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	negative 5 and een vyf de minus 6 and 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	negative 7 and drie kwarts minus links hakkie negative 4 and sewe agstes regs hakkie is gelyk aan
2	$- 24.15 - (13.7) =$	negative 24.15 minus left parenthesis 13.7 right parenthesis equals	negative 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 negative 4 regs hakkie maal 3 is gelyk aan negative 12
4	$- 12 \div 3 = - 4$	negative 12 divided by 3 equals negative 4	negative 12 divided by 3 is gelyk aan negative 4
5	$- 12 \div (- 4) = 3$	negative 12 divided by left parenthesis negative 4 right parenthesis equals 3	negative 12 divided by links hakkie negative 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 negative 5 regs hakkie
8	$- 6 \times 5$	negative 6 times 5	negative 6 maal 5
9	$- 6 \times (- 5)$	negative 6 times left parenthesis negative 5 right parenthesis	negative 6 maal links hakkie negative 5 regs hakkie
10	$- 8 \times 7$	negative 8 times 7	negative 8 maal 7
11	$- 8 \times (- 7)$	negative 8 times left parenthesis negative 7 right parenthesis	negative 8 maal links hakkie negative 7 regs hakkie
12	$8 \times (- 7)$	8 times left parenthesis negative 7 right parenthesis	8 maal links hakkie negative 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 großes M plus m hoek großes N is gelyk aan 180 graad
18	$A = \frac{1}{2} b h$	upper A equals one half b h	großes 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	Anfang Bruch area of triangle durch area of square Ende Bruch is gelyk aan Anfang Bruch 1 unit squared durch 16 units squared Ende Bruch
20	${0.6}^{2}$	0.6 squared	0,6 squared
21	${1.5}^{2}$	1.5 squared	1,5 squared
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 squared plus 5 y squared 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	ModifyingAbove großes B großes C With links regs pyltjie
26	$\vec{P Q}$	ModifyingAbove upper P upper Q With right arrow	ModifyingAbove großes P großes Q With regs pyltjie
27	$\bar{G H}$	ModifyingAbove upper G upper H With bar	ModifyingAbove großes G großes H With makron
28	$\bar{W X} ≅ \bar{Y Z}$	ModifyingAbove upper W upper X With bar approximately equals ModifyingAbove upper Y upper Z With bar	ModifyingAbove großes W großes X With makron ongeveer gelyk aan ModifyingAbove großes Y großes Z With makron
29	$∠ B E F$	angle upper B upper E upper F	hoek großes B großes E großes F
30	$∠ B E D$	angle upper B upper E upper D	hoek großes B großes E großes D
31	$∠ D E F$	angle upper D upper E upper F	hoek großes D großes E großes 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 Anfang Bruch negative b plus of minus Anfang Wurzel b squared minus 4 a c Ende Wurzel durch 2 a Ende Bruch
33	$y = x^{2} + 8 x + 16$	y equals x squared plus 8 x plus 16	y is gelyk aan x squared 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 hoch x Grundlinie 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 cubed 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 squared plus 1 regs hakkie links hakkie x squared plus 3 regs hakkie
38	$y = {0.5}^{x}$	y equals 0.5 Superscript x	y is gelyk aan 0,5 hoch 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 Anfang Bruch 3 durch x Ende Bruch
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 squared
44	$y = x^{2}$	y equals x squared	y is gelyk aan x squared
45	$y = 3^{x - 1}$	y equals 3 Superscript x minus 1	y is gelyk aan 3 hoch 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 squared 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 Anfang Bruch 1 durch x Ende Bruch
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 sestien des
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 Unterschrift n regs pyltjie oneindigheid großes E Index n Grundlinie is gelyk aan union Unterschrift n groter of gelyk aan 1 intersection Unterschrift k groter of gelyk aan n großes E Index k Grundlinie komma limsup Unterschrift n regs pyltjie oneindigheid großes E Index n Grundlinie is gelyk aan intersection Unterschrift n groter of gelyk aan 1 union Unterschrift k groter of gelyk aan n großes E Index k Grundlinie 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	StartLayout 1. Row 1. Column links hakkie i regs hakkie 2. Column Schreibschrift großes S element van Schreibschrift großes A kommapunt 2. Row 1. Column links hakkie ii regs hakkie 2. Column if großes E element van Schreibschrift großes A then großes E overbar element van Schreibschrift großes A kommapunt 3. Row 1. Column links hakkie iii regs hakkie 2. Column if großes E 1 komma großes E 2 element van Schreibschrift großes A then großes E 1 eenheid großes E 2 element van Schreibschrift großes A punt EndLayout
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	StartLayout 1. Row 1. Column Blank 2. Column Blank 3. Column links hakkie normales großes A punt 1 regs hakkie großes I f großes A element van Schreibschrift großes F t h e n 0 kleiner of gelyk aan großes P links krulhakkie großes A regs krulhakkie kleiner of gelyk aan 1 punt 4. Column links hakkie 1 regs hakkie 2. Row 1. Column Blank 2. Column Blank 3. Column links hakkie normales großes A punt 2 regs hakkie großes P links krulhakkie Schreibschrift großes S regs krulhakkie is gelyk aan 1 punt 4. Column links hakkie 2 regs hakkie 3. Row 1. Column Blank 2. Column Blank 3. Column links hakkie normales großes A punt 3 regs hakkie großes I f links krulhakkie großes E Index n Grundlinie komma n groter of gelyk aan 1 regs krulhakkie element van Schreibschrift großes F is a sequence of disjoint 4. Column links hakkie 3 regs hakkie EndLayout
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	großes P links krulhakkie großes B Index j Grundlinie afstreep großes A regs krulhakkie is gelyk aan Anfang Bruch großes P links krulhakkie großes B Index j Grundlinie regs krulhakkie großes P links krulhakkie großes A afstreep großes B Index j Grundlinie regs krulhakkie durch sigma summation Unterschrift j priem element van großes J großes P links krulhakkie großes B Index j priem Grundlinie regs krulhakkie großes P links krulhakkie großes A afstreep großes B Index j priem Grundlinie regs krulhakkie Ende Bruch 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 großes B regs hakkie is gelyk aan integraal Unterschrift großes B 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 Unterschrift n regs pyltjie oneindigheid großes E links krulhakkie StartAbsoluteValue großes X Index n Grundlinie minus großes X EndAbsoluteValue regs krulhakkie is gelyk aan großes E links krulhakkie limit Unterschrift n regs pyltjie oneindigheid StartAbsoluteValue großes X Index n Grundlinie minus großes X EndAbsoluteValue 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	StartLayout 1. Row 1. Column großes P Index my komma sigma Grundlinie links krulhakkie großes Y groter of gelyk aan l Index beta Grundlinie links hakkie großes Y overbar Index n Grundlinie komma großes S Index n Grundlinie regs hakkie regs krulhakkie is gelyk aan großes P Index my komma sigma Grundlinie links krulhakkie links hakkie großes Y minus großes Y overbar Index n Grundlinie regs hakkie divided by links hakkie großes S dot links hakkie 1 plus Anfang Bruch 1 durch n Ende Bruch regs hakkie hoch 1 divided by 2 Grundlinie regs hakkie groter of gelyk aan minus t Index beta Grundlinie links blokhakkie n minus 1 regs blokhakkie regs krulhakkie is gelyk aan beta komma 2. Row 1. Column Blank 2. Column links hakkie 1 regs hakkie EndLayout
