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Category: Algebra

I-have-five-envelopes-numbered-3-4-5-6-7-all-hidden-in-a-box-i-picked-an-envelope-If-its-prime-then-i-get-the-square-of-that-number-in-Naira-Otherwise-without-replacement-i-picked-another-env

Question Number 7168 by Tawakalitu. last updated on 14/Aug/16 $${I}\:{have}\:{five}\:{envelopes}\:{numbered}\:\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7}\:{all}\:{hidden}\:{in}\:{a} \\ $$$${box},\:{i}\:{picked}\:{an}\:{envelope}\:.\:\:{If}\:{its}\:{prime}\:{then}\:{i}\:{get}\:{the}\: \\ $$$${square}\:{of}\:{that}\:{number}\:{in}\:{Naira}.\:{Otherwise}\:\left({without}\:\right. \\ $$$$\left.{replacement}\right)\:{i}\:{picked}\:{another}\:{envelope}\:{and}\:{then}\:{get}\:{the} \\ $$$${sum}\:{of}\:{the}\:{squares}\:{of}\:{the}\:{two}\:{numbers}\:{picked}\:\left({in}\:{Naira}\right) \\ $$$${what}\:{is}\:{the}\:{chance}\:{of}\:{me}\:{getting}\:\:{N}\mathrm{25}\:\:? \\ $$$$ \\ $$ Commented…

30-teams-participated-in-the-football-tournament-At-the-end-of-the-competition-it-turned-out-that-in-Any-group-of-three-teams-it-is-possible-to-single-out-two-teams-which-score-equal-point-in-thre

Question Number 7165 by Tawakalitu. last updated on 15/Aug/16 $$\mathrm{30}\:{teams}\:{participated}\:{in}\:{the}\:{football}\:{tournament}\:.\:{At}\:{the}\: \\ $$$${end}\:{of}\:{the}\:{competition}\:{it}\:{turned}\:{out}\:{that}\:{in} \\ $$$${Any}\:{group}\:{of}\:{three}\:\:{teams}\:{it}\:{is}\:{possible}\:{to}\:{single}\:{out}\:{two} \\ $$$${teams}\:{which}\:{score}\:{equal}\:{point}\:{in}\:{three}\:{games}.\: \\ $$$${within}\:{this}\:{group}\:\left(\mathrm{3}\:{points}\:{are}\:{given}\:{for}\:{the}\:{victory},\:\right. \\ $$$$\left.\mathrm{1}\:{point}\:{for}\:{the}\:{draw}\:,\:\mathrm{0}\:{point}\:{for}\:{the}\:{defeat}\:\right).\: \\ $$$${what}\:{is}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{draws}\:{that}\:{can}\:{occur} \\ $$$${in}\:{such}\:{a}\:{tournament}\:? \\…

for-p-q-R-satisfying-p-4-q-4-4pq-find-the-range-of-p-q-when-1-no-restriction-2-0-p-1-0-q-1-

Question Number 138235 by mr W last updated on 11/Apr/21 $${for}\:{p},{q}\in\mathbb{R}\:{satisfying}\:{p}^{\mathrm{4}} +{q}^{\mathrm{4}} =\mathrm{4}{pq} \\ $$$${find}\:{the}\:{range}\:{of}\:{p}+{q}\:{when} \\ $$$$\left.\mathrm{1}\right)\:{no}\:{restriction} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{0}\leqslant{p}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{q}\leqslant\mathrm{1} \\ $$ Answered by mr W…

Question-72689

Question Number 72689 by aliesam last updated on 31/Oct/19 Answered by Tanmay chaudhury last updated on 01/Nov/19 $${IMO}\:\mathrm{2001}\:{question}… \\ $$$${this}\:{question}\:{appeared}\:{in}\:{IMO}\:\mathrm{2001}…{so}\:{pls}\:{search} \\ $$$${you}\:{will}\:{get}\:{solution} \\ $$ Commented…

Question-7147

Question Number 7147 by Tawakalitu. last updated on 13/Aug/16 Commented by Yozzii last updated on 13/Aug/16 $${u}\left({n}\right)=\left(−\mathrm{1}+\mathrm{2}\right)+\left(−\mathrm{3}+\mathrm{4}\right)+\left(−\mathrm{5}+\mathrm{6}\right)+…+\left(−\left(\mathrm{2}{n}−\mathrm{1}\right)+\mathrm{2}{n}\right) \\ $$$${u}\left({n}\right)=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{2}{n}+\mathrm{1}+\mathrm{2}{n}\right)={n} \\ $$$${u}\left(\frac{\mathrm{10}^{\mathrm{9}} }{\mathrm{2}}\right)=\frac{\mathrm{10}^{\mathrm{9}} }{\mathrm{2}}…

Question-7138

Question Number 7138 by Tawakalitu. last updated on 12/Aug/16 Answered by Yozzii last updated on 13/Aug/16 $${x}^{{x}^{\mathrm{2}} } =\mathrm{3}\:\:\left({x}>\mathrm{0}\right) \\ $$$${Let}\:{x}^{\mathrm{2}} ={e}^{{k}} \Rightarrow{x}={e}^{{k}/\mathrm{2}} \\ $$$$\therefore{e}^{\left({k}/\mathrm{2}\right){e}^{{k}}…