If you add Hillary to the friend count, that's 24. So there are 16 boys and 8 girls
Answer:
4 x 13
Step-by-step explanation:
GCD of 28 and 24 is 4
28 = 4 x 7
24 = 4 x 6
u take the 4 out
4 (7 + 6)
4 x 13
Answer: ![w=\frac{12}{13}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B12%7D%7B13%7D)
Step-by-step explanation:
To solve for w, we want to isolate the variable.
[add both sides by 2 and w]
[convert to same denominator]
[add]
[multiply both sides by 6/13]
![w=\frac{12}{13}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B12%7D%7B13%7D)
Now we know that
.
Step-by-step explanation:
Given:
and ![f(0) = 0](https://tex.z-dn.net/?f=f%280%29%20%3D%200)
We can solve for f(x) by writing
![\displaystyle f(x) = \int f'(x)dx=\int x^2e^{2x^3}dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cint%20f%27%28x%29dx%3D%5Cint%20x%5E2e%5E%7B2x%5E3%7Ddx)
Let ![u = 2x^3](https://tex.z-dn.net/?f=u%20%3D%202x%5E3)
![\:\:\:\:du=6x^2dx](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3Adu%3D6x%5E2dx)
Then
![\displaystyle f(x) = \int x^2e^{2x^3}dx = \dfrac{1}{6}\int e^u du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cint%20x%5E2e%5E%7B2x%5E3%7Ddx%20%3D%20%5Cdfrac%7B1%7D%7B6%7D%5Cint%20e%5Eu%20du)
![\displaystyle \:\:\:\:\:\:\:=\frac{1}{6}e^{2x^3} + k](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%5Cfrac%7B1%7D%7B6%7De%5E%7B2x%5E3%7D%20%2B%20k)
We know that f(0) = 0 so we can find the value for k:
![f(0) = \frac{1}{6}(1) + k \Rightarrow k = -\frac{1}{6}](https://tex.z-dn.net/?f=f%280%29%20%3D%20%5Cfrac%7B1%7D%7B6%7D%281%29%20%2B%20k%20%5CRightarrow%20k%20%3D%20-%5Cfrac%7B1%7D%7B6%7D)
Therefore,
![\displaystyle f(x) = \frac{1}{6} \left(e^{2x^3} - 1 \right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B6%7D%20%5Cleft%28e%5E%7B2x%5E3%7D%20-%201%20%5Cright%29)