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Question Number 149462 Answers: 1 Comments: 0

Question Number 149469 Answers: 1 Comments: 0

Compare: 1900^(3/4) + 99^(3/4) and 1999^(3/4)

$$\mathrm{Compare}: \\ $$$$\mathrm{1900}^{\frac{\mathrm{3}}{\mathrm{4}}} \:+\:\:\mathrm{99}^{\frac{\mathrm{3}}{\mathrm{4}}} \:\:\:\boldsymbol{\mathrm{and}}\:\:\:\mathrm{1999}^{\frac{\mathrm{3}}{\mathrm{4}}} \\ $$

Question Number 149463 Answers: 1 Comments: 0

Let the independent random variables X_1 and X_2 have binomial distribution with parameters n_1 =3,p=2/3 and n_2 =4 p=1/2 respectively. Compute P(X_1 =X_2 )

$$\mathrm{Let}\:\mathrm{the}\:\mathrm{independent}\:\mathrm{random}\:\mathrm{variables} \\ $$$$\mathrm{X}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{X}_{\mathrm{2}} \:\mathrm{have}\:\mathrm{binomial}\:\mathrm{distribution} \\ $$$$\mathrm{with}\:\mathrm{parameters}\:\mathrm{n}_{\mathrm{1}} =\mathrm{3},\mathrm{p}=\mathrm{2}/\mathrm{3}\:\mathrm{and}\:\mathrm{n}_{\mathrm{2}} =\mathrm{4} \\ $$$$\mathrm{p}=\mathrm{1}/\mathrm{2}\:\:\mathrm{respectively}.\: \\ $$$$\mathrm{Compute}\:\mathrm{P}\left(\mathrm{X}_{\mathrm{1}} =\mathrm{X}_{\mathrm{2}} \right) \\ $$

Question Number 149458 Answers: 1 Comments: 3

Question Number 149457 Answers: 1 Comments: 0

Question Number 149454 Answers: 0 Comments: 0

Question Number 149424 Answers: 1 Comments: 0

geometric series ((b_4 ∙b_7 ∙b_(10) )/(b_1 ∙b_3 ∙b_5 )) = 2^(12) find (b_5 /b_2 ) = ?

$${geometric}\:{series}\:\:\frac{{b}_{\mathrm{4}} \centerdot{b}_{\mathrm{7}} \centerdot{b}_{\mathrm{10}} }{{b}_{\mathrm{1}} \centerdot{b}_{\mathrm{3}} \centerdot{b}_{\mathrm{5}} }\:=\:\mathrm{2}^{\mathrm{12}} \\ $$$${find}\:\:\:\frac{{b}_{\mathrm{5}} }{{b}_{\mathrm{2}} }\:=\:? \\ $$

Question Number 149423 Answers: 1 Comments: 0

((2207 - (1/(2207 - (1/(2207 - ...))))))^(1/8) = ?

$$\sqrt[{\mathrm{8}}]{\mathrm{2207}\:-\:\frac{\mathrm{1}}{\mathrm{2207}\:-\:\frac{\mathrm{1}}{\mathrm{2207}\:-\:...}}}\:\:=\:? \\ $$

Question Number 149415 Answers: 1 Comments: 1

show that ∫_0 ^∞ (((sint−tcost)/t^3 ))^2 dt=(Π/(15))

$$\mathrm{show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{sint}−\mathrm{tcost}}{\mathrm{t}^{\mathrm{3}} }\right)^{\mathrm{2}} \mathrm{dt}=\frac{\Pi}{\mathrm{15}} \\ $$

Question Number 149410 Answers: 1 Comments: 0

((log_2 2^(20) + log_2 20 ∙ log_2 5 - 2 log_2 2^5 )/(log_2 20 + 2 log_2 5)) = ?