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	großes L is gelyk aan Start 5 By 6 Matrix 1. Row 1. Column 1 2. Column negative 1 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 2. Row 1. Column Blank 2. Column 1 3. Column negative 1 4. Column Blank 5. Column 0 6. Column Blank 3. Row 1. Column Blank 2. Column Blank 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 4. Row 1. Column Blank 2. Column 0 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 5. Row 1. Column Blank 2. Column Blank 3. Column Blank 4. Column Blank 5. Column 1 6. Column negative 1 EndMatrix 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	Anfang Wurzel n Ende Wurzel links blokhakkie großes Y overbar Index n Grundlinie minus links hakkie my plus z Index beta Grundlinie sigma regs hakkie regs blokhakkie divided by großes S Index n Grundlinie tilde Anfang Bruch großes U plus Anfang Wurzel n Ende Wurzel z Index 1 minus beta Grundlinie durch links hakkie chi squared links blokhakkie n minus 1 regs blokhakkie divided by links hakkie n minus 1 regs hakkie regs hakkie hoch 1 divided by 2 Grundlinie Ende Bruch tilde t links blokhakkie n minus 1 kommapunt Anfang Wurzel n Ende Wurzel z Index 1 minus beta Grundlinie 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	StartLayout 1. Row 1. Column gamma 2. Column is gelyk aan großes P links krulhakkie großes E Index p komma q Grundlinie deelversameling van links hakkie großes X Index links hakkie r regs hakkie Grundlinie komma großes X Index links hakkie s regs hakkie Grundlinie regs krulhakkie 2. Row 1. Column Blank 2. Column is gelyk aan Anfang Bruch n factorial durch links hakkie r minus 1 regs hakkie factorial Ende Bruch sigma summation Unterschrift j is gelyk aan 0 Überschrift s minus r minus 1 links hakkie negative 1 regs hakkie hoch j Grundlinie Anfang Bruch p hoch r plus j Grundlinie durch links hakkie n minus r minus j regs hakkie factorial j factorial Ende Bruch großes I Index 1 minus q Grundlinie links hakkie n minus s plus 1 komma s minus r minus j regs hakkie punt EndLayout
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	großes S Index i Grundlinie StartBinomialOrMatrix t Choose x EndBinomialOrMatrix is gelyk aan Start 2 By 2 Matrix 1. Row 1. Column 1 divided by m 2. Column 0 2. Row 1. Column a Index i Grundlinie 2. Column r Index i Grundlinie EndMatrix StartBinomialOrMatrix t Choose x EndBinomialOrMatrix plus StartBinomialOrMatrix links hakkie i minus 1 regs hakkie divided by m Choose b Index i Grundlinie EndBinomialOrMatrix 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 hoch 4 minus 2 s Grundlinie kleiner of gelyk aan Anfang Bruch 1 durch 2 großes T Ende Bruch integraal Subscript negative großes T Superscript großes T Baseline links hakkie f links hakkie t plus h regs hakkie minus f links hakkie t regs hakkie regs hakkie squared normales d t kleiner of gelyk aan c 2 h hoch 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	großes C links hakkie 0 regs hakkie minus großes C links hakkie h regs hakkie assimtoties gelyk aan c h hoch 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	großes S links hakkie omega regs hakkie is gelyk aan limit Unterschrift großes T regs pyltjie oneindigheid Anfang Bruch 1 durch 2 großes T Ende Bruch StartAbsoluteValue integraal Subscript negative großes T Superscript großes T Baseline komma f komma links hakkie komma t komma regs hakkie komma normales e hoch kursives i t omega Grundlinie komma normales d komma t EndAbsoluteValue squared 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 Subscript 0 Superscript 1 Baseline integraal Subscript 0 Superscript 1 Baseline links blokhakkie StartAbsoluteValue f links hakkie t regs hakkie minus f links hakkie u regs hakkie EndAbsoluteValue squared plus StartAbsoluteValue t minus u EndAbsoluteValue squared regs blokhakkie hoch negative s divided by 2 Grundlinie normales d t normales 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	serifenloses großes E links hakkie sigma summation Unterschrift großes I element van großes E Index k plus 1 Grundlinie StartAbsoluteValue großes I EndAbsoluteValue hoch s Grundlinie regs hakkie is gelyk aan serifenloses großes E links hakkie sigma summation Unterschrift großes I element van großes E Index k Grundlinie StartAbsoluteValue großes I EndAbsoluteValue hoch s Grundlinie regs hakkie serifenloses großes E links hakkie großes R 1 hoch s Grundlinie plus großes R 2 hoch s Grundlinie 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 Anfang Wurzel links hakkie x 2 minus x 1 regs hakkie squared plus links hakkie y 2 minus y 1 regs hakkie squared Ende Wurzel
73	$ℝ$	double struck upper R	mit Doppelstrich großes R
74	$ℝ = (- \infty, \infty)$	double struck upper R equals left parenthesis negative infinity comma infinity right parenthesis	mit Doppelstrich großes R is gelyk aan links hakkie negative oneindigheid komma oneindigheid regs hakkie
75	${1, 2, 3}$	StartSet 1 comma 2 comma 3 EndSet	StartSet 1 komma 2 komma 3 EndSet
76	$1 \in S$	1 element of upper S	1 element van großes S
77	$3 \in S$	3 element of upper S	3 element van großes S
78	$4 \notin S$	4 not an element of upper S	4 nie 'n element van großes 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 Anfang Wurzel 3 x minus 1 Ende Wurzel plus links hakkie 1 plus x regs hakkie squared
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 Anfang Bruch links hakkie b plus c regs hakkie squared durch d Ende Bruch plus Anfang Bruch links hakkie e plus f regs hakkie squared durch g Ende Bruch
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 squared links hakkie c minus b regs hakkie squared regs blokhakkie plus links blokhakkie links hakkie d plus e regs hakkie squared links hakkie f minus e regs hakkie squared 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 squared regs blokhakkie plus links blokhakkie links hakkie f minus e regs hakkie squared 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 squared 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 squared
85	$x = a + b^{2}$	x equals a plus b squared	x is gelyk aan a plus b squared
86	$\frac{\frac{1}{2}}{\frac{3}{4}} = \frac{2}{3}$	StartFraction one half Over three fourths EndFraction equals two thirds	Anfang Bruch een helfte durch drie kwarts Ende Bruch 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 Anfang Bruch x squared durch 2 factorial Ende Bruch plus Anfang Bruch x hoch 4 Grundlinie durch 4 factorial Ende Bruch 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 Anfang Bruch negative b plus of minus Anfang Wurzel b squared minus 4 a c Ende Wurzel durch 2 a Ende Bruch
90	$x + y^{\frac{2}{k + 1}}$	x plus y Superscript StartFraction 2 Over k plus 1 EndFraction	x plus y hoch Anfang Bruch 2 durch k plus 1 Ende Bruch
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 Unterschrift x regs pyltjie 0 Anfang Bruch sinus x durch x Ende Bruch 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 Anfang Wurzel links hakkie x 2 minus x 1 regs hakkie squared plus links hakkie y 2 minus y 1 regs hakkie squared Ende Wurzel
