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Question Number 176102 Answers: 2 Comments: 0

Prove that 4n<2^n for all n≥5

$$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\:\:\:\:\mathrm{4}\boldsymbol{\mathrm{n}}<\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{n}}\geqslant\mathrm{5} \\ $$

Question Number 176101 Answers: 0 Comments: 6

x^2 − 4y^2 = 3z^2 [ x, y, z ∈ N ] HCF(x, y, z) = 1 like (4, 1, 2) x, y, z < 100 solve by computer programing

$${x}^{\mathrm{2}} \:−\:\mathrm{4}{y}^{\mathrm{2}} \:=\:\mathrm{3}{z}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\left[\:{x},\:{y},\:{z}\:\in\:\mathbb{N}\:\right]\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{HCF}\left({x},\:{y},\:{z}\right)\:=\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{like}\:\left(\mathrm{4},\:\mathrm{1},\:\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x},\:{y},\:{z}\:<\:\mathrm{100} \\ $$$${solve}\:{by}\:{computer}\:{programing} \\ $$

Question Number 176100 Answers: 2 Comments: 0

Q : in AB^Δ C : A = 90^o and , m_( b) ^2 + m_( c) ^( 2) = 100. find the value of ” a ” . note : ⟨ m_( a) := the median corresponding to ” A ” . −−− m.n−−−

$$ \\ $$$$\:\:\:\:\:{Q}\:: \\ $$$$\:\:\:\:\:{in}\:\:{A}\overset{\Delta} {{B}C}\::\:{A}\:=\:\mathrm{90}^{\mathrm{o}} \:\:\:{and}\:,\:{m}_{\:{b}} ^{\mathrm{2}} \:+\:{m}_{\:{c}} ^{\:\mathrm{2}} \:=\:\mathrm{100}.\:\:\:\:\:\:\:\:\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{find}\:\:{the}\:\:{value}\:{of}\:\:\:''\:\:\:{a}\:\:\:''\:. \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{note}\::\:\:\langle\:{m}_{\:{a}} \::=\:{the}\:{median}\:{corresponding}\:\:{to}\:''\:{A}\:''\:. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:−−−\:\:\boldsymbol{{m}}.\boldsymbol{{n}}−−− \\ $$

Question Number 176098 Answers: 1 Comments: 0

The deviations of a set of numbers from 12 are 3, −2, 1, 0, −1, 4, 0, 1 and 2. Calculate the mean and standard deviation of the numbers.

$$\mathrm{The}\:\mathrm{deviations}\:\mathrm{of}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{numbers} \\ $$$$\mathrm{from}\:\mathrm{12}\:\mathrm{are}\: \\ $$$$\:\:\:\:\:\mathrm{3},\:−\mathrm{2},\:\mathrm{1},\:\mathrm{0},\:−\mathrm{1},\:\mathrm{4},\:\mathrm{0},\:\mathrm{1}\:\mathrm{and}\:\mathrm{2}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\: \\ $$$$\mathrm{deviation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}. \\ $$

Question Number 176095 Answers: 0 Comments: 1

In △ABC the following relationship holds: an_a ≥ (s (b + c) − 2bc) cos (A/2)

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship}\:\mathrm{holds}: \\ $$$$\mathrm{an}_{\boldsymbol{\mathrm{a}}} \:\geqslant\:\left(\mathrm{s}\:\left(\mathrm{b}\:+\:\mathrm{c}\right)\:−\:\mathrm{2bc}\right)\:\mathrm{cos}\:\frac{\mathrm{A}}{\mathrm{2}} \\ $$

Question Number 176094 Answers: 0 Comments: 0

Question Number 176092 Answers: 0 Comments: 3

∠AOB triangle equilareral de cote a (A;B) : centres de cercles de rayon r 𝛉 =∡ GOH EF=a_0 Determiner l aire de l espace delimite par AFOEBHG comme il est marque sur l image ci−joint en fonction de: a,r,a_0 et 𝛉

$$\angle{AOB}\:\:\:{triangle}\:{equilareral}\:{de}\:{cote}\:\boldsymbol{{a}} \\ $$$$\left({A};\mathrm{B}\right)\::\:\mathrm{c}{e}\mathrm{ntres}\:\mathrm{de}\:\mathrm{cercles}\:\mathrm{de}\:\mathrm{rayon}\:\boldsymbol{\mathrm{r}} \\ $$$$\boldsymbol{\theta}\:=\measuredangle\:\:{GOH}\:\:\:\mathrm{EF}=\boldsymbol{{a}}_{\mathrm{0}} \\ $$$${Determiner}\:{l}\:{aire}\:{de}\:{l}\:{espace}\:{delimite}\:{par} \\ $$$$\:\:\boldsymbol{\mathrm{AFOEBHG}}\:{comme}\:{il}\:{est}\:{marque}\:{sur}\:{l}\:{image}\:{ci}−{joint}\: \\ $$$${en}\:{fonction}\:{de}:\:\boldsymbol{{a}},\boldsymbol{{r}},\boldsymbol{{a}}_{\mathrm{0}} \:{et}\:\boldsymbol{\theta} \\ $$

