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Question Number 168040 Answers: 0 Comments: 4

Question Number 168035 Answers: 0 Comments: 3

In an examination, the probability of charles scoring the highest mark in Maths, Physics and Chemistry are 0.90, 0.75 and 0.80 respectively. Calculate the probability that he will get the highest mark in at least 3 subjects.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{examination},\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{charles} \\ $$$$\mathrm{scoring}\:\mathrm{the}\:\mathrm{highest}\:\mathrm{mark}\:\mathrm{in}\:\mathrm{Maths},\:\mathrm{Physics} \\ $$$$\mathrm{and}\:\mathrm{Chemistry}\:\mathrm{are}\:\mathrm{0}.\mathrm{90},\:\mathrm{0}.\mathrm{75}\:\mathrm{and}\:\mathrm{0}.\mathrm{80}\:\mathrm{respectively}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{he}\:\mathrm{will}\:\mathrm{get} \\ $$$$\mathrm{the}\:\mathrm{highest}\:\mathrm{mark}\:\mathrm{in}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{subjects}. \\ $$

Question Number 168166 Answers: 1 Comments: 0

lim_(x→0) ((sin (sin x)−x ((1−x))^(1/3) )/x^5 ) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)−{x}\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}}}{{x}^{\mathrm{5}} }\:=? \\ $$

Question Number 168026 Answers: 1 Comments: 1

Math question for anyone who has a bonus code solution. Question. Find the smallest numbers that are divisible by 15 remain 9 and divide by 25 remain 19 and divide by 18 remain 12 remain and divide by 36 remain 30 remain and divide above 40 remain 34 remain Whoever solves it on the sheet, put his photo in the comment again.

$$ \\ $$Math question for anyone who has a bonus code solution. Question. Find the smallest numbers that are divisible by 15 remain 9 and divide by 25 remain 19 and divide by 18 remain 12 remain and divide by 36 remain 30 remain and divide above 40 remain 34 remain Whoever solves it on the sheet, put his photo in the comment again.

Question Number 168014 Answers: 1 Comments: 0

lim_(x→0) ((5e^x +5e^(−x) −10)/(4x^2 ))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{5}{e}^{{x}} +\mathrm{5}{e}^{−{x}} −\mathrm{10}}{\mathrm{4}{x}^{\mathrm{2}} }=? \\ $$

Question Number 168013 Answers: 2 Comments: 0

Question Number 168011 Answers: 2 Comments: 0

Solve (2x+5y+1)dx − (5x+2y−1)dy=0 Mastermind

$${Solve}\: \\ $$$$\left(\mathrm{2}{x}+\mathrm{5}{y}+\mathrm{1}\right){dx}\:−\:\left(\mathrm{5}{x}+\mathrm{2}{y}−\mathrm{1}\right){dy}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168009 Answers: 1 Comments: 0

lim_(x→∞) (((√(4x^2 −4x+1))+3x)/( (√(x^2 +x−5))+x))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$

Question Number 168004 Answers: 1 Comments: 0

lim_(x→∞) (√(4x^2 −16x+1))−2x+3=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$

Question Number 168000 Answers: 0 Comments: 0

Divide a^(5/2) −5a^2 b^(1/3) +10a^(3/2) b^(2/3) −10ab+5a^(1/2) b^(4/3) by a^(1/2) −b^(1/3)

$${Divide}\:{a}^{\frac{\mathrm{5}}{\mathrm{2}}} −\mathrm{5}{a}^{\mathrm{2}} {b}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{10}{a}^{\frac{\mathrm{3}}{\mathrm{2}}} {b}^{\frac{\mathrm{2}}{\mathrm{3}}} −\mathrm{10}{ab}+\mathrm{5}{a}^{\frac{\mathrm{1}}{\mathrm{2}}} {b}^{\frac{\mathrm{4}}{\mathrm{3}}} \:{by}\:{a}^{\frac{\mathrm{1}}{\mathrm{2}}} −{b}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$

Question Number 167997 Answers: 0 Comments: 0

xy+3x+2y=−6 yx+y+3z=−3 zx+2z+x=2 find x and y and z

$${xy}+\mathrm{3}{x}+\mathrm{2}{y}=−\mathrm{6} \\ $$$${yx}+{y}+\mathrm{3}{z}=−\mathrm{3} \\ $$$${zx}+\mathrm{2}{z}+{x}=\mathrm{2} \\ $$$${find}\:{x}\:{and}\:{y}\:{and}\:{z} \\ $$$$ \\ $$