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	großes F Index n Grundlinie is gelyk aan großes F Index n minus 1 Grundlinie plus großes F Index 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	fettes großes Pi is gelyk aan Start 6 By 6 Matrix 1. Row 1. Column pi 11 2. Column pi 12 3. Column pi 12 4. Column 0 5. Column 0 6. Column 0 2. Row 1. Column pi 12 2. Column pi 11 3. Column pi 12 4. Column 0 5. Column 0 6. Column 0 3. Row 1. Column pi 12 2. Column pi 12 3. Column pi 11 4. Column 0 5. Column 0 6. Column 0 4. Row 1. Column 0 2. Column 0 3. Column 0 4. Column pi 44 5. Column 0 6. Column 0 5. Row 1. Column 0 2. Column 0 3. Column 0 4. Column 0 5. Column pi 44 6. Column 0 6. Row 1. Column 0 2. Column 0 3. Column 0 4. Column 0 5. Column 0 6. Column pi 44 EndMatrix
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 Anfang Bruch c 11 plus c 12 durch links hakkie c 11 minus c 12 regs hakkie links hakkie c 11 plus 2 c 12 regs hakkie Ende Bruch
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	großes S i normales großes O 2 plus 6 normales großes H normales großes F regs pyltjie normales großes H 2 großes S i normales großes F 6 plus 2 normales großes H 2 normales großes 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	Anfang Bruch d durch d x Ende Bruch links hakkie großes E links hakkie x regs hakkie großes A links hakkie x regs hakkie Anfang Bruch d w links hakkie x regs hakkie durch d x Ende Bruch 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 Index gas Grundlinie is gelyk aan minus een helfte links hakkie Anfang Bruch großes P Index seal Grundlinie durch großes P Index max Grundlinie Ende Bruch regs hakkie links hakkie Anfang Bruch 1 durch großes T Index seal Grundlinie Ende Bruch 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	großes B Index p Grundlinie is gelyk aan Anfang Anfang Bruch Anfang Bruch 7 minus v squared durch 3 Ende Bruch links hakkie 1 plus Anfang Bruch c squared durch a squared Ende Bruch plus Anfang Bruch c hoch 4 Grundlinie durch a hoch 4 Grundlinie Ende Bruch regs hakkie plus Anfang Bruch links hakkie 3 minus v regs hakkie squared c squared durch links hakkie 1 plus v regs hakkie a squared Ende Bruch durch durch links hakkie 1 minus v regs hakkie links hakkie 1 minus Anfang Bruch c hoch 4 Grundlinie durch a hoch 4 Grundlinie Ende Bruch regs hakkie links hakkie 1 minus Anfang Bruch c squared durch a squared Ende Bruch regs hakkie Ende Ende Bruch
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	großes Q Index tank hoch series Grundlinie is gelyk aan Anfang Bruch 1 durch großes R Index s Grundlinie Ende Bruch Anfang Wurzel Anfang Bruch großes L Index s Grundlinie durch großes C Index s Grundlinie Ende Bruch Ende Wurzel
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	großes Delta phi Index peak Grundlinie is gelyk aan tangens hoch negative 1 Grundlinie links hakkie k squared großes Q Index tank hoch series Grundlinie 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 Anfang Bruch großes W durch großes L squared Ende Bruch Anfang Wurzel Anfang Bruch großes E durch rho Ende Bruch Ende Wurzel Anfang Wurzel links hakkie 1 plus 0.293 Anfang Bruch großes L squared durch EW squared Ende Bruch sigma regs hakkie Ende Wurzel
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 Index n Grundlinie links hakkie x regs hakkie is gelyk aan gamma Index n Grundlinie links hakkie hiperboliese kosinus k Index n Grundlinie x minus kosinus k Index n Grundlinie x regs hakkie plus links hakkie hiperboliese sinus k Index n Grundlinie x minus sinus k Index n Grundlinie 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	StartLayout 1. Row 1. Column großes B 2. Column is gelyk aan Anfang Anfang Bruch Anfang Bruch großes F 0 durch m Ende Bruch durch durch Anfang Wurzel links hakkie omega 0 squared minus omega squared regs hakkie squared plus 4 n squared omega squared Ende Wurzel Ende Ende Bruch 2. Row 1. Column Blank 2. Column is gelyk aan Anfang Anfang Bruch Anfang Bruch großes F 0 durch k Ende Bruch durch durch Anfang Wurzel links hakkie 1 minus links hakkie omega divided by omega 0 squared regs hakkie squared regs hakkie squared plus 4 links hakkie n divided by omega 0 regs hakkie squared links hakkie omega divided by omega 0 regs hakkie squared Ende Wurzel Ende Ende Bruch EndLayout
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	normales p links hakkie großes A a n d großes B regs hakkie is gelyk aan normales p links hakkie großes A regs hakkie normales p links hakkie großes B afstreep großes 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	großes P großes M großes F links hakkie x regs hakkie eweredig aan links hakkie Anfang Bruch 1 durch x Ende Bruch regs hakkie hoch 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 Anfang Bruch 1 durch Anfang Wurzel 2 pi Ende Wurzel Ende Bruch exp links hakkie minus x squared 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	Anfang Bruch d x durch d theta Ende Bruch is gelyk aan Anfang Bruch beta durch kosinus squared theta Ende Bruch
109	$s / \sqrt{2 (n - 1)}$	s divided by StartRoot 2 left parenthesis n minus 1 right parenthesis EndRoot	s divided by Anfang Wurzel 2 links hakkie n minus 1 regs hakkie Ende Wurzel

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	negative 5 and een vyf de minus 6 and 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	negative 7 and drie kwarts minus left p'ren negative 4 and sewe agstes right p'ren is gelyk aan
2	$- 24.15 - (13.7) =$	negative 24.15 minus left p'ren 13.7 right p'ren equals	negative 24,15 minus left p'ren 13,7 right p'ren is gelyk aan
3	$(- 4) \times 3 = - 12$	left p'ren negative 4 right p'ren times 3 equals negative 12	left p'ren negative 4 right p'ren maal 3 is gelyk aan negative 12
4	$- 12 \div 3 = - 4$	negative 12 divided by 3 equals negative 4	negative 12 divided by 3 is gelyk aan negative 4
5	$- 12 \div (- 4) = 3$	negative 12 divided by left p'ren negative 4 right p'ren equals 3	negative 12 divided by left p'ren negative 4 right p'ren 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 left p'ren negative 5 right p'ren
8	$- 6 \times 5$	negative 6 times 5	negative 6 maal 5
9	$- 6 \times (- 5)$	negative 6 times left p'ren negative 5 right p'ren	negative 6 maal left p'ren negative 5 right p'ren
10	$- 8 \times 7$	negative 8 times 7	negative 8 maal 7
11	$- 8 \times (- 7)$	negative 8 times left p'ren negative 7 right p'ren	negative 8 maal left p'ren negative 7 right p'ren
12	$8 \times (- 7)$	8 times left p'ren negative 7 right p'ren	8 maal left p'ren negative 7 right p'ren
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 großes M plus m hoek großes N is gelyk aan 180 graad
18	$A = \frac{1}{2} b h$	upper A equals one half b h	großes 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	Anfang Bruch area of triangle durch area of square Ende Bruch is gelyk aan Anfang Bruch 1 unit squared durch 16 units squared Ende Bruch
20	${0.6}^{2}$	0.6 squared	0,6 squared
21	${1.5}^{2}$	1.5 squared	1,5 squared
22	$4 (2 x + 3 x)$	4 left p'ren 2 x plus 3 x right p'ren	4 left p'ren 2 x plus 3 x right p'ren
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 squared plus 5 y squared minus 2
24	$(5 + 9) - 4 + 3 =$	left p'ren 5 plus 9 right p'ren minus 4 plus 3 equals	left p'ren 5 plus 9 right p'ren minus 4 plus 3 is gelyk aan
25	$\overset{\leftrightarrow}{B C}$	ModAbove upper B upper C With left right arrow	ModAbove großes B großes C With links regs pyltjie
26	$\vec{P Q}$	ModAbove upper P upper Q With right arrow	ModAbove großes P großes Q With regs pyltjie
