Question Number 6610 by Temp last updated on 05/Jul/16 $$\mathrm{If}\:\mathrm{you}\:\mathrm{have}\:\mathrm{a}\:\mathrm{real}\:\mathrm{continuous}\:\mathrm{function}\:{f}\left({x}\right), \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{take}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{between} \\ $$$${f}\left({x}\right)\:\mathrm{and}\:{f}\left({x}+\mathrm{1}\right),\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{average} \\ $$$$\mathrm{distance}\:\mathrm{within}\:{a}\leqslant{x}\leqslant{b}? \\ $$ Commented by Temp last updated on 05/Jul/16…
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Question Number 6609 by Temp last updated on 05/Jul/16 $$\mathrm{You}\:\mathrm{have}\:\mathrm{a}\:\mathrm{1×1}\:\mathrm{cm}\:\mathrm{square}.\:\mathrm{If}\:\mathrm{you}\:\mathrm{pick} \\ $$$$\mathrm{two}\:\mathrm{random}\:\mathrm{points}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{square}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{average}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{those}\:\mathrm{points}? \\ $$ Commented by prakash jain last updated on…
Question Number 72145 by Maclaurin Stickker last updated on 25/Oct/19 $${prove}\:{that}: \\ $$$$\mathrm{cos}\:\alpha×\mathrm{cos}\:\mathrm{2}\alpha×{cos}\:\mathrm{2}^{\mathrm{2}} \alpha…{cos}\:\mathrm{2}^{{n}} \alpha \\ $$$$=\frac{\mathrm{sin}\:\mathrm{2}^{{n}+\mathrm{1}} \alpha}{\mathrm{2}^{{n}+\mathrm{1}} \mathrm{sin}\:\alpha} \\ $$$$ \\ $$ Commented by…
Question Number 6605 by WAI LIN last updated on 05/Jul/16 $${Let}\:{c}\:{be}\:{a}\:{constant}.\:{Using}\:{Var}\left({X}\right)\:=\:{E}\:\left[\left({X}−\:{E}\:\left[{X}\right]\right)^{\mathrm{2}} \right],\:{show}\:{that} \\ $$$$\left({a}\right)\:{Var}\left({c}\:{X}\right)\:=\:{c}^{\mathrm{2}} \:{Var}\left({X}\right); \\ $$$$\left({b}\right)\:{Var}\:\left(\:{c}+{X}\right)\:=\:{Var}\left({X}\right). \\ $$ Commented by prakash jain last updated…
Question Number 137678 by otchereabdullai@gmail.com last updated on 05/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{4x}−\mathrm{5}=\mathrm{a}+\left(\mathrm{a}+\mathrm{b}\right)^{\mathrm{2}} \\ $$ Commented by mr W last updated on 05/Apr/21 $${LHS}\:{is}\:{a}\:{function}!\:{you}\:{can}\:{not}\: \\…
Question Number 6604 by WAI LIN last updated on 05/Jul/16 $${If}\:{the}\:{density}\:{function}\:{of}\:{X}\:{equals} \\ $$$${f}\left({x}\right)\:=\:\begin{cases}{{c}\:{e}^{−\mathrm{2}{x}} \:,\:\mathrm{0}<{x}<\infty}\\{\mathrm{0}\:,\:\:\:\:\:\:\:\:\:\:{x}<\mathrm{0}}\end{cases} \\ $$$${find}\:{c}.\:{What}\:{is}\:{P}\left\{{X}>\mathrm{2}\right\}? \\ $$ Commented by prakash jain last updated on…
Question Number 6602 by cindycastro last updated on 05/Jul/16 $$\%{ml} \\ $$ Commented by Temp last updated on 05/Jul/16 $$=\frac{{ml}}{\mathrm{100}} \\ $$ Terms of Service…
Question Number 6599 by WAI LIN last updated on 05/Jul/16 $${Prove}\:{that}\:\underset{{j}=\mathrm{1}} {\overset{{N}} {\sum}}\left({X}_{{j}} −\mathrm{1}\right)^{\mathrm{2}} \:=\underset{{j}=\mathrm{1}} {\overset{{N}} {\sum}}\:{X}_{{j}} ^{\mathrm{2}} \:−\:\mathrm{2}\:\underset{{j}=\mathrm{1}} {\overset{{N}} {\sum}}\:{X}_{{j}} \:+\:{N}. \\ $$ Answered…
Question Number 137668 by mnjuly1970 last updated on 05/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{advanced}\:…\:…\:…\:…\:{calculus}…. \\ $$$$\:\:{prove}\:{that}:::::\:\ast\ast\ast\ast\ast \\ $$$$\:\:\:\:\boldsymbol{\Omega}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\Gamma\left({n}+\mathrm{1}\right)\Gamma\left({x}+\mathrm{1}\right)}{\left({n}+\mathrm{1}\right)\Gamma\left({n}+{x}+\mathrm{2}\right)}=\psi'\left({x}+\mathrm{1}\right) \\ $$$${proof}:: \\ $$$$\:\:\:\:\Omega=\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\frac{\beta\:\left({n}+\mathrm{1},{x}+\mathrm{1}\right)}{{n}+\mathrm{1}}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left\{\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)}\int_{\mathrm{0}} ^{\:\mathrm{1}}…