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Question Number 183424 Answers: 0 Comments: 0

Among the natural numbers not greater than 22 , the probability that the modulus of the difference of any two of the 3 randomly selected numbers is greater than 5 is equal to which of the following? a)15/22 b)1/7 c)1/22 d)1

$$\mathrm{Among}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{not} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{22}\:,\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{modulus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{any}\: \\ $$$$\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{3}\:\mathrm{randomly}\:\mathrm{selected}\:\mathrm{numbers} \\ $$$$\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{1}\left.\mathrm{5}/\mathrm{22}\:\:\:\mathrm{b}\right)\mathrm{1}/\mathrm{7}\:\:\:\mathrm{c}\right)\mathrm{1}/\mathrm{22}\:\:\:\mathrm{d}\right)\mathrm{1} \\ $$

Question Number 183631 Answers: 1 Comments: 1

determiner r? AB=6 AE=5

$${determiner}\:\:\:\boldsymbol{{r}}? \\ $$$${AB}=\mathrm{6}\:\:\:\:\:{AE}=\mathrm{5} \\ $$

Question Number 183633 Answers: 1 Comments: 1

Montrer que ((a/b))^2 =(c/d)+1

$${Montrer}\:{que} \\ $$$$\left(\frac{{a}}{{b}}\right)^{\mathrm{2}} =\frac{{c}}{{d}}+\mathrm{1} \\ $$

Question Number 183420 Answers: 2 Comments: 0

prove that Σ_(x=0) ^∞ ((4^x . x)/(x!)) = 4 e^4

$${prove}\:{that}\:\underset{{x}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{4}^{{x}} \:.\:{x}}{{x}!}\:=\:\mathrm{4}\:{e}^{\mathrm{4}} \\ $$

Question Number 183419 Answers: 0 Comments: 2

Question Number 183413 Answers: 0 Comments: 0

Question Number 183411 Answers: 0 Comments: 2

Question Number 183409 Answers: 0 Comments: 3

Question Number 183405 Answers: 0 Comments: 2

Question Number 183393 Answers: 3 Comments: 0

Question Number 183389 Answers: 2 Comments: 0

Question Number 183382 Answers: 2 Comments: 4

Question Number 183381 Answers: 1 Comments: 2

((3n^5 + 4n^4 − 7n^3 + 5n^2 − 5)/(n + 1)) There can be no residue: a)0 b)2 c)4 d)5 e)9

$$\frac{\mathrm{3n}^{\mathrm{5}} \:+\:\mathrm{4n}^{\mathrm{4}} \:−\:\mathrm{7n}^{\mathrm{3}} \:+\:\mathrm{5n}^{\mathrm{2}} \:−\:\mathrm{5}}{\mathrm{n}\:+\:\mathrm{1}} \\ $$$$\mathrm{There}\:\mathrm{can}\:\mathrm{be}\:\mathrm{no}\:\mathrm{residue}: \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{0}\left.\:\left.\:\:\mathrm{b}\right)\mathrm{2}\:\:\:\mathrm{c}\right)\mathrm{4}\:\:\:\mathrm{d}\right)\mathrm{5}\:\:\:\mathrm{e}\right)\mathrm{9} \\ $$

Question Number 183380 Answers: 0 Comments: 1

a>0 , b>0 { (((x−1)^2 + (y−7)^2 = a^2 )),(((x−2)^2 + (y−3)^2 = b^2 )) :} Find: (a+b)_(min) = ?

$$\mathrm{a}>\mathrm{0}\:,\:\mathrm{b}>\mathrm{0} \\ $$$$\begin{cases}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}−\mathrm{7}\right)^{\mathrm{2}} \:=\:\mathrm{a}^{\mathrm{2}} }\\{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}−\mathrm{3}\right)^{\mathrm{2}} \:=\:\mathrm{b}^{\mathrm{2}} }\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\left(\mathrm{a}+\mathrm{b}\right)_{\boldsymbol{\mathrm{min}}} \:=\:? \\ $$

Question Number 183594 Answers: 1 Comments: 0

log _(0.5) (√(1+x)) + 3log _(0.25) (1−x)= log _(1/16) (1−x^2 )^2 +2

$$\:\:\:\:\:\mathrm{log}\:_{\mathrm{0}.\mathrm{5}} \:\sqrt{\mathrm{1}+{x}}\:+\:\mathrm{3log}\:_{\mathrm{0}.\mathrm{25}} \left(\mathrm{1}−{x}\right)=\:\mathrm{log}\:_{\mathrm{1}/\mathrm{16}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{2}\: \\ $$

