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AllQuestion and Answers: Page 717

Question Number 145722 Answers: 0 Comments: 0

Question Number 145721 Answers: 0 Comments: 0

if a;b∈N ; a≠b and a+b=2x find (a∙b)_(max) =?

$${if}\:\:{a};{b}\in\mathbb{N}\:\:;\:\:{a}\neq{b}\:\:{and}\:\:{a}+{b}=\mathrm{2}{x} \\ $$$${find}\:\:\left({a}\centerdot{b}\right)_{\boldsymbol{{m}}{ax}} =? \\ $$

Question Number 145718 Answers: 0 Comments: 1

F_1 = 3 N ; F_2 = 4 N ; F_3 = 6 N F_(max) - F_(min) = ?

$${F}_{\mathrm{1}} \:=\:\mathrm{3}\:{N}\:\:;\:\:{F}_{\mathrm{2}} \:=\:\mathrm{4}\:{N}\:\:;\:{F}_{\mathrm{3}} \:=\:\mathrm{6}\:{N} \\ $$$${F}_{\boldsymbol{{max}}} \:\:-\:\:{F}_{\boldsymbol{{min}}} =\:? \\ $$

Question Number 145716 Answers: 0 Comments: 0

can we use the pearson′s correlation and chi−square test for hypothesis interchangably? both test is used to find significant relationship between two variables.

$${can}\:{we}\:{use}\:{the}\:{pearson}'{s}\:{correlation}\:{and}\:{chi}−{square} \\ $$$${test}\:{for}\:{hypothesis}\:{interchangably}? \\ $$$${both}\:{test}\:{is}\:{used}\:{to}\:{find}\:{significant}\:{relationship} \\ $$$${between}\:{two}\:{variables}. \\ $$

Question Number 145715 Answers: 4 Comments: 1

Question Number 146130 Answers: 0 Comments: 0

(2^k +1)(3^k +2)≡0(mod k+5) min k=? (k∈N)

$$\:\:\left(\mathrm{2}^{\mathrm{k}} +\mathrm{1}\right)\left(\mathrm{3}^{\mathrm{k}} +\mathrm{2}\right)\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{k}+\mathrm{5}\right) \\ $$$$\:\mathrm{min}\:\mathrm{k}=?\:\:\:\left(\mathrm{k}\in\mathbb{N}\right) \\ $$

Question Number 145701 Answers: 2 Comments: 1

Question Number 145687 Answers: 0 Comments: 0

if q≥3 ; a>-1 then: (1+a)^q ≥ (1+2a)(1+a)^(q-2) ≥ 1+qa

$${if}\:\:{q}\geqslant\mathrm{3}\:;\:{a}>-\mathrm{1}\:\:{then}: \\ $$$$\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+\mathrm{2}{a}\right)\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}-\mathrm{2}} \:\geqslant\:\mathrm{1}+{qa} \\ $$

Question Number 145683 Answers: 1 Comments: 0

((3 ((360))^(1/(√4)) −2 ((162))^(1/(!3)) )/( (√(10))−(√2))) =?

$$\:\frac{\mathrm{3}\:\sqrt[{\sqrt{\mathrm{4}}}]{\mathrm{360}}\:−\mathrm{2}\:\sqrt[{!\mathrm{3}}]{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}\:=? \\ $$

Question Number 145678 Answers: 0 Comments: 0

let X_1 and X_(2 ) be independent random variable of uniform distribution . If it is known that X_i ∼uniform (0,1) and let S = X_1 + X_2 Determine the Probability density function from S!

$${let}\:{X}_{\mathrm{1}} \:{and}\:{X}_{\mathrm{2}\:} \:{be}\:{independent}\:{random}\:{variable}\: \\ $$$${of}\:{uniform}\:{distribution}\:.\:{If}\:{it}\:{is}\:{known}\:{that} \\ $$$${X}_{{i}} \sim{uniform}\:\left(\mathrm{0},\mathrm{1}\right)\:{and}\:{let}\:{S}\:=\:{X}_{\mathrm{1}} \:+\:{X}_{\mathrm{2}} \\ $$$${Determine}\:{the}\:{Probability}\:{density}\:{function} \\ $$$${from}\:{S}! \\ $$

Question Number 145676 Answers: 2 Comments: 0

... advanced ......calculus... prove that: Σ_(n=1) ^∞ (((−1)^(n−1) )/(n^( 3) ((( 2n)),(( n)) ))) = (2/5) ζ (3 )

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:......{calculus}... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\:\mathrm{3}} \:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:\:{n}}\end{pmatrix}}\:=\:\frac{\mathrm{2}}{\mathrm{5}}\:\zeta\:\left(\mathrm{3}\:\right) \\ $$$$ \\ $$

Question Number 145675 Answers: 3 Comments: 0

the probabilty density function is known as follows : f(x) = {_(0 , x other) ^(cx^3 , 0 < x < 4) define P(1 < x < 2)!

$${the}\:{probabilty}\:{density}\:{function} \\ $$$${is}\:{known}\:{as}\:{follows}\:: \\ $$$${f}\left({x}\right)\:=\:\left\{_{\mathrm{0}\:\:\:,\:{x}\:{other}} ^{{cx}^{\mathrm{3}} \:\:\:,\:\mathrm{0}\:<\:{x}\:<\:\mathrm{4}} \right. \\ $$$${define}\:{P}\left(\mathrm{1}\:<\:{x}\:<\:\mathrm{2}\right)! \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 145674 Answers: 0 Comments: 0

the probability density function with two continous random variable X and Y is a follows : f(x,y) = {_(0 , x other) ^(2x + 2y , 0 < x < 1, 0 < y < 1) determine the correlation coefficient between X and Y!

