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Question Number 178064 by aurpeyz last updated on 12/Oct/22 $${A}\:{group}\:{of}\:{n}\:{people}\:{is}\:{categorized}\:{as}\:{follows}. \\ $$$$\mathrm{14}\:{people}\:{are}\:{shorter}\:{than}\:\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}\:{feet} \\ $$$$\mathrm{9}\:{people}\:{are}\:{taller}\:{than}\:\mathrm{6}\:{feet} \\ $$$$\mathrm{12}\:{people}\:{are}\:{under}\:\mathrm{21}\:{years}\:{old}. \\ $$$${if}\:{each}\:{person}\:{in}\:{the}\:{group}\:{is}\:{in}\:{at}\:{least} \\ $$$${one}\:{of}\:{the}\:{three}\:{categories}.\:{then}\:{n}\:{can}\:{be} \\ $$$${any}\:{integer}\:{between}\: \\ $$$${a}.\:\mathrm{9}\:{and}\:\mathrm{14}\:{inclusive} \\…

Question Number 112522 by mathdave last updated on 08/Sep/20 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} \mathrm{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−{x}^{\mathrm{4}} }{dx}=\frac{\mathrm{7}}{\mathrm{8}}\zeta\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{3}} }{\mathrm{32}} \\ $$ Terms of Service Privacy Policy…

Question Number 112521 by Khalmohmmad last updated on 08/Sep/20 $$\mathrm{2}^{\mathrm{x}} =\mathrm{4x}\:\:\:\:\:\: \\ $$ Commented by Khalmohmmad last updated on 08/Sep/20 $$\mathrm{Thank}\:\mathrm{you}\:\mathrm{Myborder} \\ $$ Commented by…

Question Number 46977 by 23kpratik last updated on 03/Nov/18 $$\mathrm{3}{x}+\mathrm{2}\equiv\mathrm{0}\left({mod}\:\mathrm{7}\right) \\ $$ Commented by maxmathsup by imad last updated on 03/Nov/18 $$\mathrm{3}{x}+\mathrm{2}\:=\mathrm{7}{k}\:\:{let}\:{consider}\:{the}\:{congruence}\:{modulo}\:\mathrm{3}\:\Rightarrow\overset{.} {\mathrm{3}}{x}\:+\overset{.} {\mathrm{2}}\:=\overset{.} {\mathrm{7}}{k}\:\Rightarrow…

Question Number 178039 by Alol last updated on 12/Oct/22 Terms of Service Privacy Policy Contact: info@tinkutara.com