27	$\bar{G H}$	ModAbove upper G upper H With bar	ModAbove großes G großes H With makron
28	$\bar{W X} ≅ \bar{Y Z}$	ModAbove upper W upper X With bar approximately equals ModAbove upper Y upper Z With bar	ModAbove großes W großes X With makron ongeveer gelyk aan ModAbove großes Y großes Z With makron
29	$∠ B E F$	angle upper B upper E upper F	hoek großes B großes E großes F
30	$∠ B E D$	angle upper B upper E upper D	hoek großes B großes E großes D
31	$∠ D E F$	angle upper D upper E upper F	hoek großes D großes E großes 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 Anfang Bruch negative b plus of minus Anfang Wurzel b squared minus 4 a c Ende Wurzel durch 2 a Ende Bruch
33	$y = x^{2} + 8 x + 16$	y equals x squared plus 8 x plus 16	y is gelyk aan x squared 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 left p'ren 3 hoch x Grund right p'ren
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 cubed 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 left p'ren x squared plus 1 right p'ren left p'ren x squared plus 3 right p'ren
38	$y = {0.5}^{x}$	y equals 0.5 Sup x	y is gelyk aan 0,5 hoch 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 Anfang Bruch 3 durch x Ende Bruch
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 left p'ren x plus 4 right p'ren left p'ren x plus 4 right p'ren
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 left p'ren 4 x minus 3 right p'ren left p'ren x plus 1 right p'ren
43	$y = 20 x - 4 x^{2}$	y equals 20 x minus 4 x squared	y is gelyk aan 20 x minus 4 x squared
44	$y = x^{2}$	y equals x squared	y is gelyk aan x squared
45	$y = 3^{x - 1}$	y equals 3 Sup x minus 1	y is gelyk aan 3 hoch 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 left p'ren x plus 3 right p'ren
47	$y = 4 x^{2} - x - 3$	y equals 4 x squared minus x minus 3	y is gelyk aan 4 x squared 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 Anfang Bruch 1 durch x Ende Bruch
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 left p'ren 5 minus x right p'ren
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 left p'ren x minus 3 right p'ren plus 6 left p'ren 1 minus x right p'ren
51	$0.25 > \frac{5}{16}$	0.25 greater than five sixteenths	0,25 groter as vyf sestien des
52	$32 \cdot (5 \cdot 7)$	32 dot left p'ren 5 dot 7 right p'ren	32 punt left p'ren 5 punt 7 right p'ren
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	left p'ren een helfte maal een helfte maal pi maal 2 right p'ren plus left p'ren 2 maal een helfte maal pi maal 5 right p'ren
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 Unterschrift n regs pyltjie oneindigheid großes E Index n Grund is gelyk aan union Unterschrift n groter of gelyk aan 1 intersection Unterschrift k groter of gelyk aan n großes E Index k Grund komma limsup Unterschrift n regs pyltjie oneindigheid großes E Index n Grund is gelyk aan intersection Unterschrift n groter of gelyk aan 1 union Unterschrift k groter of gelyk aan n großes E Index k Grund 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	StartLayout 1. Row 1. Column left p'ren i right p'ren 2. Column Schreibschrift großes S element van Schreibschrift großes A kommapunt 2. Row 1. Column left p'ren ii right p'ren 2. Column if großes E element van Schreibschrift großes A then großes E overbar element van Schreibschrift großes A kommapunt 3. Row 1. Column left p'ren iii right p'ren 2. Column if großes E 1 komma großes E 2 element van Schreibschrift großes A then großes E 1 eenheid großes E 2 element van Schreibschrift großes A punt EndLayout
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	StartLayout 1. Row 1. Column Blank 2. Column Blank 3. Column left p'ren normales großes A punt 1 right p'ren großes I f großes A element van Schreibschrift großes F t h e n 0 kleiner of gelyk aan großes P links krulhakkie großes A regs krulhakkie kleiner of gelyk aan 1 punt 4. Column left p'ren 1 right p'ren 2. Row 1. Column Blank 2. Column Blank 3. Column left p'ren normales großes A punt 2 right p'ren großes P links krulhakkie Schreibschrift großes S regs krulhakkie is gelyk aan 1 punt 4. Column left p'ren 2 right p'ren 3. Row 1. Column Blank 2. Column Blank 3. Column left p'ren normales großes A punt 3 right p'ren großes I f links krulhakkie großes E Index n Grund komma n groter of gelyk aan 1 regs krulhakkie element van Schreibschrift großes F is a sequence of disjoint 4. Column left p'ren 3 right p'ren EndLayout
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	großes P links krulhakkie großes B Index j Grund afstreep großes A regs krulhakkie is gelyk aan Anfang Bruch großes P links krulhakkie großes B Index j Grund regs krulhakkie großes P links krulhakkie großes A afstreep großes B Index j Grund regs krulhakkie durch sigma summation Unterschrift j priem element van großes J großes P links krulhakkie großes B Index j priem Grund regs krulhakkie großes P links krulhakkie großes A afstreep großes B Index j priem Grund regs krulhakkie Ende Bruch 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 left p'ren großes B right p'ren is gelyk aan integraal Unterschrift großes B f left p'ren x right p'ren d my 2 left p'ren x right p'ren
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 Unterschrift n regs pyltjie oneindigheid großes E links krulhakkie StartAbsoluteValue großes X Index n Grund minus großes X EndAbsoluteValue regs krulhakkie is gelyk aan großes E links krulhakkie limit Unterschrift n regs pyltjie oneindigheid StartAbsoluteValue großes X Index n Grund minus großes X EndAbsoluteValue 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	StartLayout 1. Row 1. Column großes P Index my komma sigma Grund links krulhakkie großes Y groter of gelyk aan l Index beta Grund left p'ren großes Y overbar Index n Grund komma großes S Index n Grund right p'ren regs krulhakkie is gelyk aan großes P Index my komma sigma Grund links krulhakkie left p'ren großes Y minus großes Y overbar Index n Grund right p'ren divided by left p'ren großes S dot left p'ren 1 plus Anfang Bruch 1 durch n Ende Bruch right p'ren hoch 1 divided by 2 Grund right p'ren groter of gelyk aan minus t Index beta Grund left brack n minus 1 right brack regs krulhakkie is gelyk aan beta komma 2. Row 1. Column Blank 2. Column left p'ren 1 right p'ren EndLayout
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	großes L is gelyk aan Start 5 By 6 Matrix 1. Row 1. Column 1 2. Column negative 1 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 2. Row 1. Column Blank 2. Column 1 3. Column negative 1 4. Column Blank 5. Column 0 6. Column Blank 3. Row 1. Column Blank 2. Column Blank 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 4. Row 1. Column Blank 2. Column 0 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 5. Row 1. Column Blank 2. Column Blank 3. Column Blank 4. Column Blank 5. Column 1 6. Column negative 1 EndMatrix 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	Anfang Wurzel n Ende Wurzel left brack großes Y overbar Index n Grund minus left p'ren my plus z Index beta Grund sigma right p'ren right brack divided by großes S Index n Grund tilde Anfang Bruch großes U plus Anfang Wurzel n Ende Wurzel z Index 1 minus beta Grund durch 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 hoch 1 divided by 2 Grund Ende Bruch tilde t left brack n minus 1 kommapunt Anfang Wurzel n Ende Wurzel z Index 1 minus beta Grund right brack 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	StartLayout 1. Row 1. Column gamma 2. Column is gelyk aan großes P links krulhakkie großes E Index p komma q Grund deelversameling van left p'ren großes X Index left p'ren r right p'ren Grund komma großes X Index left p'ren s right p'ren Grund regs krulhakkie 2. Row 1. Column Blank 2. Column is gelyk aan Anfang Bruch n factorial durch left p'ren r minus 1 right p'ren factorial Ende Bruch sigma summation Unterschrift j is gelyk aan 0 Überschrift s minus r minus 1 left p'ren negative 1 right p'ren hoch j Grund Anfang Bruch p hoch r plus j Grund durch left p'ren n minus r minus j right p'ren factorial j factorial Ende Bruch großes I Index 1 minus q Grund left p'ren n minus s plus 1 komma s minus r minus j right p'ren punt EndLayout
