The answer to the problem is 36
A is the awnser,because it is asking for the area of the square figure not the triangular figure in the middle.
Answer:
a) n= 1045 computers
b) n= 442 computers
c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.
Step-by-step explanation:
Hello!
The variable of interest is
X: Number of computers that use the new operating system.
You need to find the best sample size to take so that the proportion of computers that use the new operating system can be estimated with a 99% CI and a margin of error no greater than 4%.
The confidence interval for the population proportion is:
p' ±
* 

a) In this item there is no known value for the sample proportion (p') when something like this happens, you have to assume the "worst-case scenario" that is, that the proportion of success and failure of the trial are the same, i.e. p'=q'=0.5
The margin of error of the interval is:
d=
* 



![n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2](https://tex.z-dn.net/?f=n%3D%20%5Bp%27%281-p%27%29%5D%2A%28%5Cfrac%7BZ_%7B1-%5Calpha%20%2F2%7D%7D%7Bd%7D%20%29%5E2)
![n=[0.5(1-0.5)]*(\frac{2.586}{0.04} )^2= 1044.9056](https://tex.z-dn.net/?f=n%3D%5B0.5%281-0.5%29%5D%2A%28%5Cfrac%7B2.586%7D%7B0.04%7D%20%29%5E2%3D%201044.9056)
n= 1045 computers
b) This time there is a known value for the sample proportion: p'= 0.88, using the same confidence level and required margin of error:
![n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2](https://tex.z-dn.net/?f=n%3D%20%5Bp%27%281-p%27%29%5D%2A%28%5Cfrac%7BZ_%7B1-%5Calpha%20%2F2%7D%7D%7Bd%7D%20%29%5E2)
![n= [0.88*0.12]*(\frac{{2.586}}{0.04})^2= 441.3681](https://tex.z-dn.net/?f=n%3D%20%5B0.88%2A0.12%5D%2A%28%5Cfrac%7B%7B2.586%7D%7D%7B0.04%7D%29%5E2%3D%20441.3681)
n= 442 computers
c) The additional information in part b affected the required sample size, it was drastically decreased in comparison with the sample size calculated in a).
I hope it helps!
Answer:
3/2
Step-by-step explanation:
The composition of transformations has you dilate the line by a factor of 1/2, then by a factor of 3. Then the line is rotated about the origin.
The scale factor of the result will be the product of the dilation factors:
(3)(1/2) = 3/2
The scale factor of the transformation is 3/2.
She drove 2 hours at 35 miles per hour for a total of 35 * 2 = 70 miles.
She drove 3 hours at 48 miles per hour for a total of 48 * 3 = 144 miles.
Her total miles were: 70 + 144 = 214.
Her total driving time was 3 + 2 = 5 hours.
Divide her total miles by total time for her average speed:
214 / 5 = 42.8 miles per hour average speed.
Not sure if you need to round the answer or not.