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Question Number 178488    Answers: 1   Comments: 0

I have two children. One is a boy born on a Tuesday. What is the probbility I have two boys

$$ \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{two}\:\mathrm{children}.\:\mathrm{One}\:\mathrm{is}\:\mathrm{a}\:\mathrm{boy} \\ $$$$\mathrm{born}\:\mathrm{on}\:\mathrm{a}\:\mathrm{Tuesday}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{probbility}\:\mathrm{I}\:\mathrm{have}\:\mathrm{two}\:\mathrm{boys} \\ $$

Question Number 178487    Answers: 3   Comments: 0

∫ (dx/(cot^3 x sin^7 x)) =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{{dx}}{\mathrm{cot}\:^{\mathrm{3}} {x}\:\mathrm{sin}\:^{\mathrm{7}} {x}}\:=? \\ $$

Question Number 178486    Answers: 1   Comments: 0

Reduce (((2n)!)/(1×3×5×...×(2n−1)))

$$\:{Reduce}\:\frac{\left(\mathrm{2}{n}\right)!}{\mathrm{1}×\mathrm{3}×\mathrm{5}×...×\left(\mathrm{2}{n}−\mathrm{1}\right)}\: \\ $$

Question Number 177492    Answers: 0   Comments: 0

If 0<a≤b then: ∫_( a) ^( b) ∫_( a) ^( b) ((dx dy)/( (√(xy (x + y))))) ≤ ((b−a)/2) ∙ log ((b/a)) + log^2 ((b/a))

$$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}: \\ $$$$\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\:\frac{\mathrm{dx}\:\mathrm{dy}}{\:\sqrt{\mathrm{xy}\:\left(\mathrm{x}\:+\:\mathrm{y}\right)}}\:\:\leqslant\:\:\frac{\mathrm{b}−\mathrm{a}}{\mathrm{2}}\:\centerdot\:\mathrm{log}\:\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\:+\:\mathrm{log}^{\mathrm{2}} \:\left(\frac{\mathrm{b}}{\mathrm{a}}\right) \\ $$

Question Number 177493    Answers: 1   Comments: 2

find the laplace transform of f(t)=ln(t)

$${find}\:{the}\:{laplace}\:{transform}\:{of} \\ $$$${f}\left({t}\right)={ln}\left({t}\right) \\ $$

Question Number 181603    Answers: 0   Comments: 0

calcul Σ_(n=1) ^(+oo) U_n : U_n =(1/n)(E((√(n+1)) −E((√n) )

$${calcul}\:\:\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}{U}_{{n}} : \\ $$$${U}_{{n}} =\frac{\mathrm{1}}{{n}}\left({E}\left(\sqrt{{n}+\mathrm{1}}\:−{E}\left(\sqrt{{n}}\:\right)\right.\right. \\ $$

Question Number 177456    Answers: 2   Comments: 0

Question Number 177446    Answers: 1   Comments: 1

Question Number 177442    Answers: 3   Comments: 0

Question Number 177437    Answers: 0   Comments: 0

Question Number 177432    Answers: 2   Comments: 10

Question Number 177431    Answers: 0   Comments: 0

Question Number 177415    Answers: 2   Comments: 0

Question Number 177403    Answers: 2   Comments: 1

if david wears shorts and short sleeves to play outside what temperature would it most likely be?

$${if}\:{david}\:{wears}\:{shorts}\:{and}\:{short}\:{sleeves}\:{to}\:{play}\:{outside}\:{what}\:{temperature}\:{would}\:{it}\:{most}\:{likely}\:{be}? \\ $$

Question Number 177400    Answers: 3   Comments: 2

∫((√(9a^2 −1))/a)da Evaluate

$$\int\frac{\sqrt{\mathrm{9a}^{\mathrm{2}} −\mathrm{1}}}{\mathrm{a}}\mathrm{da} \\ $$$$ \\ $$$$\mathrm{Evaluate} \\ $$