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	großes S Index i Grund StartBinomialOrMatrix t Choose x EndBinomialOrMatrix is gelyk aan Start 2 By 2 Matrix 1. Row 1. Column 1 divided by m 2. Column 0 2. Row 1. Column a Index i Grund 2. Column r Index i Grund EndMatrix StartBinomialOrMatrix t Choose x EndBinomialOrMatrix plus StartBinomialOrMatrix left p'ren i minus 1 right p'ren divided by m Choose b Index i Grund EndBinomialOrMatrix 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 hoch 4 minus 2 s Grund kleiner of gelyk aan Anfang Bruch 1 durch 2 großes T Ende Bruch integraal Sub negative großes T Sup großes 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 normales d t kleiner of gelyk aan c 2 h hoch 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	großes C left p'ren 0 right p'ren minus großes C left p'ren h right p'ren assimtoties gelyk aan c h hoch 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	großes S left p'ren omega right p'ren is gelyk aan limit Unterschrift großes T regs pyltjie oneindigheid Anfang Bruch 1 durch 2 großes T Ende Bruch StartAbsoluteValue integraal Sub negative großes T Sup großes T Base komma f komma left p'ren komma t komma right p'ren komma normales e hoch kursives i t omega Grund komma normales d komma t EndAbsoluteValue squared 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 Sub 0 Sup 1 Base integraal 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 hoch negative s divided by 2 Grund normales d t normales 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	serifenloses großes E left p'ren sigma summation Unterschrift großes I element van großes E Index k plus 1 Grund StartAbsoluteValue großes I EndAbsoluteValue hoch s Grund right p'ren is gelyk aan serifenloses großes E left p'ren sigma summation Unterschrift großes I element van großes E Index k Grund StartAbsoluteValue großes I EndAbsoluteValue hoch s Grund right p'ren serifenloses großes E left p'ren großes R 1 hoch s Grund plus großes R 2 hoch s Grund right p'ren punt
70	$(x_{1}, y_{1})$	left p'ren x 1 comma y 1 right p'ren	left p'ren x 1 komma y 1 right p'ren
71	$(x_{2}, y_{2})$	left p'ren x 2 comma y 2 right p'ren	left p'ren x 2 komma y 2 right p'ren
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 Anfang Wurzel 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 Ende Wurzel
73	$ℝ$	double struck upper R	mit Doppelstrich großes R
74	$ℝ = (- \infty, \infty)$	double struck upper R equals left p'ren negative infinity comma infinity right p'ren	mit Doppelstrich großes R is gelyk aan left p'ren negative oneindigheid komma oneindigheid right p'ren
75	${1, 2, 3}$	StartSet 1 comma 2 comma 3 EndSet	StartSet 1 komma 2 komma 3 EndSet
76	$1 \in S$	1 element of upper S	1 element van großes S
77	$3 \in S$	3 element of upper S	3 element van großes S
78	$4 \notin S$	4 not an element of upper S	4 nie 'n element van großes 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 Anfang Wurzel 3 x minus 1 Ende Wurzel plus left p'ren 1 plus x right p'ren squared
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 Anfang Bruch left p'ren b plus c right p'ren squared durch d Ende Bruch plus Anfang Bruch left p'ren e plus f right p'ren squared durch g Ende Bruch
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 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
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 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
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 left brack left p'ren a plus b right p'ren squared right brack
84	$x = {(a + b)}^{2}$	x equals left p'ren a plus b right p'ren squared	x is gelyk aan left p'ren a plus b right p'ren squared
85	$x = a + b^{2}$	x equals a plus b squared	x is gelyk aan a plus b squared
86	$\frac{\frac{1}{2}}{\frac{3}{4}} = \frac{2}{3}$	StartFrac one half Over three fourths EndFrac equals two thirds	Anfang Bruch een helfte durch drie kwarts Ende Bruch 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 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 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 Anfang Bruch x squared durch 2 factorial Ende Bruch plus Anfang Bruch x hoch 4 Grund durch 4 factorial Ende Bruch 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 Anfang Bruch negative b plus of minus Anfang Wurzel b squared minus 4 a c Ende Wurzel durch 2 a Ende Bruch
90	$x + y^{\frac{2}{k + 1}}$	x plus y Sup StartFrac 2 Over k plus 1 EndFrac	x plus y hoch Anfang Bruch 2 durch k plus 1 Ende Bruch
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 Unterschrift x regs pyltjie 0 Anfang Bruch sinus x durch x Ende Bruch 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 Anfang Wurzel 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 Ende Wurzel
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	großes F Index n Grund is gelyk aan großes F Index n minus 1 Grund plus großes F Index 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	fettes großes Pi is gelyk aan Start 6 By 6 Matrix 1. Row 1. Column pi 11 2. Column pi 12 3. Column pi 12 4. Column 0 5. Column 0 6. Column 0 2. Row 1. Column pi 12 2. Column pi 11 3. Column pi 12 4. Column 0 5. Column 0 6. Column 0 3. Row 1. Column pi 12 2. Column pi 12 3. Column pi 11 4. Column 0 5. Column 0 6. Column 0 4. Row 1. Column 0 2. Column 0 3. Column 0 4. Column pi 44 5. Column 0 6. Column 0 5. Row 1. Column 0 2. Column 0 3. Column 0 4. Column 0 5. Column pi 44 6. Column 0 6. Row 1. Column 0 2. Column 0 3. Column 0 4. Column 0 5. Column 0 6. Column pi 44 EndMatrix
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 Anfang Bruch c 11 plus c 12 durch left p'ren c 11 minus c 12 right p'ren left p'ren c 11 plus 2 c 12 right p'ren Ende Bruch
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	großes S i normales großes O 2 plus 6 normales großes H normales großes F regs pyltjie normales großes H 2 großes S i normales großes F 6 plus 2 normales großes H 2 normales großes 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	Anfang Bruch d durch d x Ende Bruch left p'ren großes E left p'ren x right p'ren großes A left p'ren x right p'ren Anfang Bruch d w left p'ren x right p'ren durch d x Ende Bruch right p'ren plus p left p'ren x right p'ren 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 Index gas Grund is gelyk aan minus een helfte left p'ren Anfang Bruch großes P Index seal Grund durch großes P Index max Grund Ende Bruch right p'ren left p'ren Anfang Bruch 1 durch großes T Index seal Grund Ende Bruch right p'ren
