Question and Answers Forum

AllQuestion and Answers: Page 1180

Question Number 99194 Answers: 1 Comments: 0

Question Number 99193 Answers: 1 Comments: 4

Question Number 99175 Answers: 2 Comments: 0

A man and a woman have 3 boys and 3 girls. (i) in how many ways will they sit in a row such that the 3 boys and 3 girls are inbetween the man and woman. (ii) Say the man decides of the 3 boys and 3 girls he has 2 of the kids should help him out in a project, in how many ways can this be done, if heyoungest boy and oldest girl can′t join.

$$\:\:\mathrm{A}\:\mathrm{man}\:\mathrm{and}\:\mathrm{a}\:\mathrm{woman}\:\mathrm{have}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}.\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{will}\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{the}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{are}\:\mathrm{inbetween}\:\mathrm{the}\:\mathrm{man}\:\mathrm{and}\:\mathrm{woman}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Say}\:\mathrm{the}\:\mathrm{man}\:\mathrm{decides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{he}\:\mathrm{has}\:\mathrm{2}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{kids}\:\mathrm{should}\:\mathrm{help}\:\mathrm{him}\:\mathrm{out}\:\mathrm{in}\:\mathrm{a}\:\mathrm{project}, \\ $$$$\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{done},\:\mathrm{if}\:\mathrm{heyoungest}\:\mathrm{boy}\:\mathrm{and}\:\mathrm{oldest} \\ $$$$\mathrm{girl}\:\mathrm{can}'\mathrm{t}\:\mathrm{join}. \\ $$

Question Number 99171 Answers: 0 Comments: 3

Question Number 99168 Answers: 1 Comments: 0

Question Number 99159 Answers: 0 Comments: 2

Question Number 99154 Answers: 4 Comments: 0

Question Number 99146 Answers: 1 Comments: 0

1) explicit f(a) =∫_1 ^(√3) arctan((a/x))dx with a>0 2) calculate ∫_1 ^(√3) arctan((2/x))dx and ∫_1 ^(√3) arctan((3/x))dx

$$\left.\mathrm{1}\right)\:\mathrm{explicit}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\:\mathrm{arctan}\left(\frac{\mathrm{a}}{\mathrm{x}}\right)\mathrm{dx}\:\:\mathrm{with}\:\mathrm{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\mathrm{dx}\:\mathrm{and}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\:\mathrm{arctan}\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\mathrm{dx} \\ $$

Question Number 99142 Answers: 1 Comments: 0

If 4 dice are thrown together, then the probability that the sum of the numbers appearing on them is 13, is

$$\mathrm{If}\:\mathrm{4}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{thrown}\:\mathrm{together},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers} \\ $$$$\mathrm{appearing}\:\mathrm{on}\:\mathrm{them}\:\mathrm{is}\:\mathrm{13},\:\mathrm{is} \\ $$

Question Number 99141 Answers: 1 Comments: 0

The probability that in a random arrangement of the letters of the word ′UNIVERSITY′ the two I′ do not come together is

$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{in}\:\mathrm{a}\:\mathrm{random} \\ $$$$\mathrm{arrangement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word} \\ $$$$'\mathrm{UNIVERSITY}'\:\mathrm{the}\:\mathrm{two}\:\mathrm{I}'\:\mathrm{do}\:\mathrm{not}\:\mathrm{come} \\ $$$$\mathrm{together}\:\mathrm{is} \\ $$

Question Number 99139 Answers: 1 Comments: 0

One ticket is selected at random from 100 tickets numbered 00, 01, 02, ..., 99 Suppose A and B are the sum and product of the digit found on the ticket. Then P (A = 7/B= 0) is given by

$$\mathrm{One}\:\mathrm{ticket}\:\mathrm{is}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from} \\ $$$$\mathrm{100}\:\mathrm{tickets}\:\mathrm{numbered}\:\mathrm{00},\:\mathrm{01},\:\mathrm{02},\:...,\:\mathrm{99} \\ $$$$\mathrm{Suppose}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{and}\: \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digit}\:\mathrm{found}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ticket}. \\ $$$$\mathrm{Then}\:{P}\:\left({A}\:=\:\mathrm{7}/{B}=\:\mathrm{0}\right)\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$

Question Number 99138 Answers: 1 Comments: 0

If A and B are independent events and P(C)=0, then

$$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{independent}\:\mathrm{events}\:\mathrm{and} \\ $$$${P}\left({C}\right)=\mathrm{0},\:\mathrm{then} \\ $$

Question Number 99137 Answers: 0 Comments: 0

If m rupee coins and n ten paise coins are placed in a line, then the probability that the extreme coins are ten paise coins is

$$\mathrm{If}\:{m}\:\mathrm{rupee}\:\mathrm{coins}\:\mathrm{and}\:{n}\:\mathrm{ten}\:\mathrm{paise}\:\mathrm{coins} \\ $$$$\mathrm{are}\:\mathrm{placed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{line},\:\mathrm{then}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{extreme}\:\mathrm{coins}\:\mathrm{are}\:\mathrm{ten}\:\mathrm{paise}\:\mathrm{coins} \\ $$$$\mathrm{is} \\ $$

Question Number 99136 Answers: 0 Comments: 0

Three persons A, B, C are to speak at a function along with five others. If they all speak in random order, the probqbility that A speaks before B and B speaks before C is

$$\mathrm{Three}\:\mathrm{persons}\:{A},\:{B},\:{C}\:\:\mathrm{are}\:\mathrm{to}\:\mathrm{speak}\:\mathrm{at}\:\mathrm{a} \\ $$$$\mathrm{function}\:\mathrm{along}\:\mathrm{with}\:\mathrm{five}\:\mathrm{others}.\:\mathrm{If}\:\mathrm{they} \\ $$$$\mathrm{all}\:\mathrm{speak}\:\mathrm{in}\:\mathrm{random}\:\mathrm{order},\:\mathrm{the}\:\mathrm{probqbility} \\ $$$$\mathrm{that}\:{A}\:\mathrm{speaks}\:\mathrm{before}\:{B}\:\mathrm{and}\:{B}\:\mathrm{speaks}\: \\ $$$$\mathrm{before}\:{C}\:\mathrm{is} \\ $$

Question Number 99133 Answers: 0 Comments: 0

Equilibrate it using oxydation′s number (NH_4 )_2 Cr_2 O_7 →N_2 +H_2 O+Cr_(2 ) O_7

$${Equilibrate}\:{it}\:{using}\:{oxydation}'{s} \\ $$$${number} \\ $$$$\left({NH}_{\mathrm{4}} \right)_{\mathrm{2}} {Cr}_{\mathrm{2}} {O}_{\mathrm{7}} \rightarrow{N}_{\mathrm{2}} +{H}_{\mathrm{2}} {O}+{Cr}_{\mathrm{2}\:\:} {O}_{\mathrm{7}} \\ $$

Question Number 99123 Answers: 2 Comments: 1

Question Number 99120 Answers: 0 Comments: 2

prove that: ∫_(−(1/2)) ^∞ e^(−(4x^6 +12x^5 +15x^4 +10x^3 +4x^2 +x)) dx =((e)^(1/8) /3)[((Γ((1/6))^((−1)/2) )/(2(2)^(1/3) ))1F2(_(1/3,2/3) ^(1/6) ∣((−1)/(69/2)) ) +((Γ(5/6))/(128(4)^(1/3) ))1F2(_(4/3,5/3) ^(5/6) ∣((−1)/(69/2))) −((√π)/(16))12(_(2/3,4/3) ^(1/2) ∣((−1)/(69/2)))

