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…
Question Number 204141 by Tawa11 last updated on 06/Feb/24 Answered by AST last updated on 07/Feb/24 $${A}_{\mathrm{3}} \cap{A}_{−\mathrm{3}} =\left(−\infty,−\mathrm{3}\right]=\cap_{{i}=−\mathrm{3}} ^{\mathrm{3}} \\ $$ Commented by Tawa11…
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Question Number 203634 by cortano12 last updated on 24/Jan/24 $$\:\:\: \\ $$ Answered by Frix last updated on 24/Jan/24 $$\frac{\mathrm{2}^{{n}^{\mathrm{2}} } −\mathrm{1}}{\mathrm{2}^{{n}} −\mathrm{1}}\approx\mathrm{2}^{{n}^{\mathrm{2}} −{n}} \:\Rightarrow\:{k}=\mathrm{271}…
Question Number 203490 by cortano12 last updated on 20/Jan/24 $$\:\:\:\:\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) \\ $$$${x}\equiv\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}\right)^{\mathrm{250}} ×\mathrm{1}×\mathrm{3}×\mathrm{5}\left({mod}\:\mathrm{8}\right)\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right) \\ $$$${x}=\mathrm{125}{q}\equiv\mathrm{7}\left({mod}\:\mathrm{8}\right)\Rightarrow\mathrm{5}{q}\equiv\mathrm{15}\left({mod}\:\mathrm{8}\right)\Rightarrow{q}\equiv\mathrm{3}\left({mod}\:\mathrm{8}\right)…
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Question Number 200284 by depressiveshrek last updated on 16/Nov/23 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{set}\:{A}\:\mathrm{containing}\:{n} \\ $$$$\mathrm{elements},\:\mid\mathcal{P}\left({A}\right)\mid=\mathrm{2}^{{n}} . \\ $$ Answered by AST last updated on 16/Nov/23 $${C}_{\mathrm{0}} ^{{n}} +^{{n}}…
Question Number 199624 by pascal889 last updated on 06/Nov/23 Commented by mr W last updated on 06/Nov/23 $${you}\:{have}\:{posted}\:{the}\:{same}\:{question} \\ $$$${one}\:{time}\:{and}\:{a}\:{comment}\:{was}\:{given}. \\ $$$${why}\:{don}'{t}\:{you}\:{check}\:{if}\:{your}\:{question} \\ $$$${is}\:{wrong}?\:{maybe}\:{the}\:{question}\:{is} \\…
Question Number 198550 by HomeAlone last updated on 21/Oct/23 Commented by HomeAlone last updated on 21/Oct/23 $${also}\:{C}_{\mathrm{2}} \:{using}\:{F}\:{and}\:\mathrm{oxygen}\:\boldsymbol{\mathrm{gx}}_{\mathrm{2}} \\ $$ Terms of Service Privacy Policy…
Question Number 198380 by pascal889 last updated on 18/Oct/23 Commented by Rasheed.Sindhi last updated on 18/Oct/23 $$\mathbb{U}=? \\ $$$${Universal}\:{set}\:{is}\:{not}\:{given} \\ $$ Commented by AST last…