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Question Number 105812 Answers: 1 Comments: 0

In a by-election 20% of the electorate voted for Mr X. If 5 voters are chosen at random from this electorate, what is the probability that 20% of the sample voted for Mr X ? (a) 1 (b) (1/5) (c) (1/(625)) (d) ((256)/(625))

$$\mathrm{In}\:\mathrm{a}\:\mathrm{by}-\mathrm{election}\:\mathrm{20\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{electorate}\:\mathrm{voted}\:\mathrm{for}\:\mathrm{Mr}\:\mathrm{X}. \\ $$$$\mathrm{If}\:\mathrm{5}\:\mathrm{voters}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{this}\:\mathrm{electorate},\:\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{20\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sample}\:\mathrm{voted}\:\mathrm{for}\:\mathrm{Mr}\:\mathrm{X}\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{1}\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{1}}{\mathrm{5}}\:\:\:\:\left(\mathrm{c}\right)\:\frac{\mathrm{1}}{\mathrm{625}}\:\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{256}}{\mathrm{625}} \\ $$

Question Number 105807 Answers: 0 Comments: 0

Question Number 105806 Answers: 0 Comments: 0

Question Number 105805 Answers: 0 Comments: 0

Question Number 105803 Answers: 3 Comments: 1

The sum of two numbers are 20 and their LCM is 24. What are the two numbers?

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{numbers}\:\mathrm{are}\:\mathrm{20}\:\mathrm{and} \\ $$$$\mathrm{their}\:\mathrm{LCM}\:\mathrm{is}\:\mathrm{24}. \\ $$$$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{numbers}? \\ $$

Question Number 105810 Answers: 0 Comments: 0

Question Number 105799 Answers: 1 Comments: 0

Question Number 105791 Answers: 1 Comments: 1

From 1 to 12345, how many numbers contain the digit 0? Find the number of zeros in all these numbers. Example: 10020 has three zeros.

$${From}\:\mathrm{1}\:{to}\:\mathrm{12345},\:{how}\:{many}\:{numbers} \\ $$$${contain}\:{the}\:{digit}\:\mathrm{0}?\:{Find}\:{the}\:{number} \\ $$$${of}\:{zeros}\:{in}\:{all}\:{these}\:{numbers}. \\ $$$${Example}:\:\mathrm{10020}\:{has}\:{three}\:{zeros}. \\ $$

Question Number 105781 Answers: 1 Comments: 1

Please, I need help. Exercise We have : J_n = ∫_0 ^( (π/4)) tan^n (x) dx 1) Establish a recurrence relation between J_(n+2) and J_n . 2) Calculate J_0 and J_1 , then deduce the expression of J_n as a function of n. The deduction of the last question, please.

$$\mathrm{Please},\:\mathrm{I}\:\mathrm{need}\:\mathrm{help}. \\ $$$$\mathrm{Exercise} \\ $$$$\mathrm{We}\:\mathrm{have}\:: \\ $$$$\mathrm{J}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \mathrm{tan}^{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Establish}\:\mathrm{a}\:\mathrm{recurrence}\:\mathrm{relation} \\ $$$$\mathrm{between}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}+\mathrm{2}} \:\mathrm{and}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}} . \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Calculate}\:\boldsymbol{\mathrm{J}}_{\mathrm{0}} \:\mathrm{and}\:\boldsymbol{\mathrm{J}}_{\mathrm{1}} ,\:\mathrm{then} \\ $$$$\mathrm{deduce}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{of}\:\boldsymbol{\mathrm{J}}_{\boldsymbol{\mathrm{n}}} \:\mathrm{as}\:\mathrm{a} \\ $$$$\mathrm{function}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}. \\ $$$$\mathrm{The}\:\mathrm{deduction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last} \\ $$$$\mathrm{question},\:\mathrm{please}. \\ $$

Question Number 105771 Answers: 0 Comments: 0

lim_(n→∞) (((∫_0 ^1 x^2 (x+n)^n )/((n+1)^n )) dx)=?

