Question Number 203832 by depressiveshrek last updated on 29/Jan/24 $$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10}\:\mathrm{do}\:\mathrm{not} \\ $$$$\mathrm{have}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$ Answered by nikif99 last updated on 30/Jan/24 $${Total}\:{number}\:{of}\:{bit}\:{strings}\:{of}\:{length}\:\mathrm{10} \\ $$$${is}\:\mathrm{2}^{\mathrm{10}} =\mathrm{1024}\:\left(\mathrm{0}−\mathrm{1023}\right).…
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Question Number 202584 by cortano12 last updated on 30/Dec/23 $$\:\:\: \\ $$ Answered by dimentri last updated on 30/Dec/23 $$\mathrm{2}\:\begin{pmatrix}{\mathrm{m}}\\{\mathrm{2}}\end{pmatrix}\:−\:\mathrm{4m}\:=\:\mathrm{84} \\ $$$$\:\mathrm{m}^{\mathrm{2}} −\mathrm{5m}−\mathrm{84}\:=\:\mathrm{0} \\ $$$$\:\mathrm{m}\:=\:\mathrm{12}\:…
Question Number 202598 by cortano12 last updated on 30/Dec/23 Answered by MM42 last updated on 30/Dec/23 $$\mathrm{780}\: \\ $$$$ \\ $$ Commented by MM42 last…
Question Number 202374 by Calculusboy last updated on 25/Dec/23 Commented by Frix last updated on 25/Dec/23 $${x}^{\mathrm{3}} +{px}+{q}=\mathrm{0} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{3}} {\sum}}\:\frac{\left(\mathrm{1}+{x}_{{k}} \right)^{\mathrm{2}} }{\left(\mathrm{1}−{x}_{{k}} \right)^{\mathrm{2}}…
Question Number 202257 by cortano12 last updated on 23/Dec/23 Commented by Frix last updated on 23/Dec/23 Each wife is specific �� Commented by mr W last updated on 22/Apr/24…
Question Number 201839 by depressiveshrek last updated on 14/Dec/23 Commented by depressiveshrek last updated on 14/Dec/23 $${The}\:{last}\:{one}\:{means}: \\ $$$$\underset{{i}=\mathrm{0}} {\overset{{k}} {\sum}}{i}^{\mathrm{2}} \begin{pmatrix}{{k}}\\{{i}}\end{pmatrix}={k}\left({k}+\mathrm{1}\right)\mathrm{2}^{{k}−\mathrm{2}} \\ $$ Terms…
Question Number 200051 by cortano12 last updated on 13/Nov/23 $$ \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{arrange}\:\mathrm{3}\:\mathrm{red} \\ $$$$\:\mathrm{balls}\:\mathrm{and}\:\mathrm{9}\:\mathrm{black}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{2} \\ $$$$\mathrm{black}\:\mathrm{balls}\:\mathrm{between}\:\mathrm{2}\:\mathrm{adjacent}\:\mathrm{red} \\ $$$$\mathrm{balls}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{180}×\mathrm{8}!\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{240}×\mathrm{7}!\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{364}×\mathrm{6}! \\ $$$$\:\left(\mathrm{d}\right)\:\mathrm{282}×\mathrm{4}!\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{144}×\mathrm{5}!\: \\…
Question Number 199353 by mr W last updated on 01/Nov/23 $${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{exactly}\:{a}\: \\ $$$${group}\:{of}\:{exactly}\:\mathrm{3}\:{people}\:{born}\:{on}\:{the} \\ $$$${same}\:{day}\:{of}\:{the}\:{week}? \\ $$ Commented by AST last updated on…
Question Number 199337 by cortano12 last updated on 01/Nov/23 Answered by mr W last updated on 01/Nov/23 $$\left.\mathrm{3}\right) \\ $$$${odd}:\:\mathrm{5}×\mathrm{6}^{\mathrm{5}} \\ $$$${even}:\:\mathrm{2}×\mathrm{6}^{\mathrm{5}} \\ $$$$\frac{{odd}}{{even}}=\frac{\mathrm{5}}{\mathrm{2}} \\…