Question Number 132854 by EDWIN88 last updated on 17/Feb/21 $$\mathrm{It}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to}\:\mathrm{seat}\:\mathrm{5}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{women}\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{even}\: \\ $$$$\mathrm{place}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{such}\:\mathrm{arrangements}\:\mathrm{are} \\ $$$$\mathrm{possible}\:?\: \\ $$ Answered by bramlexs22 last updated on 17/Feb/21…
Question Number 67281 by Tony Lin last updated on 25/Aug/19 Commented by mr W last updated on 25/Aug/19 $${I}\:{get}\:\mathrm{3}{C}_{\mathrm{2}} ^{\mathrm{5}} +\mathrm{3}{C}_{\mathrm{2}} ^{\mathrm{5}} +\mathrm{12}=\mathrm{72} \\ $$…
Question Number 132726 by 676597498 last updated on 16/Feb/21 $$\mathrm{use}\:\mathrm{error}\:\mathrm{fxn} \\ $$$$\mathrm{use}\:\mathrm{polar}\:\mathrm{coordinates}\:\mathrm{to}\:\mathrm{find} \\ $$$$\int\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1468 by havandip last updated on 11/Aug/15 $$ \\ $$ Answered by 123456 last updated on 11/Aug/15 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)=\mathrm{L} \\ $$$$\forall\epsilon>\mathrm{0},\exists\mathrm{M}\in\mathbb{R},\forall{x}<\mathrm{M},\mid{f}\left({x}\right)−\mathrm{L}\mid<\epsilon \\ $$…
Question Number 132439 by liberty last updated on 14/Feb/21 $$ \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{particular} \\ $$$$\mathrm{machine}\:\mathrm{will}\:\mathrm{make}\:\mathrm{product}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{90\%}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{running}\:\mathrm{well},\:\:\mathrm{but}\:\mathrm{will}\:\mathrm{do}\:\mathrm{so}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\:\mathrm{rate}\:\mathrm{of}\:\mathrm{only}\:\mathrm{30\%}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{not}\:\mathrm{running}\:\mathrm{well}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{machine}\:\mathrm{is}\: \\…
Question Number 132382 by liberty last updated on 13/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{x}^{\mathrm{10}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{8}} \\ $$ Answered by EDWIN88 last updated on 13/Feb/21 $$\mathrm{by}\:\mathrm{multinomial}\:\mathrm{theorem}\:;\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{10}} \\…
Question Number 132174 by EDWIN88 last updated on 12/Feb/21 Commented by EDWIN88 last updated on 12/Feb/21 $$\mathrm{old}\:\mathrm{unswered} \\ $$ Commented by mr W last updated…
Question Number 1074 by Yugi last updated on 05/Jun/15 $${Prove}\:{by}\:{induction}\:{the}\:{following}\:{result}\:{where}\:{N}\:{is}\:{a}\:{positive}\:{even}\:{integer}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}_{\mathrm{1}} ^{\mathrm{2}} +{S}_{\mathrm{2}} ^{\mathrm{2}} =\mathrm{2}^{{N}} \\ $$$${where}\:\:\:\:{S}_{\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{\frac{{N}}{\mathrm{2}}+\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \begin{pmatrix}{{N}}\\{\mathrm{2}\left({r}−\mathrm{1}\right)}\end{pmatrix}\:\:\:\:{and}\:\:\:\:\:\:{S}_{\mathrm{2}} =\underset{{r}=\mathrm{1}} {\overset{{N}/\mathrm{2}} {\sum}}\left(−\mathrm{1}\right)^{{r}+\mathrm{1}}…
Question Number 66549 by aditya@345 last updated on 17/Aug/19 $$\frac{\mathrm{n}^{\mathrm{2}} !}{\left(\mathrm{n}!\right)^{\mathrm{n}} }=\mathrm{natural}\:\mathrm{number}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131994 by liberty last updated on 10/Feb/21 Commented by liberty last updated on 10/Feb/21 $$\mathrm{old}\:\mathrm{unswered} \\ $$ Answered by EDWIN88 last updated on…