Question and Answers Forum

A ballot box contains 7 balls(3 are black). we draw successively and reputing(inside) 5 balls. What is the number of possibilities to have one black ball?

$${A}\:{ballot}\:{box}\:{contains}\:\mathrm{7}\:{balls}\left(\mathrm{3}\:{are}\:\right. \\ $$$$\left.{black}\right).\:{we}\:{draw}\:{successively}\:{and} \\ $$$${reputing}\left({inside}\right)\:\mathrm{5}\:{balls}. \\ $$$${What}\:{is}\:{the}\:{number}\:{of}\:{possibilities}\: \\ $$$${to}\:{have}\:{one}\:{black}\:{ball}? \\ $$

Question Number 104984 Answers: 0 Comments: 1

Question Number 104872 Answers: 0 Comments: 0

solve for a and b: { ((a+b=60°)),((tana=(√2)tanb)) :}

$${solve}\:{for}\:{a}\:{and}\:{b}: \\ $$$$\begin{cases}{{a}+{b}=\mathrm{60}°}\\{{tana}=\sqrt{\mathrm{2}}{tanb}}\end{cases} \\ $$

Question Number 104871 Answers: 2 Comments: 0

Question Number 104987 Answers: 1 Comments: 2

Question Number 104860 Answers: 1 Comments: 0

(1−aT)(1−bT).....(1−yT)(1−zT) ????

$$\left(\mathrm{1}−{aT}\right)\left(\mathrm{1}−{bT}\right).....\left(\mathrm{1}−{yT}\right)\left(\mathrm{1}−{zT}\right)\:\:\:\:???? \\ $$

Question Number 104859 Answers: 2 Comments: 0

Question Number 104858 Answers: 1 Comments: 1

(1−a^3 )(1−b^3 )......(1−x^3 )(1−y^3 )(1−z^3 ) ????

$$\:\:\left(\mathrm{1}−{a}^{\mathrm{3}} \right)\left(\mathrm{1}−{b}^{\mathrm{3}} \right)......\left(\mathrm{1}−{x}^{\mathrm{3}} \right)\left(\mathrm{1}−{y}^{\mathrm{3}} \right)\left(\mathrm{1}−{z}^{\mathrm{3}} \right)\:\:\:\:\:\:\:\:???? \\ $$

Question Number 104857 Answers: 3 Comments: 0

y′=((y−x)/(y+x)) y(0)=0

$$\:\:{y}'=\frac{{y}−{x}}{{y}+{x}}\:\:\:\:\:\:\:{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 104856 Answers: 1 Comments: 0

lim_(z→0) (z^− /z) , lim_(z→i) (((z^− )^4 )/z^4 ) ,lim_(z→0) ((sinz)/z)

$$\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\overset{−} {{z}}}{{z}}\:\:\:\:,\:\:\:\:\underset{{z}\rightarrow{i}} {\mathrm{lim}}\:\frac{\left(\overset{−} {{z}}\right)^{\mathrm{4}} }{{z}^{\mathrm{4}} }\:\:,\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{sinz}}{{z}}\: \\ $$

Question Number 104845 Answers: 1 Comments: 0

solve y′ = y−x−1+(x−y+2)^(−1)

$${solve}\:{y}'\:=\:{y}−{x}−\mathrm{1}+\left({x}−{y}+\mathrm{2}\right)^{−\mathrm{1}} \\ $$

Question Number 104841 Answers: 3 Comments: 3

Question Number 104838 Answers: 1 Comments: 0

lim_(x→0) ((cos ^3 (8x)−1)/(6x^2 )) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\:^{\mathrm{3}} \left(\mathrm{8}{x}\right)−\mathrm{1}}{\mathrm{6}{x}^{\mathrm{2}} }\:? \\ $$

Question Number 104835 Answers: 2 Comments: 0

{ ((log _p (q) = x^2 )),((log _q (p^3 ) = x )) :} find x

$$\begin{cases}{\mathrm{log}\:_{{p}} \left({q}\right)\:=\:{x}^{\mathrm{2}} }\\{\mathrm{log}\:_{{q}} \left({p}^{\mathrm{3}} \right)\:=\:{x}\:}\end{cases} \\ $$$${find}\:{x}\: \\ $$

Question Number 104832 Answers: 1 Comments: 0

{ ((x+y+(x^2 /y^2 ) = 7)),(((((x−y)x^2 )/y^2 ) = 12 )) :}

$$\begin{cases}{{x}+{y}+\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:=\:\mathrm{7}}\\{\frac{\left({x}−{y}\right){x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:=\:\mathrm{12}\:}\end{cases} \\ $$

Question Number 104826 Answers: 1 Comments: 1

∫3^(x+2) ∙lnsin3^x dx=???

$$\int\mathrm{3}^{{x}+\mathrm{2}} \centerdot{lnsin}\mathrm{3}^{{x}} {dx}=??? \\ $$

Question Number 104821 Answers: 2 Comments: 0

3+8+15+24+35+... find sum of 50^(th) −term

$$\mathrm{3}+\mathrm{8}+\mathrm{15}+\mathrm{24}+\mathrm{35}+...\: \\ $$$${find}\:{sum}\:{of}\:\mathrm{50}^{{th}} −{term}\: \\ $$

Question Number 104812 Answers: 1 Comments: 0

lim_(x→∞) ((((3/x)))/(((2/x)+5)^2 −25)) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\frac{\mathrm{3}}{{x}}\right)}{\left(\frac{\mathrm{2}}{{x}}+\mathrm{5}\right)^{\mathrm{2}} −\mathrm{25}}\:? \\ $$

Question Number 104799 Answers: 0 Comments: 1

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