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Question Number 171386 Answers: 0 Comments: 0

A fair coin is flipped 3 times and a random variable X is defined to be 3 times the number of heads minus 2 times the number of tails. Find the probability mass function of X. (Write it in table format).

$$ \\ $$A fair coin is flipped 3 times and a random variable X is defined to be 3 times the number of heads minus 2 times the number of tails. Find the probability mass function of X. (Write it in table format).

Question Number 171385 Answers: 3 Comments: 0

lim_(x→∞) ((rx^5 −4x^3 +3)/(sx^5 −2x+1)) = (1/4) 2r+3s=?

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

Question Number 171377 Answers: 0 Comments: 0

Question Number 171376 Answers: 0 Comments: 4

lim_(x→x^(tanx) ) tanx((x/e^(tanx) ))^(tanx) =?

$$\underset{{x}\rightarrow{x}^{{tanx}} } {\mathrm{lim}}\:{tanx}\left(\frac{{x}}{{e}^{{tanx}} }\right)^{{tanx}} =? \\ $$

Question Number 171371 Answers: 3 Comments: 0

∫_(−∞) ^(+∞) (dx/(1+x^4 ))=?

$$\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{4}} }=? \\ $$

Question Number 171370 Answers: 0 Comments: 0

∫_0 ^(𝛑/2) x^3 (√(cos(x)))dx

$$\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{\mathrm{x}}^{\mathrm{3}} \sqrt{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 171367 Answers: 0 Comments: 0

Question Number 171366 Answers: 0 Comments: 0

Question Number 171362 Answers: 1 Comments: 0

A rectangle is divided into 40 equal parts. How many of these parts should be shadded in other to cover three-five of the rectangle

$$ \\ $$$$\mathrm{A}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{40}\:\mathrm{equal}\: \\ $$$$\:\mathrm{parts}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{parts}\: \\ $$$$\mathrm{should}\:\mathrm{be}\:\mathrm{shadded}\:\mathrm{in}\:\mathrm{other}\:\mathrm{to}\:\mathrm{cover}\: \\ $$$$\:\mathrm{three}-\mathrm{five}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle} \\ $$$$\: \\ $$

Question Number 171379 Answers: 0 Comments: 1

f(x)= { ((2x+3 ;x>0)),((3x−5 ;x≤0)) :} ((df(x))/dx)=?

$${f}\left({x}\right)=\begin{cases}{\mathrm{2}{x}+\mathrm{3}\:\:\:;{x}>\mathrm{0}}\\{\mathrm{3}{x}−\mathrm{5}\:\:;{x}\leqslant\mathrm{0}}\end{cases} \\ $$$$\frac{{df}\left({x}\right)}{{dx}}=? \\ $$

Question Number 171360 Answers: 1 Comments: 0

Solve for real numbers: log_9 x ∙ log_2 (7 − x) = 1

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{log}_{\mathrm{9}} \:\mathrm{x}\:\:\centerdot\:\:\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{7}\:−\:\mathrm{x}\right)\:=\:\mathrm{1} \\ $$

Question Number 171359 Answers: 1 Comments: 0

A heavenly body has mass one third of the earth and its radius is half as that of the earth. if a stone weights 200N on the earth′s surface, find its weight on that heavenly body.

$$\mathrm{A}\:\mathrm{heavenly}\:\mathrm{body}\:\mathrm{has}\:\mathrm{mass}\:\mathrm{one}\:\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{and}\:\mathrm{its} \\ $$$$\:\mathrm{radius}\:\mathrm{is}\:\mathrm{half}\:\mathrm{as}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{if}\:\mathrm{a}\:\mathrm{stone}\:\mathrm{weights}\:\mathrm{200N}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{earth}'\mathrm{s}\:\mathrm{surface},\:\mathrm{find}\:\mathrm{its}\:\mathrm{weight}\:\mathrm{on}\:\mathrm{that}\:\mathrm{heavenly}\:\mathrm{body}. \\ $$

Question Number 171356 Answers: 0 Comments: 0

Solve 1) (2x−y)dx+(4x−2y+4)dy=0 2) (2x−y+4)dy+(x−2y+5)dx=0

$${Solve} \\ $$$$\left.\mathrm{1}\right)\:\left(\mathrm{2}{x}−{y}\right){dx}+\left(\mathrm{4}{x}−\mathrm{2}{y}+\mathrm{4}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\left(\mathrm{2}{x}−{y}+\mathrm{4}\right){dy}+\left({x}−\mathrm{2}{y}+\mathrm{5}\right){dx}=\mathrm{0} \\ $$