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	großes B Index p Grund is gelyk aan Anfang Anfang Bruch Anfang Bruch 7 minus v squared durch 3 Ende Bruch left p'ren 1 plus Anfang Bruch c squared durch a squared Ende Bruch plus Anfang Bruch c hoch 4 Grund durch a hoch 4 Grund Ende Bruch right p'ren plus Anfang Bruch left p'ren 3 minus v right p'ren squared c squared durch left p'ren 1 plus v right p'ren a squared Ende Bruch durch durch left p'ren 1 minus v right p'ren left p'ren 1 minus Anfang Bruch c hoch 4 Grund durch a hoch 4 Grund Ende Bruch right p'ren left p'ren 1 minus Anfang Bruch c squared durch a squared Ende Bruch right p'ren Ende Ende Bruch
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	großes Q Index tank hoch series Grund is gelyk aan Anfang Bruch 1 durch großes R Index s Grund Ende Bruch Anfang Wurzel Anfang Bruch großes L Index s Grund durch großes C Index s Grund Ende Bruch Ende Wurzel
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	großes Delta phi Index peak Grund is gelyk aan tangens hoch negative 1 Grund left p'ren k squared großes Q Index tank hoch series Grund right p'ren
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 Anfang Bruch großes W durch großes L squared Ende Bruch Anfang Wurzel Anfang Bruch großes E durch rho Ende Bruch Ende Wurzel Anfang Wurzel left p'ren 1 plus 0.293 Anfang Bruch großes L squared durch EW squared Ende Bruch sigma right p'ren Ende Wurzel
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 Index n Grund left p'ren x right p'ren is gelyk aan gamma Index n Grund left p'ren hiperboliese kosinus k Index n Grund x minus kosinus k Index n Grund x right p'ren plus left p'ren hiperboliese sinus k Index n Grund x minus sinus k Index n Grund x right p'ren
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	StartLayout 1. Row 1. Column großes B 2. Column is gelyk aan Anfang Anfang Bruch Anfang Bruch großes F 0 durch m Ende Bruch durch durch Anfang Wurzel left p'ren omega 0 squared minus omega squared right p'ren squared plus 4 n squared omega squared Ende Wurzel Ende Ende Bruch 2. Row 1. Column Blank 2. Column is gelyk aan Anfang Anfang Bruch Anfang Bruch großes F 0 durch k Ende Bruch durch durch Anfang Wurzel 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 Ende Wurzel Ende Ende Bruch EndLayout
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	normales p left p'ren großes A a n d großes B right p'ren is gelyk aan normales p left p'ren großes A right p'ren normales p left p'ren großes B afstreep großes A right p'ren
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	großes P großes M großes F left p'ren x right p'ren eweredig aan left p'ren Anfang Bruch 1 durch x Ende Bruch right p'ren hoch 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 left p'ren x right p'ren is gelyk aan Anfang Bruch 1 durch Anfang Wurzel 2 pi Ende Wurzel Ende Bruch exp left p'ren minus x squared skuinsstreep 2 right p'ren
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	Anfang Bruch d x durch d theta Ende Bruch is gelyk aan Anfang Bruch beta durch kosinus squared theta Ende Bruch
109	$s / \sqrt{2 (n - 1)}$	s divided by StartRoot 2 left p'ren n minus 1 right p'ren EndRoot	s divided by Anfang Wurzel 2 left p'ren n minus 1 right p'ren Ende Wurzel

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	negative 5 and een vyf de minus 6 and 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	negative 7 and drie kwarts minus L p'ren negative 4 and sewe agstes R p'ren is gelyk aan
2	$- 24.15 - (13.7) =$	negative 24.15 minus L p'ren 13.7 R p'ren equals	negative 24,15 minus L p'ren 13,7 R p'ren is gelyk aan
3	$(- 4) \times 3 = - 12$	L p'ren negative 4 R p'ren times 3 equals negative 12	L p'ren negative 4 R p'ren maal 3 is gelyk aan negative 12
4	$- 12 \div 3 = - 4$	negative 12 divided by 3 equals negative 4	negative 12 divided by 3 is gelyk aan negative 4
5	$- 12 \div (- 4) = 3$	negative 12 divided by L p'ren negative 4 R p'ren equals 3	negative 12 divided by L p'ren negative 4 R p'ren 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 L p'ren negative 5 R p'ren
8	$- 6 \times 5$	negative 6 times 5	negative 6 maal 5
9	$- 6 \times (- 5)$	negative 6 times L p'ren negative 5 R p'ren	negative 6 maal L p'ren negative 5 R p'ren
10	$- 8 \times 7$	negative 8 times 7	negative 8 maal 7
11	$- 8 \times (- 7)$	negative 8 times L p'ren negative 7 R p'ren	negative 8 maal L p'ren negative 7 R p'ren
12	$8 \times (- 7)$	8 times L p'ren negative 7 R p'ren	8 maal L p'ren negative 7 R p'ren
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 großes M plus m hoek großes N is gelyk aan 180 graad
18	$A = \frac{1}{2} b h$	upper A equals one half b h	großes 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	Bruch area of triangle durch area of square Ende Bruch is gelyk aan Bruch 1 unit squared durch 16 units squared Ende Bruch
20	${0.6}^{2}$	0.6 squared	0,6 squared
21	${1.5}^{2}$	1.5 squared	1,5 squared
22	$4 (2 x + 3 x)$	4 L p'ren 2 x plus 3 x R p'ren	4 L p'ren 2 x plus 3 x R p'ren
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 squared plus 5 y squared minus 2
24	$(5 + 9) - 4 + 3 =$	L p'ren 5 plus 9 R p'ren minus 4 plus 3 equals	L p'ren 5 plus 9 R p'ren minus 4 plus 3 is gelyk aan
25	$\overset{\leftrightarrow}{B C}$	ModAbove upper B upper C With L R arrow	ModAbove großes B großes C With L R arrow
26	$\vec{P Q}$	ModAbove upper P upper Q With R arrow	ModAbove großes P großes Q With R arrow
27	$\bar{G H}$	ModAbove upper G upper H With bar	ModAbove großes G großes H With makron
28	$\bar{W X} ≅ \bar{Y Z}$	ModAbove upper W upper X With bar approximately equals ModAbove upper Y upper Z With bar	ModAbove großes W großes X With makron ongeveer gelyk aan ModAbove großes Y großes Z With makron
29	$∠ B E F$	angle upper B upper E upper F	hoek großes B großes E großes F
30	$∠ B E D$	angle upper B upper E upper D	hoek großes B großes E großes D
31	$∠ D E F$	angle upper D upper E upper F	hoek großes D großes E großes 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 Bruch negative b plus of minus Wurzel b squared minus 4 a c Ende Wurzel durch 2 a Ende Bruch
33	$y = x^{2} + 8 x + 16$	y equals x squared plus 8 x plus 16	y is gelyk aan x squared 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 L p'ren 3 hoch x Grund R p'ren
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 cubed 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 L p'ren x squared plus 1 R p'ren L p'ren x squared plus 3 R p'ren
38	$y = {0.5}^{x}$	y equals 0.5 Sup x	y is gelyk aan 0,5 hoch 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 Bruch 3 durch x Ende Bruch
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 L p'ren x plus 4 R p'ren L p'ren x plus 4 R p'ren
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 L p'ren 4 x minus 3 R p'ren L p'ren x plus 1 R p'ren
43	$y = 20 x - 4 x^{2}$	y equals 20 x minus 4 x squared	y is gelyk aan 20 x minus 4 x squared
44	$y = x^{2}$	y equals x squared	y is gelyk aan x squared
45	$y = 3^{x - 1}$	y equals 3 Sup x minus 1	y is gelyk aan 3 hoch 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 L p'ren x plus 3 R p'ren
47	$y = 4 x^{2} - x - 3$	y equals 4 x squared minus x minus 3	y is gelyk aan 4 x squared 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 Bruch 1 durch x Ende Bruch
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 L p'ren 5 minus x R p'ren
