Afrikaans Mathspeak Steve Noble's samples.

Afrikaans Mathspeak Steve Noble's samples. Locale: af, Style: Verbose.

0	$- 5 \frac{1}{5} - 6 \frac{2}{3} =$	negative 5 and one fifth minus 6 and two thirds equals	negatief 5 en een vyfde minus 6 en twee derdes is gelyk aan
1	$- 7 \frac{3}{4} - (- 4 \frac{7}{8}) =$	negative 7 and three fourths minus left parenthesis negative 4 and seven eighths right parenthesis equals	negatief 7 en drie kwarte minus links hakkie negatief 4 en sewe agstes regs hakkie is gelyk aan
2	$- 24.15 - (13.7) =$	negative 24.15 minus left parenthesis 13.7 right parenthesis equals	negatief 24,15 minus links hakkie 13,7 regs hakkie is gelyk aan
3	$(- 4) \times 3 = - 12$	left parenthesis negative 4 right parenthesis times 3 equals negative 12	links hakkie negatief 4 regs hakkie maal 3 is gelyk aan negatief 12
4	$- 12 \div 3 = - 4$	negative 12 divided by 3 equals negative 4	negatief 12 gedeel deur 3 is gelyk aan negatief 4
5	$- 12 \div (- 4) = 3$	negative 12 divided by left parenthesis negative 4 right parenthesis equals 3	negatief 12 gedeel deur links hakkie negatief 4 regs hakkie is gelyk aan 3
6	$6 \times 5$	6 times 5	6 maal 5
7	$6 \times (- 5)$	6 times left parenthesis negative 5 right parenthesis	6 maal links hakkie negatief 5 regs hakkie
8	$- 6 \times 5$	negative 6 times 5	negatief 6 maal 5
9	$- 6 \times (- 5)$	negative 6 times left parenthesis negative 5 right parenthesis	negatief 6 maal links hakkie negatief 5 regs hakkie
10	$- 8 \times 7$	negative 8 times 7	negatief 8 maal 7
11	$- 8 \times (- 7)$	negative 8 times left parenthesis negative 7 right parenthesis	negatief 8 maal links hakkie negatief 7 regs hakkie
12	$8 \times (- 7)$	8 times left parenthesis negative 7 right parenthesis	8 maal links hakkie negatief 7 regs hakkie
13	$8 \times 7$	8 times 7	8 maal 7
14	$m ∠ 1 = 30°$	m angle 1 equals 30 degree	m hoek 1 is gelyk aan 30 graad
15	$m ∠ 2 = 60°$	m angle 2 equals 60 degree	m hoek 2 is gelyk aan 60 graad
16	$m ∠ 1 + m ∠ 2 = 90°$	m angle 1 plus m angle 2 equals 90 degree	m hoek 1 plus m hoek 2 is gelyk aan 90 graad
17	$m ∠ M + m ∠ N = 180°$	m angle upper M plus m angle upper N equals 180 degree	m hoek hoofletter M plus m hoek hoofletter N is gelyk aan 180 graad
18	$A = \frac{1}{2} b h$	upper A equals one half b h	hoofletter A is gelyk aan een helfte b h
19	$\frac{area of triangle}{area of square} = \frac{{1 unit}^{2}}{{16 units}^{2}}$	StartFraction area of triangle Over area of square EndFraction equals StartFraction 1 unit squared Over 16 units squared EndFraction	BeginBreuk area of triangle Oor area of square EndBreuk is gelyk aan BeginBreuk 1 unit kwadraat Oor 16 units kwadraat EndBreuk
20	${0.6}^{2}$	0.6 squared	0,6 kwadraat
21	${1.5}^{2}$	1.5 squared	1,5 kwadraat
22	$4 (2 x + 3 x)$	4 left parenthesis 2 x plus 3 x right parenthesis	4 links hakkie 2 x plus 3 x regs hakkie
23	$36 + 4 y - 1 y^{2} + 5 y^{2} - 2$	36 plus 4 y minus 1 y squared plus 5 y squared minus 2	36 plus 4 y minus 1 y kwadraat plus 5 y kwadraat minus 2
24	$(5 + 9) - 4 + 3 =$	left parenthesis 5 plus 9 right parenthesis minus 4 plus 3 equals	links hakkie 5 plus 9 regs hakkie minus 4 plus 3 is gelyk aan
25	$\overset{\leftrightarrow}{B C}$	ModifyingAbove upper B upper C With left right arrow	pas boonste aan hoofletter B hoofletter C met links regs pyltjie
26	$\vec{P Q}$	ModifyingAbove upper P upper Q With right arrow	pas boonste aan hoofletter P hoofletter Q met regs pyltjie
27	$\bar{G H}$	ModifyingAbove upper G upper H With bar	pas boonste aan hoofletter G hoofletter H met makron
28	$\bar{W X} ≅ \bar{Y Z}$	ModifyingAbove upper W upper X With bar approximately equals ModifyingAbove upper Y upper Z With bar	pas boonste aan hoofletter W hoofletter X met makron ongeveer gelyk aan pas boonste aan hoofletter Y hoofletter Z met makron
29	$∠ B E F$	angle upper B upper E upper F	hoek hoofletter B hoofletter E hoofletter F
30	$∠ B E D$	angle upper B upper E upper D	hoek hoofletter B hoofletter E hoofletter D
31	$∠ D E F$	angle upper D upper E upper F	hoek hoofletter D hoofletter E hoofletter F
32	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	x equals StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction	x is gelyk aan BeginBreuk negatief b plus of minus Begin wortel b kwadraat minus 4 a c End wortel Oor 2 a EndBreuk
33	$y = x^{2} + 8 x + 16$	y equals x squared plus 8 x plus 16	y is gelyk aan x kwadraat plus 8 x plus 16
34	$y = \frac{1}{3} (3^{x})$	y equals one third left parenthesis 3 Superscript x Baseline right parenthesis	y is gelyk aan een derde links hakkie 3 Superskrif x Basislyn regs hakkie
35	$y = 10 - 2 x$	y equals 10 minus 2 x	y is gelyk aan 10 minus 2 x
36	$y = 2 x^{3} + 5$	y equals 2 x cubed plus 5	y is gelyk aan 2 x kubbiek plus 5
37	$y = (x^{2} + 1) (x^{2} + 3)$	y equals left parenthesis x squared plus 1 right parenthesis left parenthesis x squared plus 3 right parenthesis	y is gelyk aan links hakkie x kwadraat plus 1 regs hakkie links hakkie x kwadraat plus 3 regs hakkie
38	$y = {0.5}^{x}$	y equals 0.5 Superscript x	y is gelyk aan 0,5 Superskrif x
39	$y = 22 - 2 x$	y equals 22 minus 2 x	y is gelyk aan 22 minus 2 x
40	$y = \frac{3}{x}$	y equals StartFraction 3 Over x EndFraction	y is gelyk aan BeginBreuk 3 Oor x EndBreuk
41	$y = (x + 4) (x + 4)$	y equals left parenthesis x plus 4 right parenthesis left parenthesis x plus 4 right parenthesis	y is gelyk aan links hakkie x plus 4 regs hakkie links hakkie x plus 4 regs hakkie
42	$y = (4 x - 3) (x + 1)$	y equals left parenthesis 4 x minus 3 right parenthesis left parenthesis x plus 1 right parenthesis	y is gelyk aan links hakkie 4 x minus 3 regs hakkie links hakkie x plus 1 regs hakkie
43	$y = 20 x - 4 x^{2}$	y equals 20 x minus 4 x squared	y is gelyk aan 20 x minus 4 x kwadraat
44	$y = x^{2}$	y equals x squared	y is gelyk aan x kwadraat
45	$y = 3^{x - 1}$	y equals 3 Superscript x minus 1	y is gelyk aan 3 Superskrif x minus 1
46	$y = 16 - 2 (x + 3)$	y equals 16 minus 2 left parenthesis x plus 3 right parenthesis	y is gelyk aan 16 minus 2 links hakkie x plus 3 regs hakkie
47	$y = 4 x^{2} - x - 3$	y equals 4 x squared minus x minus 3	y is gelyk aan 4 x kwadraat minus x minus 3
48	$y = x + \frac{1}{x}$	y equals x plus StartFraction 1 Over x EndFraction	y is gelyk aan x plus BeginBreuk 1 Oor x EndBreuk
49	$y = 4 x (5 - x)$	y equals 4 x left parenthesis 5 minus x right parenthesis	y is gelyk aan 4 x links hakkie 5 minus x regs hakkie
50	$y = 2 (x - 3) + 6 (1 - x)$	y equals 2 left parenthesis x minus 3 right parenthesis plus 6 left parenthesis 1 minus x right parenthesis	y is gelyk aan 2 links hakkie x minus 3 regs hakkie plus 6 links hakkie 1 minus x regs hakkie
51	$0.25 > \frac{5}{16}$	0.25 greater than five sixteenths	0,25 groter as vyf sestiendes
52	$32 \cdot (5 \cdot 7)$	32 dot left parenthesis 5 dot 7 right parenthesis	32 punt links hakkie 5 punt 7 regs hakkie
53	$(\frac{1}{2} \times \frac{1}{2} \times π \times 2) + (2 \times \frac{1}{2} \times π \times 5)$	left parenthesis one half times one half times pi times 2 right parenthesis plus left parenthesis 2 times one half times pi times 5 right parenthesis	links hakkie een helfte maal een helfte maal pi maal 2 regs hakkie plus links hakkie 2 maal een helfte maal pi maal 5 regs hakkie
54	$\underset{n \to \infty}{liminf} E_{n} = ⋃_{n \geq 1} ⋂_{k \geq n} E_{k}, \underset{n \to \infty}{limsup} E_{n} = ⋂_{n \geq 1} ⋃_{k \geq n} E_{k} .$	liminf Underscript n right arrow infinity Endscripts upper E Subscript n Baseline equals union Underscript n greater than or equals 1 Endscripts intersection Underscript k greater than or equals n Endscripts upper E Subscript k Baseline comma limsup Underscript n right arrow infinity Endscripts upper E Subscript n Baseline equals intersection Underscript n greater than or equals 1 Endscripts union Underscript k greater than or equals n Endscripts upper E Subscript k Baseline period	liminf Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E Onderskrif n Basislyn is gelyk aan n ary union Onderskrif n groter of gelyk aan 1 End skrifte n ary intersection Onderskrif k groter of gelyk aan n End skrifte hoofletter E Onderskrif k Basislyn komma limsup Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E Onderskrif n Basislyn is gelyk aan n ary intersection Onderskrif n groter of gelyk aan 1 End skrifte n ary union Onderskrif k groter of gelyk aan n End skrifte hoofletter E Onderskrif k Basislyn punt
55	$\begin{array}{l} (i) & 𝒮 \in 𝒜; \\ (ii) & if E \in 𝒜 then \overline{E} \in 𝒜; \\ (iii) & if E_{1}, E_{2} \in 𝒜 then E_{1} \cup E_{2} \in 𝒜 . \end{array}$	StartLayout 1st Row 1st Column left parenthesis i right parenthesis 2nd Column script upper S element of script upper A semicolon 2nd Row 1st Column left parenthesis ii right parenthesis 2nd Column if upper E element of script upper A then upper E overbar element of script upper A semicolon 3rd Row 1st Column left parenthesis iii right parenthesis 2nd Column if upper E 1 comma upper E 2 element of script upper A then upper E 1 union upper E 2 element of script upper A period EndLayout	Begin uitleg 1. Ry 1. Kolom links hakkie i regs hakkie 2. Kolom skrif hoofletter S element van skrif hoofletter A kommapunt 2. Ry 1. Kolom links hakkie ii regs hakkie 2. Kolom if hoofletter E element van skrif hoofletter A then hoofletter E bostaaf element van skrif hoofletter A kommapunt 3. Ry 1. Kolom links hakkie iii regs hakkie 2. Kolom if hoofletter E 1 komma hoofletter E 2 element van skrif hoofletter A then hoofletter E 1 eenheid hoofletter E 2 element van skrif hoofletter A punt End uitleg
56	$\begin{array}{l} (A . 1) If A \in ℱ then 0 \leq P {A} \leq 1 . & (1) \\ (A . 2) P {𝒮} = 1 . & (2) \\ (A . 3) If {E_{n}, n \geq 1} \in ℱ is a sequence of disjoint & (3) \end{array}$	StartLayout 1st Row 1st Column Blank 2nd Column Blank 3rd Column left parenthesis normal upper A period 1 right parenthesis upper I f upper A element of script upper F t h e n 0 less than or equals upper P left brace upper A right brace less than or equals 1 period 4th Column left parenthesis 1 right parenthesis 2nd Row 1st Column Blank 2nd Column Blank 3rd Column left parenthesis normal upper A period 2 right parenthesis upper P left brace script upper S right brace equals 1 period 4th Column left parenthesis 2 right parenthesis 3rd Row 1st Column Blank 2nd Column Blank 3rd Column left parenthesis normal upper A period 3 right parenthesis upper I f left brace upper E Subscript n Baseline comma n greater than or equals 1 right brace element of script upper F is a sequence of disjoint 4th Column left parenthesis 3 right parenthesis EndLayout	Begin uitleg 1. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 1 regs hakkie hoofletter I f hoofletter A element van skrif hoofletter F t h e n 0 kleiner of gelyk aan hoofletter P links krulhakkie hoofletter A regs krulhakkie kleiner of gelyk aan 1 punt 4. Kolom links hakkie 1 regs hakkie 2. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 2 regs hakkie hoofletter P links krulhakkie skrif hoofletter S regs krulhakkie is gelyk aan 1 punt 4. Kolom links hakkie 2 regs hakkie 3. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 3 regs hakkie hoofletter I f links krulhakkie hoofletter E Onderskrif n Basislyn komma n groter of gelyk aan 1 regs krulhakkie element van skrif hoofletter F is a sequence of disjoint 4. Kolom links hakkie 3 regs hakkie End uitleg
57	$P {B_{j} \| A} = \frac{P {B_{j}} P {A \| B_{j}}}{\sum_{j' \in J} P {B_{j'}} P {A \| B_{j'}}} .$	upper P left brace upper B Subscript j Baseline vertical bar upper A right brace equals StartFraction upper P left brace upper B Subscript j Baseline right brace upper P left brace upper A vertical bar upper B Subscript j Baseline right brace Over sigma summation Underscript j prime element of upper J Endscripts upper P left brace upper B Subscript j prime Baseline right brace upper P left brace upper A vertical bar upper B Subscript j prime Baseline right brace EndFraction period	hoofletter P links krulhakkie hoofletter B Onderskrif j Basislyn afstreep hoofletter A regs krulhakkie is gelyk aan BeginBreuk hoofletter P links krulhakkie hoofletter B Onderskrif j Basislyn regs krulhakkie hoofletter P links krulhakkie hoofletter A afstreep hoofletter B Onderskrif j Basislyn regs krulhakkie Oor som Onderskrif j priem element van hoofletter J End skrifte hoofletter P links krulhakkie hoofletter B Onderskrif j priem Basislyn regs krulhakkie hoofletter P links krulhakkie hoofletter A afstreep hoofletter B Onderskrif j priem Basislyn regs krulhakkie EndBreuk punt
58	$μ_{1} (B) = \int_{B} f (x) d μ_{2} (x)$	mu 1 left parenthesis upper B right parenthesis equals integral Underscript upper B Endscripts f left parenthesis x right parenthesis d mu 2 left parenthesis x right parenthesis	my 1 links hakkie hoofletter B regs hakkie is gelyk aan integraal Onderskrif hoofletter B End skrifte f links hakkie x regs hakkie d my 2 links hakkie x regs hakkie
59	$lim_{n \to \infty} E {\| X_{n} - X \|} = E {lim_{n \to \infty} \| X_{n} - X \|} = 0 .$	limit Underscript n right arrow infinity Endscripts upper E left brace StartAbsoluteValue upper X Subscript n Baseline minus upper X EndAbsoluteValue right brace equals upper E left brace limit Underscript n right arrow infinity Endscripts StartAbsoluteValue upper X Subscript n Baseline minus upper X EndAbsoluteValue right brace equals 0 period	limit Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E links krulhakkie begin absolute Waarde hoofletter X Onderskrif n Basislyn minus hoofletter X End Absolute Waarde regs krulhakkie is gelyk aan hoofletter E links krulhakkie limit Onderskrif n regs pyltjie oneindigheid End skrifte begin absolute Waarde hoofletter X Onderskrif n Basislyn minus hoofletter X End Absolute Waarde regs krulhakkie is gelyk aan 0 punt
