Question Number 182199 by depressiveshrek last updated on 05/Dec/22 $${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{7}\right\} \\ $$$${If}\:{we}\:{multiply}\:{atleast}\:\mathrm{2}\:{numbers} \\ $$$${from}\:{this}\:{set}\:{with}\:{each}\:{other},\:{what} \\ $$$${are}\:{the}\:{chances}\:{of}\:{the}\:{product}\:{to} \\ $$$${turn}\:{out}\:{to}\:{be}\:{divisible}\:{by}\:\mathrm{3}? \\ $$ Answered by Acem last updated…
Question Number 50960 by kaivan.ahmadi last updated on 22/Dec/18 $$\mathrm{4}\:\:\:\left(\mathrm{3}\right)\:\:\:\:\mathrm{2} \\ $$$$\mathrm{5}\:\:\:\:\mathrm{3}\:\:\:\left(?\right)\:\:\mathrm{1}\:\:\:\:\mathrm{1} \\ $$$$\mathrm{6}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\left(\mathrm{8}\right)\:\:\:\:?\:\:\:\:\:?\:\:\:\:\:\mathrm{1} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{each}\:\:\:? \\ $$ Terms of Service Privacy Policy…
Question Number 116356 by bemath last updated on 03/Oct/20 $$\mathrm{Let}\:\mathrm{S}\:=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},…,\mathrm{48},\mathrm{49}\right\}\:.\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{select}\:\mathrm{n}\:\mathrm{numbers}\: \\ $$$$\mathrm{from}\:\mathrm{S}\:\mathrm{and}\:\mathrm{arrange}\:\mathrm{them}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of} \\ $$$$\mathrm{any}\:\mathrm{two}\:\mathrm{adjacent}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}\:\mathrm{100}? \\ $$ Terms…
Question Number 181313 by a.lgnaoui last updated on 23/Nov/22 $${Montrer}\:{que} \\ $$$$\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{2}^{{n}+\mathrm{2}} \:\:\:{est}\:{divisible}\:{par}\:\mathrm{7} \\ $$ Answered by mr W last updated on 23/Nov/22 $$\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}}…
Question Number 115742 by bemath last updated on 28/Sep/20 $${what}\:{the}\:{cooefficient}\:{of}\:{x}^{\mathrm{10}} \:{from} \\ $$$$\left(\mathrm{1}+{x}\right)×\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)×\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right)×…×\left(\mathrm{1}+\mathrm{2020}{x}^{\mathrm{2020}} \right) \\ $$ Answered by mr W last updated on…
Question Number 180877 by Sheshdevsahu last updated on 18/Nov/22 $$\boldsymbol{\mathrm{Q}}.\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{integers}}\:\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}}\:>\:\mathrm{1}\:\boldsymbol{\mathrm{satisfy}}. \\ $$$$\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{b}}} .\boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{a}}} \:+\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{b}}} \:+\:\boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{a}}} \:=\:\mathrm{5329} \\ $$ Commented by MJS_new last updated…
Question Number 180776 by Acem last updated on 17/Nov/22 $${Simplify}\:\:\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}}\: \\ $$$$ \\ $$ Answered by BaliramKumar last updated on 17/Nov/22 $$\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}\:} \\ $$$$\sqrt{\mathrm{2}\sqrt{\mathrm{2}\:}\:+\:\mathrm{3}\:} \\…
Question Number 180746 by Acem last updated on 16/Nov/22 Answered by MJS_new last updated on 16/Nov/22 $$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{200}}\right)^{\mathrm{200}} >\mathrm{2} \\ $$$$\mathrm{because}\:\mathrm{we}\:\mathrm{know} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}}\right)^{\mathrm{1}} =\mathrm{2} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}}…
Question Number 115033 by bobhans last updated on 23/Sep/20 $${If}\:{a}\:{and}\:{b}\:{positive}\:{real}\:{number}\:{where} \\ $$$${a}^{\mathrm{505}} \:+\:{b}^{\mathrm{505}} \:=\:\mathrm{1},\:{then}\:{minimum}\:{value} \\ $$$${a}^{\mathrm{2020}} \:+\:{b}^{\mathrm{2020}} \:{is}\:\_\_ \\ $$ Answered by 1549442205PVT last updated…
Question Number 180115 by universe last updated on 07/Nov/22 Answered by mr W last updated on 07/Nov/22 $$\mathrm{7}×\mathrm{6}×\mathrm{4}×\mathrm{5}×\mathrm{2}=\mathrm{1680} \\ $$$$=\mathrm{40}×\mathrm{42}=\left(\mathrm{42}−\mathrm{1}\right)\left(\mathrm{41}+\mathrm{1}\right)=\mathrm{41}^{\mathrm{2}} −\mathrm{1} \\ $$$$\Rightarrow\:\left({d}\right) \\ $$…