Question Number 177378    Answers: 1   Comments: 0

Question Number 177451    Answers: 1   Comments: 1

Question Number 177361    Answers: 1   Comments: 0

4(16^((x+4)) × 5.2^(2x) =13

$$\mathrm{4}\left(\mathrm{16}^{\left({x}+\mathrm{4}\right)} \:×\:\mathrm{5}.\mathrm{2}^{\mathrm{2}{x}} =\mathrm{13}\right. \\ $$

Question Number 177360    Answers: 1   Comments: 0

1/2 log_4 36 ×log_6 64

$$\mathrm{1}/\mathrm{2}\:{log}_{\mathrm{4}} \mathrm{36}\:×{log}_{\mathrm{6}} \mathrm{64} \\ $$

Question Number 177375    Answers: 0   Comments: 5

soit k un entier naturel non nul ,S un nombre fini de nombres premiers impair −Demontrer qu il existe au plus une maniere(a rotation et symetrie axiale) de disposer les elements de S sur un cercle de sorte que le priduit de 2 nombres places l′un a cote de l′autre soit toujours de la forme (x^2 +x+k),x un entier naturel non nul. Extrait de Olimpiad de Mathematiques (France 2022).

$$\mathrm{soit}\:\mathrm{k}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}\:,\mathrm{S}\:\mathrm{un}\:\mathrm{nombre}\:\mathrm{fini}\:\mathrm{de}\: \\ $$$$\mathrm{nombres}\:\mathrm{premiers}\:\mathrm{impair} \\ $$$$−\mathrm{Demontrer}\:\mathrm{qu}\:\mathrm{il}\:\mathrm{existe}\:\mathrm{au}\:\mathrm{plus}\:\mathrm{une}\:\mathrm{maniere}\left(\mathrm{a}\:\mathrm{rotation}\:\mathrm{et}\:\mathrm{symetrie}\:\mathrm{axiale}\right) \\ $$$$\mathrm{de}\:\mathrm{disposer}\:\mathrm{les}\:\mathrm{elements}\:\mathrm{de}\:\mathrm{S}\:\mathrm{sur}\:\mathrm{un}\:\mathrm{cercle}\:\mathrm{de}\:\mathrm{sorte}\:\mathrm{que}\:\mathrm{le}\:\mathrm{priduit}\:\mathrm{de}\:\mathrm{2}\:\mathrm{nombres}\: \\ $$$$\mathrm{places}\:\mathrm{l}'\mathrm{un}\:\mathrm{a}\:\mathrm{cote}\:\mathrm{de}\:\mathrm{l}'\mathrm{autre}\:\mathrm{soit}\:\mathrm{toujours}\:\mathrm{de}\:\mathrm{la}\:\mathrm{forme}\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{k}}\right),\mathrm{x}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}. \\ $$$$\:\:\:\:\:\:\:{Extrait}\:{de}\:{Olimpiad}\:{de}\:{Mathematiques}\:\left({France}\:\mathrm{2022}\right). \\ $$$$ \\ $$

Question Number 177353    Answers: 4   Comments: 1

Question Number 177336    Answers: 0   Comments: 3

A tank GM by 4m by 3m. calculate one−third of its volume. please help!

$$\mathrm{A}\:\mathrm{tank}\:\mathrm{GM}\:\mathrm{by}\:\mathrm{4m}\:\mathrm{by}\:\mathrm{3m}.\:\mathrm{calculate} \\ $$$$\mathrm{one}−\mathrm{third}\:\mathrm{of}\:\mathrm{its}\:\mathrm{volume}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}! \\ $$

Question Number 177331    Answers: 1   Comments: 0

a+b+c=0 a^2 +b^2 +c^2 =4 a^4 +b^4 +c^4 =?

$${a}+{b}+{c}=\mathrm{0} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{4} \\ $$$${a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} =? \\ $$

Question Number 177332    Answers: 1   Comments: 1

Question Number 177320    Answers: 1   Comments: 0

Question Number 177306    Answers: 2   Comments: 0

Resoudre l equaation acos x+bsin x=c (a,b,c)∈R^3

$${Resoudre}\:{l}\:{equaation} \\ $$$$\:\:{a}\mathrm{cos}\:{x}+{b}\mathrm{sin}\:{x}={c} \\ $$$$\left({a},{b},{c}\right)\in\mathbb{R}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$

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