60	$\begin{array}{l} P_{μ, σ} {Y \geq l_{β} ({\overline{Y}}_{n}, S_{n})} = P_{μ, σ} {(Y - {\overline{Y}}_{n}) / (S \cdot {(1 + \frac{1}{n})}^{1 / 2}) \geq - t_{β} [n - 1]} = β, \\ (1) \end{array}$	StartLayout 1st Row 1st Column upper P Subscript mu comma sigma Baseline left brace upper Y greater than or equals l Subscript beta Baseline left parenthesis upper Y overbar Subscript n Baseline comma upper S Subscript n Baseline right parenthesis right brace equals upper P Subscript mu comma sigma Baseline left brace left parenthesis upper Y minus upper Y overbar Subscript n Baseline right parenthesis divided by left parenthesis upper S dot left parenthesis 1 plus StartFraction 1 Over n EndFraction right parenthesis Superscript 1 divided by 2 Baseline right parenthesis greater than or equals minus t Subscript beta Baseline left bracket n minus 1 right bracket right brace equals beta comma 2nd Row 1st Column Blank 2nd Column left parenthesis 1 right parenthesis EndLayout	Begin uitleg 1. Ry 1. Kolom hoofletter P Onderskrif my komma sigma Basislyn links krulhakkie hoofletter Y groter of gelyk aan l Onderskrif beta Basislyn links hakkie hoofletter Y bostaaf Onderskrif n Basislyn komma hoofletter S Onderskrif n Basislyn regs hakkie regs krulhakkie is gelyk aan hoofletter P Onderskrif my komma sigma Basislyn links krulhakkie links hakkie hoofletter Y minus hoofletter Y bostaaf Onderskrif n Basislyn regs hakkie gedeel deur links hakkie hoofletter S dot links hakkie 1 plus BeginBreuk 1 Oor n EndBreuk regs hakkie Superskrif 1 gedeel deur 2 Basislyn regs hakkie groter of gelyk aan minus t Onderskrif beta Basislyn links blokhakkie n minus 1 regs blokhakkie regs krulhakkie is gelyk aan beta komma 2. Ry 1. Kolom leeg 2. Kolom links hakkie 1 regs hakkie End uitleg
61	$L = (\begin{matrix} 1 & - 1 \\ 1 & - 1 & 0 \\ 0 \\ 1 & - 1 \end{matrix}) .$	upper L equals Start 5 By 6 Matrix 1st Row 1st Column 1 2nd Column negative 1 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 2nd Row 1st Column Blank 2nd Column 1 3rd Column negative 1 4th Column Blank 5th Column 0 6th Column Blank 3rd Row 1st Column Blank 2nd Column Blank 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 4th Row 1st Column Blank 2nd Column 0 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 5th Row 1st Column Blank 2nd Column Blank 3rd Column Blank 4th Column Blank 5th Column 1 6th Column negative 1 EndMatrix period	hoofletter L is gelyk aan Begin 5 By 6 Matriks 1. Ry 1. Kolom 1 2. Kolom negatief 1 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 2. Ry 1. Kolom leeg 2. Kolom 1 3. Kolom negatief 1 4. Kolom Leeg 5. Kolom 0 6. Kolom Leeg 3. Ry 1. Kolom leeg 2. Kolom Leeg 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 4. Ry 1. Kolom leeg 2. Kolom 0 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 5. Ry 1. Kolom leeg 2. Kolom Leeg 3. Kolom Leeg 4. Kolom Leeg 5. Kolom 1 6. Kolom negatief 1 End Matriks punt
62	$\sqrt{n} [{\overline{Y}}_{n} - (μ + z_{β} σ)] / S_{n} ~ \frac{U + \sqrt{n} z_{1 - β}}{(χ^{2} [n - 1] / (n - 1))^{1 / 2}} ~ t [n - 1; \sqrt{n} z_{1 - β}],$	StartRoot n EndRoot left bracket upper Y overbar Subscript n Baseline minus left parenthesis mu plus z Subscript beta Baseline sigma right parenthesis right bracket divided by upper S Subscript n Baseline tilde StartFraction upper U plus StartRoot n EndRoot z Subscript 1 minus beta Baseline Over left parenthesis chi squared left bracket n minus 1 right bracket divided by left parenthesis n minus 1 right parenthesis right parenthesis Superscript 1 divided by 2 Baseline EndFraction tilde t left bracket n minus 1 semicolon StartRoot n EndRoot z Subscript 1 minus beta Baseline right bracket comma	Begin wortel n End wortel links blokhakkie hoofletter Y bostaaf Onderskrif n Basislyn minus links hakkie my plus z Onderskrif beta Basislyn sigma regs hakkie regs blokhakkie gedeel deur hoofletter S Onderskrif n Basislyn tilde BeginBreuk hoofletter U plus Begin wortel n End wortel z Onderskrif 1 minus beta Basislyn Oor links hakkie chi kwadraat links blokhakkie n minus 1 regs blokhakkie gedeel deur links hakkie n minus 1 regs hakkie regs hakkie Superskrif 1 gedeel deur 2 Basislyn EndBreuk tilde t links blokhakkie n minus 1 kommapunt Begin wortel n End wortel z Onderskrif 1 minus beta Basislyn regs blokhakkie komma
63	$\begin{array}{l} γ & = P {E_{p, q} \subset (X_{(r)}, X_{(s)}} \\ = \frac{n!}{(r - 1)!} \sum_{j = 0}^{s - r - 1} (- 1)^{j} \frac{p^{r + j}}{(n - r - j)! j!} I_{1 - q} (n - s + 1, s - r - j) . \end{array}$	StartLayout 1st Row 1st Column gamma 2nd Column equals upper P left brace upper E Subscript p comma q Baseline subset of left parenthesis upper X Subscript left parenthesis r right parenthesis Baseline comma upper X Subscript left parenthesis s right parenthesis Baseline right brace 2nd Row 1st Column Blank 2nd Column equals StartFraction n factorial Over left parenthesis r minus 1 right parenthesis factorial EndFraction sigma summation Underscript j equals 0 Overscript s minus r minus 1 Endscripts left parenthesis negative 1 right parenthesis Superscript j Baseline StartFraction p Superscript r plus j Baseline Over left parenthesis n minus r minus j right parenthesis factorial j factorial EndFraction upper I Subscript 1 minus q Baseline left parenthesis n minus s plus 1 comma s minus r minus j right parenthesis period EndLayout	Begin uitleg 1. Ry 1. Kolom gamma 2. Kolom is gelyk aan hoofletter P links krulhakkie hoofletter E Onderskrif p komma q Basislyn deelversameling van links hakkie hoofletter X Onderskrif links hakkie r regs hakkie Basislyn komma hoofletter X Onderskrif links hakkie s regs hakkie Basislyn regs krulhakkie 2. Ry 1. Kolom leeg 2. Kolom is gelyk aan BeginBreuk n faktoriaal Oor links hakkie r minus 1 regs hakkie faktoriaal EndBreuk som Onderskrif j is gelyk aan 0 Boskrif s minus r minus 1 End skrifte links hakkie negatief 1 regs hakkie Superskrif j Basislyn BeginBreuk p Superskrif r plus j Basislyn Oor links hakkie n minus r minus j regs hakkie faktoriaal j faktoriaal EndBreuk hoofletter I Onderskrif 1 minus q Basislyn links hakkie n minus s plus 1 komma s minus r minus j regs hakkie punt End uitleg
64	$S_{i} [\begin{matrix} t \\ x \end{matrix}] = [\begin{matrix} 1 / m & 0 \\ a_{i} & r_{i} \end{matrix}] [\begin{matrix} t \\ x \end{matrix}] + [\begin{matrix} (i - 1) / m \\ b_{i} \end{matrix}],$	upper S Subscript i Baseline StartBinomialOrMatrix t Choose x EndBinomialOrMatrix equals Start 2 By 2 Matrix 1st Row 1st Column 1 divided by m 2nd Column 0 2nd Row 1st Column a Subscript i Baseline 2nd Column r Subscript i Baseline EndMatrix StartBinomialOrMatrix t Choose x EndBinomialOrMatrix plus StartBinomialOrMatrix left parenthesis i minus 1 right parenthesis divided by m Choose b Subscript i Baseline EndBinomialOrMatrix comma	hoofletter S Onderskrif i Basislyn Begin Binomiaal of Matriks t Kies x End Binomiaal of Matriks is gelyk aan Begin 2 By 2 Matriks 1. Ry 1. Kolom 1 gedeel deur m 2. Kolom 0 2. Ry 1. Kolom a Onderskrif i Basislyn 2. Kolom r Onderskrif i Basislyn End Matriks Begin Binomiaal of Matriks t Kies x End Binomiaal of Matriks plus Begin Binomiaal of Matriks links hakkie i minus 1 regs hakkie gedeel deur m Kies b Onderskrif i Basislyn End Binomiaal of Matriks komma
65	$c_{1} h^{4 - 2 s} \leq \frac{1}{2 T} \int_{- T}^{T} {(f (t + h) - f (t))}^{2} d t \leq c_{2} h^{4 - 2 s}$	c 1 h Superscript 4 minus 2 s Baseline less than or equals StartFraction 1 Over 2 upper T EndFraction integral Subscript negative upper T Superscript upper T Baseline left parenthesis f left parenthesis t plus h right parenthesis minus f left parenthesis t right parenthesis right parenthesis squared normal d t less than or equals c 2 h Superscript 4 minus 2 s	c 1 h Superskrif 4 minus 2 s Basislyn kleiner of gelyk aan BeginBreuk 1 Oor 2 hoofletter T EndBreuk integraal Onderskrif negatief hoofletter T Boskrif hoofletter T Basislyn links hakkie f links hakkie t plus h regs hakkie minus f links hakkie t regs hakkie regs hakkie kwadraat normaal d t kleiner of gelyk aan c 2 h Superskrif 4 minus 2 s
66	$C (0) - C (h) ≃ c h^{4 - 2 s}$	upper C left parenthesis 0 right parenthesis minus upper C left parenthesis h right parenthesis asymptotically equals c h Superscript 4 minus 2 s	hoofletter C links hakkie 0 regs hakkie minus hoofletter C links hakkie h regs hakkie assimtoties gelyk aan c h Superskrif 4 minus 2 s
67	$S (ω) = \lim_{T \to \infty} \frac{1}{2 T} {\|\int_{- T}^{T} f (t) e^{it ω} d t\|}^{2} .$	upper S left parenthesis omega right parenthesis equals limit Underscript upper T right arrow infinity Endscripts StartFraction 1 Over 2 upper T EndFraction StartAbsoluteValue integral Subscript negative upper T Superscript upper T Baseline comma f comma left parenthesis comma t comma right parenthesis comma normal e Superscript italic i t omega Baseline comma normal d comma t EndAbsoluteValue squared period	hoofletter S links hakkie omega regs hakkie is gelyk aan limit Onderskrif hoofletter T regs pyltjie oneindigheid End skrifte BeginBreuk 1 Oor 2 hoofletter T EndBreuk begin absolute Waarde integraal Onderskrif negatief hoofletter T Boskrif hoofletter T Basislyn komma f komma links hakkie komma t komma regs hakkie komma normaal e Superskrif kursief i t omega Basislyn komma normaal d komma t End Absolute Waarde kwadraat punt
68	$\int_{0}^{1} \int_{0}^{1} {[\| f (t) - f (u) \|^{2} + \| t - u \|^{2}]}^{- s / 2} d t d u < \infty$	integral Subscript 0 Superscript 1 Baseline integral Subscript 0 Superscript 1 Baseline left bracket StartAbsoluteValue f left parenthesis t right parenthesis minus f left parenthesis u right parenthesis EndAbsoluteValue squared plus StartAbsoluteValue t minus u EndAbsoluteValue squared right bracket Superscript negative s divided by 2 Baseline normal d t normal d u less than infinity	integraal Onderskrif 0 Boskrif 1 Basislyn integraal Onderskrif 0 Boskrif 1 Basislyn links blokhakkie begin absolute Waarde f links hakkie t regs hakkie minus f links hakkie u regs hakkie End Absolute Waarde kwadraat plus begin absolute Waarde t minus u End Absolute Waarde kwadraat regs blokhakkie Superskrif negatief s gedeel deur 2 Basislyn normaal d t normaal d u kleiner as oneindigheid
69	$E (\sum_{I \in E_{k + 1}} \| I \|^{s}) = E (\sum_{I \in E_{k}} \| I \|^{s}) E (R_{1}^{s} + R_{2}^{s}) .$	sans serif upper E left parenthesis sigma summation Underscript upper I element of upper E Subscript k plus 1 Baseline Endscripts StartAbsoluteValue upper I EndAbsoluteValue Superscript s Baseline right parenthesis equals sans serif upper E left parenthesis sigma summation Underscript upper I element of upper E Subscript k Baseline Endscripts StartAbsoluteValue upper I EndAbsoluteValue Superscript s Baseline right parenthesis sans serif upper E left parenthesis upper R 1 Superscript s Baseline plus upper R 2 Superscript s Baseline right parenthesis period	sans serif hoofletter E links hakkie som Onderskrif hoofletter I element van hoofletter E Onderskrif k plus 1 Basislyn End skrifte begin absolute Waarde hoofletter I End Absolute Waarde Superskrif s Basislyn regs hakkie is gelyk aan sans serif hoofletter E links hakkie som Onderskrif hoofletter I element van hoofletter E Onderskrif k Basislyn End skrifte begin absolute Waarde hoofletter I End Absolute Waarde Superskrif s Basislyn regs hakkie sans serif hoofletter E links hakkie hoofletter R 1 Superskrif s Basislyn plus hoofletter R 2 Superskrif s Basislyn regs hakkie punt
70	$(x_{1}, y_{1})$	left parenthesis x 1 comma y 1 right parenthesis	links hakkie x 1 komma y 1 regs hakkie
71	$(x_{2}, y_{2})$	left parenthesis x 2 comma y 2 right parenthesis	links hakkie x 2 komma y 2 regs hakkie
72	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$	d equals StartRoot left parenthesis x 2 minus x 1 right parenthesis squared plus left parenthesis y 2 minus y 1 right parenthesis squared EndRoot	d is gelyk aan Begin wortel links hakkie x 2 minus x 1 regs hakkie kwadraat plus links hakkie y 2 minus y 1 regs hakkie kwadraat End wortel
73	$ℝ$	double struck upper R	hoofletter R dubbelgeslaan
74	$ℝ = (- \infty, \infty)$	double struck upper R equals left parenthesis negative infinity comma infinity right parenthesis	hoofletter R dubbelgeslaan is gelyk aan links hakkie negatief oneindigheid komma oneindigheid regs hakkie
75	${1, 2, 3}$	StartSet 1 comma 2 comma 3 EndSet	begin versameling 1 komma 2 komma 3 End versameling
76	$1 \in S$	1 element of upper S	1 element van hoofletter S
77	$3 \in S$	3 element of upper S	3 element van hoofletter S
78	$4 \notin S$	4 not an element of upper S	4 nie 'n element van hoofletter S
79	$a = \sqrt{3 x - 1} + {(1 + x)}^{2}$	a equals StartRoot 3 x minus 1 EndRoot plus left parenthesis 1 plus x right parenthesis squared	a is gelyk aan Begin wortel 3 x minus 1 End wortel plus links hakkie 1 plus x regs hakkie kwadraat
80	$a = \frac{{(b + c)}^{2}}{d} + \frac{{(e + f)}^{2}}{g}$	a equals StartFraction left parenthesis b plus c right parenthesis squared Over d EndFraction plus StartFraction left parenthesis e plus f right parenthesis squared Over g EndFraction	a is gelyk aan BeginBreuk links hakkie b plus c regs hakkie kwadraat Oor d EndBreuk plus BeginBreuk links hakkie e plus f regs hakkie kwadraat Oor g EndBreuk
81	$x = [{(a + b)}^{2} {(c - b)}^{2}] + [{(d + e)}^{2} {(f - e)}^{2}]$	x equals left bracket left parenthesis a plus b right parenthesis squared left parenthesis c minus b right parenthesis squared right bracket plus left bracket left parenthesis d plus e right parenthesis squared left parenthesis f minus e right parenthesis squared right bracket	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat links hakkie c minus b regs hakkie kwadraat regs blokhakkie plus links blokhakkie links hakkie d plus e regs hakkie kwadraat links hakkie f minus e regs hakkie kwadraat regs blokhakkie
