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Category: Arithmetic

A-certain-preliminary-science-class-contains-50-students-all-of-whom-take-Mathematics-18-study-Chemistry-17-study-Biology-24-study-Physics-Of-those-taking-three-subjects-5-study-Physics-and-Chemi

Question Number 198321 by necx122 last updated on 17/Oct/23 $${A}\:{certain}\:{preliminary}\:{science}\:{class} \\ $$$${contains}\:\mathrm{50}\:{students}\:{all}\:{of}\:{whom}\:{take} \\ $$$${Mathematics}.\:\mathrm{18}\:{study}\:{Chemistry},\:\mathrm{17} \\ $$$${study}\:{Biology},\:\mathrm{24}\:{study}\:{Physics}.\:{Of} \\ $$$${those}\:{taking}\:{three}\:{subjects},\:\mathrm{5}\:{study} \\ $$$${Physics}\:{and}\:{Chemistry},\:\mathrm{7}\:{study}\:{Physics} \\ $$$${and}\:{Biology}\:{and}\:\mathrm{6}\:{study}\:{Chemistry} \\ $$$${and}\:{Biology}\:{while}\:\mathrm{2}\:{take}\:{all}\:{four}\:{subjects}. \\…

An-analysis-of-100-personal-injury-claims-made-upon-a-motor-insurance-company-revealed-that-loss-or-injury-in-respect-of-an-eye-an-arm-or-leg-occurred-in-30-50-and-70-cases-respectively-Claims-inv

Question Number 198319 by necx122 last updated on 17/Oct/23 $${An}\:{analysis}\:{of}\:\mathrm{100}\:{personal}\:{injury} \\ $$$${claims}\:{made}\:{upon}\:{a}\:{motor}\:{insurance} \\ $$$${company}\:{revealed}\:{that}\:{loss}\:{or}\:{injury} \\ $$$${in}\:{respect}\:{of}\:{an}\:{eye},\:{an}\:{arm}\:{or}\:{leg} \\ $$$${occurred}\:{in}\:\mathrm{30},\:\mathrm{50}\:{and}\:\mathrm{70}\:{cases},\:{respectively}. \\ $$$${Claims}\:{involving}\:{the}\:{loss}\:{or}\:{injury}\:{to} \\ $$$${two}\:{of}\:{these}\:{number}\:\mathrm{44}.\:{How}\:{many} \\ $$$${claims}\:{involved}\:{loss}\:{or}\:{injury}\:{to}\:{all} \\…

A-father-reduced-the-quantity-of-food-bought-for-the-family-by-10-when-he-found-that-the-cost-of-living-had-increased-by-15-What-is-the-fractional-increase-in-the-family-food-bill-

Question Number 198067 by necx122 last updated on 09/Oct/23 $${A}\:{father}\:{reduced}\:{the}\:{quantity}\:{of}\:{food} \\ $$$${bought}\:{for}\:{the}\:{family}\:{by}\:\mathrm{10\%}\:{when}\:{he} \\ $$$${found}\:{that}\:{the}\:{cost}\:{of}\:{living}\:{had} \\ $$$${increased}\:{by}\:\mathrm{15\%}.\:{What}\:{is}\:{the}\:{fractional} \\ $$$${increase}\:{in}\:{the}\:{family}\:{food}\:{bill}? \\ $$ Answered by yogamulyadi last updated…

If-f-x-sin-x-x-and-S-n-k-1-n-f-kpi-pi-f-kpi-pi-gt-1-Prove-that-lim-n-S-n-1-f-pi-

Question Number 197323 by Erico last updated on 13/Sep/23 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\:\mathrm{and}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\mathrm{f}\left(\mathrm{k}\pi+\frac{\pi}{\alpha}\right)+\mathrm{f}\left(\mathrm{k}\pi−\frac{\pi}{\alpha}\right)\right]\:\:\:\:\left(\alpha>\mathrm{1}\right) \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{n}\rightarrow+\infty} {\:\mathrm{lim}}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\mathrm{1}−\mathrm{f}\left(\frac{\pi}{\alpha}\right) \\ $$ Answered by witcher3 last updated on…

calcul-0-ln-cht-sh-t-dt-

Question Number 197247 by Erico last updated on 11/Sep/23 $$\mathrm{calcul}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{{ln}\left({cht}\right)}{{sh}\left({t}\right)}{dt} \\ $$ Answered by witcher3 last updated on 11/Sep/23 $$=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{ch}\left(\mathrm{t}\right)\right)\mathrm{sh}\left(\mathrm{t}\right)}{\mathrm{1}−\mathrm{ch}^{\mathrm{2}} \left(\mathrm{x}\right)}…