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Question Number 147906 Answers: 1 Comments: 0

4 bad apples are mixed accidentally with 20 good apples. Obtain the probability distribution of the numbers of bad apples in a draw of 2 apples at random

$$\mathrm{4}\:{bad}\:{apples}\:{are}\:{mixed}\:{accidentally} \\ $$$${with}\:\mathrm{20}\:{good}\:{apples}.\:{Obtain}\:{the} \\ $$$$\:{probability}\:{distribution}\:{of}\:{the}\: \\ $$$${numbers}\:{of}\:{bad}\:{apples}\:{in}\:{a}\:{draw}\:{of}\: \\ $$$$\mathrm{2}\:{apples}\:{at}\:{random} \\ $$

Question Number 147905 Answers: 1 Comments: 0

Question Number 147904 Answers: 1 Comments: 0

Question Number 147895 Answers: 0 Comments: 0

Question Number 147894 Answers: 2 Comments: 0

x^2 - 3x + 4 = 0 ⇒ x^2 + ((16)/x^2 ) = ?

$${x}^{\mathrm{2}} \:-\:\mathrm{3}{x}\:+\:\mathrm{4}\:=\:\mathrm{0}\:\:\Rightarrow\:\:{x}^{\mathrm{2}} \:+\:\frac{\mathrm{16}}{{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 147893 Answers: 0 Comments: 2

x + 1 + (1/x) = 4 ⇒ x + 1 - (1/x) = ?

$${x}\:+\:\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{4}\:\:\Rightarrow\:\:{x}\:+\:\mathrm{1}\:-\:\frac{\mathrm{1}}{{x}}\:=\:? \\ $$

Question Number 147892 Answers: 1 Comments: 0

if x;y;z>1 then: (√((((x−1)(y−1)(z−1))/((x+1)(y+1)(z+1))) )) < ((xyz)/8)

$${if}\:\:\:{x};{y};{z}>\mathrm{1}\:\:\:{then}: \\ $$$$\sqrt{\frac{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)\left({z}−\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)\left({y}+\mathrm{1}\right)\left({z}+\mathrm{1}\right)}\:}\:<\:\frac{{xyz}}{\mathrm{8}} \\ $$

Question Number 147884 Answers: 0 Comments: 0

∫_0 ^1 e^(−x) x^a dx a>0

$$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−{x}} {x}^{{a}} {dx}\:\:{a}>\mathrm{0} \\ $$$$ \\ $$

Question Number 147882 Answers: 2 Comments: 0

if ((6(√3) + 10))^(1/3) − ((6(√3) − 10))^(1/3) = x find (x^3 /(10−3x)) = ?

$${if}\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:+\:\mathrm{10}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:−\:\mathrm{10}}\:=\:\boldsymbol{{x}} \\ $$$${find}\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{10}−\mathrm{3}{x}}\:=\:? \\ $$

Question Number 147879 Answers: 1 Comments: 0

Question Number 147878 Answers: 1 Comments: 0

Find the sum to n term: 1.2.3 + 4.5.6 + 7.8.9 + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\:\mathrm{n}\:\:\mathrm{term}:\:\:\:\:\:\mathrm{1}.\mathrm{2}.\mathrm{3}\:\:+\:\:\mathrm{4}.\mathrm{5}.\mathrm{6}\:\:+\:\:\mathrm{7}.\mathrm{8}.\mathrm{9}\:\:+\:\:... \\ $$

Question Number 147873 Answers: 1 Comments: 0

Question Number 147877 Answers: 1 Comments: 2

Find the sum to close form. (1/(1.2.3)) + (1/(4.5.6)) + (1/(7.8.9)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{close}\:\mathrm{form}. \\ $$$$\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:\:\:+\:\:\:...\:\:\: \\ $$

Question Number 147867 Answers: 3 Comments: 0

∫secx dx=?

$$\int\mathrm{sec}{x}\:{dx}=? \\ $$

Question Number 147863 Answers: 1 Comments: 0

calculate Σ_(n=0) ^∞ ((n!^2 )/((2n)!))