82	$x = [{(a + b)}^{2}] + [{(f - e)}^{2}]$	x equals left bracket left parenthesis a plus b right parenthesis squared right bracket plus left bracket left parenthesis f minus e right parenthesis squared right bracket	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat regs blokhakkie plus links blokhakkie links hakkie f minus e regs hakkie kwadraat regs blokhakkie
83	$x = [{(a + b)}^{2}]$	x equals left bracket left parenthesis a plus b right parenthesis squared right bracket	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat regs blokhakkie
84	$x = {(a + b)}^{2}$	x equals left parenthesis a plus b right parenthesis squared	x is gelyk aan links hakkie a plus b regs hakkie kwadraat
85	$x = a + b^{2}$	x equals a plus b squared	x is gelyk aan a plus b kwadraat
86	$\frac{\frac{1}{2}}{\frac{3}{4}} = \frac{2}{3}$	StartFraction one half Over three fourths EndFraction equals two thirds	BeginBreuk een helfte Oor drie kwarte EndBreuk is gelyk aan twee derdes
87	$2 ((x + 1) (x + 3) - 4 ((x - 1) (x + 2) - 3)) = y$	2 left parenthesis left parenthesis x plus 1 right parenthesis left parenthesis x plus 3 right parenthesis minus 4 left parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x plus 2 right parenthesis minus 3 right parenthesis right parenthesis equals y	2 links hakkie links hakkie x plus 1 regs hakkie links hakkie x plus 3 regs hakkie minus 4 links hakkie links hakkie x minus 1 regs hakkie links hakkie x plus 2 regs hakkie minus 3 regs hakkie regs hakkie is gelyk aan y
88	$\cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \dots$	cosine x equals 1 minus StartFraction x squared Over 2 factorial EndFraction plus StartFraction x Superscript 4 Baseline Over 4 factorial EndFraction minus ellipsis	kosinus x is gelyk aan 1 minus BeginBreuk x kwadraat Oor 2 faktoriaal EndBreuk plus BeginBreuk x Superskrif 4 Basislyn Oor 4 faktoriaal EndBreuk minus ellipsis
89	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	x equals StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction	x is gelyk aan BeginBreuk negatief b plus of minus Begin wortel b kwadraat minus 4 a c End wortel Oor 2 a EndBreuk
90	$x + y^{\frac{2}{k + 1}}$	x plus y Superscript StartFraction 2 Over k plus 1 EndFraction	x plus y Superskrif BeginBreuk 2 Oor k plus 1 EndBreuk
91	$\lim_{x \to 0} \frac{\sin x}{x} = 1$	limit Underscript x right arrow 0 Endscripts StartFraction sine x Over x EndFraction equals 1	limit Onderskrif x regs pyltjie 0 End skrifte BeginBreuk sinus x Oor x EndBreuk is gelyk aan 1
92	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$	d equals StartRoot left parenthesis x 2 minus x 1 right parenthesis squared plus left parenthesis y 2 minus y 1 right parenthesis squared EndRoot	d is gelyk aan Begin wortel links hakkie x 2 minus x 1 regs hakkie kwadraat plus links hakkie y 2 minus y 1 regs hakkie kwadraat End wortel
93	$F_{n} = F_{n - 1} + F_{n - 2}$	upper F Subscript n Baseline equals upper F Subscript n minus 1 Baseline plus upper F Subscript n minus 2	hoofletter F Onderskrif n Basislyn is gelyk aan hoofletter F Onderskrif n minus 1 Basislyn plus hoofletter F Onderskrif n minus 2
94	$Π = (\begin{matrix} π_{11} & π_{12} & π_{12} & 0 & 0 & 0 \\ π_{12} & π_{11} & π_{12} & 0 & 0 & 0 \\ π_{12} & π_{12} & π_{11} & 0 & 0 & 0 \\ 0 & 0 & 0 & π_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & π_{44} & 0 \\ 0 & 0 & 0 & 0 & 0 & π_{44} \end{matrix})$	bold upper Pi equals Start 6 By 6 Matrix 1st Row 1st Column pi 11 2nd Column pi 12 3rd Column pi 12 4th Column 0 5th Column 0 6th Column 0 2nd Row 1st Column pi 12 2nd Column pi 11 3rd Column pi 12 4th Column 0 5th Column 0 6th Column 0 3rd Row 1st Column pi 12 2nd Column pi 12 3rd Column pi 11 4th Column 0 5th Column 0 6th Column 0 4th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column pi 44 5th Column 0 6th Column 0 5th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column 0 5th Column pi 44 6th Column 0 6th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column 0 5th Column 0 6th Column pi 44 EndMatrix	vetgedruk hoofletter Pi is gelyk aan Begin 6 By 6 Matriks 1. Ry 1. Kolom pi 11 2. Kolom pi 12 3. Kolom pi 12 4. Kolom 0 5. Kolom 0 6. Kolom 0 2. Ry 1. Kolom pi 12 2. Kolom pi 11 3. Kolom pi 12 4. Kolom 0 5. Kolom 0 6. Kolom 0 3. Ry 1. Kolom pi 12 2. Kolom pi 12 3. Kolom pi 11 4. Kolom 0 5. Kolom 0 6. Kolom 0 4. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom pi 44 5. Kolom 0 6. Kolom 0 5. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom 0 5. Kolom pi 44 6. Kolom 0 6. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom 0 5. Kolom 0 6. Kolom pi 44 End Matriks
95	$s_{11} = \frac{c_{11} + c_{12}}{(c_{11} - c_{12}) (c_{11} + 2 c_{12})}$	s 11 equals StartFraction c 11 plus c 12 Over left parenthesis c 11 minus c 12 right parenthesis left parenthesis c 11 plus 2 c 12 right parenthesis EndFraction	s 11 is gelyk aan BeginBreuk c 11 plus c 12 Oor links hakkie c 11 minus c 12 regs hakkie links hakkie c 11 plus 2 c 12 regs hakkie EndBreuk
96	$Si O_{2} + 6 H F \to H_{2} Si F_{6} + 2 H_{2} O$	upper S i normal upper O 2 plus 6 normal upper H normal upper F right arrow normal upper H 2 upper S i normal upper F 6 plus 2 normal upper H 2 normal upper O	hoofletter S i normaal hoofletter O 2 plus 6 normaal hoofletter H normaal hoofletter F regs pyltjie normaal hoofletter H 2 hoofletter S i normaal hoofletter F 6 plus 2 normaal hoofletter H 2 normaal hoofletter O
97	$\frac{d}{d x} (E (x) A (x) \frac{d w (x)}{d x}) + p (x) = 0$	StartFraction d Over d x EndFraction left parenthesis upper E left parenthesis x right parenthesis upper A left parenthesis x right parenthesis StartFraction d w left parenthesis x right parenthesis Over d x EndFraction right parenthesis plus p left parenthesis x right parenthesis equals 0	BeginBreuk d Oor d x EndBreuk links hakkie hoofletter E links hakkie x regs hakkie hoofletter A links hakkie x regs hakkie BeginBreuk d w links hakkie x regs hakkie Oor d x EndBreuk regs hakkie plus p links hakkie x regs hakkie is gelyk aan 0
98	${TCS}_{gas} = - \frac{1}{2} (\frac{P_{seal}}{P_{max}}) (\frac{1}{T_{seal}})$	TCS Subscript gas Baseline equals minus one half left parenthesis StartFraction upper P Subscript seal Baseline Over upper P Subscript max Baseline EndFraction right parenthesis left parenthesis StartFraction 1 Over upper T Subscript seal Baseline EndFraction right parenthesis	TCS Onderskrif gas Basislyn is gelyk aan minus een helfte links hakkie BeginBreuk hoofletter P Onderskrif seal Basislyn Oor hoofletter P Onderskrif max Basislyn EndBreuk regs hakkie links hakkie BeginBreuk 1 Oor hoofletter T Onderskrif seal Basislyn EndBreuk regs hakkie
99	$B_{p} = \frac{\frac{7 - v^{2}}{3} (1 + \frac{c^{2}}{a^{2}} + \frac{c^{4}}{a^{4}}) + \frac{{(3 - v)}^{2} c^{2}}{(1 + v) a^{2}}}{(1 - v) (1 - \frac{c^{4}}{a^{4}}) (1 - \frac{c^{2}}{a^{2}})}$	upper B Subscript p Baseline equals StartStartFraction StartFraction 7 minus v squared Over 3 EndFraction left parenthesis 1 plus StartFraction c squared Over a squared EndFraction plus StartFraction c Superscript 4 Baseline Over a Superscript 4 Baseline EndFraction right parenthesis plus StartFraction left parenthesis 3 minus v right parenthesis squared c squared Over left parenthesis 1 plus v right parenthesis a squared EndFraction OverOver left parenthesis 1 minus v right parenthesis left parenthesis 1 minus StartFraction c Superscript 4 Baseline Over a Superscript 4 Baseline EndFraction right parenthesis left parenthesis 1 minus StartFraction c squared Over a squared EndFraction right parenthesis EndEndFraction	hoofletter B Onderskrif p Basislyn is gelyk aan BeginBeginBreuk BeginBreuk 7 minus v kwadraat Oor 3 EndBreuk links hakkie 1 plus BeginBreuk c kwadraat Oor a kwadraat EndBreuk plus BeginBreuk c Superskrif 4 Basislyn Oor a Superskrif 4 Basislyn EndBreuk regs hakkie plus BeginBreuk links hakkie 3 minus v regs hakkie kwadraat c kwadraat Oor links hakkie 1 plus v regs hakkie a kwadraat EndBreuk OorOor links hakkie 1 minus v regs hakkie links hakkie 1 minus BeginBreuk c Superskrif 4 Basislyn Oor a Superskrif 4 Basislyn EndBreuk regs hakkie links hakkie 1 minus BeginBreuk c kwadraat Oor a kwadraat EndBreuk regs hakkie EndEndBreuk
100	$Q_{tank}^{series} = \frac{1}{R_{s}} \sqrt{\frac{L_{s}}{C_{s}}}$	upper Q Subscript tank Superscript series Baseline equals StartFraction 1 Over upper R Subscript s Baseline EndFraction StartRoot StartFraction upper L Subscript s Baseline Over upper C Subscript s Baseline EndFraction EndRoot	hoofletter Q Onderskrif tank Superskrif series Basislyn is gelyk aan BeginBreuk 1 Oor hoofletter R Onderskrif s Basislyn EndBreuk Begin wortel BeginBreuk hoofletter L Onderskrif s Basislyn Oor hoofletter C Onderskrif s Basislyn EndBreuk End wortel
101	$Δ ϕ_{peak} = {tan}^{- 1} (k^{2} Q_{tank}^{series})$	upper Delta phi Subscript peak Baseline equals tangent Superscript negative 1 Baseline left parenthesis k squared upper Q Subscript tank Superscript series Baseline right parenthesis	hoofletter Delta phi Onderskrif peak Basislyn is gelyk aan tangens Superskrif negatief 1 Basislyn links hakkie k kwadraat hoofletter Q Onderskrif tank Superskrif series Basislyn regs hakkie
102	$f = 1.013 \frac{W}{L^{2}} \sqrt{\frac{E}{ρ}} \sqrt{(1 + 0.293 \frac{L^{2}}{{EW}^{2}} σ)}$	f equals 1.013 StartFraction upper W Over upper L squared EndFraction StartRoot StartFraction upper E Over rho EndFraction EndRoot StartRoot left parenthesis 1 plus 0.293 StartFraction upper L squared Over EW squared EndFraction sigma right parenthesis EndRoot	f is gelyk aan 1.013 BeginBreuk hoofletter W Oor hoofletter L kwadraat EndBreuk Begin wortel BeginBreuk hoofletter E Oor rho EndBreuk End wortel Begin wortel links hakkie 1 plus 0.293 BeginBreuk hoofletter L kwadraat Oor EW kwadraat EndBreuk sigma regs hakkie End wortel
103	$u_{n} (x) = γ_{n} (\cosh k_{n} x - \cos k_{n} x) + (\sinh k_{n} x - \sin k_{n} x)$	u Subscript n Baseline left parenthesis x right parenthesis equals gamma Subscript n Baseline left parenthesis hyperbolic cosine k Subscript n Baseline x minus cosine k Subscript n Baseline x right parenthesis plus left parenthesis hyperbolic sine k Subscript n Baseline x minus sine k Subscript n Baseline x right parenthesis	u Onderskrif n Basislyn links hakkie x regs hakkie is gelyk aan gamma Onderskrif n Basislyn links hakkie hiperboliese kosinus k Onderskrif n Basislyn x minus kosinus k Onderskrif n Basislyn x regs hakkie plus links hakkie hiperboliese sinus k Onderskrif n Basislyn x minus sinus k Onderskrif n Basislyn x regs hakkie
104	$\begin{matrix} B & = \frac{\frac{F_{0}}{m}}{\sqrt{(ω_{0}^{2} - ω^{2})^{2} + 4 n^{2} ω^{2}}} \\ = \frac{\frac{F_{0}}{k}}{\sqrt{(1 - (ω / ω_{0}^{2})^{2})^{2} + 4 (n / ω_{0})^{2} (ω / ω_{0})^{2}}} \end{matrix}$	StartLayout 1st Row 1st Column upper B 2nd Column equals StartStartFraction StartFraction upper F 0 Over m EndFraction OverOver StartRoot left parenthesis omega 0 squared minus omega squared right parenthesis squared plus 4 n squared omega squared EndRoot EndEndFraction 2nd Row 1st Column Blank 2nd Column equals StartStartFraction StartFraction upper F 0 Over k EndFraction OverOver StartRoot left parenthesis 1 minus left parenthesis omega divided by omega 0 squared right parenthesis squared right parenthesis squared plus 4 left parenthesis n divided by omega 0 right parenthesis squared left parenthesis omega divided by omega 0 right parenthesis squared EndRoot EndEndFraction EndLayout	Begin uitleg 1. Ry 1. Kolom hoofletter B 2. Kolom is gelyk aan BeginBeginBreuk BeginBreuk hoofletter F 0 Oor m EndBreuk OorOor Begin wortel links hakkie omega 0 kwadraat minus omega kwadraat regs hakkie kwadraat plus 4 n kwadraat omega kwadraat End wortel EndEndBreuk 2. Ry 1. Kolom leeg 2. Kolom is gelyk aan BeginBeginBreuk BeginBreuk hoofletter F 0 Oor k EndBreuk OorOor Begin wortel links hakkie 1 minus links hakkie omega gedeel deur omega 0 kwadraat regs hakkie kwadraat regs hakkie kwadraat plus 4 links hakkie n gedeel deur omega 0 regs hakkie kwadraat links hakkie omega gedeel deur omega 0 regs hakkie kwadraat End wortel EndEndBreuk End uitleg
105	$p (A and B) = p (A) p (B \| A)$	normal p left parenthesis upper A a n d upper B right parenthesis equals normal p left parenthesis upper A right parenthesis normal p left parenthesis upper B vertical bar upper A right parenthesis	normaal p links hakkie hoofletter A a n d hoofletter B regs hakkie is gelyk aan normaal p links hakkie hoofletter A regs hakkie normaal p links hakkie hoofletter B afstreep hoofletter A regs hakkie
106	$PMF (x) \propto {(\frac{1}{x})}^{α}$	upper P upper M upper F left parenthesis x right parenthesis proportional to left parenthesis StartFraction 1 Over x EndFraction right parenthesis Superscript alpha	hoofletter P hoofletter M hoofletter F links hakkie x regs hakkie eweredig aan links hakkie BeginBreuk 1 Oor x EndBreuk regs hakkie Superskrif alfa
107	$f (x) = \frac{1}{\sqrt{2 π}} exp (- x^{2} /2)$	f left parenthesis x right parenthesis equals StartFraction 1 Over StartRoot 2 pi EndRoot EndFraction exp left parenthesis minus x squared slash 2 right parenthesis	f links hakkie x regs hakkie is gelyk aan BeginBreuk 1 Oor Begin wortel 2 pi End wortel EndBreuk exp links hakkie minus x kwadraat skuinsstreep 2 regs hakkie
108	$\frac{d x}{d θ} = \frac{β}{{cos}^{2} θ}$	StartFraction d x Over d theta EndFraction equals StartFraction beta Over cosine squared theta EndFraction	BeginBreuk d x Oor d theta EndBreuk is gelyk aan BeginBreuk beta Oor kosinus kwadraat theta EndBreuk
109	$s / \sqrt{2 (n - 1)}$	s divided by StartRoot 2 left parenthesis n minus 1 right parenthesis EndRoot	s gedeel deur Begin wortel 2 links hakkie n minus 1 regs hakkie End wortel

Afrikaans Mathspeak Steve Noble's samples. Locale: af, Style: Brief.