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 L p'ren x minus 3 R p'ren plus 6 L p'ren 1 minus x R p'ren
51	$0.25 > \frac{5}{16}$	0.25 greater than five sixteenths	0,25 groter as vyf sestien des
52	$32 \cdot (5 \cdot 7)$	32 dot L p'ren 5 dot 7 R p'ren	32 punt L p'ren 5 punt 7 R p'ren
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	L p'ren een helfte maal een helfte maal pi maal 2 R p'ren plus L p'ren 2 maal een helfte maal pi maal 5 R p'ren
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 Unterschrift n R arrow oneindigheid großes E Index n Grund is gelyk aan union Unterschrift n groter of gelyk aan 1 intersection Unterschrift k groter of gelyk aan n großes E Index k Grund komma limsup Unterschrift n R arrow oneindigheid großes E Index n Grund is gelyk aan intersection Unterschrift n groter of gelyk aan 1 union Unterschrift k groter of gelyk aan n großes E Index k Grund 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	Layout 1. Row 1. Column L p'ren i R p'ren 2. Column Schreibschrift großes S element van Schreibschrift großes A kommapunt 2. Row 1. Column L p'ren ii R p'ren 2. Column if großes E element van Schreibschrift großes A then großes E overbar element van Schreibschrift großes A kommapunt 3. Row 1. Column L p'ren iii R p'ren 2. Column if großes E 1 komma großes E 2 element van Schreibschrift großes A then großes E 1 eenheid großes E 2 element van Schreibschrift großes A punt EndLayout
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	Layout 1. Row 1. Column Blank 2. Column Blank 3. Column L p'ren normales großes A punt 1 R p'ren großes I f großes A element van Schreibschrift großes F t h e n 0 kleiner of gelyk aan großes P L brace großes A R brace kleiner of gelyk aan 1 punt 4. Column L p'ren 1 R p'ren 2. Row 1. Column Blank 2. Column Blank 3. Column L p'ren normales großes A punt 2 R p'ren großes P L brace Schreibschrift großes S R brace is gelyk aan 1 punt 4. Column L p'ren 2 R p'ren 3. Row 1. Column Blank 2. Column Blank 3. Column L p'ren normales großes A punt 3 R p'ren großes I f L brace großes E Index n Grund komma n groter of gelyk aan 1 R brace element van Schreibschrift großes F is a sequence of disjoint 4. Column L p'ren 3 R p'ren EndLayout
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	großes P L brace großes B Index j Grund afstreep großes A R brace is gelyk aan Bruch großes P L brace großes B Index j Grund R brace großes P L brace großes A afstreep großes B Index j Grund R brace durch sigma summation Unterschrift j priem element van großes J großes P L brace großes B Index j priem Grund R brace großes P L brace großes A afstreep großes B Index j priem Grund R brace Ende Bruch 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 L p'ren großes B R p'ren is gelyk aan integraal Unterschrift großes B f L p'ren x R p'ren d my 2 L p'ren x R p'ren
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 Unterschrift n R arrow oneindigheid großes E L brace AbsoluteValue großes X Index n Grund minus großes X EndAbsoluteValue R brace is gelyk aan großes E L brace limit Unterschrift n R arrow oneindigheid AbsoluteValue großes X Index n Grund minus großes X EndAbsoluteValue R brace 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	Layout 1. Row 1. Column großes P Index my komma sigma Grund L brace großes Y groter of gelyk aan l Index beta Grund L p'ren großes Y overbar Index n Grund komma großes S Index n Grund R p'ren R brace is gelyk aan großes P Index my komma sigma Grund L brace L p'ren großes Y minus großes Y overbar Index n Grund R p'ren divided by L p'ren großes S dot L p'ren 1 plus Bruch 1 durch n Ende Bruch R p'ren hoch 1 divided by 2 Grund R p'ren groter of gelyk aan minus t Index beta Grund L brack n minus 1 R brack R brace is gelyk aan beta komma 2. Row 1. Column Blank 2. Column L p'ren 1 R p'ren EndLayout
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	großes L is gelyk aan 5 By 6 Matrix 1. Row 1. Column 1 2. Column negative 1 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 2. Row 1. Column Blank 2. Column 1 3. Column negative 1 4. Column Blank 5. Column 0 6. Column Blank 3. Row 1. Column Blank 2. Column Blank 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 4. Row 1. Column Blank 2. Column 0 3. Column Blank 4. Column Blank 5. Column Blank 6. Column Blank 5. Row 1. Column Blank 2. Column Blank 3. Column Blank 4. Column Blank 5. Column 1 6. Column negative 1 EndMatrix 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	Wurzel n Ende Wurzel L brack großes Y overbar Index n Grund minus L p'ren my plus z Index beta Grund sigma R p'ren R brack divided by großes S Index n Grund tilde Bruch großes U plus Wurzel n Ende Wurzel z Index 1 minus beta Grund durch 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 hoch 1 divided by 2 Grund Ende Bruch tilde t L brack n minus 1 kommapunt Wurzel n Ende Wurzel z Index 1 minus beta Grund R brack 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	Layout 1. Row 1. Column gamma 2. Column is gelyk aan großes P L brace großes E Index p komma q Grund deelversameling van L p'ren großes X Index L p'ren r R p'ren Grund komma großes X Index L p'ren s R p'ren Grund R brace 2. Row 1. Column Blank 2. Column is gelyk aan Bruch n factorial durch L p'ren r minus 1 R p'ren factorial Ende Bruch sigma summation Unterschrift j is gelyk aan 0 Überschrift s minus r minus 1 L p'ren negative 1 R p'ren hoch j Grund Bruch p hoch r plus j Grund durch L p'ren n minus r minus j R p'ren factorial j factorial Ende Bruch großes I Index 1 minus q Grund L p'ren n minus s plus 1 komma s minus r minus j R p'ren punt EndLayout
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	großes S Index i Grund BinomialOrMatrix t Choose x EndBinomialOrMatrix is gelyk aan 2 By 2 Matrix 1. Row 1. Column 1 divided by m 2. Column 0 2. Row 1. Column a Index i Grund 2. Column r Index i Grund EndMatrix BinomialOrMatrix t Choose x EndBinomialOrMatrix plus BinomialOrMatrix L p'ren i minus 1 R p'ren divided by m Choose b Index i Grund EndBinomialOrMatrix 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 hoch 4 minus 2 s Grund kleiner of gelyk aan Bruch 1 durch 2 großes T Ende Bruch integraal Sub negative großes T Sup großes 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 normales d t kleiner of gelyk aan c 2 h hoch 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	großes C L p'ren 0 R p'ren minus großes C L p'ren h R p'ren assimtoties gelyk aan c h hoch 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	großes S L p'ren omega R p'ren is gelyk aan limit Unterschrift großes T R arrow oneindigheid Bruch 1 durch 2 großes T Ende Bruch AbsoluteValue integraal Sub negative großes T Sup großes T Base komma f komma L p'ren komma t komma R p'ren komma normales e hoch kursives i t omega Grund komma normales d komma t EndAbsoluteValue squared 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 Sub 0 Sup 1 Base integraal 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 hoch negative s divided by 2 Grund normales d t normales 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	serifenloses großes E L p'ren sigma summation Unterschrift großes I element van großes E Index k plus 1 Grund AbsoluteValue großes I EndAbsoluteValue hoch s Grund R p'ren is gelyk aan serifenloses großes E L p'ren sigma summation Unterschrift großes I element van großes E Index k Grund AbsoluteValue großes I EndAbsoluteValue hoch s Grund R p'ren serifenloses großes E L p'ren großes R 1 hoch s Grund plus großes R 2 hoch s Grund R p'ren punt