$${the}\:{probability}\:{density}\:{function}\:{with}\:{two}\:{continous}\:{random} \\ $$$${variable}\:{X}\:{and}\:{Y}\:{is}\:{a}\:{follows}\:: \\ $$$$ \\ $$$${f}\left({x},{y}\right)\:=\:\left\{_{\mathrm{0}\:\:,\:{x}\:{other}} ^{\mathrm{2}{x}\:+\:\mathrm{2}{y}\:\:,\:\mathrm{0}\:<\:{x}\:<\:\mathrm{1},\:\mathrm{0}\:<\:{y}\:<\:\mathrm{1}} \right. \\ $$$$ \\ $$$${determine}\:{the}\:{correlation}\:{coefficient} \\ $$$${between}\:{X}\:{and}\:{Y}! \\ $$

Question Number 145671 Answers: 6 Comments: 1

Question Number 145664 Answers: 2 Comments: 0

S=Σ_(k=0) ^n (−1)^k k^3 =?

$$\mathrm{S}=\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \mathrm{k}^{\mathrm{3}} =? \\ $$

Question Number 145668 Answers: 1 Comments: 0

Compare: sin(43°) and sin(40°)+sin(3°)

$${Compare}: \\ $$$${sin}\left(\mathrm{43}°\right)\:\:{and}\:\:{sin}\left(\mathrm{40}°\right)+{sin}\left(\mathrm{3}°\right) \\ $$

Question Number 145666 Answers: 1 Comments: 0

Question Number 145665 Answers: 1 Comments: 0

Question Number 145660 Answers: 1 Comments: 0

Question Number 145652 Answers: 2 Comments: 0

Question Number 145646 Answers: 1 Comments: 0

Find the arc lenght of the function y^2 = (x^3 /a) where a is a constant for 0≤x≤((7a)/3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{y}^{\mathrm{2}} \:=\:\frac{{x}^{\mathrm{3}} }{{a}}\:\mathrm{where}\:{a}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{for} \\ $$$$\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{7}{a}}{\mathrm{3}} \\ $$

Question Number 145645 Answers: 0 Comments: 0

∫_0 ^a x^(−(x/a)) dx

$$\int_{\mathrm{0}} ^{{a}} {x}^{−\frac{{x}}{{a}}} {dx} \\ $$

Question Number 145641 Answers: 0 Comments: 0

Let g:R→R be given by g(x) = 3 + 4x .Prove by induction that, for all positive integers n, g^n (x) = (4^n −1) + 4^n (x). If for every positive integer k, we inteprete g^(−k) as the inverse of the function g^k .Prove that the above formula holds alsl for all negative integers n.

$$\mathrm{Let}\:\mathrm{g}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{given}\:\mathrm{by}\:\mathrm{g}\left({x}\right)\:=\:\mathrm{3}\:+\:\mathrm{4}{x}\:.\mathrm{Prove}\:\mathrm{by}\:\mathrm{induction} \\ $$$$\mathrm{that},\:\mathrm{for}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:{n},\: \\ $$$$\mathrm{g}^{{n}} \left({x}\right)\:=\:\left(\mathrm{4}^{{n}} −\mathrm{1}\right)\:+\:\mathrm{4}^{{n}} \left({x}\right). \\ $$$$\mathrm{If}\:\mathrm{for}\:\mathrm{every}\:\mathrm{positive}\:\mathrm{integer}\:{k},\:\mathrm{we}\:\mathrm{inteprete}\:\mathrm{g}^{−{k}} \:\mathrm{as}\:\mathrm{the}\:\mathrm{inverse} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{g}^{{k}} .\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{above}\:\mathrm{formula}\:\mathrm{holds}\:\mathrm{alsl} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{negative}\:\mathrm{integers}\:{n}. \\ $$

Question Number 145620 Answers: 1 Comments: 0

(d/dx)(((x+((x+((x+...))^(1/3) ))^(1/3) ))^(1/3) )=?

$$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+...}}}\right)=? \\ $$

Question Number 145615 Answers: 0 Comments: 2

Let a,b,c > 0 and abc = 1. Prove that (a^3 /((a+1)^2 ))+(b^3 /((b+1)^2 ))+(c^3 /((c+1)^2 )) ≥((a+b+c)/4)

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{abc}\:=\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{3}} }{\left({a}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{{b}^{\mathrm{3}} }{\left({b}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{{c}^{\mathrm{3}} }{\left({c}+\mathrm{1}\right)^{\mathrm{2}} }\:\geqslant\frac{{a}+{b}+{c}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 145602 Answers: 5 Comments: 0

.....Advanced .........Calculus..... Q:: Find the value of :: determinant ((( i :: 𝛗 := ∫_0 ^( 1) Ln ( Γ ( 2 + x ) )dx = ? )),(( ii :: Ω := Σ_(n=1) ^∞ (( 1)/( n ( 2n + 3 ))) = ?))) .....m.n.july.1970..... ■

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....\mathrm{Advanced}\:.........\mathrm{Calculus}..... \\ $$$$\:\:\:\mathrm{Q}::\:\:\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{array}{|c|c|}{\:{i}\:::\:\:\:\boldsymbol{\phi}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Ln}\:\left(\:\Gamma\:\left(\:\mathrm{2}\:+\:{x}\:\right)\:\right){dx}\:=\:?\:\:\:\:}\\{\:{ii}\:::\:\:\:\Omega\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{1}}{\:{n}\:\left(\:\mathrm{2}{n}\:+\:\mathrm{3}\:\right)}\:=\:?}\\\hline\end{array} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....{m}.{n}.{july}.\mathrm{1970}.....\:\:\:\:\blacksquare \\ $$$$ \\ $$

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