0	$- 5 \frac{1}{5} - 6 \frac{2}{3} =$	negative 5 and one fifth minus 6 and two thirds equals	negatief 5 en een vyfde minus 6 en twee derdes is gelyk aan
1	$- 7 \frac{3}{4} - (- 4 \frac{7}{8}) =$	negative 7 and three fourths minus left p'ren negative 4 and seven eighths right p'ren equals	negatief 7 en drie kwarte minus links hakkie negatief 4 en sewe agstes regs hakkie is gelyk aan
2	$- 24.15 - (13.7) =$	negative 24.15 minus left p'ren 13.7 right p'ren equals	negatief 24,15 minus links hakkie 13,7 regs hakkie is gelyk aan
3	$(- 4) \times 3 = - 12$	left p'ren negative 4 right p'ren times 3 equals negative 12	links hakkie negatief 4 regs hakkie maal 3 is gelyk aan negatief 12
4	$- 12 \div 3 = - 4$	negative 12 divided by 3 equals negative 4	negatief 12 gedeel deur 3 is gelyk aan negatief 4
5	$- 12 \div (- 4) = 3$	negative 12 divided by left p'ren negative 4 right p'ren equals 3	negatief 12 gedeel deur links hakkie negatief 4 regs hakkie is gelyk aan 3
6	$6 \times 5$	6 times 5	6 maal 5
7	$6 \times (- 5)$	6 times left p'ren negative 5 right p'ren	6 maal links hakkie negatief 5 regs hakkie
8	$- 6 \times 5$	negative 6 times 5	negatief 6 maal 5
9	$- 6 \times (- 5)$	negative 6 times left p'ren negative 5 right p'ren	negatief 6 maal links hakkie negatief 5 regs hakkie
10	$- 8 \times 7$	negative 8 times 7	negatief 8 maal 7
11	$- 8 \times (- 7)$	negative 8 times left p'ren negative 7 right p'ren	negatief 8 maal links hakkie negatief 7 regs hakkie
12	$8 \times (- 7)$	8 times left p'ren negative 7 right p'ren	8 maal links hakkie negatief 7 regs hakkie
13	$8 \times 7$	8 times 7	8 maal 7
14	$m ∠ 1 = 30°$	m angle 1 equals 30 degree	m hoek 1 is gelyk aan 30 graad
15	$m ∠ 2 = 60°$	m angle 2 equals 60 degree	m hoek 2 is gelyk aan 60 graad
16	$m ∠ 1 + m ∠ 2 = 90°$	m angle 1 plus m angle 2 equals 90 degree	m hoek 1 plus m hoek 2 is gelyk aan 90 graad
17	$m ∠ M + m ∠ N = 180°$	m angle upper M plus m angle upper N equals 180 degree	m hoek hoofletter M plus m hoek hoofletter N is gelyk aan 180 graad
18	$A = \frac{1}{2} b h$	upper A equals one half b h	hoofletter A is gelyk aan een helfte b h
19	$\frac{area of triangle}{area of square} = \frac{{1 unit}^{2}}{{16 units}^{2}}$	StartFrac area of triangle Over area of square EndFrac equals StartFrac 1 unit squared Over 16 units squared EndFrac	BeginBreuk area of triangle Oor area of square EndBreuk is gelyk aan BeginBreuk 1 unit kwadraat Oor 16 units kwadraat EndBreuk
20	${0.6}^{2}$	0.6 squared	0,6 kwadraat
21	${1.5}^{2}$	1.5 squared	1,5 kwadraat
22	$4 (2 x + 3 x)$	4 left p'ren 2 x plus 3 x right p'ren	4 links hakkie 2 x plus 3 x regs hakkie
23	$36 + 4 y - 1 y^{2} + 5 y^{2} - 2$	36 plus 4 y minus 1 y squared plus 5 y squared minus 2	36 plus 4 y minus 1 y kwadraat plus 5 y kwadraat minus 2
24	$(5 + 9) - 4 + 3 =$	left p'ren 5 plus 9 right p'ren minus 4 plus 3 equals	links hakkie 5 plus 9 regs hakkie minus 4 plus 3 is gelyk aan
25	$\overset{\leftrightarrow}{B C}$	ModAbove upper B upper C With left right arrow	pas aan bo hoofletter B hoofletter C met links regs pyltjie
26	$\vec{P Q}$	ModAbove upper P upper Q With right arrow	pas aan bo hoofletter P hoofletter Q met regs pyltjie
27	$\bar{G H}$	ModAbove upper G upper H With bar	pas aan bo hoofletter G hoofletter H met makron
28	$\bar{W X} ≅ \bar{Y Z}$	ModAbove upper W upper X With bar approximately equals ModAbove upper Y upper Z With bar	pas aan bo hoofletter W hoofletter X met makron ongeveer gelyk aan pas aan bo hoofletter Y hoofletter Z met makron
29	$∠ B E F$	angle upper B upper E upper F	hoek hoofletter B hoofletter E hoofletter F
30	$∠ B E D$	angle upper B upper E upper D	hoek hoofletter B hoofletter E hoofletter D
31	$∠ D E F$	angle upper D upper E upper F	hoek hoofletter D hoofletter E hoofletter F
32	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	x equals StartFrac negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFrac	x is gelyk aan BeginBreuk negatief b plus of minus Begin wortel b kwadraat minus 4 a c End wortel Oor 2 a EndBreuk
33	$y = x^{2} + 8 x + 16$	y equals x squared plus 8 x plus 16	y is gelyk aan x kwadraat plus 8 x plus 16
34	$y = \frac{1}{3} (3^{x})$	y equals one third left p'ren 3 Sup x Base right p'ren	y is gelyk aan een derde links hakkie 3 Sup x Basis regs hakkie
35	$y = 10 - 2 x$	y equals 10 minus 2 x	y is gelyk aan 10 minus 2 x
36	$y = 2 x^{3} + 5$	y equals 2 x cubed plus 5	y is gelyk aan 2 x kubbiek plus 5
37	$y = (x^{2} + 1) (x^{2} + 3)$	y equals left p'ren x squared plus 1 right p'ren left p'ren x squared plus 3 right p'ren	y is gelyk aan links hakkie x kwadraat plus 1 regs hakkie links hakkie x kwadraat plus 3 regs hakkie
38	$y = {0.5}^{x}$	y equals 0.5 Sup x	y is gelyk aan 0,5 Sup x
39	$y = 22 - 2 x$	y equals 22 minus 2 x	y is gelyk aan 22 minus 2 x
40	$y = \frac{3}{x}$	y equals StartFrac 3 Over x EndFrac	y is gelyk aan BeginBreuk 3 Oor x EndBreuk
41	$y = (x + 4) (x + 4)$	y equals left p'ren x plus 4 right p'ren left p'ren x plus 4 right p'ren	y is gelyk aan links hakkie x plus 4 regs hakkie links hakkie x plus 4 regs hakkie
42	$y = (4 x - 3) (x + 1)$	y equals left p'ren 4 x minus 3 right p'ren left p'ren x plus 1 right p'ren	y is gelyk aan links hakkie 4 x minus 3 regs hakkie links hakkie x plus 1 regs hakkie
43	$y = 20 x - 4 x^{2}$	y equals 20 x minus 4 x squared	y is gelyk aan 20 x minus 4 x kwadraat
44	$y = x^{2}$	y equals x squared	y is gelyk aan x kwadraat
45	$y = 3^{x - 1}$	y equals 3 Sup x minus 1	y is gelyk aan 3 Sup x minus 1
46	$y = 16 - 2 (x + 3)$	y equals 16 minus 2 left p'ren x plus 3 right p'ren	y is gelyk aan 16 minus 2 links hakkie x plus 3 regs hakkie
47	$y = 4 x^{2} - x - 3$	y equals 4 x squared minus x minus 3	y is gelyk aan 4 x kwadraat minus x minus 3
48	$y = x + \frac{1}{x}$	y equals x plus StartFrac 1 Over x EndFrac	y is gelyk aan x plus BeginBreuk 1 Oor x EndBreuk
49	$y = 4 x (5 - x)$	y equals 4 x left p'ren 5 minus x right p'ren	y is gelyk aan 4 x links hakkie 5 minus x regs hakkie
50	$y = 2 (x - 3) + 6 (1 - x)$	y equals 2 left p'ren x minus 3 right p'ren plus 6 left p'ren 1 minus x right p'ren	y is gelyk aan 2 links hakkie x minus 3 regs hakkie plus 6 links hakkie 1 minus x regs hakkie
51	$0.25 > \frac{5}{16}$	0.25 greater than five sixteenths	0,25 groter as vyf sestiendes
52	$32 \cdot (5 \cdot 7)$	32 dot left p'ren 5 dot 7 right p'ren	32 punt links hakkie 5 punt 7 regs hakkie
53	$(\frac{1}{2} \times \frac{1}{2} \times π \times 2) + (2 \times \frac{1}{2} \times π \times 5)$	left p'ren one half times one half times pi times 2 right p'ren plus left p'ren 2 times one half times pi times 5 right p'ren	links hakkie een helfte maal een helfte maal pi maal 2 regs hakkie plus links hakkie 2 maal een helfte maal pi maal 5 regs hakkie
54	$\underset{n \to \infty}{liminf} E_{n} = ⋃_{n \geq 1} ⋂_{k \geq n} E_{k}, \underset{n \to \infty}{limsup} E_{n} = ⋂_{n \geq 1} ⋃_{k \geq n} E_{k} .$	liminf Underscript n right arrow infinity Endscripts upper E Sub n Base equals union Underscript n greater than or equals 1 Endscripts intersection Underscript k greater than or equals n Endscripts upper E Sub k Base comma limsup Underscript n right arrow infinity Endscripts upper E Sub n Base equals intersection Underscript n greater than or equals 1 Endscripts union Underscript k greater than or equals n Endscripts upper E Sub k Base period	liminf Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E Onderskrif n Basis is gelyk aan n ary union Onderskrif n groter of gelyk aan 1 End skrifte n ary intersection Onderskrif k groter of gelyk aan n End skrifte hoofletter E Onderskrif k Basis komma limsup Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E Onderskrif n Basis is gelyk aan n ary intersection Onderskrif n groter of gelyk aan 1 End skrifte n ary union Onderskrif k groter of gelyk aan n End skrifte hoofletter E Onderskrif k Basis punt
55	$\begin{array}{l} (i) & 𝒮 \in 𝒜; \\ (ii) & if E \in 𝒜 then \overline{E} \in 𝒜; \\ (iii) & if E_{1}, E_{2} \in 𝒜 then E_{1} \cup E_{2} \in 𝒜 . \end{array}$	StartLayout 1st Row 1st Column left p'ren i right p'ren 2nd Column script upper S element of script upper A semicolon 2nd Row 1st Column left p'ren ii right p'ren 2nd Column if upper E element of script upper A then upper E overbar element of script upper A semicolon 3rd Row 1st Column left p'ren iii right p'ren 2nd Column if upper E 1 comma upper E 2 element of script upper A then upper E 1 union upper E 2 element of script upper A period EndLayout	Begin uitleg 1. Ry 1. Kolom links hakkie i regs hakkie 2. Kolom skrif hoofletter S element van skrif hoofletter A kommapunt 2. Ry 1. Kolom links hakkie ii regs hakkie 2. Kolom if hoofletter E element van skrif hoofletter A then hoofletter E bostaaf element van skrif hoofletter A kommapunt 3. Ry 1. Kolom links hakkie iii regs hakkie 2. Kolom if hoofletter E 1 komma hoofletter E 2 element van skrif hoofletter A then hoofletter E 1 eenheid hoofletter E 2 element van skrif hoofletter A punt End uitleg
56	$\begin{array}{l} (A . 1) If A \in ℱ then 0 \leq P {A} \leq 1 . & (1) \\ (A . 2) P {𝒮} = 1 . & (2) \\ (A . 3) If {E_{n}, n \geq 1} \in ℱ is a sequence of disjoint & (3) \end{array}$	StartLayout 1st Row 1st Column Blank 2nd Column Blank 3rd Column left p'ren normal upper A period 1 right p'ren upper I f upper A element of script upper F t h e n 0 less than or equals upper P left brace upper A right brace less than or equals 1 period 4th Column left p'ren 1 right p'ren 2nd Row 1st Column Blank 2nd Column Blank 3rd Column left p'ren normal upper A period 2 right p'ren upper P left brace script upper S right brace equals 1 period 4th Column left p'ren 2 right p'ren 3rd Row 1st Column Blank 2nd Column Blank 3rd Column left p'ren normal upper A period 3 right p'ren upper I f left brace upper E Sub n Base comma n greater than or equals 1 right brace element of script upper F is a sequence of disjoint 4th Column left p'ren 3 right p'ren EndLayout	Begin uitleg 1. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 1 regs hakkie hoofletter I f hoofletter A element van skrif hoofletter F t h e n 0 kleiner of gelyk aan hoofletter P links krulhakkie hoofletter A regs krulhakkie kleiner of gelyk aan 1 punt 4. Kolom links hakkie 1 regs hakkie 2. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 2 regs hakkie hoofletter P links krulhakkie skrif hoofletter S regs krulhakkie is gelyk aan 1 punt 4. Kolom links hakkie 2 regs hakkie 3. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 3 regs hakkie hoofletter I f links krulhakkie hoofletter E Onderskrif n Basis komma n groter of gelyk aan 1 regs krulhakkie element van skrif hoofletter F is a sequence of disjoint 4. Kolom links hakkie 3 regs hakkie End uitleg
57	$P {B_{j} \| A} = \frac{P {B_{j}} P {A \| B_{j}}}{\sum_{j' \in J} P {B_{j'}} P {A \| B_{j'}}} .$	upper P left brace upper B Sub j Base vertical bar upper A right brace equals StartFrac upper P left brace upper B Sub j Base right brace upper P left brace upper A vertical bar upper B Sub j Base right brace Over sigma summation Underscript j prime element of upper J Endscripts upper P left brace upper B Sub j prime Base right brace upper P left brace upper A vertical bar upper B Sub j prime Base right brace EndFrac period	hoofletter P links krulhakkie hoofletter B Onderskrif j Basis afstreep hoofletter A regs krulhakkie is gelyk aan BeginBreuk hoofletter P links krulhakkie hoofletter B Onderskrif j Basis regs krulhakkie hoofletter P links krulhakkie hoofletter A afstreep hoofletter B Onderskrif j Basis regs krulhakkie Oor som Onderskrif j priem element van hoofletter J End skrifte hoofletter P links krulhakkie hoofletter B Onderskrif j priem Basis regs krulhakkie hoofletter P links krulhakkie hoofletter A afstreep hoofletter B Onderskrif j priem Basis regs krulhakkie EndBreuk punt
58	$μ_{1} (B) = \int_{B} f (x) d μ_{2} (x)$	mu 1 left p'ren upper B right p'ren equals integral Underscript upper B Endscripts f left p'ren x right p'ren d mu 2 left p'ren x right p'ren	my 1 links hakkie hoofletter B regs hakkie is gelyk aan integraal Onderskrif hoofletter B End skrifte f links hakkie x regs hakkie d my 2 links hakkie x regs hakkie
59	$lim_{n \to \infty} E {\| X_{n} - X \|} = E {lim_{n \to \infty} \| X_{n} - X \|} = 0 .$	limit Underscript n right arrow infinity Endscripts upper E left brace StartAbsoluteValue upper X Sub n Base minus upper X EndAbsoluteValue right brace equals upper E left brace limit Underscript n right arrow infinity Endscripts StartAbsoluteValue upper X Sub n Base minus upper X EndAbsoluteValue right brace equals 0 period	limit Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E links krulhakkie begin absolute Waarde hoofletter X Onderskrif n Basis minus hoofletter X End Absolute Waarde regs krulhakkie is gelyk aan hoofletter E links krulhakkie limit Onderskrif n regs pyltjie oneindigheid End skrifte begin absolute Waarde hoofletter X Onderskrif n Basis minus hoofletter X End Absolute Waarde regs krulhakkie is gelyk aan 0 punt
60	$\begin{array}{l} P_{μ, σ} {Y \geq l_{β} ({\overline{Y}}_{n}, S_{n})} = P_{μ, σ} {(Y - {\overline{Y}}_{n}) / (S \cdot {(1 + \frac{1}{n})}^{1 / 2}) \geq - t_{β} [n - 1]} = β, \\ (1) \end{array}$	StartLayout 1st Row 1st Column upper P Sub mu comma sigma Base left brace upper Y greater than or equals l Sub beta Base left p'ren upper Y overbar Sub n Base comma upper S Sub n Base right p'ren right brace equals upper P Sub mu comma sigma Base left brace left p'ren upper Y minus upper Y overbar Sub n Base right p'ren divided by left p'ren upper S dot left p'ren 1 plus StartFrac 1 Over n EndFrac right p'ren Sup 1 divided by 2 Base right p'ren greater than or equals minus t Sub beta Base left brack n minus 1 right brack right brace equals beta comma 2nd Row 1st Column Blank 2nd Column left p'ren 1 right p'ren EndLayout	Begin uitleg 1. Ry 1. Kolom hoofletter P Onderskrif my komma sigma Basis links krulhakkie hoofletter Y groter of gelyk aan l Onderskrif beta Basis links hakkie hoofletter Y bostaaf Onderskrif n Basis komma hoofletter S Onderskrif n Basis regs hakkie regs krulhakkie is gelyk aan hoofletter P Onderskrif my komma sigma Basis links krulhakkie links hakkie hoofletter Y minus hoofletter Y bostaaf Onderskrif n Basis regs hakkie gedeel deur links hakkie hoofletter S dot links hakkie 1 plus BeginBreuk 1 Oor n EndBreuk regs hakkie Sup 1 gedeel deur 2 Basis regs hakkie groter of gelyk aan minus t Onderskrif beta Basis links blokhakkie n minus 1 regs blokhakkie regs krulhakkie is gelyk aan beta komma 2. Ry 1. Kolom leeg 2. Kolom links hakkie 1 regs hakkie End uitleg
