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Question Number 87253    Answers: 1   Comments: 0

Three pair of socks are placed in a box.If two socks are drawn at random from the box What is the probability (a)of drawing a match pair (b)of drawing a socks for the left and right feet (c)of drawing two socks of the right feet d)drawing two socks of left feet (e)drawing socks of the same feet

$${Three}\:{pair}\:{of}\:{socks}\:{are} \\ $$$${placed}\:{in}\:{a}\:{box}.{If}\:{two} \\ $$$${socks}\:{are}\:{drawn}\:{at} \\ $$$${random}\:{from}\:{the}\:{box} \\ $$$${What}\:{is}\:{the}\:{probability} \\ $$$$\left({a}\right){of}\:{drawing}\:\:{a}\:{match} \\ $$$${pair} \\ $$$$\left({b}\right){of}\:{drawing}\:{a}\:{socks} \\ $$$${for}\:{the}\:{left}\:{and}\:{right} \\ $$$${feet} \\ $$$$\left({c}\right){of}\:{drawing}\:{two}\:{socks}\:{of} \\ $$$${the}\:{right}\:{feet} \\ $$$$\left.{d}\right){drawing}\:{two}\:{socks}\:{of} \\ $$$${left}\:{feet} \\ $$$$\left({e}\right){drawing}\:{socks}\:{of}\:{the} \\ $$$${same}\:{feet} \\ $$$$ \\ $$

Question Number 87224    Answers: 1   Comments: 7

how to simply the boolean algebra (X+Y+Z)(X′ +Y+Z) (X+Y′+Z)

$$\mathrm{how}\:\mathrm{to}\:\mathrm{simply}\:\mathrm{the}\: \\ $$$$\mathrm{boolean}\:\mathrm{algebra}\:\left(\mathrm{X}+\mathrm{Y}+\mathrm{Z}\right)\left(\mathrm{X}'\:+\mathrm{Y}+\mathrm{Z}\right) \\ $$$$\left(\mathrm{X}+\mathrm{Y}'+\mathrm{Z}\right)\: \\ $$

Question Number 87130    Answers: 0   Comments: 5

find the slope for the curve r = 3 sin 2θ at θ =(π/4) ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{at}\:\theta\:=\frac{\pi}{\mathrm{4}}\:? \\ $$

Question Number 87093    Answers: 0   Comments: 6

⌊((x−1)/4)⌋+⌊((x−2)/3)⌋=⌊((x−3)/2)⌋

$$\lfloor\frac{{x}−\mathrm{1}}{\mathrm{4}}\rfloor+\lfloor\frac{{x}−\mathrm{2}}{\mathrm{3}}\rfloor=\lfloor\frac{{x}−\mathrm{3}}{\mathrm{2}}\rfloor \\ $$

Question Number 87050    Answers: 0   Comments: 3

what are the roots of the system of equation (x/y)+(y/(x+1)) = (4/3) and x+y + xy = 5 ?

$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}+\mathrm{1}}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{x}+\mathrm{y}\:+\:\mathrm{xy}\:=\:\mathrm{5}\:? \\ $$

Question Number 87028    Answers: 0   Comments: 0

solve D.E (dy/dx)+((ysec^3 y)/x)=x^2 y^2

$${solve}\:{D}.{E} \\ $$$$\frac{{dy}}{{dx}}+\frac{{y}\mathrm{sec}\:^{\mathrm{3}} {y}}{{x}}={x}^{\mathrm{2}} {y}^{\mathrm{2}} \\ $$

Question Number 87009    Answers: 2   Comments: 0

solve 7⌊x+3⌋^2 −3⌊x⌋+6=5 mod 11

$${solve} \\ $$$$\mathrm{7}\lfloor{x}+\mathrm{3}\rfloor^{\mathrm{2}} −\mathrm{3}\lfloor{x}\rfloor+\mathrm{6}=\mathrm{5}\:{mod}\:\mathrm{11} \\ $$

Question Number 86924    Answers: 1   Comments: 0

Question Number 86903    Answers: 0   Comments: 0

Question Number 86825    Answers: 1   Comments: 1

a^3 +(1/a^3 )=18 a^4 +(1/a^4 )=?

$${a}^{\mathrm{3}} +\frac{\mathrm{1}}{{a}^{\mathrm{3}} }=\mathrm{18} \\ $$$${a}^{\mathrm{4}} +\frac{\mathrm{1}}{{a}^{\mathrm{4}} }=? \\ $$

Question Number 86779    Answers: 1   Comments: 0

ssolve 1)x−[x]≥0 2)x−[x]≤0 3)x+[x]≥0 4)x+[x]≤0

$${ssolve} \\ $$$$\left.\mathrm{1}\right){x}−\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){x}−\left[{x}\right]\leqslant\mathrm{0} \\ $$$$\left.\mathrm{3}\right){x}+\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{4}\right){x}+\left[{x}\right]\leqslant\mathrm{0}\: \\ $$

Question Number 86741    Answers: 1   Comments: 4

{ ((x+10y+50z=500)),((x+y+z=100)) :} find x,y,z

$$\begin{cases}{{x}+\mathrm{10}{y}+\mathrm{50}{z}=\mathrm{500}}\\{{x}+{y}+{z}=\mathrm{100}}\end{cases} \\ $$$$ \\ $$$${find}\:{x},{y},{z} \\ $$

