Answer:
g(x) = x^2 - 7
Step-by-step explanation:
gf(x) = x^2 + 6x + 2
Converting to vertex form:-
g(fx) = (x + 3)^2 - 9 + 2
= (x + 3)^2 - 7.
As you replace the x in g(x) with f(x) in order to get g(f(x) then,
since f(x) = (x + 3), g(x) is x^2 - 7 (answer)
Answer:
48
Step-by-step explanation:
Take the second derivative, utilizing quotient and chain rule.
![{g}^{'} = - \frac{8}{(2x - 1)^{3} } \\ {g''} = \frac{48}{(2x - 1)^{4} } \\ {g''(1)} = \frac{48}{(2(1) - 1)^{4} } = \frac{48}{1} = 48](https://tex.z-dn.net/?f=%20%7Bg%7D%5E%7B%27%7D%20%20%3D%20%20%20-%20%5Cfrac%7B8%7D%7B%282x%20-%201%29%5E%7B3%7D%20%7D%20%5C%5C%20%20%7Bg%27%27%7D%20%20%3D%20%20%20%5Cfrac%7B48%7D%7B%282x%20-%201%29%5E%7B4%7D%20%7D%20%20%5C%5C%20%7Bg%27%27%281%29%7D%20%20%3D%20%20%20%5Cfrac%7B48%7D%7B%282%281%29%20-%201%29%5E%7B4%7D%20%7D%20%20%3D%20%20%5Cfrac%7B48%7D%7B1%7D%20%20%3D%2048)
Using the normal distribution, it is found that the mean is of
and the standard deviation is of
.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, we have that the p-value of Z when X = 30 is of 0.1, hence, when X = 30, Z = -1.28, so:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-1.28 = \frac{30 - \mu}{\sigma}](https://tex.z-dn.net/?f=-1.28%20%3D%20%5Cfrac%7B30%20-%20%5Cmu%7D%7B%5Csigma%7D)
![30 - \mu = -1.28\sigma](https://tex.z-dn.net/?f=30%20-%20%5Cmu%20%3D%20-1.28%5Csigma)
![\mu = 30 + 1.28\sigma](https://tex.z-dn.net/?f=%5Cmu%20%3D%2030%20%2B%201.28%5Csigma)
The p-value of Z when X = 32.5 is of 0.2, hence when X = 32.5, Z = -0.84, hence:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-0.84 = \frac{32.5 - \mu}{\sigma}](https://tex.z-dn.net/?f=-0.84%20%3D%20%5Cfrac%7B32.5%20-%20%5Cmu%7D%7B%5Csigma%7D)
![32.5 - \mu = -0.84\sigma](https://tex.z-dn.net/?f=32.5%20-%20%5Cmu%20%3D%20-0.84%5Csigma)
![\mu = 32.5 + 0.84\sigma](https://tex.z-dn.net/?f=%5Cmu%20%3D%2032.5%20%2B%200.84%5Csigma)
Hence:
![30 + 1.28\sigma = 32.5 + 0.84\sigma](https://tex.z-dn.net/?f=30%20%2B%201.28%5Csigma%20%3D%2032.5%20%2B%200.84%5Csigma)
![0.44\sigma = 2.5](https://tex.z-dn.net/?f=0.44%5Csigma%20%3D%202.5)
![\sigma = \frac{2.5}{0.44}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Cfrac%7B2.5%7D%7B0.44%7D)
![\sigma = 5.68](https://tex.z-dn.net/?f=%5Csigma%20%3D%205.68)
![\mu = 32.5 + 0.84(5.68) = 37.27](https://tex.z-dn.net/?f=%5Cmu%20%3D%2032.5%20%2B%200.84%285.68%29%20%3D%2037.27)
More can be learned about the normal distribution at brainly.com/question/27643290
#SPJ1
We are given with
<span>mXZ = 140∘
mXSZ = 220∘
and YX and YZ are tangents to circle A at X and Z.
According to the theorems on circles, the angles formed by the intersection of the two tangents is half the difference between of the measure of the arcs subtended by the tangents. So,
</span>∠XYZ = (220 - 140) /2 = 40∘<span />
Answer:
Answer is *Y*
Step-by-step explanation: