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Category: Set Theory

Q-Choose-at-least-some-members-frome-the-set-A-14-15-20-22-23-28-so-that-whith-confidence-includes-three-consecutive-members-

Question Number 209746 by MM42 last updated on 21/Jul/24 $$\left.{Q}\right){Choose}\:{at}\:{least}\:{some}\:{members} \\ $$$${frome}\:{the}\:{set}\:{A}=\left\{\mathrm{14},\mathrm{15},…,\mathrm{20},\mathrm{22},\mathrm{23},…,\mathrm{28}\right\} \\ $$$${so}\:{that}\:{whith}\:{confidence}\:\:{includes}\:{three}\:{consecutive} \\ $$$${members}? \\ $$ Commented by MM42 last updated on 20/Jul/24…

Find-f-x-x-0-dt-t-e-f-t-

Question Number 209246 by Erico last updated on 05/Jul/24 $$\mathrm{Find}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{t}+\mathrm{e}^{\mathrm{f}\left(\mathrm{t}\right)} } \\ $$ Answered by mr W last updated on 06/Jul/24 $${f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}}…

Question-207864

Question Number 207864 by efronzo1 last updated on 29/May/24 $$\:\:\:\:\:\underbrace{\:} \\ $$ Answered by Rasheed.Sindhi last updated on 29/May/24 $$\mathrm{2}^{\mathrm{5}{m}} \centerdot\mathrm{5}^{\mathrm{2}{n}} \centerdot{k}=\mathrm{2020}^{\mathrm{2020}} =\left(\mathrm{2}^{\mathrm{2}} .\mathrm{5}.\mathrm{101}\right)^{\mathrm{2020}} \\…

2-students-are-passing-a-test-of-n-questions-with-the-same-chance-to-find-each-one-Show-the-chance-that-they-both-don-t-find-a-same-question-is-3-4-n-

Question Number 207372 by sniper237 last updated on 12/May/24 $$\mathrm{2}\:{students}\:{are}\:{passing}\: \\ $$$${a}\:{test}\:{of}\:\:{n}\:{questions}\:{with} \\ $$$${the}\:{same}\:{chance}\:{to}\:{find}\:{each}\:{one} \\ $$$${Show}\:\:{the}\:{chance}\:{that}\:{they}\:{both} \\ $$$$\:{don}'{t}\:{find}\:{a}\:{same}\:{question}\:{is}\:\:\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \\ $$ Commented by A5T last updated…

1-3-5-7-9-2005-mod-1000-

Question Number 203490 by cortano12 last updated on 20/Jan/24 $$\:\:\:\:\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×…×\mathrm{2005}\:=\:…\:\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$ Answered by AST last updated on 20/Jan/24 $${x}=\mathrm{1}×\mathrm{3}×\mathrm{5}…×\mathrm{2005}\equiv\mathrm{0}\left({mod}\:\mathrm{125}\right) \\ $$$${x}\equiv\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}\right)^{\mathrm{250}} ×\mathrm{1}×\mathrm{3}×\mathrm{5}\left({mod}\:\mathrm{8}\right)\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right) \\ $$$${x}=\mathrm{125}{q}\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right)\Rightarrow\mathrm{5}{q}\equiv\mathrm{15}\left({mod}\:\mathrm{8}\right)\Rightarrow{q}\equiv\mathrm{3}\left({mod}\:\mathrm{8}\right)…