61	$L = (\begin{matrix} 1 & - 1 \\ 1 & - 1 & 0 \\ 0 \\ 1 & - 1 \end{matrix}) .$	upper L equals Start 5 By 6 Matrix 1st Row 1st Column 1 2nd Column negative 1 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 2nd Row 1st Column Blank 2nd Column 1 3rd Column negative 1 4th Column Blank 5th Column 0 6th Column Blank 3rd Row 1st Column Blank 2nd Column Blank 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 4th Row 1st Column Blank 2nd Column 0 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 5th Row 1st Column Blank 2nd Column Blank 3rd Column Blank 4th Column Blank 5th Column 1 6th Column negative 1 EndMatrix period	hoofletter L is gelyk aan Begin 5 By 6 Matriks 1. Ry 1. Kolom 1 2. Kolom negatief 1 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 2. Ry 1. Kolom leeg 2. Kolom 1 3. Kolom negatief 1 4. Kolom Leeg 5. Kolom 0 6. Kolom Leeg 3. Ry 1. Kolom leeg 2. Kolom Leeg 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 4. Ry 1. Kolom leeg 2. Kolom 0 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 5. Ry 1. Kolom leeg 2. Kolom Leeg 3. Kolom Leeg 4. Kolom Leeg 5. Kolom 1 6. Kolom negatief 1 End Matriks punt
62	$\sqrt{n} [{\overline{Y}}_{n} - (μ + z_{β} σ)] / S_{n} ~ \frac{U + \sqrt{n} z_{1 - β}}{(χ^{2} [n - 1] / (n - 1))^{1 / 2}} ~ t [n - 1; \sqrt{n} z_{1 - β}],$	StartRoot n EndRoot left brack upper Y overbar Sub n Base minus left p'ren mu plus z Sub beta Base sigma right p'ren right brack divided by upper S Sub n Base tilde StartFrac upper U plus StartRoot n EndRoot z Sub 1 minus beta Base Over left p'ren chi squared left brack n minus 1 right brack divided by left p'ren n minus 1 right p'ren right p'ren Sup 1 divided by 2 Base EndFrac tilde t left brack n minus 1 semicolon StartRoot n EndRoot z Sub 1 minus beta Base right brack comma	Begin wortel n End wortel links blokhakkie hoofletter Y bostaaf Onderskrif n Basis minus links hakkie my plus z Onderskrif beta Basis sigma regs hakkie regs blokhakkie gedeel deur hoofletter S Onderskrif n Basis tilde BeginBreuk hoofletter U plus Begin wortel n End wortel z Onderskrif 1 minus beta Basis Oor links hakkie chi kwadraat links blokhakkie n minus 1 regs blokhakkie gedeel deur links hakkie n minus 1 regs hakkie regs hakkie Sup 1 gedeel deur 2 Basis EndBreuk tilde t links blokhakkie n minus 1 kommapunt Begin wortel n End wortel z Onderskrif 1 minus beta Basis regs blokhakkie komma
63	$\begin{array}{l} γ & = P {E_{p, q} \subset (X_{(r)}, X_{(s)}} \\ = \frac{n!}{(r - 1)!} \sum_{j = 0}^{s - r - 1} (- 1)^{j} \frac{p^{r + j}}{(n - r - j)! j!} I_{1 - q} (n - s + 1, s - r - j) . \end{array}$	StartLayout 1st Row 1st Column gamma 2nd Column equals upper P left brace upper E Sub p comma q Base subset of left p'ren upper X Sub left p'ren r right p'ren Base comma upper X Sub left p'ren s right p'ren Base right brace 2nd Row 1st Column Blank 2nd Column equals StartFrac n factorial Over left p'ren r minus 1 right p'ren factorial EndFrac sigma summation Underscript j equals 0 Overscript s minus r minus 1 Endscripts left p'ren negative 1 right p'ren Sup j Base StartFrac p Sup r plus j Base Over left p'ren n minus r minus j right p'ren factorial j factorial EndFrac upper I Sub 1 minus q Base left p'ren n minus s plus 1 comma s minus r minus j right p'ren period EndLayout	Begin uitleg 1. Ry 1. Kolom gamma 2. Kolom is gelyk aan hoofletter P links krulhakkie hoofletter E Onderskrif p komma q Basis deelversameling van links hakkie hoofletter X Onderskrif links hakkie r regs hakkie Basis komma hoofletter X Onderskrif links hakkie s regs hakkie Basis regs krulhakkie 2. Ry 1. Kolom leeg 2. Kolom is gelyk aan BeginBreuk n faktoriaal Oor links hakkie r minus 1 regs hakkie faktoriaal EndBreuk som Onderskrif j is gelyk aan 0 Boskrif s minus r minus 1 End skrifte links hakkie negatief 1 regs hakkie Sup j Basis BeginBreuk p Sup r plus j Basis Oor links hakkie n minus r minus j regs hakkie faktoriaal j faktoriaal EndBreuk hoofletter I Onderskrif 1 minus q Basis links hakkie n minus s plus 1 komma s minus r minus j regs hakkie punt End uitleg
64	$S_{i} [\begin{matrix} t \\ x \end{matrix}] = [\begin{matrix} 1 / m & 0 \\ a_{i} & r_{i} \end{matrix}] [\begin{matrix} t \\ x \end{matrix}] + [\begin{matrix} (i - 1) / m \\ b_{i} \end{matrix}],$	upper S Sub i Base StartBinomialOrMatrix t Choose x EndBinomialOrMatrix equals Start 2 By 2 Matrix 1st Row 1st Column 1 divided by m 2nd Column 0 2nd Row 1st Column a Sub i Base 2nd Column r Sub i Base EndMatrix StartBinomialOrMatrix t Choose x EndBinomialOrMatrix plus StartBinomialOrMatrix left p'ren i minus 1 right p'ren divided by m Choose b Sub i Base EndBinomialOrMatrix comma	hoofletter S Onderskrif i Basis Begin Binomiaal of Matriks t Kies x End Binomiaal of Matriks is gelyk aan Begin 2 By 2 Matriks 1. Ry 1. Kolom 1 gedeel deur m 2. Kolom 0 2. Ry 1. Kolom a Onderskrif i Basis 2. Kolom r Onderskrif i Basis End Matriks Begin Binomiaal of Matriks t Kies x End Binomiaal of Matriks plus Begin Binomiaal of Matriks links hakkie i minus 1 regs hakkie gedeel deur m Kies b Onderskrif i Basis End Binomiaal of Matriks komma
65	$c_{1} h^{4 - 2 s} \leq \frac{1}{2 T} \int_{- T}^{T} {(f (t + h) - f (t))}^{2} d t \leq c_{2} h^{4 - 2 s}$	c 1 h Sup 4 minus 2 s Base less than or equals StartFrac 1 Over 2 upper T EndFrac integral Sub negative upper T Sup upper T Base left p'ren f left p'ren t plus h right p'ren minus f left p'ren t right p'ren right p'ren squared normal d t less than or equals c 2 h Sup 4 minus 2 s	c 1 h Sup 4 minus 2 s Basis kleiner of gelyk aan BeginBreuk 1 Oor 2 hoofletter T EndBreuk integraal Onder negatief hoofletter T Bo hoofletter T Basis links hakkie f links hakkie t plus h regs hakkie minus f links hakkie t regs hakkie regs hakkie kwadraat normaal d t kleiner of gelyk aan c 2 h Sup 4 minus 2 s
66	$C (0) - C (h) ≃ c h^{4 - 2 s}$	upper C left p'ren 0 right p'ren minus upper C left p'ren h right p'ren asymptotically equals c h Sup 4 minus 2 s	hoofletter C links hakkie 0 regs hakkie minus hoofletter C links hakkie h regs hakkie assimtoties gelyk aan c h Sup 4 minus 2 s
67	$S (ω) = \lim_{T \to \infty} \frac{1}{2 T} {\|\int_{- T}^{T} f (t) e^{it ω} d t\|}^{2} .$	upper S left p'ren omega right p'ren equals limit Underscript upper T right arrow infinity Endscripts StartFrac 1 Over 2 upper T EndFrac StartAbsoluteValue integral Sub negative upper T Sup upper T Base comma f comma left p'ren comma t comma right p'ren comma normal e Sup italic i t omega Base comma normal d comma t EndAbsoluteValue squared period	hoofletter S links hakkie omega regs hakkie is gelyk aan limit Onderskrif hoofletter T regs pyltjie oneindigheid End skrifte BeginBreuk 1 Oor 2 hoofletter T EndBreuk begin absolute Waarde integraal Onder negatief hoofletter T Bo hoofletter T Basis komma f komma links hakkie komma t komma regs hakkie komma normaal e Sup kursief i t omega Basis komma normaal d komma t End Absolute Waarde kwadraat punt
68	$\int_{0}^{1} \int_{0}^{1} {[\| f (t) - f (u) \|^{2} + \| t - u \|^{2}]}^{- s / 2} d t d u < \infty$	integral Sub 0 Sup 1 Base integral Sub 0 Sup 1 Base left brack StartAbsoluteValue f left p'ren t right p'ren minus f left p'ren u right p'ren EndAbsoluteValue squared plus StartAbsoluteValue t minus u EndAbsoluteValue squared right brack Sup negative s divided by 2 Base normal d t normal d u less than infinity	integraal Onder 0 Bo 1 Basis integraal Onder 0 Bo 1 Basis links blokhakkie begin absolute Waarde f links hakkie t regs hakkie minus f links hakkie u regs hakkie End Absolute Waarde kwadraat plus begin absolute Waarde t minus u End Absolute Waarde kwadraat regs blokhakkie Sup negatief s gedeel deur 2 Basis normaal d t normaal d u kleiner as oneindigheid
69	$E (\sum_{I \in E_{k + 1}} \| I \|^{s}) = E (\sum_{I \in E_{k}} \| I \|^{s}) E (R_{1}^{s} + R_{2}^{s}) .$	sans serif upper E left p'ren sigma summation Underscript upper I element of upper E Sub k plus 1 Base Endscripts StartAbsoluteValue upper I EndAbsoluteValue Sup s Base right p'ren equals sans serif upper E left p'ren sigma summation Underscript upper I element of upper E Sub k Base Endscripts StartAbsoluteValue upper I EndAbsoluteValue Sup s Base right p'ren sans serif upper E left p'ren upper R 1 Sup s Base plus upper R 2 Sup s Base right p'ren period	sans serif hoofletter E links hakkie som Onderskrif hoofletter I element van hoofletter E Onderskrif k plus 1 Basis End skrifte begin absolute Waarde hoofletter I End Absolute Waarde Sup s Basis regs hakkie is gelyk aan sans serif hoofletter E links hakkie som Onderskrif hoofletter I element van hoofletter E Onderskrif k Basis End skrifte begin absolute Waarde hoofletter I End Absolute Waarde Sup s Basis regs hakkie sans serif hoofletter E links hakkie hoofletter R 1 Sup s Basis plus hoofletter R 2 Sup s Basis regs hakkie punt
70	$(x_{1}, y_{1})$	left p'ren x 1 comma y 1 right p'ren	links hakkie x 1 komma y 1 regs hakkie
71	$(x_{2}, y_{2})$	left p'ren x 2 comma y 2 right p'ren	links hakkie x 2 komma y 2 regs hakkie
72	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$	d equals StartRoot left p'ren x 2 minus x 1 right p'ren squared plus left p'ren y 2 minus y 1 right p'ren squared EndRoot	d is gelyk aan Begin wortel links hakkie x 2 minus x 1 regs hakkie kwadraat plus links hakkie y 2 minus y 1 regs hakkie kwadraat End wortel
73	$ℝ$	double struck upper R	hoofletter R dubbelgeslaan
74	$ℝ = (- \infty, \infty)$	double struck upper R equals left p'ren negative infinity comma infinity right p'ren	hoofletter R dubbelgeslaan is gelyk aan links hakkie negatief oneindigheid komma oneindigheid regs hakkie
75	${1, 2, 3}$	StartSet 1 comma 2 comma 3 EndSet	begin versameling 1 komma 2 komma 3 End versameling
76	$1 \in S$	1 element of upper S	1 element van hoofletter S
77	$3 \in S$	3 element of upper S	3 element van hoofletter S
78	$4 \notin S$	4 not an element of upper S	4 nie 'n element van hoofletter S
79	$a = \sqrt{3 x - 1} + {(1 + x)}^{2}$	a equals StartRoot 3 x minus 1 EndRoot plus left p'ren 1 plus x right p'ren squared	a is gelyk aan Begin wortel 3 x minus 1 End wortel plus links hakkie 1 plus x regs hakkie kwadraat
80	$a = \frac{{(b + c)}^{2}}{d} + \frac{{(e + f)}^{2}}{g}$	a equals StartFrac left p'ren b plus c right p'ren squared Over d EndFrac plus StartFrac left p'ren e plus f right p'ren squared Over g EndFrac	a is gelyk aan BeginBreuk links hakkie b plus c regs hakkie kwadraat Oor d EndBreuk plus BeginBreuk links hakkie e plus f regs hakkie kwadraat Oor g EndBreuk
81	$x = [{(a + b)}^{2} {(c - b)}^{2}] + [{(d + e)}^{2} {(f - e)}^{2}]$	x equals left brack left p'ren a plus b right p'ren squared left p'ren c minus b right p'ren squared right brack plus left brack left p'ren d plus e right p'ren squared left p'ren f minus e right p'ren squared right brack	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat links hakkie c minus b regs hakkie kwadraat regs blokhakkie plus links blokhakkie links hakkie d plus e regs hakkie kwadraat links hakkie f minus e regs hakkie kwadraat regs blokhakkie
82	$x = [{(a + b)}^{2}] + [{(f - e)}^{2}]$	x equals left brack left p'ren a plus b right p'ren squared right brack plus left brack left p'ren f minus e right p'ren squared right brack	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat regs blokhakkie plus links blokhakkie links hakkie f minus e regs hakkie kwadraat regs blokhakkie
83	$x = [{(a + b)}^{2}]$	x equals left brack left p'ren a plus b right p'ren squared right brack	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat regs blokhakkie
84	$x = {(a + b)}^{2}$	x equals left p'ren a plus b right p'ren squared	x is gelyk aan links hakkie a plus b regs hakkie kwadraat
85	$x = a + b^{2}$	x equals a plus b squared	x is gelyk aan a plus b kwadraat
86	$\frac{\frac{1}{2}}{\frac{3}{4}} = \frac{2}{3}$	StartFrac one half Over three fourths EndFrac equals two thirds	BeginBreuk een helfte Oor drie kwarte EndBreuk is gelyk aan twee derdes
87	$2 ((x + 1) (x + 3) - 4 ((x - 1) (x + 2) - 3)) = y$	2 left p'ren left p'ren x plus 1 right p'ren left p'ren x plus 3 right p'ren minus 4 left p'ren left p'ren x minus 1 right p'ren left p'ren x plus 2 right p'ren minus 3 right p'ren right p'ren equals y	2 links hakkie links hakkie x plus 1 regs hakkie links hakkie x plus 3 regs hakkie minus 4 links hakkie links hakkie x minus 1 regs hakkie links hakkie x plus 2 regs hakkie minus 3 regs hakkie regs hakkie is gelyk aan y
88	$\cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \dots$	cosine x equals 1 minus StartFrac x squared Over 2 factorial EndFrac plus StartFrac x Sup 4 Base Over 4 factorial EndFrac minus ellipsis	kosinus x is gelyk aan 1 minus BeginBreuk x kwadraat Oor 2 faktoriaal EndBreuk plus BeginBreuk x Sup 4 Basis Oor 4 faktoriaal EndBreuk minus ellipsis
89	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	x equals StartFrac negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFrac	x is gelyk aan BeginBreuk negatief b plus of minus Begin wortel b kwadraat minus 4 a c End wortel Oor 2 a EndBreuk
90	$x + y^{\frac{2}{k + 1}}$	x plus y Sup StartFrac 2 Over k plus 1 EndFrac	x plus y Sup BeginBreuk 2 Oor k plus 1 EndBreuk
91	$\lim_{x \to 0} \frac{\sin x}{x} = 1$	limit Underscript x right arrow 0 Endscripts StartFrac sine x Over x EndFrac equals 1	limit Onderskrif x regs pyltjie 0 End skrifte BeginBreuk sinus x Oor x EndBreuk is gelyk aan 1
92	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$	d equals StartRoot left p'ren x 2 minus x 1 right p'ren squared plus left p'ren y 2 minus y 1 right p'ren squared EndRoot	d is gelyk aan Begin wortel links hakkie x 2 minus x 1 regs hakkie kwadraat plus links hakkie y 2 minus y 1 regs hakkie kwadraat End wortel
93	$F_{n} = F_{n - 1} + F_{n - 2}$	upper F Sub n Base equals upper F Sub n minus 1 Base plus upper F Sub n minus 2	hoofletter F Onderskrif n Basis is gelyk aan hoofletter F Onderskrif n minus 1 Basis plus hoofletter F Onderskrif n minus 2
94	$Π = (\begin{matrix} π_{11} & π_{12} & π_{12} & 0 & 0 & 0 \\ π_{12} & π_{11} & π_{12} & 0 & 0 & 0 \\ π_{12} & π_{12} & π_{11} & 0 & 0 & 0 \\ 0 & 0 & 0 & π_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & π_{44} & 0 \\ 0 & 0 & 0 & 0 & 0 & π_{44} \end{matrix})$	bold upper Pi equals Start 6 By 6 Matrix 1st Row 1st Column pi 11 2nd Column pi 12 3rd Column pi 12 4th Column 0 5th Column 0 6th Column 0 2nd Row 1st Column pi 12 2nd Column pi 11 3rd Column pi 12 4th Column 0 5th Column 0 6th Column 0 3rd Row 1st Column pi 12 2nd Column pi 12 3rd Column pi 11 4th Column 0 5th Column 0 6th Column 0 4th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column pi 44 5th Column 0 6th Column 0 5th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column 0 5th Column pi 44 6th Column 0 6th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column 0 5th Column 0 6th Column pi 44 EndMatrix	vetgedruk hoofletter Pi is gelyk aan Begin 6 By 6 Matriks 1. Ry 1. Kolom pi 11 2. Kolom pi 12 3. Kolom pi 12 4. Kolom 0 5. Kolom 0 6. Kolom 0 2. Ry 1. Kolom pi 12 2. Kolom pi 11 3. Kolom pi 12 4. Kolom 0 5. Kolom 0 6. Kolom 0 3. Ry 1. Kolom pi 12 2. Kolom pi 12 3. Kolom pi 11 4. Kolom 0 5. Kolom 0 6. Kolom 0 4. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom pi 44 5. Kolom 0 6. Kolom 0 5. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom 0 5. Kolom pi 44 6. Kolom 0 6. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom 0 5. Kolom 0 6. Kolom pi 44 End Matriks