Question Number 183592 Answers: 1 Comments: 0

{ (((√(x/y)) +(√(y/z)) +(√(z/x)) = 3)),(((√(y/x)) +(√(z/y)) +(√(x/z)) = 3)),(((√(xyz)) = 1)) :}

$$\:\:\:\:\:\begin{cases}{\sqrt{\frac{{x}}{{y}}}\:+\sqrt{\frac{{y}}{{z}}}\:+\sqrt{\frac{{z}}{{x}}}\:=\:\mathrm{3}}\\{\sqrt{\frac{{y}}{{x}}}\:+\sqrt{\frac{{z}}{{y}}}\:+\sqrt{\frac{{x}}{{z}}}\:=\:\mathrm{3}}\\{\sqrt{{xyz}}\:=\:\mathrm{1}}\end{cases} \\ $$$$\: \\ $$$$ \\ $$

Question Number 183376 Answers: 2 Comments: 1

Question Number 183366 Answers: 0 Comments: 2

6 of the 23 given points in the plane lie on a circle. Let n be the number of circles passing through at least 3 of these points. What is the maximum number of n?

$$\mathrm{6}\:\mathrm{of}\:\mathrm{the}\:\mathrm{23}\:\mathrm{given}\:\mathrm{points}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{lie}\:\mathrm{on}\:\mathrm{a}\:\mathrm{circle}.\:\mathrm{Let}\:\boldsymbol{\mathrm{n}}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{circles}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{points}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{number}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}? \\ $$

Question Number 183363 Answers: 1 Comments: 0

Find: 2003∙2005^3 −2004∙2002^3

$$\mathrm{Find}: \\ $$$$\mathrm{2003}\centerdot\mathrm{2005}^{\mathrm{3}} −\mathrm{2004}\centerdot\mathrm{2002}^{\mathrm{3}} \\ $$

Question Number 183426 Answers: 2 Comments: 3

surface de la partie bleu du graphe?

$${surface}\:{de}\:{la}\:{partie}\:{bleu} \\ $$$${du}\:{graphe}? \\ $$

Question Number 183354 Answers: 0 Comments: 2

Given three point.Find the for the plane through the point P(0,1,0) Q(3,1,4) R(−1,0,1)

$${Given}\:{three}\:{point}.{Find}\:{the} \\ $$$${for}\:{the}\:{plane}\:\:{through}\:{the}\:{point} \\ $$$${P}\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\:{Q}\left(\mathrm{3},\mathrm{1},\mathrm{4}\right)\:\:{R}\left(−\mathrm{1},\mathrm{0},\mathrm{1}\right) \\ $$

Question Number 183353 Answers: 1 Comments: 0

For the function f(x)= { ((x^2 −3 if x<4)),(((x^2 /(x+4)) if x≥4)) :} Find (i) lim_(x→−4) f(x) ii)lim_(x→+4) f(x)

$${For}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3}\:{if}\:{x}<\mathrm{4}}\\{\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{4}}\:\:\:\:\:{if}\:{x}\geqslant\mathrm{4}}\end{cases} \\ $$$$\left.{Find}\:\left({i}\right)\:\underset{{x}\rightarrow−\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right)\:\:\:\:\:\:{ii}\right)\underset{{x}\rightarrow+\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right) \\ $$

Question Number 183352 Answers: 0 Comments: 0

For the function f(x)= { ((1−x^2 if x< 2)),((2x+1 if x≥2)) :} Find (i)lim_(x→^− 2) f(x) (ii) lim_(x→2^+ ) f(x)

$${For}\:{the}\:{function}\: \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{1}−{x}^{\mathrm{2}} \:{if}\:{x}<\:\mathrm{2}}\\{\mathrm{2}{x}+\mathrm{1}\:{if}\:{x}\geqslant\mathrm{2}}\end{cases} \\ $$$${Find} \\ $$$$\left({i}\right)\underset{{x}\rightarrow^{−} \mathrm{2}} {\mathrm{lim}}{f}\left({x}\right)\:\:\:\:\:\:\:\left({ii}\right)\:\underset{{x}\rightarrow\mathrm{2}^{+} } {\mathrm{lim}}\:{f}\left({x}\right) \\ $$$$ \\ $$

Question Number 183350 Answers: 3 Comments: 2

Find (a)lim_(x→∞) ((3x+2)/(x^2 −x+1)) (b)lim_(x→∞) ((√(x^2 −1))/(2x+1)) (c)lim_(x→5) (((√(3x+1)) −4)/(x−5))

$${Find}\: \\ $$$$\left({a}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{3}{x}+\mathrm{2}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}} \\ $$$$\left({b}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{\mathrm{2}{x}+\mathrm{1}} \\ $$$$\left({c}\right)\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3}{x}+\mathrm{1}}\:−\mathrm{4}}{{x}−\mathrm{5}} \\ $$

Question Number 183344 Answers: 2 Comments: 1

Question Number 183342 Answers: 3 Comments: 0

Find: 3 − (2/(3 − (2/(3 − (2/(...)))))) = ?

$$\mathrm{Find}:\:\:\:\:\:\mathrm{3}\:−\:\frac{\mathrm{2}}{\mathrm{3}\:−\:\frac{\mathrm{2}}{\mathrm{3}\:−\:\frac{\mathrm{2}}{...}}}\:=\:? \\ $$

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