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Question Number 160090 Answers: 0 Comments: 2

There are 40 oranges, 20 apples, and 20 lemons in a bag. What is the minimum number of fruits that you have to take out of the bag with your eyes closed before you are sure that one of them is an orange?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{40}\:\mathrm{oranges},\:\mathrm{20}\:\mathrm{apples},\:\mathrm{and}\: \\ $$$$\mathrm{20}\:\mathrm{lemons}\:\mathrm{in}\:\mathrm{a}\:\mathrm{bag}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{minimum}\:\mathrm{number}\:\mathrm{of}\:\mathrm{fruits}\:\mathrm{that}\:\mathrm{you}\: \\ $$$$\mathrm{have}\:\mathrm{to}\:\mathrm{take}\:\mathrm{out}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{with}\:\mathrm{your}\: \\ $$$$\mathrm{eyes}\:\mathrm{closed}\:\mathrm{before}\:\mathrm{you}\:\mathrm{are}\:\mathrm{sure}\:\mathrm{that}\: \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{them}\:\mathrm{is}\:\mathrm{an}\:\mathrm{orange}? \\ $$

Question Number 159125 Answers: 0 Comments: 3

for a, b, c >0 and a+b+c=2 find min(2ab^2 +b^3 c, 2bc^2 +c^3 a, 2ca^2 +a^3 b) or disprove that such a minimum doesn′t exist.

$${for}\:{a},\:{b},\:{c}\:>\mathrm{0}\:{and}\:{a}+{b}+{c}=\mathrm{2} \\ $$$${find}\:{min}\left(\mathrm{2}{ab}^{\mathrm{2}} +{b}^{\mathrm{3}} {c},\:\mathrm{2}{bc}^{\mathrm{2}} +{c}^{\mathrm{3}} {a},\:\mathrm{2}{ca}^{\mathrm{2}} +{a}^{\mathrm{3}} {b}\right) \\ $$$${or}\:{disprove}\:{that}\:{such}\:{a}\:{minimum} \\ $$$${doesn}'{t}\:{exist}. \\ $$

Question Number 159106 Answers: 0 Comments: 0

∫_0 ^π ((sin(nz))/(z^4 sin(πz)))dz

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{sin}\left({nz}\right)}{\mathrm{z}^{\mathrm{4}} \mathrm{sin}\left(\pi{z}\right)}{dz} \\ $$

Question Number 159099 Answers: 1 Comments: 0

Question Number 159097 Answers: 0 Comments: 0

f(x)=log_(2 ) ^x (((x^2 −1)/( (√(x+1)))))+∣x∣^2

$${f}\left({x}\right)={log}_{\mathrm{2}\:} ^{{x}} \left(\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\:\sqrt{{x}+\mathrm{1}}}\right)+\mid{x}\mid^{\mathrm{2}} \\ $$

Question Number 159092 Answers: 1 Comments: 0

Question Number 159087 Answers: 0 Comments: 0

Question Number 159086 Answers: 0 Comments: 0

Question Number 159085 Answers: 1 Comments: 0

Question Number 159080 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (1/(n!(n^4 +n^2 +1)))=?

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}!\left(\mathrm{n}^{\mathrm{4}} +\mathrm{n}^{\mathrm{2}} +\mathrm{1}\right)}=? \\ $$

Question Number 159079 Answers: 1 Comments: 0

Prove that 2+(√3) , (((√3)−2)/3) and (1/( (√3)−5)) are the number irrational

$${Prove}\:{that}\:\:\mathrm{2}+\sqrt{\mathrm{3}}\:,\:\frac{\sqrt{\mathrm{3}}−\mathrm{2}}{\mathrm{3}}\:\:{and}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}−\mathrm{5}}\: \\ $$$${are}\:{the}\:{number}\:{irrational} \\ $$

Question Number 159078 Answers: 0 Comments: 0

1) Prove by recurrence that for n≥28, n!≥11^n 2) On subtract the limit of the suite (((n!)/(10^n ))) when n tended at +∞

$$\left.\mathrm{1}\right)\:{Prove}\:{by}\:{recurrence}\:{that}\: \\ $$$${for}\:{n}\geqslant\mathrm{28},\:\:\:{n}!\geqslant\mathrm{11}^{{n}} \: \\ $$$$\left.\mathrm{2}\right)\:{On}\:{subtract}\:{the}\:{limit}\:{of}\:{the}\: \\ $$$${suite}\:\left(\frac{{n}!}{\mathrm{10}^{{n}} }\right)\:{when}\:{n}\:{tended}\:{at}\:+\infty \\ $$

Question Number 159072 Answers: 0 Comments: 1

Question Number 159071 Answers: 1 Comments: 0

Determine the cardinality and power set of B = {{a,b,c},{d,e},{f,g,h,i}

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{cardinality}\:\mathrm{and}\:\mathrm{power} \\ $$$$\mathrm{set}\:\mathrm{of} \\ $$$${B}\:=\:\left\{\left\{{a},{b},{c}\right\},\left\{{d},{e}\right\},\left\{{f},{g},{h},{i}\right\}\right. \\ $$

Question Number 159070 Answers: 1 Comments: 0

Ω:= ∫_0 ^( ∞) ( H_( (i/x)) + H_( −(i/x)) ) dx=?

$$ \\ $$$$ \\ $$$$\:\:\:\:\Omega:=\:\int_{\mathrm{0}} ^{\:\infty} \left(\:\mathrm{H}_{\:\frac{{i}}{{x}}} \:+\:\mathrm{H}_{\:−\frac{{i}}{{x}}} \:\right)\:{dx}=? \\ $$$$ \\ $$

Question Number 159069 Answers: 0 Comments: 0

Question Number 159066 Answers: 0 Comments: 1

16/4(2+2)=?

$$\mathrm{16}/\mathrm{4}\left(\mathrm{2}+\mathrm{2}\right)=? \\ $$

Question Number 159057 Answers: 1 Comments: 1

Solve for positive integers: a^3 + 9b^2 + 9c^2 = 2017 where a ≥ b ≥ c

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}: \\ $$$$\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{9b}^{\mathrm{2}} \:+\:\mathrm{9c}^{\mathrm{2}} \:=\:\mathrm{2017} \\ $$$$\mathrm{where}\:\:\mathrm{a}\:\geqslant\:\mathrm{b}\:\geqslant\:\mathrm{c} \\ $$$$ \\ $$

Question Number 159049 Answers: 2 Comments: 0

solve the following equation: sin^( 6) (x) +cos^( 6) (x)+sin^4 (x)+cos^( 4) (x)=(3/4)

$$ \\ $$$$\:\:\:\:\:\:{solve}\:{the}\:{following}\:{equation}: \\ $$$$\: \\ $$$${sin}^{\:\mathrm{6}} \left({x}\right)\:+{cos}^{\:\mathrm{6}} \left({x}\right)+{sin}^{\mathrm{4}} \left({x}\right)+{cos}^{\:\mathrm{4}} \left({x}\right)=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$ \\ $$

Question Number 159046 Answers: 1 Comments: 2

Question Number 159030 Answers: 1 Comments: 0

(arcsin (cos 93°))^2 =?

$$\:\left(\mathrm{arcsin}\:\left(\mathrm{cos}\:\mathrm{93}°\right)\right)^{\mathrm{2}} =? \\ $$

Question Number 159029 Answers: 0 Comments: 2

In a box of marbles, the ratio of red marble to total marble is 2 :5, the ratio of green marble to the total marble is 3:10 . If the marbles that are neither red nor green are blue, how many marbles are in the box if there are 40 marbles in the box

$$\:\mathrm{In}\:\mathrm{a}\:\mathrm{box}\:\mathrm{of}\:\mathrm{marbles},\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{red} \\ $$$$\mathrm{marble}\:\mathrm{to}\:\mathrm{total}\:\mathrm{marble}\:\mathrm{is}\:\mathrm{2}\::\mathrm{5},\:\mathrm{the}\: \\ $$$$\mathrm{ratio}\:\mathrm{of}\:\mathrm{green}\:\mathrm{marble}\:\mathrm{to}\:\mathrm{the}\:\mathrm{total}\: \\ $$$$\mathrm{marble}\:\mathrm{is}\:\mathrm{3}:\mathrm{10}\:.\:\mathrm{If}\:\mathrm{the}\:\mathrm{marbles}\:\mathrm{that}\:\mathrm{are} \\ $$$$\mathrm{neither}\:\mathrm{red}\:\mathrm{nor}\:\mathrm{green}\:\mathrm{are}\:\mathrm{blue},\:\mathrm{how}\: \\ $$$$\mathrm{many}\:\mathrm{marbles}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{box}\:\mathrm{if}\:\mathrm{there} \\ $$$$\mathrm{are}\:\mathrm{40}\:\mathrm{marbles}\:\mathrm{in}\:\mathrm{the}\:\mathrm{box} \\ $$

Question Number 159027 Answers: 0 Comments: 1

A mountain trail is 12.1 mile long. If a hiker walks along the trail at rate of 1.96 miles per hour approximatly, how many hours will the hiker walk the entire trail

$$\mathrm{A}\:\mathrm{mountain}\:\mathrm{trail}\:\mathrm{is}\:\mathrm{12}.\mathrm{1}\:\mathrm{mile}\:\mathrm{long}.\:\mathrm{If} \\ $$$$\mathrm{a}\:\mathrm{hiker}\:\mathrm{walks}\:\mathrm{along}\:\mathrm{the}\:\mathrm{trail}\:\mathrm{at}\:\mathrm{rate}\:\mathrm{of} \\ $$$$\mathrm{1}.\mathrm{96}\:\mathrm{miles}\:\mathrm{per}\:\mathrm{hour}\:\mathrm{approximatly},\: \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{hours}\:\mathrm{will}\:\mathrm{the}\:\mathrm{hiker}\:\mathrm{walk}\: \\ $$$$\mathrm{the}\:\mathrm{entire}\:\mathrm{trail} \\ $$$$ \\ $$

Question Number 159035 Answers: 0 Comments: 12

Question Number 159021 Answers: 1 Comments: 0

Question Number 159034 Answers: 1 Comments: 0

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