95	$s_{11} = \frac{c_{11} + c_{12}}{(c_{11} - c_{12}) (c_{11} + 2 c_{12})}$	s 11 equals StartFrac c 11 plus c 12 Over left p'ren c 11 minus c 12 right p'ren left p'ren c 11 plus 2 c 12 right p'ren EndFrac	s 11 is gelyk aan BeginBreuk c 11 plus c 12 Oor links hakkie c 11 minus c 12 regs hakkie links hakkie c 11 plus 2 c 12 regs hakkie EndBreuk
96	$Si O_{2} + 6 H F \to H_{2} Si F_{6} + 2 H_{2} O$	upper S i normal upper O 2 plus 6 normal upper H normal upper F right arrow normal upper H 2 upper S i normal upper F 6 plus 2 normal upper H 2 normal upper O	hoofletter S i normaal hoofletter O 2 plus 6 normaal hoofletter H normaal hoofletter F regs pyltjie normaal hoofletter H 2 hoofletter S i normaal hoofletter F 6 plus 2 normaal hoofletter H 2 normaal hoofletter O
97	$\frac{d}{d x} (E (x) A (x) \frac{d w (x)}{d x}) + p (x) = 0$	StartFrac d Over d x EndFrac left p'ren upper E left p'ren x right p'ren upper A left p'ren x right p'ren StartFrac d w left p'ren x right p'ren Over d x EndFrac right p'ren plus p left p'ren x right p'ren equals 0	BeginBreuk d Oor d x EndBreuk links hakkie hoofletter E links hakkie x regs hakkie hoofletter A links hakkie x regs hakkie BeginBreuk d w links hakkie x regs hakkie Oor d x EndBreuk regs hakkie plus p links hakkie x regs hakkie is gelyk aan 0
98	${TCS}_{gas} = - \frac{1}{2} (\frac{P_{seal}}{P_{max}}) (\frac{1}{T_{seal}})$	TCS Sub gas Base equals minus one half left p'ren StartFrac upper P Sub seal Base Over upper P Sub max Base EndFrac right p'ren left p'ren StartFrac 1 Over upper T Sub seal Base EndFrac right p'ren	TCS Onderskrif gas Basis is gelyk aan minus een helfte links hakkie BeginBreuk hoofletter P Onderskrif seal Basis Oor hoofletter P Onderskrif max Basis EndBreuk regs hakkie links hakkie BeginBreuk 1 Oor hoofletter T Onderskrif seal Basis EndBreuk regs hakkie
99	$B_{p} = \frac{\frac{7 - v^{2}}{3} (1 + \frac{c^{2}}{a^{2}} + \frac{c^{4}}{a^{4}}) + \frac{{(3 - v)}^{2} c^{2}}{(1 + v) a^{2}}}{(1 - v) (1 - \frac{c^{4}}{a^{4}}) (1 - \frac{c^{2}}{a^{2}})}$	upper B Sub p Base equals StartStartFrac StartFrac 7 minus v squared Over 3 EndFrac left p'ren 1 plus StartFrac c squared Over a squared EndFrac plus StartFrac c Sup 4 Base Over a Sup 4 Base EndFrac right p'ren plus StartFrac left p'ren 3 minus v right p'ren squared c squared Over left p'ren 1 plus v right p'ren a squared EndFrac OverOver left p'ren 1 minus v right p'ren left p'ren 1 minus StartFrac c Sup 4 Base Over a Sup 4 Base EndFrac right p'ren left p'ren 1 minus StartFrac c squared Over a squared EndFrac right p'ren EndEndFrac	hoofletter B Onderskrif p Basis is gelyk aan BeginBeginBreuk BeginBreuk 7 minus v kwadraat Oor 3 EndBreuk links hakkie 1 plus BeginBreuk c kwadraat Oor a kwadraat EndBreuk plus BeginBreuk c Sup 4 Basis Oor a Sup 4 Basis EndBreuk regs hakkie plus BeginBreuk links hakkie 3 minus v regs hakkie kwadraat c kwadraat Oor links hakkie 1 plus v regs hakkie a kwadraat EndBreuk OorOor links hakkie 1 minus v regs hakkie links hakkie 1 minus BeginBreuk c Sup 4 Basis Oor a Sup 4 Basis EndBreuk regs hakkie links hakkie 1 minus BeginBreuk c kwadraat Oor a kwadraat EndBreuk regs hakkie EndEndBreuk
100	$Q_{tank}^{series} = \frac{1}{R_{s}} \sqrt{\frac{L_{s}}{C_{s}}}$	upper Q Sub tank Sup series Base equals StartFrac 1 Over upper R Sub s Base EndFrac StartRoot StartFrac upper L Sub s Base Over upper C Sub s Base EndFrac EndRoot	hoofletter Q Onderskrif tank Sup series Basis is gelyk aan BeginBreuk 1 Oor hoofletter R Onderskrif s Basis EndBreuk Begin wortel BeginBreuk hoofletter L Onderskrif s Basis Oor hoofletter C Onderskrif s Basis EndBreuk End wortel
101	$Δ ϕ_{peak} = {tan}^{- 1} (k^{2} Q_{tank}^{series})$	upper Delta phi Sub peak Base equals tangent Sup negative 1 Base left p'ren k squared upper Q Sub tank Sup series Base right p'ren	hoofletter Delta phi Onderskrif peak Basis is gelyk aan tangens Sup negatief 1 Basis links hakkie k kwadraat hoofletter Q Onderskrif tank Sup series Basis regs hakkie
102	$f = 1.013 \frac{W}{L^{2}} \sqrt{\frac{E}{ρ}} \sqrt{(1 + 0.293 \frac{L^{2}}{{EW}^{2}} σ)}$	f equals 1.013 StartFrac upper W Over upper L squared EndFrac StartRoot StartFrac upper E Over rho EndFrac EndRoot StartRoot left p'ren 1 plus 0.293 StartFrac upper L squared Over EW squared EndFrac sigma right p'ren EndRoot	f is gelyk aan 1.013 BeginBreuk hoofletter W Oor hoofletter L kwadraat EndBreuk Begin wortel BeginBreuk hoofletter E Oor rho EndBreuk End wortel Begin wortel links hakkie 1 plus 0.293 BeginBreuk hoofletter L kwadraat Oor EW kwadraat EndBreuk sigma regs hakkie End wortel
103	$u_{n} (x) = γ_{n} (\cosh k_{n} x - \cos k_{n} x) + (\sinh k_{n} x - \sin k_{n} x)$	u Sub n Base left p'ren x right p'ren equals gamma Sub n Base left p'ren hyperbolic cosine k Sub n Base x minus cosine k Sub n Base x right p'ren plus left p'ren hyperbolic sine k Sub n Base x minus sine k Sub n Base x right p'ren	u Onderskrif n Basis links hakkie x regs hakkie is gelyk aan gamma Onderskrif n Basis links hakkie hiperboliese kosinus k Onderskrif n Basis x minus kosinus k Onderskrif n Basis x regs hakkie plus links hakkie hiperboliese sinus k Onderskrif n Basis x minus sinus k Onderskrif n Basis x regs hakkie
104	$\begin{matrix} B & = \frac{\frac{F_{0}}{m}}{\sqrt{(ω_{0}^{2} - ω^{2})^{2} + 4 n^{2} ω^{2}}} \\ = \frac{\frac{F_{0}}{k}}{\sqrt{(1 - (ω / ω_{0}^{2})^{2})^{2} + 4 (n / ω_{0})^{2} (ω / ω_{0})^{2}}} \end{matrix}$	StartLayout 1st Row 1st Column upper B 2nd Column equals StartStartFrac StartFrac upper F 0 Over m EndFrac OverOver StartRoot left p'ren omega 0 squared minus omega squared right p'ren squared plus 4 n squared omega squared EndRoot EndEndFrac 2nd Row 1st Column Blank 2nd Column equals StartStartFrac StartFrac upper F 0 Over k EndFrac OverOver StartRoot left p'ren 1 minus left p'ren omega divided by omega 0 squared right p'ren squared right p'ren squared plus 4 left p'ren n divided by omega 0 right p'ren squared left p'ren omega divided by omega 0 right p'ren squared EndRoot EndEndFrac EndLayout	Begin uitleg 1. Ry 1. Kolom hoofletter B 2. Kolom is gelyk aan BeginBeginBreuk BeginBreuk hoofletter F 0 Oor m EndBreuk OorOor Begin wortel links hakkie omega 0 kwadraat minus omega kwadraat regs hakkie kwadraat plus 4 n kwadraat omega kwadraat End wortel EndEndBreuk 2. Ry 1. Kolom leeg 2. Kolom is gelyk aan BeginBeginBreuk BeginBreuk hoofletter F 0 Oor k EndBreuk OorOor Begin wortel links hakkie 1 minus links hakkie omega gedeel deur omega 0 kwadraat regs hakkie kwadraat regs hakkie kwadraat plus 4 links hakkie n gedeel deur omega 0 regs hakkie kwadraat links hakkie omega gedeel deur omega 0 regs hakkie kwadraat End wortel EndEndBreuk End uitleg
105	$p (A and B) = p (A) p (B \| A)$	normal p left p'ren upper A a n d upper B right p'ren equals normal p left p'ren upper A right p'ren normal p left p'ren upper B vertical bar upper A right p'ren	normaal p links hakkie hoofletter A a n d hoofletter B regs hakkie is gelyk aan normaal p links hakkie hoofletter A regs hakkie normaal p links hakkie hoofletter B afstreep hoofletter A regs hakkie
106	$PMF (x) \propto {(\frac{1}{x})}^{α}$	upper P upper M upper F left p'ren x right p'ren proportional to left p'ren StartFrac 1 Over x EndFrac right p'ren Sup alpha	hoofletter P hoofletter M hoofletter F links hakkie x regs hakkie eweredig aan links hakkie BeginBreuk 1 Oor x EndBreuk regs hakkie Sup alfa
107	$f (x) = \frac{1}{\sqrt{2 π}} exp (- x^{2} /2)$	f left p'ren x right p'ren equals StartFrac 1 Over StartRoot 2 pi EndRoot EndFrac exp left p'ren minus x squared slash 2 right p'ren	f links hakkie x regs hakkie is gelyk aan BeginBreuk 1 Oor Begin wortel 2 pi End wortel EndBreuk exp links hakkie minus x kwadraat skuinsstreep 2 regs hakkie
108	$\frac{d x}{d θ} = \frac{β}{{cos}^{2} θ}$	StartFrac d x Over d theta EndFrac equals StartFrac beta Over cosine squared theta EndFrac	BeginBreuk d x Oor d theta EndBreuk is gelyk aan BeginBreuk beta Oor kosinus kwadraat theta EndBreuk
109	$s / \sqrt{2 (n - 1)}$	s divided by StartRoot 2 left p'ren n minus 1 right p'ren EndRoot	s gedeel deur Begin wortel 2 links hakkie n minus 1 regs hakkie End wortel

Afrikaans Mathspeak Steve Noble's samples. Locale: af, Style: Superbrief.

0	$- 5 \frac{1}{5} - 6 \frac{2}{3} =$	negative 5 and one fifth minus 6 and two thirds equals	negatief 5 en een vyfde minus 6 en twee derdes is gelyk aan
1	$- 7 \frac{3}{4} - (- 4 \frac{7}{8}) =$	negative 7 and three fourths minus L p'ren negative 4 and seven eighths R p'ren equals	negatief 7 en drie kwarte minus links hakkie negatief 4 en sewe agstes regs hakkie is gelyk aan
2	$- 24.15 - (13.7) =$	negative 24.15 minus L p'ren 13.7 R p'ren equals	negatief 24,15 minus links hakkie 13,7 regs hakkie is gelyk aan
3	$(- 4) \times 3 = - 12$	L p'ren negative 4 R p'ren times 3 equals negative 12	links hakkie negatief 4 regs hakkie maal 3 is gelyk aan negatief 12
4	$- 12 \div 3 = - 4$	negative 12 divided by 3 equals negative 4	negatief 12 gedeel deur 3 is gelyk aan negatief 4
5	$- 12 \div (- 4) = 3$	negative 12 divided by L p'ren negative 4 R p'ren equals 3	negatief 12 gedeel deur links hakkie negatief 4 regs hakkie is gelyk aan 3
6	$6 \times 5$	6 times 5	6 maal 5
7	$6 \times (- 5)$	6 times L p'ren negative 5 R p'ren	6 maal links hakkie negatief 5 regs hakkie
8	$- 6 \times 5$	negative 6 times 5	negatief 6 maal 5
9	$- 6 \times (- 5)$	negative 6 times L p'ren negative 5 R p'ren	negatief 6 maal links hakkie negatief 5 regs hakkie
10	$- 8 \times 7$	negative 8 times 7	negatief 8 maal 7
11	$- 8 \times (- 7)$	negative 8 times L p'ren negative 7 R p'ren	negatief 8 maal links hakkie negatief 7 regs hakkie
12	$8 \times (- 7)$	8 times L p'ren negative 7 R p'ren	8 maal links hakkie negatief 7 regs hakkie
13	$8 \times 7$	8 times 7	8 maal 7
14	$m ∠ 1 = 30°$	m angle 1 equals 30 degree	m hoek 1 is gelyk aan 30 graad
15	$m ∠ 2 = 60°$	m angle 2 equals 60 degree	m hoek 2 is gelyk aan 60 graad
16	$m ∠ 1 + m ∠ 2 = 90°$	m angle 1 plus m angle 2 equals 90 degree	m hoek 1 plus m hoek 2 is gelyk aan 90 graad
17	$m ∠ M + m ∠ N = 180°$	m angle upper M plus m angle upper N equals 180 degree	m hoek hoofletter M plus m hoek hoofletter N is gelyk aan 180 graad
18	$A = \frac{1}{2} b h$	upper A equals one half b h	hoofletter A is gelyk aan een helfte b h
19	$\frac{area of triangle}{area of square} = \frac{{1 unit}^{2}}{{16 units}^{2}}$	Frac area of triangle Over area of square EndFrac equals Frac 1 unit squared Over 16 units squared EndFrac	Breuk area of triangle Oor area of square End breuk is gelyk aan Breuk 1 unit kwadraat Oor 16 units kwadraat End breuk
20	${0.6}^{2}$	0.6 squared	0,6 kwadraat
21	${1.5}^{2}$	1.5 squared	1,5 kwadraat
22	$4 (2 x + 3 x)$	4 L p'ren 2 x plus 3 x R p'ren	4 links hakkie 2 x plus 3 x regs hakkie
23	$36 + 4 y - 1 y^{2} + 5 y^{2} - 2$	36 plus 4 y minus 1 y squared plus 5 y squared minus 2	36 plus 4 y minus 1 y kwadraat plus 5 y kwadraat minus 2
24	$(5 + 9) - 4 + 3 =$	L p'ren 5 plus 9 R p'ren minus 4 plus 3 equals	links hakkie 5 plus 9 regs hakkie minus 4 plus 3 is gelyk aan
25	$\overset{\leftrightarrow}{B C}$	ModAbove upper B upper C With L R arrow	pas aan bo hoofletter B hoofletter C met links regs pyltjie
26	$\vec{P Q}$	ModAbove upper P upper Q With R arrow	pas aan bo hoofletter P hoofletter Q met regs pyltjie
27	$\bar{G H}$	ModAbove upper G upper H With bar	pas aan bo hoofletter G hoofletter H met makron
28	$\bar{W X} ≅ \bar{Y Z}$	ModAbove upper W upper X With bar approximately equals ModAbove upper Y upper Z With bar	pas aan bo hoofletter W hoofletter X met makron ongeveer gelyk aan pas aan bo hoofletter Y hoofletter Z met makron
29	$∠ B E F$	angle upper B upper E upper F	hoek hoofletter B hoofletter E hoofletter F
30	$∠ B E D$	angle upper B upper E upper D	hoek hoofletter B hoofletter E hoofletter D
31	$∠ D E F$	angle upper D upper E upper F	hoek hoofletter D hoofletter E hoofletter F
32	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	x equals Frac negative b plus or minus Root b squared minus 4 a c EndRoot Over 2 a EndFrac	x is gelyk aan Breuk negatief b plus of minus Wortel b kwadraat minus 4 a c End wortel Oor 2 a End breuk
33	$y = x^{2} + 8 x + 16$	y equals x squared plus 8 x plus 16	y is gelyk aan x kwadraat plus 8 x plus 16
34	$y = \frac{1}{3} (3^{x})$	y equals one third L p'ren 3 Sup x Base R p'ren	y is gelyk aan een derde links hakkie 3 Sup x Basis regs hakkie
35	$y = 10 - 2 x$	y equals 10 minus 2 x	y is gelyk aan 10 minus 2 x
36	$y = 2 x^{3} + 5$	y equals 2 x cubed plus 5	y is gelyk aan 2 x kubbiek plus 5
37	$y = (x^{2} + 1) (x^{2} + 3)$	y equals L p'ren x squared plus 1 R p'ren L p'ren x squared plus 3 R p'ren	y is gelyk aan links hakkie x kwadraat plus 1 regs hakkie links hakkie x kwadraat plus 3 regs hakkie
38	$y = {0.5}^{x}$	y equals 0.5 Sup x	y is gelyk aan 0,5 Sup x
39	$y = 22 - 2 x$	y equals 22 minus 2 x	y is gelyk aan 22 minus 2 x
40	$y = \frac{3}{x}$	y equals Frac 3 Over x EndFrac	y is gelyk aan Breuk 3 Oor x End breuk
41	$y = (x + 4) (x + 4)$	y equals L p'ren x plus 4 R p'ren L p'ren x plus 4 R p'ren	y is gelyk aan links hakkie x plus 4 regs hakkie links hakkie x plus 4 regs hakkie
42	$y = (4 x - 3) (x + 1)$	y equals L p'ren 4 x minus 3 R p'ren L p'ren x plus 1 R p'ren	y is gelyk aan links hakkie 4 x minus 3 regs hakkie links hakkie x plus 1 regs hakkie
43	$y = 20 x - 4 x^{2}$	y equals 20 x minus 4 x squared	y is gelyk aan 20 x minus 4 x kwadraat
44	$y = x^{2}$	y equals x squared	y is gelyk aan x kwadraat
45	$y = 3^{x - 1}$	y equals 3 Sup x minus 1	y is gelyk aan 3 Sup x minus 1
46	$y = 16 - 2 (x + 3)$	y equals 16 minus 2 L p'ren x plus 3 R p'ren	y is gelyk aan 16 minus 2 links hakkie x plus 3 regs hakkie
47	$y = 4 x^{2} - x - 3$	y equals 4 x squared minus x minus 3	y is gelyk aan 4 x kwadraat minus x minus 3
48	$y = x + \frac{1}{x}$	y equals x plus Frac 1 Over x EndFrac	y is gelyk aan x plus Breuk 1 Oor x End breuk
49	$y = 4 x (5 - x)$	y equals 4 x L p'ren 5 minus x R p'ren	y is gelyk aan 4 x links hakkie 5 minus x regs hakkie
50	$y = 2 (x - 3) + 6 (1 - x)$	y equals 2 L p'ren x minus 3 R p'ren plus 6 L p'ren 1 minus x R p'ren	y is gelyk aan 2 links hakkie x minus 3 regs hakkie plus 6 links hakkie 1 minus x regs hakkie
51	$0.25 > \frac{5}{16}$	0.25 greater than five sixteenths	0,25 groter as vyf sestiendes
52	$32 \cdot (5 \cdot 7)$	32 dot L p'ren 5 dot 7 R p'ren	32 punt links hakkie 5 punt 7 regs hakkie
53	$(\frac{1}{2} \times \frac{1}{2} \times π \times 2) + (2 \times \frac{1}{2} \times π \times 5)$	L p'ren one half times one half times pi times 2 R p'ren plus L p'ren 2 times one half times pi times 5 R p'ren	links hakkie een helfte maal een helfte maal pi maal 2 regs hakkie plus links hakkie 2 maal een helfte maal pi maal 5 regs hakkie
