The slope-intercept form:

The formula of a slope:

We have the points (-4, 47) and (2, -16). Substitute:

Therefore we have:

Put the coordinates of the point (2, -16) to the equation:

Answer: 
The valid conclusions for the manager based on the considered test is given by: Option
<h3>When do we perform one sample z-test?</h3>
One sample z-test is performed if the sample size is large enough (n > 30) and we want to know if the sample comes from the specific population.
For this case, we're specified that:
- Population mean =
= $150 - Population standard deviation =
= $30.20 - Sample mean =
= $160 - Sample size = n = 40 > 30
- Level of significance =
= 2.5% = 0.025 - We want to determine if the average customer spends more in his store than the national average.
Forming hypotheses:
- Null Hypothesis: Nullifies what we're trying to determine. Assumes that the average customer doesn't spend more in the store than the national average. Symbolically, we get:

- Alternate hypothesis: Assumes that customer spends more in his store than the national average. Symbolically

where
is the hypothesized population mean of the money his customer spends in his store.
The z-test statistic we get is:

The test is single tailed, (right tailed).
The critical value of z at level of significance 0.025 is 1.96
Since we've got 2.904 > 1.96, so we reject the null hypothesis.
(as for right tailed test, we reject null hypothesis if the test statistic is > critical value).
Thus, we accept the alternate hypothesis that customer spends more in his store than the national average.
Learn more about one-sample z-test here:
brainly.com/question/21477856
Answer:
x=13
Step-by-step explanation:
First, you add the x's together: 2x+x=3x
Now you have:3x-1=38
Add 1 to both sides: 3x=39
1 cancel on the left side of the equation
Divide 3 on both sides: x=39/3
3 cancels on the left side and 39 divided by 3 is 13:
x=13
Hope this helps!
notice, the circle is missing 1/4, so the area of it is just 3/4 of the whole area of the circle.
![\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=8 \end{cases}\implies A=\pi 8^2\implies A=64\pi \\\\\\ \stackrel{whole}{\cfrac{4}{4}}-\stackrel{one~quarter}{\cfrac{1}{4}}=\cfrac{3}{4}~\hfill \cfrac{3}{4}\cdot 64\pi \implies 48\pi \implies \stackrel{\pi =3.14}{150.72} \\\\\\ ~\hspace{34em}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D8%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%208%5E2%5Cimplies%20A%3D64%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bwhole%7D%7B%5Ccfrac%7B4%7D%7B4%7D%7D-%5Cstackrel%7Bone~quarter%7D%7B%5Ccfrac%7B1%7D%7B4%7D%7D%3D%5Ccfrac%7B3%7D%7B4%7D~%5Chfill%20%5Ccfrac%7B3%7D%7B4%7D%5Ccdot%2064%5Cpi%20%5Cimplies%2048%5Cpi%20%5Cimplies%20%5Cstackrel%7B%5Cpi%20%3D3.14%7D%7B150.72%7D%20%5C%5C%5C%5C%5C%5C%20~%5Chspace%7B34em%7D)
Answer:
A:80 B:30
Step-by-step explanation: