Question Number 178395 by mr W last updated on 16/Oct/22 $${How}\:{many}\:\mathrm{5}\:{digit}\:{numbers}\:{with} \\ $$$${different}\:{digits}\:{are}\:{multiple}\:{of}\:\mathrm{9}? \\ $$ Answered by cortano1 last updated on 16/Oct/22 $$\left(\mathrm{1}\right)\mathrm{1}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}\Rightarrow\mathrm{5}! \\ $$$$\left(\mathrm{2}\right)\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{8}\Rightarrow\mathrm{5}!…
Question Number 112812 by Aina Samuel Temidayo last updated on 09/Sep/20 $$\mathrm{There}\:\mathrm{are}\:\mathrm{2016}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{drawn}\:\mathrm{on} \\ $$$$\mathrm{a}\:\mathrm{board}\:\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{are} \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\mathrm{one}\:\mathrm{another}.\:\frac{\mathrm{3}}{\mathrm{8}}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{meet}\:\mathrm{at}\:\mathrm{a}\:\mathrm{point}\:\mathrm{and}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{ones}\:\mathrm{intersect}\:\mathrm{with}\:\mathrm{all} \\ $$$$\mathrm{other}\:\mathrm{lines}\:\mathrm{on}\:\mathrm{the}\:\mathrm{board}.\:\mathrm{Determine} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{intersections} \\…
Question Number 178173 by cortano1 last updated on 13/Oct/22 Answered by Acem last updated on 13/Oct/22 $$\:{No}.\mathrm{1},\:{NumWrds}_{\mathrm{5}\ell{s}} =\:{P}_{\mathrm{21}} ^{\:\mathrm{3}} ×{P}_{\mathrm{5}} ^{\:\mathrm{2}} =\:\mathrm{159}\:\mathrm{600}\:{words} \\ $$$$ \\…
Question Number 112538 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by floor(10²Eta[1]) last updated on 08/Sep/20 $$=\mathrm{log}_{\mathrm{n}} \mathrm{2}+\mathrm{2log}_{\mathrm{n}} \mathrm{2}+\mathrm{3log}_{\mathrm{n}} \mathrm{2}+…+\mathrm{2015log}_{\mathrm{n}} \mathrm{2} \\ $$$$=\mathrm{log}_{\mathrm{n}}…
Question Number 112534 by Aina Samuel Temidayo last updated on 08/Sep/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{points}\:\mathrm{to}\:\mathrm{be}\:\mathrm{distributed}\:\mathrm{within} \\ $$$$\mathrm{a}\:\mathrm{3}×\mathrm{6}\:\mathrm{to}\:\mathrm{ensure}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{two} \\ $$$$\mathrm{points}\:\mathrm{whose}\:\mathrm{distance}\:\mathrm{apart}\:\mathrm{is}\:\mathrm{less} \\ $$$$\mathrm{than}\:\sqrt{\mathrm{2}}? \\ $$ Commented by Aina…
Question Number 112533 by Aina Samuel Temidayo last updated on 08/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{number}\:\mathrm{of}\:\mathrm{n} \\ $$$$\mathrm{integers}\:\mathrm{to}\:\mathrm{be}\:\mathrm{selected}\:\mathrm{from} \\ $$$$\mathrm{S}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},…\mathrm{11}\right\}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{difference} \\ $$$$\mathrm{of}\:\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{n}\:\mathrm{integers}\:\mathrm{is}\:\mathrm{7}. \\ $$ Commented by Aina Samuel Temidayo…
Question Number 112531 by Aina Samuel Temidayo last updated on 08/Sep/20 $$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{cardboard}\:\mathrm{is}\:\mathrm{8cm}\:\mathrm{long} \\ $$$$\mathrm{and}\:\mathrm{6cm}\:\mathrm{wide}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{beads}\:\mathrm{you}\:\mathrm{can}\:\mathrm{arrange}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{board}\:\mathrm{such}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{beads}\:\mathrm{that}\:\mathrm{are}\:\mathrm{less}\:\mathrm{than} \\ $$$$\sqrt{\mathrm{10}}\mathrm{cm}\:\mathrm{apart}. \\ $$ Commented…
Question Number 112195 by 675480065 last updated on 06/Sep/20 $$\underset{\mathrm{n}=\mathrm{1}\:} {\overset{\mathrm{11}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} \left(\mathrm{4n}+\mathrm{2}\right)}{\mathrm{4n}\left(\mathrm{n}+\mathrm{1}\right)} \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$ Answered by MJS_new last updated on 06/Sep/20 $$\mathrm{simply}\:\mathrm{calculate}\:\mathrm{it}!\:\mathrm{it}'\mathrm{s}\:\mathrm{only}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{11}…
Question Number 177597 by cortano1 last updated on 07/Oct/22 Answered by mr W last updated on 07/Oct/22 $$\boldsymbol{{method}}\:\mathrm{1}:\:\boldsymbol{{without}}\:\boldsymbol{{using}}\:\boldsymbol{{formula}} \\ $$$$\mathrm{1}×\mathrm{1}×{C}_{\mathrm{3}} ^{\mathrm{6}} ×\mathrm{2}^{\mathrm{3}} \\ $$$$+\left[\mathrm{1}×\left(−\mathrm{1}\right)+\mathrm{3}×\mathrm{1}\right]×{C}_{\mathrm{2}} ^{\mathrm{6}}…
Question Number 111937 by bemath last updated on 05/Sep/20 Answered by bobhans last updated on 05/Sep/20 $$\:\mathrm{let}\:\mathrm{the}\:\mathrm{first}\:\mathrm{five}\:\mathrm{question}\:\mathrm{is}\:\mathrm{number}\::\: \\ $$$$\mathrm{1};\:\mathrm{2};\:\mathrm{3};\:\mathrm{4};\:\mathrm{5}\: \\ $$$$\mathrm{case}\left(\mathrm{1}\right)\:\Rightarrow\:\mathrm{C}\:_{\mathrm{4}} ^{\mathrm{5}} \:×\:\mathrm{C}\:_{\mathrm{4}} ^{\mathrm{5}} \:=\:\mathrm{25}\:…