54	$\underset{n \to \infty}{liminf} E_{n} = ⋃_{n \geq 1} ⋂_{k \geq n} E_{k}, \underset{n \to \infty}{limsup} E_{n} = ⋂_{n \geq 1} ⋃_{k \geq n} E_{k} .$	liminf Underscript n R arrow infinity Endscripts upper E Sub n Base equals union Underscript n greater than or equals 1 Endscripts intersection Underscript k greater than or equals n Endscripts upper E Sub k Base comma limsup Underscript n R arrow infinity Endscripts upper E Sub n Base equals intersection Underscript n greater than or equals 1 Endscripts union Underscript k greater than or equals n Endscripts upper E Sub k Base period	liminf Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E Onderskrif n Basis is gelyk aan n ary union Onderskrif n groter of gelyk aan 1 End skrifte n ary intersection Onderskrif k groter of gelyk aan n End skrifte hoofletter E Onderskrif k Basis komma limsup Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E Onderskrif n Basis is gelyk aan n ary intersection Onderskrif n groter of gelyk aan 1 End skrifte n ary union Onderskrif k groter of gelyk aan n End skrifte hoofletter E Onderskrif k Basis punt
55	$\begin{array}{l} (i) & 𝒮 \in 𝒜; \\ (ii) & if E \in 𝒜 then \overline{E} \in 𝒜; \\ (iii) & if E_{1}, E_{2} \in 𝒜 then E_{1} \cup E_{2} \in 𝒜 . \end{array}$	Layout 1st Row 1st Column L p'ren i R p'ren 2nd Column script upper S element of script upper A semicolon 2nd Row 1st Column L p'ren ii R p'ren 2nd Column if upper E element of script upper A then upper E overbar element of script upper A semicolon 3rd Row 1st Column L p'ren iii R p'ren 2nd Column if upper E 1 comma upper E 2 element of script upper A then upper E 1 union upper E 2 element of script upper A period EndLayout	uitleg 1. Ry 1. Kolom links hakkie i regs hakkie 2. Kolom skrif hoofletter S element van skrif hoofletter A kommapunt 2. Ry 1. Kolom links hakkie ii regs hakkie 2. Kolom if hoofletter E element van skrif hoofletter A then hoofletter E bostaaf element van skrif hoofletter A kommapunt 3. Ry 1. Kolom links hakkie iii regs hakkie 2. Kolom if hoofletter E 1 komma hoofletter E 2 element van skrif hoofletter A then hoofletter E 1 eenheid hoofletter E 2 element van skrif hoofletter A punt End uitleg
56	$\begin{array}{l} (A . 1) If A \in ℱ then 0 \leq P {A} \leq 1 . & (1) \\ (A . 2) P {𝒮} = 1 . & (2) \\ (A . 3) If {E_{n}, n \geq 1} \in ℱ is a sequence of disjoint & (3) \end{array}$	Layout 1st Row 1st Column Blank 2nd Column Blank 3rd Column L p'ren normal upper A period 1 R p'ren upper I f upper A element of script upper F t h e n 0 less than or equals upper P L brace upper A R brace less than or equals 1 period 4th Column L p'ren 1 R p'ren 2nd Row 1st Column Blank 2nd Column Blank 3rd Column L p'ren normal upper A period 2 R p'ren upper P L brace script upper S R brace equals 1 period 4th Column L p'ren 2 R p'ren 3rd Row 1st Column Blank 2nd Column Blank 3rd Column L p'ren normal upper A period 3 R p'ren upper I f L brace upper E Sub n Base comma n greater than or equals 1 R brace element of script upper F is a sequence of disjoint 4th Column L p'ren 3 R p'ren EndLayout	uitleg 1. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 1 regs hakkie hoofletter I f hoofletter A element van skrif hoofletter F t h e n 0 kleiner of gelyk aan hoofletter P links krulhakkie hoofletter A regs krulhakkie kleiner of gelyk aan 1 punt 4. Kolom links hakkie 1 regs hakkie 2. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 2 regs hakkie hoofletter P links krulhakkie skrif hoofletter S regs krulhakkie is gelyk aan 1 punt 4. Kolom links hakkie 2 regs hakkie 3. Ry 1. Kolom leeg 2. Kolom leeg 3. Kolom links hakkie normaal hoofletter A punt 3 regs hakkie hoofletter I f links krulhakkie hoofletter E Onderskrif n Basis komma n groter of gelyk aan 1 regs krulhakkie element van skrif hoofletter F is a sequence of disjoint 4. Kolom links hakkie 3 regs hakkie End uitleg
57	$P {B_{j} \| A} = \frac{P {B_{j}} P {A \| B_{j}}}{\sum_{j' \in J} P {B_{j'}} P {A \| B_{j'}}} .$	upper P L brace upper B Sub j Base vertical bar upper A R brace equals Frac upper P L brace upper B Sub j Base R brace upper P L brace upper A vertical bar upper B Sub j Base R brace Over sigma summation Underscript j prime element of upper J Endscripts upper P L brace upper B Sub j prime Base R brace upper P L brace upper A vertical bar upper B Sub j prime Base R brace EndFrac period	hoofletter P links krulhakkie hoofletter B Onderskrif j Basis afstreep hoofletter A regs krulhakkie is gelyk aan Breuk hoofletter P links krulhakkie hoofletter B Onderskrif j Basis regs krulhakkie hoofletter P links krulhakkie hoofletter A afstreep hoofletter B Onderskrif j Basis regs krulhakkie Oor som Onderskrif j priem element van hoofletter J End skrifte hoofletter P links krulhakkie hoofletter B Onderskrif j priem Basis regs krulhakkie hoofletter P links krulhakkie hoofletter A afstreep hoofletter B Onderskrif j priem Basis regs krulhakkie End breuk punt
58	$μ_{1} (B) = \int_{B} f (x) d μ_{2} (x)$	mu 1 L p'ren upper B R p'ren equals integral Underscript upper B Endscripts f L p'ren x R p'ren d mu 2 L p'ren x R p'ren	my 1 links hakkie hoofletter B regs hakkie is gelyk aan integraal Onderskrif hoofletter B End skrifte f links hakkie x regs hakkie d my 2 links hakkie x regs hakkie
59	$lim_{n \to \infty} E {\| X_{n} - X \|} = E {lim_{n \to \infty} \| X_{n} - X \|} = 0 .$	limit Underscript n R arrow infinity Endscripts upper E L brace AbsoluteValue upper X Sub n Base minus upper X EndAbsoluteValue R brace equals upper E L brace limit Underscript n R arrow infinity Endscripts AbsoluteValue upper X Sub n Base minus upper X EndAbsoluteValue R brace equals 0 period	limit Onderskrif n regs pyltjie oneindigheid End skrifte hoofletter E links krulhakkie Absolute Waarde hoofletter X Onderskrif n Basis minus hoofletter X End Absolute Waarde regs krulhakkie is gelyk aan hoofletter E links krulhakkie limit Onderskrif n regs pyltjie oneindigheid End skrifte Absolute Waarde hoofletter X Onderskrif n Basis minus hoofletter X End Absolute Waarde regs krulhakkie is gelyk aan 0 punt
60	$\begin{array}{l} P_{μ, σ} {Y \geq l_{β} ({\overline{Y}}_{n}, S_{n})} = P_{μ, σ} {(Y - {\overline{Y}}_{n}) / (S \cdot {(1 + \frac{1}{n})}^{1 / 2}) \geq - t_{β} [n - 1]} = β, \\ (1) \end{array}$	Layout 1st Row 1st Column upper P Sub mu comma sigma Base L brace upper Y greater than or equals l Sub beta Base L p'ren upper Y overbar Sub n Base comma upper S Sub n Base R p'ren R brace equals upper P Sub mu comma sigma Base L brace L p'ren upper Y minus upper Y overbar Sub n Base R p'ren divided by L p'ren upper S dot L p'ren 1 plus Frac 1 Over n EndFrac R p'ren Sup 1 divided by 2 Base R p'ren greater than or equals minus t Sub beta Base L brack n minus 1 R brack R brace equals beta comma 2nd Row 1st Column Blank 2nd Column L p'ren 1 R p'ren EndLayout	uitleg 1. Ry 1. Kolom hoofletter P Onderskrif my komma sigma Basis links krulhakkie hoofletter Y groter of gelyk aan l Onderskrif beta Basis links hakkie hoofletter Y bostaaf Onderskrif n Basis komma hoofletter S Onderskrif n Basis regs hakkie regs krulhakkie is gelyk aan hoofletter P Onderskrif my komma sigma Basis links krulhakkie links hakkie hoofletter Y minus hoofletter Y bostaaf Onderskrif n Basis regs hakkie gedeel deur links hakkie hoofletter S dot links hakkie 1 plus Breuk 1 Oor n End breuk regs hakkie Sup 1 gedeel deur 2 Basis regs hakkie groter of gelyk aan minus t Onderskrif beta Basis links blokhakkie n minus 1 regs blokhakkie regs krulhakkie is gelyk aan beta komma 2. Ry 1. Kolom leeg 2. Kolom links hakkie 1 regs hakkie End uitleg
61	$L = (\begin{matrix} 1 & - 1 \\ 1 & - 1 & 0 \\ 0 \\ 1 & - 1 \end{matrix}) .$	upper L equals 5 By 6 Matrix 1st Row 1st Column 1 2nd Column negative 1 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 2nd Row 1st Column Blank 2nd Column 1 3rd Column negative 1 4th Column Blank 5th Column 0 6th Column Blank 3rd Row 1st Column Blank 2nd Column Blank 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 4th Row 1st Column Blank 2nd Column 0 3rd Column Blank 4th Column Blank 5th Column Blank 6th Column Blank 5th Row 1st Column Blank 2nd Column Blank 3rd Column Blank 4th Column Blank 5th Column 1 6th Column negative 1 EndMatrix period	hoofletter L is gelyk aan 5 By 6 Matriks 1. Ry 1. Kolom 1 2. Kolom negatief 1 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 2. Ry 1. Kolom leeg 2. Kolom 1 3. Kolom negatief 1 4. Kolom Leeg 5. Kolom 0 6. Kolom Leeg 3. Ry 1. Kolom leeg 2. Kolom Leeg 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 4. Ry 1. Kolom leeg 2. Kolom 0 3. Kolom Leeg 4. Kolom Leeg 5. Kolom Leeg 6. Kolom Leeg 5. Ry 1. Kolom leeg 2. Kolom Leeg 3. Kolom Leeg 4. Kolom Leeg 5. Kolom 1 6. Kolom negatief 1 End Matriks punt
62	$\sqrt{n} [{\overline{Y}}_{n} - (μ + z_{β} σ)] / S_{n} ~ \frac{U + \sqrt{n} z_{1 - β}}{(χ^{2} [n - 1] / (n - 1))^{1 / 2}} ~ t [n - 1; \sqrt{n} z_{1 - β}],$	Root n EndRoot L brack upper Y overbar Sub n Base minus L p'ren mu plus z Sub beta Base sigma R p'ren R brack divided by upper S Sub n Base tilde Frac upper U plus Root n EndRoot z Sub 1 minus beta Base Over L p'ren chi squared L brack n minus 1 R brack divided by L p'ren n minus 1 R p'ren R p'ren Sup 1 divided by 2 Base EndFrac tilde t L brack n minus 1 semicolon Root n EndRoot z Sub 1 minus beta Base R brack comma	Wortel n End wortel links blokhakkie hoofletter Y bostaaf Onderskrif n Basis minus links hakkie my plus z Onderskrif beta Basis sigma regs hakkie regs blokhakkie gedeel deur hoofletter S Onderskrif n Basis tilde Breuk hoofletter U plus Wortel n End wortel z Onderskrif 1 minus beta Basis Oor links hakkie chi kwadraat links blokhakkie n minus 1 regs blokhakkie gedeel deur links hakkie n minus 1 regs hakkie regs hakkie Sup 1 gedeel deur 2 Basis End breuk tilde t links blokhakkie n minus 1 kommapunt Wortel n End wortel z Onderskrif 1 minus beta Basis regs blokhakkie komma
63	$\begin{array}{l} γ & = P {E_{p, q} \subset (X_{(r)}, X_{(s)}} \\ = \frac{n!}{(r - 1)!} \sum_{j = 0}^{s - r - 1} (- 1)^{j} \frac{p^{r + j}}{(n - r - j)! j!} I_{1 - q} (n - s + 1, s - r - j) . \end{array}$	Layout 1st Row 1st Column gamma 2nd Column equals upper P L brace upper E Sub p comma q Base subset of L p'ren upper X Sub L p'ren r R p'ren Base comma upper X Sub L p'ren s R p'ren Base R brace 2nd Row 1st Column Blank 2nd Column equals Frac n factorial Over L p'ren r minus 1 R p'ren factorial EndFrac sigma summation Underscript j equals 0 Overscript s minus r minus 1 Endscripts L p'ren negative 1 R p'ren Sup j Base Frac p Sup r plus j Base Over L p'ren n minus r minus j R p'ren factorial j factorial EndFrac upper I Sub 1 minus q Base L p'ren n minus s plus 1 comma s minus r minus j R p'ren period EndLayout	uitleg 1. Ry 1. Kolom gamma 2. Kolom is gelyk aan hoofletter P links krulhakkie hoofletter E Onderskrif p komma q Basis deelversameling van links hakkie hoofletter X Onderskrif links hakkie r regs hakkie Basis komma hoofletter X Onderskrif links hakkie s regs hakkie Basis regs krulhakkie 2. Ry 1. Kolom leeg 2. Kolom is gelyk aan Breuk n faktoriaal Oor links hakkie r minus 1 regs hakkie faktoriaal End breuk som Onderskrif j is gelyk aan 0 Boskrif s minus r minus 1 End skrifte links hakkie negatief 1 regs hakkie Sup j Basis Breuk p Sup r plus j Basis Oor links hakkie n minus r minus j regs hakkie faktoriaal j faktoriaal End breuk hoofletter I Onderskrif 1 minus q Basis links hakkie n minus s plus 1 komma s minus r minus j regs hakkie punt End uitleg
64	$S_{i} [\begin{matrix} t \\ x \end{matrix}] = [\begin{matrix} 1 / m & 0 \\ a_{i} & r_{i} \end{matrix}] [\begin{matrix} t \\ x \end{matrix}] + [\begin{matrix} (i - 1) / m \\ b_{i} \end{matrix}],$	upper S Sub i Base BinomialOrMatrix t Choose x EndBinomialOrMatrix equals 2 By 2 Matrix 1st Row 1st Column 1 divided by m 2nd Column 0 2nd Row 1st Column a Sub i Base 2nd Column r Sub i Base EndMatrix BinomialOrMatrix t Choose x EndBinomialOrMatrix plus BinomialOrMatrix L p'ren i minus 1 R p'ren divided by m Choose b Sub i Base EndBinomialOrMatrix comma	hoofletter S Onderskrif i Basis Binomiaal of Matriks t Kies x End Binomiaal of Matriks is gelyk aan 2 By 2 Matriks 1. Ry 1. Kolom 1 gedeel deur m 2. Kolom 0 2. Ry 1. Kolom a Onderskrif i Basis 2. Kolom r Onderskrif i Basis End Matriks Binomiaal of Matriks t Kies x End Binomiaal of Matriks plus Binomiaal of Matriks links hakkie i minus 1 regs hakkie gedeel deur m Kies b Onderskrif i Basis End Binomiaal of Matriks komma
65	$c_{1} h^{4 - 2 s} \leq \frac{1}{2 T} \int_{- T}^{T} {(f (t + h) - f (t))}^{2} d t \leq c_{2} h^{4 - 2 s}$	c 1 h Sup 4 minus 2 s Base less than or equals Frac 1 Over 2 upper T EndFrac integral Sub negative upper T Sup upper T Base L p'ren f L p'ren t plus h R p'ren minus f L p'ren t R p'ren R p'ren squared normal d t less than or equals c 2 h Sup 4 minus 2 s	c 1 h Sup 4 minus 2 s Basis kleiner of gelyk aan Breuk 1 Oor 2 hoofletter T End breuk integraal Onder negatief hoofletter T Bo hoofletter T Basis links hakkie f links hakkie t plus h regs hakkie minus f links hakkie t regs hakkie regs hakkie kwadraat normaal d t kleiner of gelyk aan c 2 h Sup 4 minus 2 s
66	$C (0) - C (h) ≃ c h^{4 - 2 s}$	upper C L p'ren 0 R p'ren minus upper C L p'ren h R p'ren asymptotically equals c h Sup 4 minus 2 s	hoofletter C links hakkie 0 regs hakkie minus hoofletter C links hakkie h regs hakkie assimtoties gelyk aan c h Sup 4 minus 2 s
67	$S (ω) = \lim_{T \to \infty} \frac{1}{2 T} {\|\int_{- T}^{T} f (t) e^{it ω} d t\|}^{2} .$	upper S L p'ren omega R p'ren equals limit Underscript upper T R arrow infinity Endscripts Frac 1 Over 2 upper T EndFrac AbsoluteValue integral Sub negative upper T Sup upper T Base comma f comma L p'ren comma t comma R p'ren comma normal e Sup italic i t omega Base comma normal d comma t EndAbsoluteValue squared period	hoofletter S links hakkie omega regs hakkie is gelyk aan limit Onderskrif hoofletter T regs pyltjie oneindigheid End skrifte Breuk 1 Oor 2 hoofletter T End breuk Absolute Waarde integraal Onder negatief hoofletter T Bo hoofletter T Basis komma f komma links hakkie komma t komma regs hakkie komma normaal e Sup kursief i t omega Basis komma normaal d komma t End Absolute Waarde kwadraat punt
68	$\int_{0}^{1} \int_{0}^{1} {[\| f (t) - f (u) \|^{2} + \| t - u \|^{2}]}^{- s / 2} d t d u < \infty$	integral Sub 0 Sup 1 Base integral Sub 0 Sup 1 Base L brack AbsoluteValue f L p'ren t R p'ren minus f L p'ren u R p'ren EndAbsoluteValue squared plus AbsoluteValue t minus u EndAbsoluteValue squared R brack Sup negative s divided by 2 Base normal d t normal d u less than infinity	integraal Onder 0 Bo 1 Basis integraal Onder 0 Bo 1 Basis links blokhakkie Absolute Waarde f links hakkie t regs hakkie minus f links hakkie u regs hakkie End Absolute Waarde kwadraat plus Absolute Waarde t minus u End Absolute Waarde kwadraat regs blokhakkie Sup negatief s gedeel deur 2 Basis normaal d t normaal d u kleiner as oneindigheid