$$\underset{{n}\rightarrow\infty} {{lim}}\:\left(\frac{\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{\mathrm{2}} \left({x}+{n}\right)^{{n}} }{\left({n}+\mathrm{1}\right)^{{n}} }\:{dx}\right)=? \\ $$

Question Number 105769 Answers: 2 Comments: 1

Question Number 105766 Answers: 1 Comments: 0

If p = sin ((π/(18)))sin (((5π)/(18)))sin (((7π)/(18))) find the value of p.

$${If}\:{p}\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{18}}\right)\mathrm{sin}\:\left(\frac{\mathrm{5}\pi}{\mathrm{18}}\right)\mathrm{sin}\:\left(\frac{\mathrm{7}\pi}{\mathrm{18}}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{p}. \\ $$

Question Number 105764 Answers: 4 Comments: 1

(1)If cos (α+β) = (4/5) and sin (α−β) = (5/(13)) where 0 < α< (π/4). Find tan 2α . (2) cos^4 ((π/8))+cos^4 (((3π)/8))+cos^4 (((5π)/8))+cos^4 (((7π)/8))?

$$\left(\mathrm{1}\right){If}\:\mathrm{cos}\:\left(\alpha+\beta\right)\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:{and}\:\mathrm{sin}\:\left(\alpha−\beta\right)\:=\:\frac{\mathrm{5}}{\mathrm{13}} \\ $$$${where}\:\mathrm{0}\:<\:\alpha<\:\frac{\pi}{\mathrm{4}}.\:{Find}\:\mathrm{tan}\:\mathrm{2}\alpha\:. \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right)? \\ $$

Question Number 105759 Answers: 2 Comments: 1

If α and β are the solution of equation a tan θ + b sec θ = c . find the value of tan (α+β).

$${If}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{solution}\:{of} \\ $$$${equation}\:{a}\:\mathrm{tan}\:\theta\:+\:{b}\:\mathrm{sec}\:\theta\:=\:{c}\:.\: \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{tan}\:\left(\alpha+\beta\right). \\ $$

Question Number 105755 Answers: 2 Comments: 0

∫ (dx/(√(x(√x) −x^2 ))) ?

$$\int\:\frac{{dx}}{\sqrt{{x}\sqrt{{x}}\:−{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 105753 Answers: 1 Comments: 1

∫ ((x^2 +sin^2 x)/(x^2 +cos^2 x)) dx

$$\int\:\frac{{x}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} +\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 105748 Answers: 2 Comments: 0

lim_(x→∞) (((x−1)^(100) (6x+1)^(100) )/((3x+5)^(200) ))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{100}} \left(\mathrm{6x}+\mathrm{1}\right)^{\mathrm{100}} }{\left(\mathrm{3x}+\mathrm{5}\right)^{\mathrm{200}} }=? \\ $$

Question Number 105743 Answers: 1 Comments: 1

Question Number 105742 Answers: 0 Comments: 0

Let a differentiable function f:R→R satisfies ∣f′(x)∣≤1 for all x∈[0,2] and f(0)=f(2)=1 Prove that 1≤∫_0 ^2 f(x)dx≤3

$$\mathrm{Let}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{function}\:\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\mathrm{satisfies}\:\mid\mathrm{f}'\left(\mathrm{x}\right)\mid\leqslant\mathrm{1}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{2}\right]\:\mathrm{and} \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{f}\left(\mathrm{2}\right)=\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{1}\leqslant\int_{\mathrm{0}} ^{\mathrm{2}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\leqslant\mathrm{3}\: \\ $$

Question Number 105738 Answers: 1 Comments: 0

(x tan ((y/x))−y sec^2 ((y/x))) dx−x sec^2 ((y/x))dy=0

$$\left({x}\:\mathrm{tan}\:\left(\frac{{y}}{{x}}\right)−{y}\:\mathrm{sec}\:^{\mathrm{2}} \left(\frac{{y}}{{x}}\right)\right)\:{dx}−{x}\:\mathrm{sec}\:^{\mathrm{2}} \left(\frac{{y}}{{x}}\right){dy}=\mathrm{0} \\ $$