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{n}!^{\mathrm{2}} }{\left(\mathrm{2n}\right)!} \\ $$$$ \\ $$

Question Number 147862 Answers: 1 Comments: 0

calculate Σ_(n=0) ^∞ (n^2 /3^n )

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{n}} } \\ $$

Question Number 147861 Answers: 0 Comments: 0

resoudre dans Z^2 x^2 −y^2 =3x

$$\mathrm{resoudre}\:\mathrm{dans}\:\mathrm{Z}^{\mathrm{2}} \:\:\:\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \:=\mathrm{3x} \\ $$

Question Number 147876 Answers: 1 Comments: 0

Question Number 147842 Answers: 0 Comments: 2

x ; y ; z > 0 { ((x+y^2 +z^3 = 3)),((y+z^2 +x^3 = 3)),((z+x^2 +y^3 = 3)) :} ⇒ x ; y ; z = ?

$${x}\:;\:{y}\:;\:{z}\:>\:\mathrm{0} \\ $$$$\begin{cases}{{x}+{y}^{\mathrm{2}} +{z}^{\mathrm{3}} \:=\:\mathrm{3}}\\{{y}+{z}^{\mathrm{2}} +{x}^{\mathrm{3}} \:=\:\mathrm{3}}\\{{z}+{x}^{\mathrm{2}} +{y}^{\mathrm{3}} \:=\:\mathrm{3}}\end{cases}\:\:\Rightarrow\:\:{x}\:;\:{y}\:;\:{z}\:=\:? \\ $$

Question Number 147837 Answers: 1 Comments: 0

Evaluate ∫((sin^8 θ−cos^8 θ)/(1−2sin^2 θcos^2 θ)) dθ

$${Evaluate} \\ $$$$\int\frac{\mathrm{sin}\:^{\mathrm{8}} \theta−\mathrm{cos}\:^{\mathrm{8}} \theta}{\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \theta\mathrm{cos}\:^{\mathrm{2}} \theta}\:{d}\theta \\ $$$$ \\ $$

Question Number 147835 Answers: 0 Comments: 0

prove that ∫cos 2θlog(((cos θ+sin θ)/(cos θ−sin θ)))=(1/2)sin 2θlog[tan ((π/4)+θ)+(1/2)log (cos 2θ)

$${prove}\:{that}\: \\ $$$$\:\:\int\mathrm{cos}\:\mathrm{2}\theta{log}\left(\frac{\mathrm{cos}\:\theta+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\right)=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}\theta{log}\left[\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}+\theta\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:\left(\mathrm{cos}\:\mathrm{2}\theta\right)\right. \\ $$$$ \\ $$

Question Number 147828 Answers: 1 Comments: 0

Σ_(p=0) ^n psh(a+bp)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{psh}\left(\mathrm{a}+\mathrm{bp}\right) \\ $$

Question Number 147820 Answers: 1 Comments: 0

Σ_(p=0) ^n sh^2 (a+pb)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{sh}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$

Question Number 147819 Answers: 1 Comments: 0

Σ_(p=0) ^n ch^2 (a+pb)

$$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{ch}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$

Question Number 147811 Answers: 1 Comments: 0

Question Number 147810 Answers: 1 Comments: 0

cos(x) ∙ cos(3x)=cos(5x) ∙ cos(7x) x = ?

$$\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\:\centerdot\:\boldsymbol{{cos}}\left(\mathrm{3}\boldsymbol{{x}}\right)=\boldsymbol{{cos}}\left(\mathrm{5}\boldsymbol{{x}}\right)\:\centerdot\:\boldsymbol{{cos}}\left(\mathrm{7}\boldsymbol{{x}}\right) \\ $$$$\boldsymbol{{x}}\:=\:? \\ $$

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