Question Number 86737    Answers: 2   Comments: 4

prove that 1/cos2x+cosx+1=((sin((5x)/2))/(2sin(x/2)))+(1/2) 2/((cos(x)+isin(x)−1)/(cos(x)+isin(x)+1))=−i tan(x) 3/((cos(5x)+isin(5x)+1)/(cos(5x)−isin(x)+1))=cos(5x)+isin(5x)

$${prove}\:{that} \\ $$$$\mathrm{1}/{cos}\mathrm{2}{x}+{cosx}+\mathrm{1}=\frac{{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}}{\mathrm{2}{sin}\frac{{x}}{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{2}/\frac{{cos}\left({x}\right)+{isin}\left({x}\right)−\mathrm{1}}{{cos}\left({x}\right)+{isin}\left({x}\right)+\mathrm{1}}=−{i}\:{tan}\left({x}\right) \\ $$$$ \\ $$$$\mathrm{3}/\frac{{cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right)+\mathrm{1}}{{cos}\left(\mathrm{5}{x}\right)−{isin}\left({x}\right)+\mathrm{1}}={cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right) \\ $$

Question Number 86723    Answers: 0   Comments: 1

Question Number 86610    Answers: 0   Comments: 4

Question Number 86602    Answers: 0   Comments: 0

Question Number 86586    Answers: 1   Comments: 4

Question Number 86541    Answers: 0   Comments: 1

Question Number 86426    Answers: 2   Comments: 0

solve in R x^3 −5=[x]

$${solve}\:{in}\:{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{5}=\left[{x}\right] \\ $$

Question Number 86396    Answers: 0   Comments: 0

Question Number 86298    Answers: 0   Comments: 5

let x^x^x^⋰ =2 x^2 =2 x=±(√2) then let x^x^x^⋰ =4 x^4 =4 x=±(4)^(1/4) =±(√2) so we had prove 2=4 right?

$${let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{2} \\ $$$${x}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}=\pm\sqrt{\mathrm{2}} \\ $$$${then}\:{let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{4} \\ $$$${x}^{\mathrm{4}} =\mathrm{4} \\ $$$${x}=\pm\sqrt[{\mathrm{4}}]{\mathrm{4}}=\pm\sqrt{\mathrm{2}} \\ $$$${so}\:{we}\:{had}\:{prove}\:\mathrm{2}=\mathrm{4}\:{right}? \\ $$

Question Number 86230    Answers: 1   Comments: 0

is (−1)^(m/n) =((((−1 )^m ))^(1/n) ) or =(((−1))^(1/n) )^m or both of them are fault and why ?

$${is}\:\:\left(−\mathrm{1}\right)^{\frac{{m}}{{n}}} \:=\left(\sqrt[{{n}}]{\left(−\mathrm{1}\:\right)^{{m}} }\right)\:{or}\:=\left(\sqrt[{{n}}]{−\mathrm{1}}\right)^{{m}} \\ $$$${or}\:{both}\:{of}\:{them}\:{are}\:{fault}\:{and}\:{why}\:? \\ $$

Question Number 86206    Answers: 0   Comments: 3

1.line:y=−x+4 ,meets : xy=1 at:A,B. ⇒ S_(OA^△ B) =? (O=origin of cordinates) 2.find :center area of region bonded by corve: (√(x/a))+(√(y/b))=1,and x,y axes. (a≠b)∈R^+

$$\mathrm{1}.\mathrm{line}:\boldsymbol{\mathrm{y}}=−\boldsymbol{\mathrm{x}}+\mathrm{4}\:\:,\mathrm{meets}\::\:\boldsymbol{\mathrm{xy}}=\mathrm{1}\:\mathrm{at}:\boldsymbol{\mathrm{A}},\boldsymbol{\mathrm{B}}. \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\mathrm{S}_{\mathrm{O}\overset{\bigtriangleup} {\mathrm{A}B}} =?\:\left(\mathrm{O}=\mathrm{origin}\:\mathrm{of}\:\mathrm{cordinates}\right) \\ $$$$\mathrm{2}.\mathrm{find}\::\mathrm{center}\:\mathrm{area}\:\mathrm{of}\:\mathrm{region}\:\mathrm{bonded}\:\mathrm{by} \\ $$$$\mathrm{corve}:\:\:\sqrt{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{a}}}}+\sqrt{\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{b}}}}=\mathrm{1},\mathrm{and}\:\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\:\mathrm{axes}. \\ $$$$\left(\boldsymbol{\mathrm{a}}\neq\boldsymbol{\mathrm{b}}\right)\in\boldsymbol{\mathrm{R}}^{+} \\ $$

Question Number 86141    Answers: 0   Comments: 5

A number n leaves a remainder of 22 when divided by 24 and remainder 30 when divided by 33. Find the least possible value of n

$$\mathrm{A}\:\mathrm{number}\:\mathrm{n}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{22}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{remainder}\:\:\mathrm{30}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{33}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{n} \\ $$

Question Number 86085    Answers: 1   Comments: 4

If X^2 +Y^2 =10 XY=5 Find (X^2 −Y^2 )

$$\mathrm{If}\:\mathrm{X}^{\mathrm{2}} +\mathrm{Y}^{\mathrm{2}} =\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{XY}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{X}^{\mathrm{2}} −\mathrm{Y}^{\mathrm{2}} \right) \\ $$

Question Number 86042    Answers: 3   Comments: 0

solve: ⌊ (√x) ⌋=⌊(x/2)⌋

$${solve}:\:\:\lfloor\:\sqrt{{x}}\:\rfloor=\lfloor\frac{{x}}{\mathrm{2}}\rfloor \\ $$

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