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Question Number 160314 Answers: 0 Comments: 2

suppose the probability of a child being a boy is 0.5. Find the probability that a family of 3 children will have (i) at least two boys (ii) exactly two boys (iii) all girls

$${suppose}\:{the}\:{probability}\:{of}\:{a}\:{child} \\ $$$${being}\:{a}\:{boy}\:{is}\:\mathrm{0}.\mathrm{5}.\:{Find}\:{the}\: \\ $$$${probability}\:{that}\:{a}\:{family}\:{of}\: \\ $$$$\:\mathrm{3}\:{children}\:{will}\:{have}\: \\ $$$$\left({i}\right)\:{at}\:{least}\:{two}\:{boys} \\ $$$$\left({ii}\right)\:{exactly}\:{two}\:{boys} \\ $$$$\left({iii}\right)\:{all}\:{girls} \\ $$

Question Number 160310 Answers: 0 Comments: 1

find the period of the function: y = tan ((πx)/k) + cos ((2πx)/(k + 5))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\mathrm{y}\:=\:\mathrm{tan}\:\frac{\pi\mathrm{x}}{\mathrm{k}}\:+\:\mathrm{cos}\:\frac{\mathrm{2}\pi\mathrm{x}}{\mathrm{k}\:+\:\mathrm{5}} \\ $$

Question Number 160330 Answers: 0 Comments: 0

(du/dx) = e^(((x/u))) find u

$$\frac{{du}}{{dx}}\:=\:{e}^{\left(\frac{{x}}{{u}}\right)} \\ $$$${find}\:{u} \\ $$

Question Number 160328 Answers: 0 Comments: 0

∫_1 ^( 2e) (√(((x^2 +1)/(ln x)) (√(ln x^2 )))) dx =?

$$\:\int_{\mathrm{1}} ^{\:\mathrm{2e}} \:\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{ln}\:\mathrm{x}}\:\sqrt{\mathrm{ln}\:\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=? \\ $$

Question Number 160305 Answers: 0 Comments: 0

Question Number 160304 Answers: 0 Comments: 0

Question Number 160302 Answers: 1 Comments: 0

Question Number 160299 Answers: 0 Comments: 0

Question Number 160291 Answers: 3 Comments: 0

Ω = ∫ ((x^2 −3x+7)/((x^2 −4x+6)^2 )) dx =?

$$\:\:\:\Omega\:=\:\int\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{7}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{6}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$

Question Number 160289 Answers: 2 Comments: 0

Σ_(n≥1) ^∞ (1/(n(2n+1)^2 ))=?

$$\underset{{n}\geqslant\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$

Question Number 160283 Answers: 0 Comments: 1

Question Number 160282 Answers: 1 Comments: 0

Find: lim_(x→b) ((b^x - x^b )/(x - b))

$$\mathrm{Find}:\:\:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\boldsymbol{\mathrm{b}}} {\mathrm{lim}}\:\frac{\mathrm{b}^{\boldsymbol{\mathrm{x}}} \:-\:\mathrm{x}^{\boldsymbol{\mathrm{b}}} }{\mathrm{x}\:-\:\mathrm{b}} \\ $$

Question Number 160281 Answers: 1 Comments: 0

∫_0 ^1 ((ln^2 (1−x)lnx)/x)dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{lnx}}}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 160276 Answers: 1 Comments: 0

∫_0 ^1 ((ln(1−x)ln(x))/(1−x))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}−\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 160270 Answers: 2 Comments: 0

Question Number 160269 Answers: 0 Comments: 1

In each square of a 5×5 board there is a lamp turned off.If we touch a lamp then that lamp and the ones in neighbouring squares(the squares which share a side)change their states.After a certain number of moves,Is it possible to turn on all lamps?Give Reason?

$${In}\:{each}\:{square}\:{of}\:{a}\:\mathrm{5}×\mathrm{5}\:{board}\:{there} \\ $$$${is}\:{a}\:{lamp}\:{turned}\:{off}.{If}\:{we}\:{touch}\:\:{a}\: \\ $$$${lamp}\:{then}\:{that}\:{lamp}\:{and}\:{the}\:{ones}\:{in}\: \\ $$$${neighbouring}\:{squares}\left({the}\:{squares}\:\right. \\ $$$$\left.{which}\:{share}\:{a}\:{side}\right){change}\:{their} \\ $$$$\:{states}.{After}\:{a}\:{certain}\:{number}\:{of}\: \\ $$$${moves},{Is}\:{it}\:{possible}\:{to}\:{turn}\:{on}\:{all}\: \\ $$$${lamps}?{Give}\:{Reason}? \\ $$$$ \\ $$$$ \\ $$

Question Number 160268 Answers: 0 Comments: 0