$$\frac{{log}_{\mathrm{2}} \:\mathrm{2}^{\mathrm{20}} \:+\:{log}_{\mathrm{2}} \:\mathrm{20}\:\centerdot\:{log}_{\mathrm{2}} \:\mathrm{5}\:-\:\mathrm{2}\:{log}_{\mathrm{2}} \:\mathrm{2}^{\mathrm{5}} }{{log}_{\mathrm{2}} \:\mathrm{20}\:+\:\mathrm{2}\:{log}_{\mathrm{2}} \:\mathrm{5}}\:=\:? \\ $$

Question Number 149408 Answers: 0 Comments: 2

cos((π/2) - (1/2) arccos (4/5)) = ?

$${cos}\left(\frac{\pi}{\mathrm{2}}\:-\:\frac{\mathrm{1}}{\mathrm{2}}\:{arccos}\:\frac{\mathrm{4}}{\mathrm{5}}\right)\:=\:? \\ $$

Question Number 149406 Answers: 0 Comments: 0

if x has a binomial distribution with n=10 and p=(1/3).Find E(e^(3x) )

$${if}\:{x}\:{has}\:{a}\:{binomial}\:{distribution}\:{with}\:{n}=\mathrm{10}\:{and}\:{p}=\frac{\mathrm{1}}{\mathrm{3}}.{Find}\:{E}\left({e}^{\mathrm{3}{x}} \right) \\ $$

Question Number 149405 Answers: 0 Comments: 2

if ∫f(x)dx = x^3 −3x^2 −c find f(−2) = ?

$${if}\:\:\:\int{f}\left({x}\right){dx}\:=\:{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −{c} \\ $$$${find}\:\:\:{f}\left(−\mathrm{2}\right)\:=\:? \\ $$

Question Number 149400 Answers: 3 Comments: 0

Question Number 149395 Answers: 1 Comments: 0

Question Number 149385 Answers: 4 Comments: 0

Question Number 149383 Answers: 1 Comments: 1

Question Number 149378 Answers: 3 Comments: 0

Question Number 149377 Answers: 1 Comments: 0

Question Number 149372 Answers: 1 Comments: 0

Question Number 149373 Answers: 1 Comments: 0

Question Number 149428 Answers: 2 Comments: 3

Question Number 149425 Answers: 1 Comments: 0

Question Number 149354 Answers: 1 Comments: 5

z>0 z^2 + 12(√z) = 5 z + 2(√z) = ?

$${z}>\mathrm{0} \\ $$$${z}^{\mathrm{2}} \:+\:\mathrm{12}\sqrt{{z}}\:=\:\mathrm{5} \\ $$$${z}\:+\:\mathrm{2}\sqrt{{z}}\:=\:? \\ $$

Question Number 149346 Answers: 2 Comments: 1

lim_(x→∞) (((3x+12)/(6x−20)))^(2x) =?

$${li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{\mathrm{3}{x}+\mathrm{12}}{\mathrm{6}{x}−\mathrm{20}}\right)^{\mathrm{2}{x}} =? \\ $$

Question Number 149342 Answers: 1 Comments: 1

is this true and is there a proof? ∀k∈N∣k>1 ((Σ_(n=1) ^(k^2 −1) (√(k+(√n))))/(Σ_(n=1) ^(k^2 −1) (√(k−(√n)))))=1+(√2)

$$\mathrm{is}\:\mathrm{this}\:\mathrm{true}\:\mathrm{and}\:\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{proof}? \\ $$$$\forall{k}\in\mathbb{N}\mid{k}>\mathrm{1} \\ $$$$\frac{\underset{{n}=\mathrm{1}} {\overset{{k}^{\mathrm{2}} −\mathrm{1}} {\sum}}\sqrt{{k}+\sqrt{{n}}}}{\underset{{n}=\mathrm{1}} {\overset{{k}^{\mathrm{2}} −\mathrm{1}} {\sum}}\sqrt{{k}−\sqrt{{n}}}}=\mathrm{1}+\sqrt{\mathrm{2}} \\ $$

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