70	$(x_{1}, y_{1})$	L p'ren x 1 comma y 1 R p'ren	L p'ren x 1 komma y 1 R p'ren
71	$(x_{2}, y_{2})$	L p'ren x 2 comma y 2 R p'ren	L p'ren x 2 komma y 2 R p'ren
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 Wurzel 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 Ende Wurzel
73	$ℝ$	double struck upper R	mit Doppelstrich großes R
74	$ℝ = (- \infty, \infty)$	double struck upper R equals L p'ren negative infinity comma infinity R p'ren	mit Doppelstrich großes R is gelyk aan L p'ren negative oneindigheid komma oneindigheid R p'ren
75	${1, 2, 3}$	Set 1 comma 2 comma 3 EndSet	Set 1 komma 2 komma 3 EndSet
76	$1 \in S$	1 element of upper S	1 element van großes S
77	$3 \in S$	3 element of upper S	3 element van großes S
78	$4 \notin S$	4 not an element of upper S	4 nie 'n element van großes 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 Wurzel 3 x minus 1 Ende Wurzel plus L p'ren 1 plus x R p'ren squared
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 Bruch L p'ren b plus c R p'ren squared durch d Ende Bruch plus Bruch L p'ren e plus f R p'ren squared durch g Ende Bruch
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 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
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 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
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 L brack L p'ren a plus b R p'ren squared R brack
84	$x = {(a + b)}^{2}$	x equals L p'ren a plus b R p'ren squared	x is gelyk aan L p'ren a plus b R p'ren squared
85	$x = a + b^{2}$	x equals a plus b squared	x is gelyk aan a plus b squared
86	$\frac{\frac{1}{2}}{\frac{3}{4}} = \frac{2}{3}$	Frac one half Over three fourths EndFrac equals two thirds	Bruch een helfte durch drie kwarts Ende Bruch 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 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 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 Bruch x squared durch 2 factorial Ende Bruch plus Bruch x hoch 4 Grund durch 4 factorial Ende Bruch 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 Bruch negative b plus of minus Wurzel b squared minus 4 a c Ende Wurzel durch 2 a Ende Bruch
90	$x + y^{\frac{2}{k + 1}}$	x plus y Sup Frac 2 Over k plus 1 EndFrac	x plus y hoch Bruch 2 durch k plus 1 Ende Bruch
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 Unterschrift x R arrow 0 Bruch sinus x durch x Ende Bruch 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 Wurzel 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 Ende Wurzel
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	großes F Index n Grund is gelyk aan großes F Index n minus 1 Grund plus großes F Index 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	fettes großes Pi is gelyk aan 6 By 6 Matrix 1. Row 1. Column pi 11 2. Column pi 12 3. Column pi 12 4. Column 0 5. Column 0 6. Column 0 2. Row 1. Column pi 12 2. Column pi 11 3. Column pi 12 4. Column 0 5. Column 0 6. Column 0 3. Row 1. Column pi 12 2. Column pi 12 3. Column pi 11 4. Column 0 5. Column 0 6. Column 0 4. Row 1. Column 0 2. Column 0 3. Column 0 4. Column pi 44 5. Column 0 6. Column 0 5. Row 1. Column 0 2. Column 0 3. Column 0 4. Column 0 5. Column pi 44 6. Column 0 6. Row 1. Column 0 2. Column 0 3. Column 0 4. Column 0 5. Column 0 6. Column pi 44 EndMatrix
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 Bruch c 11 plus c 12 durch L p'ren c 11 minus c 12 R p'ren L p'ren c 11 plus 2 c 12 R p'ren Ende Bruch
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	großes S i normales großes O 2 plus 6 normales großes H normales großes F R arrow normales großes H 2 großes S i normales großes F 6 plus 2 normales großes H 2 normales großes 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	Bruch d durch d x Ende Bruch L p'ren großes E L p'ren x R p'ren großes A L p'ren x R p'ren Bruch d w L p'ren x R p'ren durch d x Ende Bruch R p'ren plus p L p'ren x R p'ren 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 Index gas Grund is gelyk aan minus een helfte L p'ren Bruch großes P Index seal Grund durch großes P Index max Grund Ende Bruch R p'ren L p'ren Bruch 1 durch großes T Index seal Grund Ende Bruch R p'ren
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	großes B Index p Grund is gelyk aan geschachteltBruch Bruch 7 minus v squared durch 3 Ende Bruch L p'ren 1 plus Bruch c squared durch a squared Ende Bruch plus Bruch c hoch 4 Grund durch a hoch 4 Grund Ende Bruch R p'ren plus Bruch L p'ren 3 minus v R p'ren squared c squared durch L p'ren 1 plus v R p'ren a squared Ende Bruch geschachteltdurch L p'ren 1 minus v R p'ren L p'ren 1 minus Bruch c hoch 4 Grund durch a hoch 4 Grund Ende Bruch R p'ren L p'ren 1 minus Bruch c squared durch a squared Ende Bruch R p'ren geschachteltEnde Bruch
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	großes Q Index tank hoch series Grund is gelyk aan Bruch 1 durch großes R Index s Grund Ende Bruch Wurzel Bruch großes L Index s Grund durch großes C Index s Grund Ende Bruch Ende Wurzel
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	großes Delta phi Index peak Grund is gelyk aan tangens hoch negative 1 Grund L p'ren k squared großes Q Index tank hoch series Grund R p'ren
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 Bruch großes W durch großes L squared Ende Bruch Wurzel Bruch großes E durch rho Ende Bruch Ende Wurzel Wurzel L p'ren 1 plus 0.293 Bruch großes L squared durch EW squared Ende Bruch sigma R p'ren Ende Wurzel
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 Index n Grund L p'ren x R p'ren is gelyk aan gamma Index n Grund L p'ren hiperboliese kosinus k Index n Grund x minus kosinus k Index n Grund x R p'ren plus L p'ren hiperboliese sinus k Index n Grund x minus sinus k Index n Grund x R p'ren
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	Layout 1. Row 1. Column großes B 2. Column is gelyk aan geschachteltBruch Bruch großes F 0 durch m Ende Bruch geschachteltdurch Wurzel L p'ren omega 0 squared minus omega squared R p'ren squared plus 4 n squared omega squared Ende Wurzel geschachteltEnde Bruch 2. Row 1. Column Blank 2. Column is gelyk aan geschachteltBruch Bruch großes F 0 durch k Ende Bruch geschachteltdurch Wurzel 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 Ende Wurzel geschachteltEnde Bruch EndLayout
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	normales p L p'ren großes A a n d großes B R p'ren is gelyk aan normales p L p'ren großes A R p'ren normales p L p'ren großes B afstreep großes A R p'ren
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	großes P großes M großes F L p'ren x R p'ren eweredig aan L p'ren Bruch 1 durch x Ende Bruch R p'ren hoch 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 L p'ren x R p'ren is gelyk aan Bruch 1 durch Wurzel 2 pi Ende Wurzel Ende Bruch exp L p'ren minus x squared skuinsstreep 2 R p'ren
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	Bruch d x durch d theta Ende Bruch is gelyk aan Bruch beta durch kosinus squared theta Ende Bruch
109	$s / \sqrt{2 (n - 1)}$	s divided by Root 2 L p'ren n minus 1 R p'ren EndRoot	s divided by Wurzel 2 L p'ren n minus 1 R p'ren Ende Wurzel