$${prove}\:{that}: \\ $$$$\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\infty} {e}^{−\left(\mathrm{4}{x}^{\mathrm{6}} +\mathrm{12}{x}^{\mathrm{5}} +\mathrm{15}{x}^{\mathrm{4}} +\mathrm{10}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +{x}\right)} {dx} \\ $$$$=\frac{\sqrt[{\mathrm{8}}]{{e}}}{\mathrm{3}}\left[\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{6}}\right)^{\frac{−\mathrm{1}}{\mathrm{2}}} }{\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{2}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{1}/\mathrm{3},\mathrm{2}/\mathrm{3}} ^{\mathrm{1}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\:\right)\:+\frac{\Gamma\left(\mathrm{5}/\mathrm{6}\right)}{\mathrm{128}\sqrt[{\mathrm{3}}]{\mathrm{4}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{4}/\mathrm{3},\mathrm{5}/\mathrm{3}} ^{\mathrm{5}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\right)\:−\frac{\sqrt{\pi}}{\mathrm{16}}\mathrm{12}\left(_{\mathrm{2}/\mathrm{3},\mathrm{4}/\mathrm{3}} ^{\mathrm{1}/\mathrm{2}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\right)\:\right. \\ $$

Question Number 99118 Answers: 4 Comments: 0

Question Number 99117 Answers: 1 Comments: 0

let a,b,c ∈R determine the minimum value ((3a)/(b+c))+((4b)/(a+c))+((5c)/(a+b))

$${let}\:{a},{b},{c}\:\in\mathbb{R}\:{determine}\:{the}\:{minimum} \\ $$$${value} \\ $$$$ \\ $$$$\frac{\mathrm{3}{a}}{{b}+{c}}+\frac{\mathrm{4}{b}}{{a}+{c}}+\frac{\mathrm{5}{c}}{{a}+{b}} \\ $$

Question Number 99114 Answers: 1 Comments: 0

calculate: ∫(√x)sinh^(−1) (x)dx where sinh^(−1) (x) is the inverse hyperbolic sine function

$${calculate}: \\ $$$$\int\sqrt{{x}}{sinh}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$${where}\:{sinh}^{−\mathrm{1}} \left({x}\right)\:{is}\:{the}\:{inverse}\:{hyperbolic}\: \\ $$$${sine}\:{function} \\ $$$$ \\ $$$$ \\ $$

Question Number 99113 Answers: 2 Comments: 0

solve y^(′′) +5y^′ −3y =x^2 sin(3x) with y(0) =0 and y^′ (0)=−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{5y}^{'} \:−\mathrm{3y}\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{3x}\right)\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)\:=\mathrm{0}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$

Question Number 99102 Answers: 0 Comments: 21

Question Number 99097 Answers: 0 Comments: 1

Hello verry nice day for all of you god bless You pleas Can you use black Color shen You post Quation or Give answer is verry hard to read withe other colors

$${Hello}\: \\ $$$${verry}\:{nice}\:{day}\:{for}\:{all}\:{of}\:{you}\:{god}\:{bless}\:{You} \\ $$$${pleas}\:{Can}\:{you}\:{use}\:{black}\:{Color}\:{shen}\:{You}\:{post}\:{Quation}\: \\ $$$${or}\:{Give}\:{answer}\:{is}\:{verry}\:{hard}\:{to}\:{read}\:{withe}\:{other}\:{colors} \\ $$

Question Number 99095 Answers: 1 Comments: 0

Question Number 99094 Answers: 1 Comments: 0

find ((9+9((9+9((9+9((9+...))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) − (√(8−(√(8−(√(8+(√(8−(√(8−(√(8−(√(8−(√)))))))...))))))))

$$\mathrm{find}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\mathrm{9}\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+...}}}}− \\ $$$$\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}+\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{}}}}...}}}}\: \\ $$

Question Number 99089 Answers: 1 Comments: 0

((9+((9+((9+((9+...))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) ))^(1/(3 )) −(√(8−(√(8−(√(8−(√(8−...))))))))

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}+...}}}}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−\sqrt{\mathrm{8}−...}}}} \\ $$

Pg 1175 Pg 1176 Pg 1177 Pg 1178 Pg 1179 Pg 1180 Pg 1181 Pg 1182 Pg 1183 Pg 1184

Contact: info@tinkutara.com