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Question Number 57952 Answers: 1 Comments: 0

An irregular 6 faced die is thrown and the expectation that in 10 throws it will give five even numbers is twice the expectation that it will give four even numbers.How many times in 15000 sets of 10 throws would you expect it to give one even number?

$${An}\:{irregular}\:\mathrm{6}\:{faced}\:{die}\:{is}\:{thrown}\:{and} \\ $$$${the}\:{expectation}\:{that}\:{in}\:\mathrm{10}\:{throws}\:{it}\:{will} \\ $$$${give}\:{five}\:{even}\:{numbers}\:{is}\:{twice}\:{the} \\ $$$${expectation}\:{that}\:{it}\:{will}\:{give}\:{four}\:{even} \\ $$$${numbers}.{How}\:{many}\:{times}\:{in}\:\mathrm{15000} \\ $$$${sets}\:{of}\:\mathrm{10}\:{throws}\:{would}\:{you}\:{expect}\:{it} \\ $$$${to}\:{give}\:{one}\:{even}\:{number}? \\ $$

Question Number 57949 Answers: 0 Comments: 0

(0,i,j) is orthonormal A and B are two points wich verify AB =3 find the locus of point M wich verify MA +MB =6

$$\left(\mathrm{0},{i},{j}\right)\:{is}\:{orthonormal}\:\:\:{A}\:{and}\:\:{B}\:{are}\:{two}\:{points}\:{wich}\:{verify}\:{AB}\:=\mathrm{3} \\ $$$${find}\:\:{the}\:{locus}\:{of}\:{point}\:{M}\:{wich}\:{verify}\:\:{MA}\:+{MB}\:=\mathrm{6}\: \\ $$

Question Number 57948 Answers: 0 Comments: 0

let A(ξ) =∫_ξ ^ξ^2 ((arctan(1+ξt)−(π/4))/((√(2+ξt))−(√(2−ξt)))) dt find lim_(ξ →0) A(ξ) .

$${let}\:{A}\left(\xi\right)\:=\int_{\xi} ^{\xi^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left(\mathrm{1}+\xi{t}\right)−\frac{\pi}{\mathrm{4}}}{\sqrt{\mathrm{2}+\xi{t}}−\sqrt{\mathrm{2}−\xi{t}}}\:{dt} \\ $$$${find}\:{lim}_{\xi\:\rightarrow\mathrm{0}} \:\:{A}\left(\xi\right)\:. \\ $$$$ \\ $$

Question Number 57947 Answers: 0 Comments: 0

let P(x)=(1+ix)^n −1−ni with x real and n integr natural 1) find the roots of P(x) 2) factorize P(x) inside C[x] 3) factorize P(x) inside R[x] 4) decompose the fraction F(x) =((P^((1)) (x))/(P(x))) inside C(x) P^((1)) is the derivative of P .

$${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{{n}} −\mathrm{1}−{ni}\:\:\:\:{with}\:{x}\:{real}\:{and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{P}\left({x}\right)\:{inside}\:{R}\left[{x}\right] \\ $$$$\left.\mathrm{4}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)\:=\frac{{P}^{\left(\mathrm{1}\right)} \left({x}\right)}{{P}\left({x}\right)}\:{inside}\:{C}\left({x}\right) \\ $$$${P}^{\left(\mathrm{1}\right)} \:{is}\:{the}\:{derivative}\:{of}\:{P}\:. \\ $$

Question Number 57946 Answers: 0 Comments: 0

Question Number 57938 Answers: 0 Comments: 0

Question Number 57933 Answers: 0 Comments: 0

Question Number 57932 Answers: 1 Comments: 0

7+g=24

$$\mathrm{7}+{g}=\mathrm{24} \\ $$$$ \\ $$

Question Number 57931 Answers: 0 Comments: 0

What is 2^3 +6×4

$$\mathrm{What}\:\mathrm{is}\:\mathrm{2}^{\mathrm{3}} +\mathrm{6}×\mathrm{4} \\ $$

