Answer: 82
Step-by-step explanation:
H=9(-3)^2+1
Simplify both sides of the equation.
h=81+1
81+1 =82
h=82
For any single draw,
![\mathbb P(\text{white})=\dfrac6{42+6+8}=\dfrac6{56}](https://tex.z-dn.net/?f=%5Cmathbb%20P%28%5Ctext%7Bwhite%7D%29%3D%5Cdfrac6%7B42%2B6%2B8%7D%3D%5Cdfrac6%7B56%7D)
![\mathbb P(\text{gray})=\dfrac8{42+6+8}=\dfrac8{56}](https://tex.z-dn.net/?f=%5Cmathbb%20P%28%5Ctext%7Bgray%7D%29%3D%5Cdfrac8%7B42%2B6%2B8%7D%3D%5Cdfrac8%7B56%7D)
Drawing a white marble or a gray marble are disjoint events; only one of them can happen. So
![\mathbb P(\text{white or gray})=\mathbb P(\text{white})+\mathbb P(\text{gray})-\underbrace{\mathbb P(\text{white and gray})}_0](https://tex.z-dn.net/?f=%5Cmathbb%20P%28%5Ctext%7Bwhite%20or%20gray%7D%29%3D%5Cmathbb%20P%28%5Ctext%7Bwhite%7D%29%2B%5Cmathbb%20P%28%5Ctext%7Bgray%7D%29-%5Cunderbrace%7B%5Cmathbb%20P%28%5Ctext%7Bwhite%20and%20gray%7D%29%7D_0)
![\mathbb P(\text{white or gray})=\dfrac6{56}+\dfrac8{56}=\dfrac{14}{56}](https://tex.z-dn.net/?f=%5Cmathbb%20P%28%5Ctext%7Bwhite%20or%20gray%7D%29%3D%5Cdfrac6%7B56%7D%2B%5Cdfrac8%7B56%7D%3D%5Cdfrac%7B14%7D%7B56%7D)
Out of 224 draws, you should expect
![\dfrac{14}{56}\times224=56](https://tex.z-dn.net/?f=%5Cdfrac%7B14%7D%7B56%7D%5Ctimes224%3D56)
of the marbles to be either white or gray.
Answer:
![\Huge \boxed{\frac{1}{125}}](https://tex.z-dn.net/?f=%5CHuge%20%5Cboxed%7B%5Cfrac%7B1%7D%7B125%7D%7D)
Step-by-step explanation:
<h2>Order of operations</h2>
PEMDAS
Parenthesis, exponent, multiply, divide, add, and subtract from left to right.
Do exponent.
![\displaystyle \frac{1}{5^3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B5%5E3%7D)
![\displaystyle 5^3=5\times5\times5=125](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5E3%3D5%5Ctimes5%5Ctimes5%3D125)
![\displaystyle \frac{1}{125}=125](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B125%7D%3D125)
, which is our answer.
Hope this helps!
Answer:
g(x) = 6 * 3^x
Step-by-step explanation:
This is the answer because the question states that the graph is vertically stretched by a factor of 6. Since the parent function of an exponential function is f(x) = a * 3^(k(x-d)) + c, we plug in 6 for a, where we get g(x) = 6 * 3^x.
1,2,3,4,6,8,12,24 are all the factors to 24