Answer:
About 41.5%
Step-by-step explanation:
<em>Given:</em>
<em>A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape.</em>
<em>To Find:</em>
<em>What is the probability that both grapes are red?</em>
<em>Answer choices:</em>
<em>about 39.7%</em>
<em>about 41.5%</em>
<em>about 42.5%</em>
<em>about 44.5%</em>
<em>Solution:</em>
<em>Since, there are 8 green grapes and 15 red grapes, the total number of grapes is 23 .</em>
<em>As the red grapes are 15..</em>
<em>Thus,</em>
<em>The probability of choosing a red grape the first time is 15/23.</em>
<em>Because out of the total 23 grapes only 15 were red grape.</em>
<em>The probability of choosing the red grape the second time will be 14/22. Because the number of red grapes has already decreased by one and so is the total number of grapes after first choice</em>
<em>Hence, the probability of choosing or eating two red grapes will be :</em>
<em>15/23×14/22</em>
<em>=105/253</em>
<em>=0.415</em>
<em>= 41.5%</em>
<em>Therefore, the probability that both grapes are red is about 41.5%</em>
Answer:
Volume of Gold = 0.4 cubic feet.
Step-by-step explanation:
First we have to make sure the units are same as the units the answer is required in.
Answer should be given in cubic feet.
Density is given in pounds per cubic foot. And Mass is given in pounds. So units are in order. Therefore, we can go ahead with the calculation.
The Density of Gold = [Mass of Gold/Volume of Gold]
By substituting values,
ponds per cubic foot = [
pounds / Volume of gold]
Making Volume of God the subject of the equation,
Volume of Gold = [ pounds / tex]1204[/tex] ponds per cubic foot ]
Volume of Gold = 0.4 cubic feet.
Answer:
A heart will beat 140 times in 2 minutes
Step-by-step explanation:
700 ÷ 10 = 70
140 ÷ 70 = 2
Answer:
she purchased 6 first class tickets and 2 normal tickets
Step-by-step explanation:
so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check
so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.
![\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cstackrel%7Bf%28x%29%7D%7B2x%5E3-x%5E2-5x%7D~~%20-%20~~%5B%5Cstackrel%7Bg%28x%29%7D%7B-x%5E2%2B3x%7D%5D%5Cimplies%202x%5E3-x%5E2-5x%2Bx%5E2-3x%20%5C%5C%5C%5C%5C%5C%202x%5E3-8x%5Cimplies%202%28x%5E3-4x%29%5Cimplies%20%5Cdisplaystyle%202%5Cint%5Climits_%7B-2%7D%5E%7B0%7D%20%28x%5E3-4x%29dx%20%5Cimplies%202%5Cleft%5B%20%5Ccfrac%7Bx%5E4%7D%7B4%7D-2x%5E2%20%5Cright%5D_%7B-2%7D%5E%7B0%7D%5Cimplies%20%5Cboxed%7B8%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}](https://tex.z-dn.net/?f=%5Cstackrel%7Bg%28x%29%7D%7B-x%5E2%2B3x%7D~~%20-%20~~%5B%5Cstackrel%7Bf%28x%29%7D%7B2x%5E3-x%5E2-5x%7D%5D%5Cimplies%20-x%5E2%2B3x-2x%5E3%2Bx%5E2%2B5x%20%5C%5C%5C%5C%5C%5C%20-2x%5E3%2B8x%5Cimplies%202%28-x%5E3%2B4x%29%20%5C%5C%5C%5C%5C%5C%20%5Cdisplaystyle%202%5Cint%5Climits_%7B0%7D%5E%7B2%7D%20%28-x%5E3%2B4x%29dx%20%5Cimplies%202%5Cleft%5B%20-%5Ccfrac%7Bx%5E4%7D%7B4%7D%2B2x%5E2%20%5Cright%5D_%7B0%7D%5E%7B2%7D%5Cimplies%20%5Cboxed%7B8%7D%20~%5Chfill%20%5Cboxed%7B%5Cstackrel%7B%5Ctextit%7Btotal%20area%7D%7D%7B8~~%20%2B%20~~8~~%20%3D%20~~16%7D%7D)