Question Number 57930 Answers: 1 Comments: 0

solve 2.3((2/(11))+3)

$$\mathrm{solve}\:\mathrm{2}.\mathrm{3}\left(\frac{\mathrm{2}}{\mathrm{11}}+\mathrm{3}\right) \\ $$

Question Number 57925 Answers: 1 Comments: 1

solve y^(′′) −xy =0 by using integr series.

$${solve}\:{y}^{''} \:−{xy}\:=\mathrm{0}\:\:{by}\:{using}\:{integr}\:{series}. \\ $$

Question Number 57923 Answers: 0 Comments: 3

decompose the fraction F(x) =(x^n /(x^(2n) −1)) inside C(x) and R(x)

$${decompose}\:{the}\:{fraction}\:{F}\left({x}\right)\:=\frac{{x}^{{n}} }{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:{inside}\:{C}\left({x}\right)\:{and}\:{R}\left({x}\right) \\ $$

Question Number 57922 Answers: 0 Comments: 2

decompose inside C(x) the fraction F(x) =(1/((x^2 +1)^n )) with n integr natural and n≥1

$${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} }\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$${and}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 57915 Answers: 2 Comments: 0

Question Number 57914 Answers: 0 Comments: 0

Question Number 57909 Answers: 2 Comments: 0

n men and n women should be arranged alternately in a row, how many ways can this be done? if the same should be done on a table, how many ways then?

$${n}\:{men}\:{and}\:{n}\:{women}\:{should}\:{be}\:{arranged} \\ $$$${alternately}\:{in}\:{a}\:{row},\:{how}\:{many}\:{ways} \\ $$$${can}\:{this}\:{be}\:{done}?\:{if}\:{the}\:{same}\:{should} \\ $$$${be}\:{done}\:{on}\:{a}\:{table},\:{how}\:{many}\:{ways}\:{then}? \\ $$

Question Number 57902 Answers: 1 Comments: 1

prove that the equation Z^n =1 have exacly n roots given by Z_k =e^(i((2kπ)/n)) k∈[[0,n−1]]

$${prove}\:{that}\:{the}\:{equation}\:{Z}^{{n}} =\mathrm{1}\:\:{have}\:{exacly}\:{n}\:{roots}\:\:{given}\:{by} \\ $$$${Z}_{{k}} ={e}^{{i}\frac{\mathrm{2}{k}\pi}{{n}}} \:\:\:\:{k}\in\left[\left[\mathrm{0},{n}−\mathrm{1}\right]\right] \\ $$

Question Number 57900 Answers: 0 Comments: 1

let f(x) =∫_0 ^∞ ((cos(πxt))/((t^2 +3x^2 )^2 )) dt with x>0 1) find a explicit form for f(x) 2) find the value of ∫_0 ^∞ ((cos(πt))/((t^2 +3)^2 ))dt 3) let U_n =f(n) find nature of Σ U_n

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\pi{xt}\right)}{\left({t}^{\mathrm{2}} \:+\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dt}\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\pi{t}\right)}{\left({t}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{U}_{{n}} ={f}\left({n}\right)\:\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 57899 Answers: 0 Comments: 2

let f(x) =∫_0 ^(+∞) (dt/((t^2 +x^2 )^3 )) with x>0 1) find a explicit form off (x) 1) calculate ∫_0 ^∞ (dx/((t^2 +3)^3 )) and ∫_0 ^∞ (dt/((t^2 +4)^3 )) 2) find the value of A(θ) =∫_0 ^∞ (dt/((t^2 +sin^2 θ)^3 )) with 0<θ<π.

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{off}\:\left({x}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({t}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{3}} }\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:+{sin}^{\mathrm{2}} \theta\right)^{\mathrm{3}} }\:\:{with}\:\mathrm{0}<\theta<\pi. \\ $$

Question Number 57889 Answers: 0 Comments: 0