69	$E (\sum_{I \in E_{k + 1}} \| I \|^{s}) = E (\sum_{I \in E_{k}} \| I \|^{s}) E (R_{1}^{s} + R_{2}^{s}) .$	sans serif upper E L p'ren sigma summation Underscript upper I element of upper E Sub k plus 1 Base Endscripts AbsoluteValue upper I EndAbsoluteValue Sup s Base R p'ren equals sans serif upper E L p'ren sigma summation Underscript upper I element of upper E Sub k Base Endscripts AbsoluteValue upper I EndAbsoluteValue Sup s Base R p'ren sans serif upper E L p'ren upper R 1 Sup s Base plus upper R 2 Sup s Base R p'ren period	sans serif hoofletter E links hakkie som Onderskrif hoofletter I element van hoofletter E Onderskrif k plus 1 Basis End skrifte Absolute Waarde hoofletter I End Absolute Waarde Sup s Basis regs hakkie is gelyk aan sans serif hoofletter E links hakkie som Onderskrif hoofletter I element van hoofletter E Onderskrif k Basis End skrifte Absolute Waarde hoofletter I End Absolute Waarde Sup s Basis regs hakkie sans serif hoofletter E links hakkie hoofletter R 1 Sup s Basis plus hoofletter R 2 Sup s Basis regs hakkie punt
70	$(x_{1}, y_{1})$	L p'ren x 1 comma y 1 R p'ren	links hakkie x 1 komma y 1 regs hakkie
71	$(x_{2}, y_{2})$	L p'ren x 2 comma y 2 R p'ren	links hakkie x 2 komma y 2 regs hakkie
72	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$	d equals Root L p'ren x 2 minus x 1 R p'ren squared plus L p'ren y 2 minus y 1 R p'ren squared EndRoot	d is gelyk aan Wortel links hakkie x 2 minus x 1 regs hakkie kwadraat plus links hakkie y 2 minus y 1 regs hakkie kwadraat End wortel
73	$ℝ$	double struck upper R	hoofletter R dubbelgeslaan
74	$ℝ = (- \infty, \infty)$	double struck upper R equals L p'ren negative infinity comma infinity R p'ren	hoofletter R dubbelgeslaan is gelyk aan links hakkie negatief oneindigheid komma oneindigheid regs hakkie
75	${1, 2, 3}$	Set 1 comma 2 comma 3 EndSet	Versameling 1 komma 2 komma 3 End Versameling
76	$1 \in S$	1 element of upper S	1 element van hoofletter S
77	$3 \in S$	3 element of upper S	3 element van hoofletter S
78	$4 \notin S$	4 not an element of upper S	4 nie 'n element van hoofletter S
79	$a = \sqrt{3 x - 1} + {(1 + x)}^{2}$	a equals Root 3 x minus 1 EndRoot plus L p'ren 1 plus x R p'ren squared	a is gelyk aan Wortel 3 x minus 1 End wortel plus links hakkie 1 plus x regs hakkie kwadraat
80	$a = \frac{{(b + c)}^{2}}{d} + \frac{{(e + f)}^{2}}{g}$	a equals Frac L p'ren b plus c R p'ren squared Over d EndFrac plus Frac L p'ren e plus f R p'ren squared Over g EndFrac	a is gelyk aan Breuk links hakkie b plus c regs hakkie kwadraat Oor d End breuk plus Breuk links hakkie e plus f regs hakkie kwadraat Oor g End breuk
81	$x = [{(a + b)}^{2} {(c - b)}^{2}] + [{(d + e)}^{2} {(f - e)}^{2}]$	x equals L brack L p'ren a plus b R p'ren squared L p'ren c minus b R p'ren squared R brack plus L brack L p'ren d plus e R p'ren squared L p'ren f minus e R p'ren squared R brack	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat links hakkie c minus b regs hakkie kwadraat regs blokhakkie plus links blokhakkie links hakkie d plus e regs hakkie kwadraat links hakkie f minus e regs hakkie kwadraat regs blokhakkie
82	$x = [{(a + b)}^{2}] + [{(f - e)}^{2}]$	x equals L brack L p'ren a plus b R p'ren squared R brack plus L brack L p'ren f minus e R p'ren squared R brack	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat regs blokhakkie plus links blokhakkie links hakkie f minus e regs hakkie kwadraat regs blokhakkie
83	$x = [{(a + b)}^{2}]$	x equals L brack L p'ren a plus b R p'ren squared R brack	x is gelyk aan links blokhakkie links hakkie a plus b regs hakkie kwadraat regs blokhakkie
84	$x = {(a + b)}^{2}$	x equals L p'ren a plus b R p'ren squared	x is gelyk aan links hakkie a plus b regs hakkie kwadraat
85	$x = a + b^{2}$	x equals a plus b squared	x is gelyk aan a plus b kwadraat
86	$\frac{\frac{1}{2}}{\frac{3}{4}} = \frac{2}{3}$	Frac one half Over three fourths EndFrac equals two thirds	Breuk een helfte Oor drie kwarte End breuk is gelyk aan twee derdes
87	$2 ((x + 1) (x + 3) - 4 ((x - 1) (x + 2) - 3)) = y$	2 L p'ren L p'ren x plus 1 R p'ren L p'ren x plus 3 R p'ren minus 4 L p'ren L p'ren x minus 1 R p'ren L p'ren x plus 2 R p'ren minus 3 R p'ren R p'ren equals y	2 links hakkie links hakkie x plus 1 regs hakkie links hakkie x plus 3 regs hakkie minus 4 links hakkie links hakkie x minus 1 regs hakkie links hakkie x plus 2 regs hakkie minus 3 regs hakkie regs hakkie is gelyk aan y
88	$\cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \dots$	cosine x equals 1 minus Frac x squared Over 2 factorial EndFrac plus Frac x Sup 4 Base Over 4 factorial EndFrac minus ellipsis	kosinus x is gelyk aan 1 minus Breuk x kwadraat Oor 2 faktoriaal End breuk plus Breuk x Sup 4 Basis Oor 4 faktoriaal End breuk minus ellipsis
89	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	x equals Frac negative b plus or minus Root b squared minus 4 a c EndRoot Over 2 a EndFrac	x is gelyk aan Breuk negatief b plus of minus Wortel b kwadraat minus 4 a c End wortel Oor 2 a End breuk
90	$x + y^{\frac{2}{k + 1}}$	x plus y Sup Frac 2 Over k plus 1 EndFrac	x plus y Sup Breuk 2 Oor k plus 1 End breuk
91	$\lim_{x \to 0} \frac{\sin x}{x} = 1$	limit Underscript x R arrow 0 Endscripts Frac sine x Over x EndFrac equals 1	limit Onderskrif x regs pyltjie 0 End skrifte Breuk sinus x Oor x End breuk is gelyk aan 1
92	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$	d equals Root L p'ren x 2 minus x 1 R p'ren squared plus L p'ren y 2 minus y 1 R p'ren squared EndRoot	d is gelyk aan Wortel links hakkie x 2 minus x 1 regs hakkie kwadraat plus links hakkie y 2 minus y 1 regs hakkie kwadraat End wortel
93	$F_{n} = F_{n - 1} + F_{n - 2}$	upper F Sub n Base equals upper F Sub n minus 1 Base plus upper F Sub n minus 2	hoofletter F Onderskrif n Basis is gelyk aan hoofletter F Onderskrif n minus 1 Basis plus hoofletter F Onderskrif n minus 2
94	$Π = (\begin{matrix} π_{11} & π_{12} & π_{12} & 0 & 0 & 0 \\ π_{12} & π_{11} & π_{12} & 0 & 0 & 0 \\ π_{12} & π_{12} & π_{11} & 0 & 0 & 0 \\ 0 & 0 & 0 & π_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & π_{44} & 0 \\ 0 & 0 & 0 & 0 & 0 & π_{44} \end{matrix})$	bold upper Pi equals 6 By 6 Matrix 1st Row 1st Column pi 11 2nd Column pi 12 3rd Column pi 12 4th Column 0 5th Column 0 6th Column 0 2nd Row 1st Column pi 12 2nd Column pi 11 3rd Column pi 12 4th Column 0 5th Column 0 6th Column 0 3rd Row 1st Column pi 12 2nd Column pi 12 3rd Column pi 11 4th Column 0 5th Column 0 6th Column 0 4th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column pi 44 5th Column 0 6th Column 0 5th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column 0 5th Column pi 44 6th Column 0 6th Row 1st Column 0 2nd Column 0 3rd Column 0 4th Column 0 5th Column 0 6th Column pi 44 EndMatrix	vetgedruk hoofletter Pi is gelyk aan 6 By 6 Matriks 1. Ry 1. Kolom pi 11 2. Kolom pi 12 3. Kolom pi 12 4. Kolom 0 5. Kolom 0 6. Kolom 0 2. Ry 1. Kolom pi 12 2. Kolom pi 11 3. Kolom pi 12 4. Kolom 0 5. Kolom 0 6. Kolom 0 3. Ry 1. Kolom pi 12 2. Kolom pi 12 3. Kolom pi 11 4. Kolom 0 5. Kolom 0 6. Kolom 0 4. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom pi 44 5. Kolom 0 6. Kolom 0 5. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom 0 5. Kolom pi 44 6. Kolom 0 6. Ry 1. Kolom 0 2. Kolom 0 3. Kolom 0 4. Kolom 0 5. Kolom 0 6. Kolom pi 44 End Matriks
95	$s_{11} = \frac{c_{11} + c_{12}}{(c_{11} - c_{12}) (c_{11} + 2 c_{12})}$	s 11 equals Frac c 11 plus c 12 Over L p'ren c 11 minus c 12 R p'ren L p'ren c 11 plus 2 c 12 R p'ren EndFrac	s 11 is gelyk aan Breuk c 11 plus c 12 Oor links hakkie c 11 minus c 12 regs hakkie links hakkie c 11 plus 2 c 12 regs hakkie End breuk
96	$Si O_{2} + 6 H F \to H_{2} Si F_{6} + 2 H_{2} O$	upper S i normal upper O 2 plus 6 normal upper H normal upper F R arrow normal upper H 2 upper S i normal upper F 6 plus 2 normal upper H 2 normal upper O	hoofletter S i normaal hoofletter O 2 plus 6 normaal hoofletter H normaal hoofletter F regs pyltjie normaal hoofletter H 2 hoofletter S i normaal hoofletter F 6 plus 2 normaal hoofletter H 2 normaal hoofletter O
97	$\frac{d}{d x} (E (x) A (x) \frac{d w (x)}{d x}) + p (x) = 0$	Frac d Over d x EndFrac L p'ren upper E L p'ren x R p'ren upper A L p'ren x R p'ren Frac d w L p'ren x R p'ren Over d x EndFrac R p'ren plus p L p'ren x R p'ren equals 0	Breuk d Oor d x End breuk links hakkie hoofletter E links hakkie x regs hakkie hoofletter A links hakkie x regs hakkie Breuk d w links hakkie x regs hakkie Oor d x End breuk regs hakkie plus p links hakkie x regs hakkie is gelyk aan 0
98	${TCS}_{gas} = - \frac{1}{2} (\frac{P_{seal}}{P_{max}}) (\frac{1}{T_{seal}})$	TCS Sub gas Base equals minus one half L p'ren Frac upper P Sub seal Base Over upper P Sub max Base EndFrac R p'ren L p'ren Frac 1 Over upper T Sub seal Base EndFrac R p'ren	TCS Onderskrif gas Basis is gelyk aan minus een helfte links hakkie Breuk hoofletter P Onderskrif seal Basis Oor hoofletter P Onderskrif max Basis End breuk regs hakkie links hakkie Breuk 1 Oor hoofletter T Onderskrif seal Basis End breuk regs hakkie
99	$B_{p} = \frac{\frac{7 - v^{2}}{3} (1 + \frac{c^{2}}{a^{2}} + \frac{c^{4}}{a^{4}}) + \frac{{(3 - v)}^{2} c^{2}}{(1 + v) a^{2}}}{(1 - v) (1 - \frac{c^{4}}{a^{4}}) (1 - \frac{c^{2}}{a^{2}})}$	upper B Sub p Base equals NestFrac Frac 7 minus v squared Over 3 EndFrac L p'ren 1 plus Frac c squared Over a squared EndFrac plus Frac c Sup 4 Base Over a Sup 4 Base EndFrac R p'ren plus Frac L p'ren 3 minus v R p'ren squared c squared Over L p'ren 1 plus v R p'ren a squared EndFrac NestOver L p'ren 1 minus v R p'ren L p'ren 1 minus Frac c Sup 4 Base Over a Sup 4 Base EndFrac R p'ren L p'ren 1 minus Frac c squared Over a squared EndFrac R p'ren NestEndFrac	hoofletter B Onderskrif p Basis is gelyk aan genesBreuk Breuk 7 minus v kwadraat Oor 3 End breuk links hakkie 1 plus Breuk c kwadraat Oor a kwadraat End breuk plus Breuk c Sup 4 Basis Oor a Sup 4 Basis End breuk regs hakkie plus Breuk links hakkie 3 minus v regs hakkie kwadraat c kwadraat Oor links hakkie 1 plus v regs hakkie a kwadraat End breuk genesOor links hakkie 1 minus v regs hakkie links hakkie 1 minus Breuk c Sup 4 Basis Oor a Sup 4 Basis End breuk regs hakkie links hakkie 1 minus Breuk c kwadraat Oor a kwadraat End breuk regs hakkie genesEnd breuk
100	$Q_{tank}^{series} = \frac{1}{R_{s}} \sqrt{\frac{L_{s}}{C_{s}}}$	upper Q Sub tank Sup series Base equals Frac 1 Over upper R Sub s Base EndFrac Root Frac upper L Sub s Base Over upper C Sub s Base EndFrac EndRoot	hoofletter Q Onderskrif tank Sup series Basis is gelyk aan Breuk 1 Oor hoofletter R Onderskrif s Basis End breuk Wortel Breuk hoofletter L Onderskrif s Basis Oor hoofletter C Onderskrif s Basis End breuk End wortel
101	$Δ ϕ_{peak} = {tan}^{- 1} (k^{2} Q_{tank}^{series})$	upper Delta phi Sub peak Base equals tangent Sup negative 1 Base L p'ren k squared upper Q Sub tank Sup series Base R p'ren	hoofletter Delta phi Onderskrif peak Basis is gelyk aan tangens Sup negatief 1 Basis links hakkie k kwadraat hoofletter Q Onderskrif tank Sup series Basis regs hakkie
102	$f = 1.013 \frac{W}{L^{2}} \sqrt{\frac{E}{ρ}} \sqrt{(1 + 0.293 \frac{L^{2}}{{EW}^{2}} σ)}$	f equals 1.013 Frac upper W Over upper L squared EndFrac Root Frac upper E Over rho EndFrac EndRoot Root L p'ren 1 plus 0.293 Frac upper L squared Over EW squared EndFrac sigma R p'ren EndRoot	f is gelyk aan 1.013 Breuk hoofletter W Oor hoofletter L kwadraat End breuk Wortel Breuk hoofletter E Oor rho End breuk End wortel Wortel links hakkie 1 plus 0.293 Breuk hoofletter L kwadraat Oor EW kwadraat End breuk sigma regs hakkie End wortel
103	$u_{n} (x) = γ_{n} (\cosh k_{n} x - \cos k_{n} x) + (\sinh k_{n} x - \sin k_{n} x)$	u Sub n Base L p'ren x R p'ren equals gamma Sub n Base L p'ren hyperbolic cosine k Sub n Base x minus cosine k Sub n Base x R p'ren plus L p'ren hyperbolic sine k Sub n Base x minus sine k Sub n Base x R p'ren	u Onderskrif n Basis links hakkie x regs hakkie is gelyk aan gamma Onderskrif n Basis links hakkie hiperboliese kosinus k Onderskrif n Basis x minus kosinus k Onderskrif n Basis x regs hakkie plus links hakkie hiperboliese sinus k Onderskrif n Basis x minus sinus k Onderskrif n Basis x regs hakkie
104	$\begin{matrix} B & = \frac{\frac{F_{0}}{m}}{\sqrt{(ω_{0}^{2} - ω^{2})^{2} + 4 n^{2} ω^{2}}} \\ = \frac{\frac{F_{0}}{k}}{\sqrt{(1 - (ω / ω_{0}^{2})^{2})^{2} + 4 (n / ω_{0})^{2} (ω / ω_{0})^{2}}} \end{matrix}$	Layout 1st Row 1st Column upper B 2nd Column equals NestFrac Frac upper F 0 Over m EndFrac NestOver Root L p'ren omega 0 squared minus omega squared R p'ren squared plus 4 n squared omega squared EndRoot NestEndFrac 2nd Row 1st Column Blank 2nd Column equals NestFrac Frac upper F 0 Over k EndFrac NestOver Root L p'ren 1 minus L p'ren omega divided by omega 0 squared R p'ren squared R p'ren squared plus 4 L p'ren n divided by omega 0 R p'ren squared L p'ren omega divided by omega 0 R p'ren squared EndRoot NestEndFrac EndLayout	uitleg 1. Ry 1. Kolom hoofletter B 2. Kolom is gelyk aan genesBreuk Breuk hoofletter F 0 Oor m End breuk genesOor Wortel links hakkie omega 0 kwadraat minus omega kwadraat regs hakkie kwadraat plus 4 n kwadraat omega kwadraat End wortel genesEnd breuk 2. Ry 1. Kolom leeg 2. Kolom is gelyk aan genesBreuk Breuk hoofletter F 0 Oor k End breuk genesOor Wortel links hakkie 1 minus links hakkie omega gedeel deur omega 0 kwadraat regs hakkie kwadraat regs hakkie kwadraat plus 4 links hakkie n gedeel deur omega 0 regs hakkie kwadraat links hakkie omega gedeel deur omega 0 regs hakkie kwadraat End wortel genesEnd breuk End uitleg
105	$p (A and B) = p (A) p (B \| A)$	normal p L p'ren upper A a n d upper B R p'ren equals normal p L p'ren upper A R p'ren normal p L p'ren upper B vertical bar upper A R p'ren	normaal p links hakkie hoofletter A a n d hoofletter B regs hakkie is gelyk aan normaal p links hakkie hoofletter A regs hakkie normaal p links hakkie hoofletter B afstreep hoofletter A regs hakkie
106	$PMF (x) \propto {(\frac{1}{x})}^{α}$	upper P upper M upper F L p'ren x R p'ren proportional to L p'ren Frac 1 Over x EndFrac R p'ren Sup alpha	hoofletter P hoofletter M hoofletter F links hakkie x regs hakkie eweredig aan links hakkie Breuk 1 Oor x End breuk regs hakkie Sup alfa
107	$f (x) = \frac{1}{\sqrt{2 π}} exp (- x^{2} /2)$	f L p'ren x R p'ren equals Frac 1 Over Root 2 pi EndRoot EndFrac exp L p'ren minus x squared slash 2 R p'ren	f links hakkie x regs hakkie is gelyk aan Breuk 1 Oor Wortel 2 pi End wortel End breuk exp links hakkie minus x kwadraat skuinsstreep 2 regs hakkie
108	$\frac{d x}{d θ} = \frac{β}{{cos}^{2} θ}$	Frac d x Over d theta EndFrac equals Frac beta Over cosine squared theta EndFrac	Breuk d x Oor d theta End breuk is gelyk aan Breuk beta Oor kosinus kwadraat theta End breuk
109	$s / \sqrt{2 (n - 1)}$	s divided by Root 2 L p'ren n minus 1 R p'ren EndRoot	s gedeel deur Wortel 2 links hakkie n minus 1 regs hakkie End wortel