Question Number 167996 Answers: 0 Comments: 0

find dy/dx if y=((x+2)/( (√(x+1)))) by first principle

$${find}\:{dy}/{dx}\:{if}\:{y}=\frac{{x}+\mathrm{2}}{\:\sqrt{{x}+\mathrm{1}}}\:{by}\:{first}\:{principle} \\ $$

Question Number 167994 Answers: 0 Comments: 0

Question Number 167989 Answers: 2 Comments: 0

∫ ((3−cos x)/(3+cos x)) dx =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{\mathrm{3}−\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$

Question Number 167986 Answers: 1 Comments: 0

cosxcos(π/6)−sin(π/6)sinx=(π/4)

$$\mathrm{cosxcos}\frac{\pi}{\mathrm{6}}−\mathrm{sin}\frac{\pi}{\mathrm{6}}\mathrm{sinx}=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 167985 Answers: 2 Comments: 0

If af(x)+bf((1/x))=(1/x) where a≠b and x≠0 show that f(x)=((1/(a^2 −b^2 )))((a/x)−bx)

$$\mathrm{If}\:\:\mathrm{af}\left(\mathrm{x}\right)+\mathrm{bf}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{where}\: \\ $$$$\mathrm{a}\neq\mathrm{b}\:\mathrm{and}\:\:\mathrm{x}\neq\mathrm{0}\:\mathrm{show}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} }\right)\left(\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{x}}}−\boldsymbol{\mathrm{bx}}\right) \\ $$

Question Number 167983 Answers: 0 Comments: 0

lim_(x→2^x ) (((x+2)/(2−x)))=?

$$\underset{{x}\rightarrow\mathrm{2}^{{x}} } {\mathrm{lim}}\left(\frac{{x}+\mathrm{2}}{\mathrm{2}−{x}}\right)=? \\ $$

Question Number 167982 Answers: 0 Comments: 3

lim_(x→∞) (((√(4x^2 −4x+1))+3x)/( (√(x^2 +x−5))+x))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$

Question Number 167981 Answers: 1 Comments: 0

lim_(x→0) ((4^x −2^x )/(8^x −4^x ))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}^{{x}} −\mathrm{2}^{{x}} }{\mathrm{8}^{{x}} −\mathrm{4}^{{x}} }=? \\ $$

Question Number 167980 Answers: 1 Comments: 3

lim_(x→∞) (√(4x^2 −16x+1))−2x+3=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$

Question Number 167979 Answers: 1 Comments: 0

3 men and 4 women are to sit on a table. Calculate the number of possible sitting arrangements if (a) they sit in a row such that the men must not sit next to each other. (b) they sit in circular pattern and the clockwise and anticlockwise orders are considered the same.

$$\mathrm{3}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\:\mathrm{are}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{table}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{possible}\:\mathrm{sitting}\:\mathrm{arrangements}\:\mathrm{if} \\ $$$$\:\left({a}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{men}\:\mathrm{must}\:\mathrm{not}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{other}. \\ $$$$\:\left({b}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{circular}\:\mathrm{pattern}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{clockwise}\:\mathrm{and}\:\mathrm{anticlockwise} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{orders}\:\mathrm{are}\:\mathrm{considered}\:\mathrm{the}\:\mathrm{same}. \\ $$

Question Number 167978 Answers: 0 Comments: 0

(((3 2 )),((4 5)) ) [A] = determinant (((3 2)),((4 5)))

$$\begin{pmatrix}{\mathrm{3}\:\:\:\:\:\mathrm{2}\:}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{pmatrix}\:\:\left[{A}\right]\:=\begin{vmatrix}{\mathrm{3}\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{vmatrix} \\ $$

Question Number 167977 Answers: 1 Comments: 0

Prove that I_n =(1/2^(n+1) )∫_π ^(4nπ) xcos (x/2)dx=((2−π)/2^(np) )

$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\int_{\pi} ^{\mathrm{4}{n}\pi} {x}\mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx}=\frac{\mathrm{2}−\pi}{\mathrm{2}^{{np}} } \\ $$

Question Number 167976 Answers: 0 Comments: 0

Question Number 167974 Answers: 1 Comments: 0

Question Number 167970 Answers: 0 Comments: 0

Calculate: lim_(n→∞) Σ_(k=1) ^n (k^2 /n^3 )∙(k)^(1/k) =?

$$\mathrm{Calculate}:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{n}^{\mathrm{3}} }\centerdot\sqrt[{\mathrm{k}}]{\mathrm{k}}=? \\ $$

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