Question Number 176086 Answers: 0 Comments: 1

Question Number 176076 Answers: 0 Comments: 1

Question Number 176070 Answers: 0 Comments: 3

demontrer par recurrence que pour tout n>0 appartenent a l ensemble des entier naturel 3^(2n−2^(n ) ) est multiple de 7

$${demontrer}\:{par}\:{recurrence}\:{que}\:{pour}\:{tout}\:{n}>\mathrm{0}\:{appartenent}\:{a}\:{l}\:{ensemble}\:{des}\:{entier}\:{naturel}\:\mathrm{3}^{\mathrm{2}{n}−\mathrm{2}^{{n}\:} } {est}\:{multiple}\:{de}\:\mathrm{7} \\ $$

Question Number 176058 Answers: 3 Comments: 0

22^(22) what is hte last digit?

$$\mathrm{22}^{\mathrm{22}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{hte}\:\mathrm{last}\:\mathrm{digit}? \\ $$

Question Number 176056 Answers: 1 Comments: 0

Three bags labelled R, B and W cotains Red, Blue and White balls respectively of equal sizes, the ratio of the balls in the bag are R:B=2:3 and B:W= 4:5. All the balls are removed into a big bag and properly mixed together. If two balls are picked at random one after the other with replacement, find the probability of picking a) white ball and a blue b). A blue ball first and then red ball

$$\:\mathrm{Three}\:\mathrm{bags}\:\mathrm{labelled}\:\mathrm{R},\:\mathrm{B}\:\mathrm{and}\:\mathrm{W}\: \\ $$$$\:\mathrm{cotains}\:\mathrm{Red},\:\mathrm{Blue}\:\mathrm{and}\:\mathrm{White}\:\mathrm{balls}\: \\ $$$$\:\mathrm{respectively}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{sizes},\:\mathrm{the}\:\mathrm{ratio}\: \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{are}\:\:\mathrm{R}:\mathrm{B}=\mathrm{2}:\mathrm{3}\: \\ $$$$\mathrm{and}\:\mathrm{B}:\mathrm{W}=\:\mathrm{4}:\mathrm{5}.\:\mathrm{All}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{are}\: \\ $$$$\mathrm{removed}\:\mathrm{into}\:\mathrm{a}\:\mathrm{big}\:\mathrm{bag}\:\mathrm{and}\:\mathrm{properly}\: \\ $$$$\mathrm{mixed}\:\mathrm{together}.\:\mathrm{If}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{picked} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{one}\:\mathrm{after}\:\mathrm{the}\:\mathrm{other}\:\mathrm{with}\: \\ $$$$\mathrm{replacement},\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{picking}\: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{white}\:\mathrm{ball}\:\mathrm{and}\:\mathrm{a}\:\mathrm{blue} \\ $$$$\left.\mathrm{b}\right).\:\mathrm{A}\:\mathrm{blue}\:\mathrm{ball}\:\mathrm{first}\:\mathrm{and}\:\mathrm{then}\:\mathrm{red}\:\mathrm{ball} \\ $$$$ \\ $$

Question Number 176060 Answers: 2 Comments: 0

x^2 −4x+5=0

$${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}=\mathrm{0} \\ $$

Question Number 176054 Answers: 1 Comments: 0

(1/(2!)) + (2/(3!)) + (3/(4!)) + (4/(5!)) + ............. ∞ = ?

$$\frac{\mathrm{1}}{\mathrm{2}!}\:+\:\frac{\mathrm{2}}{\mathrm{3}!}\:+\:\frac{\mathrm{3}}{\mathrm{4}!}\:+\:\frac{\mathrm{4}}{\mathrm{5}!}\:+\:.............\:\infty\:=\:? \\ $$

Question Number 176049 Answers: 1 Comments: 0

calculer (−1/2+i(√(3/2)^3 ))

$${calculer}\:\left(−\mathrm{1}/\mathrm{2}+{i}\sqrt{\left.\mathrm{3}/\mathrm{2}\right)^{\mathrm{3}} }\right. \\ $$

Question Number 176037 Answers: 2 Comments: 1

If (a−b)(a + b) = 13 Find 2a + b = ?