Question Number 105734 Answers: 0 Comments: 0

(2x+(x^2 +y^2 )cot x) dx +2y dy = 0

$$\left(\mathrm{2}{x}+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\mathrm{cot}\:{x}\right)\:{dx}\:+\mathrm{2}{y}\:{dy}\:=\:\mathrm{0} \\ $$

Question Number 105722 Answers: 4 Comments: 1

∫ (√(x−(√x))) dx

$$\int\:\sqrt{{x}−\sqrt{{x}}}\:{dx}\: \\ $$

Question Number 105725 Answers: 0 Comments: 5

App updates: • Image are saved as a background task so that you dont get app not responding when saving images. • Bug Fix: Background color was ignored while sharing • Support added for Bangla • Fixes for crashes reported. Please update from playstore.

$$\mathrm{App}\:\mathrm{updates}: \\ $$$$\bullet\:\mathrm{Image}\:\mathrm{are}\:\mathrm{saved}\:\mathrm{as}\:\mathrm{a}\:\mathrm{background} \\ $$$$\:\:\:\mathrm{task}\:\mathrm{so}\:\mathrm{that}\:\mathrm{you}\:\mathrm{dont}\:\mathrm{get}\:\mathrm{app}\:\mathrm{not} \\ $$$$\:\:\:\mathrm{responding}\:\mathrm{when}\:\mathrm{saving}\:\mathrm{images}. \\ $$$$\bullet\:\mathrm{Bug}\:\mathrm{Fix}:\:\mathrm{Background}\:\mathrm{color}\:\mathrm{was}\: \\ $$$$\:\:\:\:\mathrm{ignored}\:\mathrm{while}\:\mathrm{sharing} \\ $$$$\bullet\:\mathrm{Support}\:\mathrm{added}\:\mathrm{for}\:\mathrm{Bangla} \\ $$$$\bullet\:\mathrm{Fixes}\:\mathrm{for}\:\mathrm{crashes}\:\mathrm{reported}. \\ $$$$\mathrm{Please}\:\mathrm{update}\:\mathrm{from}\:\mathrm{playstore}. \\ $$

Question Number 105710 Answers: 3 Comments: 0

(2xy+cos y) dx +(x^2 −xsiny−2y)dy=0

$$\left(\mathrm{2}{xy}+\mathrm{cos}\:{y}\right)\:{dx}\:+\left({x}^{\mathrm{2}} −{x}\mathrm{sin}{y}−\mathrm{2}{y}\right){dy}=\mathrm{0} \\ $$

Question Number 105707 Answers: 4 Comments: 1

Find a polynomial f(x) which satisfy the following conditions: i) f(x) of degree 4 ii) (x−1) is a factor of f(x) and f′(x) iii) f(0)=3 and f′(0)=−5 iv) when f(x) is divided by (x−2), the remainder is 13.

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{conditions}: \\ $$$$\left.\mathrm{i}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{of}\:\mathrm{degree}\:\mathrm{4} \\ $$$$\left.\mathrm{ii}\right)\:\left(\mathrm{x}−\mathrm{1}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}'\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{iii}\right)\:\mathrm{f}\left(\mathrm{0}\right)=\mathrm{3}\:\mathrm{and}\:\mathrm{f}'\left(\mathrm{0}\right)=−\mathrm{5} \\ $$$$\left.\mathrm{iv}\right)\:\mathrm{when}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{2}\right),\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{13}. \\ $$

Question Number 105706 Answers: 1 Comments: 0

∫_0 ^π (dx/(((√5)−cos x)^3 )) ?

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{dx}}{\left(\sqrt{\mathrm{5}}−\mathrm{cos}\:{x}\right)^{\mathrm{3}} }\:? \\ $$

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