Question Number 171346 Answers: 0 Comments: 2

solve: ((m+(mn^2 )^(1/3) +(m^2 n)^(1/3) )/(m−n)) × (((m^(1/3) −n^(1/3) ))/m^(1/3) )

$$\:\:\mathrm{solve}: \\ $$$$\:\:\:\frac{\mathrm{m}+\left(\mathrm{mn}^{\mathrm{2}} \right)^{\mathrm{1}/\mathrm{3}} +\left(\mathrm{m}^{\mathrm{2}} \mathrm{n}\right)^{\mathrm{1}/\mathrm{3}} }{\mathrm{m}−\mathrm{n}}\:×\:\frac{\left(\mathrm{m}^{\mathrm{1}/\mathrm{3}} −\mathrm{n}^{\mathrm{1}/\mathrm{3}} \right)}{\mathrm{m}^{\mathrm{1}/\mathrm{3}} } \\ $$

Question Number 171343 Answers: 0 Comments: 0

Given M=(m_(ij) +t) a real square matrix, with t∈R. Show that the determinant of M is linear function (affine) of t.

$${Given}\:{M}=\left({m}_{{ij}} +{t}\right)\:{a}\:{real}\:{square} \\ $$$${matrix},\:{with}\:{t}\in\mathbb{R}. \\ $$$${Show}\:{that}\:{the}\:{determinant}\:{of}\:{M} \\ $$$${is}\:{linear}\:{function}\:\left({affine}\right)\:{of}\:{t}. \\ $$

Question Number 171342 Answers: 1 Comments: 1

Question Number 171341 Answers: 2 Comments: 1

lim_(x→0) ((x^2 +sin3x)/(2x−sinx))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +{sin}\mathrm{3}{x}}{\mathrm{2}{x}−{sinx}}=? \\ $$

Question Number 171339 Answers: 1 Comments: 0

an integer n 1≤n≤144 is picked at random what is the probability that n is the square of an inteer?

$${an}\:{integer}\:{n}\:\mathrm{1}\leq{n}\leq\mathrm{144}\:{is}\:{picked} \\ $$$${at}\:{random}\: \\ $$$${what}\:{is}\:{the}\:{probability}\:{that} \\ $$$$\:{n}\:{is}\:{the}\:{square}\:{of}\:{an} \\ $$$${inteer}? \\ $$

Question Number 171336 Answers: 1 Comments: 0

Question Number 171332 Answers: 0 Comments: 2

A bicycle has a constant velocity of 10 m/s. A person starts from rest and runs to catch up to the bicycle in 30 s. What is the acceleration of the person?

Question Number 171331 Answers: 0 Comments: 0

Question Number 176850 Answers: 1 Comments: 0

f(x)=2(x−1) (fofo...of)_(50 times) (x)=?

$${f}\left({x}\right)=\mathrm{2}\left({x}−\mathrm{1}\right) \\ $$$$\underset{\mathrm{50}\:\mathrm{times}} {\underbrace{\left({fofo}...{of}\right)}}\left({x}\right)=? \\ $$

Question Number 176849 Answers: 0 Comments: 0

The constant term in the polynomial P(x)=(x^2 +x−7)Q(x+1)+2x+1 is −20. What is the sum of coefficients of the polynomial Q(x) ?

$$\mathrm{The}\:\mathrm{constant}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\mathrm{P}\left({x}\right)=\left({x}^{\mathrm{2}} +{x}−\mathrm{7}\right){Q}\left({x}+\mathrm{1}\right)+\mathrm{2}{x}+\mathrm{1} \\ $$$$\mathrm{is}\:−\mathrm{20}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{coefficients}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{polynomial}\:\mathrm{Q}\left({x}\right)\:? \\ $$

Question Number 176848 Answers: 1 Comments: 0

Question Number 171315 Answers: 1 Comments: 0

The tangent to the curve y=ax^2 +bx+2 at (1,(1/2)) is parallel to the normal to the curve y=x^2 +6x+10 at (−2,2). Find the values of a and b.

$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{2} \\ $$$$\mathrm{at}\:\left(\mathrm{1},\frac{\mathrm{1}}{\mathrm{2}}\right)\:\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} +\mathrm{6x}+\mathrm{10}\:\mathrm{at}\:\left(−\mathrm{2},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}. \\ $$

Question Number 171314 Answers: 1 Comments: 0

If C_r , C_s are cyclic groups such that g.c.d(r,s)=1, then show that C_r ×C_s is a cyclic group. Mastermind

$${If}\:{C}_{{r}} ,\:{C}_{{s}} \:{are}\:{cyclic}\:{groups}\:{such}\:{that} \\ $$$${g}.{c}.{d}\left({r},{s}\right)=\mathrm{1},\:{then}\:{show}\:{that}\:{C}_{{r}} ×{C}_{{s}} \:{is} \\ $$$${a}\:{cyclic}\:{group}. \\ $$$$ \\ $$$${Mastermind} \\ $$

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