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AllQuestion and Answers: Page 380

Question Number 174664    Answers: 1   Comments: 0

Question Number 174661    Answers: 1   Comments: 0

After being marked down 20 percent. a calculator sells for $10. The Original selling price was ?

$$\mathrm{After}\:\mathrm{being}\:\mathrm{marked}\:\mathrm{down}\:\mathrm{20}\:\mathrm{percent}. \\ $$$$\mathrm{a}\:\mathrm{calculator}\:\mathrm{sells}\:\mathrm{for}\:\$\mathrm{10}.\:\mathrm{The}\:\mathrm{Original} \\ $$$$\mathrm{selling}\:\mathrm{price}\:\mathrm{was}\:? \\ $$

Question Number 174655    Answers: 1   Comments: 0

Factorize a^3 − 16a − 3

$$\mathrm{Factorize}\:{a}^{\mathrm{3}} \:−\:\mathrm{16}{a}\:−\:\mathrm{3} \\ $$

Question Number 174654    Answers: 0   Comments: 1

Factorize x^9 + x^7 + 1

$$\mathrm{Factorize}\:{x}^{\mathrm{9}} \:+\:{x}^{\mathrm{7}} \:+\:\mathrm{1} \\ $$

Question Number 174649    Answers: 0   Comments: 3

Question Number 174647    Answers: 0   Comments: 0

Question Number 174635    Answers: 2   Comments: 0

Question Number 174628    Answers: 1   Comments: 2

Ω = ∫ (x/(1+csc x)) dx =?

$$\:\:\:\Omega\:=\:\int\:\frac{{x}}{\mathrm{1}+\mathrm{csc}\:{x}}\:{dx}\:=? \\ $$

Question Number 174627    Answers: 0   Comments: 0

Question Number 174626    Answers: 0   Comments: 0

Question Number 174625    Answers: 0   Comments: 0

Question Number 174624    Answers: 0   Comments: 0

Question Number 174622    Answers: 0   Comments: 1

Question Number 174620    Answers: 0   Comments: 1

Question Number 174619    Answers: 2   Comments: 0

Question Number 174613    Answers: 1   Comments: 0

In a mixture of Skettles and M&M′s, 80% of the pieces are M&M′s. A fourth of this mixture is replaced by a second mixture, resulting in combination which contain 16% Skittles in total. What was the percentage of Skittles in the second mixture?

$$\mathrm{In}\:\mathrm{a}\:\mathrm{mixture}\:\mathrm{of}\:\:\mathrm{Skettles}\:\mathrm{and}\:\mathrm{M\&M}'\mathrm{s}, \\ $$$$\mathrm{80\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pieces}\:\mathrm{are}\:\mathrm{M\&M}'\mathrm{s}.\:\mathrm{A}\:\mathrm{fourth} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{mixture}\:\mathrm{is}\:\mathrm{replaced}\:\mathrm{by}\:\mathrm{a}\:\mathrm{second} \\ $$$$\mathrm{mixture},\:\mathrm{resulting}\:\mathrm{in}\:\mathrm{combination} \\ $$$$\mathrm{which}\:\mathrm{contain}\:\mathrm{16\%}\:\mathrm{Skittles}\:\mathrm{in}\:\mathrm{total}. \\ $$$$\mathrm{What}\:\mathrm{was}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{of}\:\mathrm{Skittles} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{second}\:\mathrm{mixture}? \\ $$

Question Number 174612    Answers: 0   Comments: 1

Question Number 174611    Answers: 0   Comments: 2

Find the expected payback for a game in which you bet $8.00 on any number from 0 to 99 and if your number comes up, you win $2,000.00

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{expected}\:\mathrm{payback}\:\mathrm{for}\:\mathrm{a}\: \\ $$$$\mathrm{game}\:\mathrm{in}\:\mathrm{which}\:\mathrm{you}\:\mathrm{bet}\:\$\mathrm{8}.\mathrm{00}\:\mathrm{on}\:\mathrm{any} \\ $$$$\mathrm{number}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{99}\:\mathrm{and}\:\mathrm{if}\:\mathrm{your} \\ $$$$\mathrm{number}\:\mathrm{comes}\:\mathrm{up},\:\mathrm{you}\:\mathrm{win}\:\$\mathrm{2},\mathrm{000}.\mathrm{00} \\ $$

Question Number 174610    Answers: 0   Comments: 0

find the value of this integral: I=∫_0 ^∞ ((tan^(−1) (x))/(1+x+x^2 )) dx

$${find}\:{the}\:{value}\:{of}\:{this}\:{integral}: \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \:\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 174599    Answers: 0   Comments: 0

Question Number 174594    Answers: 1   Comments: 0

Let σ(n) be the sum of all positive divisors of the integer n and let p be any prime number. show that σ(n)<2n holds true for all n of the form n=p^2 . Mastermind

$$\mathrm{Let}\:\sigma\left(\mathrm{n}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive} \\ $$$$\mathrm{divisors}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{and}\:\mathrm{let}\:\mathrm{p}\:\mathrm{be} \\ $$$$\mathrm{any}\:\mathrm{prime}\:\mathrm{number}.\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\sigma\left(\mathrm{n}\right)<\mathrm{2n}\:\mathrm{holds}\:\mathrm{true}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{form}\:\mathrm{n}=\mathrm{p}^{\mathrm{2}} . \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174630    Answers: 1   Comments: 0

lim_(n→∞) Σ_(r=1) ^∞ (r/(n^2 +r))

$$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{r}}{{n}^{\mathrm{2}} +{r}} \\ $$

Question Number 174591    Answers: 1   Comments: 0

The drawing below shows two equilateral triangles with side length a. The triangle are horizontally shifted by (a/2). Find the intersection area A of the two triangles (grey area).

$$\mathrm{The}\:\mathrm{drawing}\:\mathrm{below}\:\mathrm{shows}\:\mathrm{two}\: \\ $$$$\mathrm{equilateral}\:\mathrm{triangles}\:\mathrm{with}\:\mathrm{side}\:\mathrm{length} \\ $$$$\boldsymbol{\mathrm{a}}.\:\mathrm{The}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{horizontally}\:\mathrm{shifted} \\ $$$$\mathrm{by}\:\frac{\mathrm{a}}{\mathrm{2}}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{area}\:\mathrm{A}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{triangles}\:\left(\mathrm{grey}\:\mathrm{area}\right). \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 174587    Answers: 0   Comments: 2

Question Number 174583    Answers: 0   Comments: 0

Your friend makes 6 field goals and 2 free throws. You make twice as many field goals as your friend and half the number of free throws. How many points do you have. explain the order of operation you followed

$$\:\mathrm{Your}\:\mathrm{friend}\:\mathrm{makes}\:\mathrm{6}\:\mathrm{field}\:\mathrm{goals}\:\mathrm{and}\: \\ $$$$\:\:\mathrm{2}\:\mathrm{free}\:\mathrm{throws}.\:\mathrm{You}\:\mathrm{make}\:\mathrm{twice}\:\mathrm{as} \\ $$$$\:\mathrm{many}\:\mathrm{field}\:\mathrm{goals}\:\mathrm{as}\:\mathrm{your}\:\mathrm{friend}\:\mathrm{and}\: \\ $$$$\:\mathrm{half}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{free}\:\mathrm{throws}.\:\mathrm{How} \\ $$$$\mathrm{many}\:\mathrm{points}\:\mathrm{do}\:\mathrm{you}\:\mathrm{have}.\:\mathrm{explain}\:\mathrm{the} \\ $$$$\mathrm{order}\:\mathrm{of}\:\mathrm{operation}\:\mathrm{you}\:\mathrm{followed} \\ $$$$\:\:\:\:\: \\ $$

Question Number 174582    Answers: 0   Comments: 0

Your friend makes 4 field goals . you make three times as many field goals as your friend plus one field goals. how many points do you have. Explain the order of operation you followed

$$\:\mathrm{Your}\:\mathrm{friend}\:\mathrm{makes}\:\mathrm{4}\:\mathrm{field}\:\mathrm{goals}\:.\:\mathrm{you} \\ $$$$\:\mathrm{make}\:\mathrm{three}\:\mathrm{times}\:\mathrm{as}\:\mathrm{many}\:\mathrm{field}\:\mathrm{goals} \\ $$$$\mathrm{as}\:\mathrm{your}\:\mathrm{friend}\:\mathrm{plus}\:\mathrm{one}\:\mathrm{field}\:\mathrm{goals}. \\ $$$$\:\mathrm{how}\:\mathrm{many}\:\mathrm{points}\:\mathrm{do}\:\mathrm{you}\:\mathrm{have}.\: \\ $$$$\mathrm{Explain}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{operation}\:\mathrm{you}\: \\ $$$$\mathrm{followed} \\ $$

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