Help Answer This Question For 20 Points

A

Step-by-step explanation:

When we rotate anything, at least one part/face of it will become spherical/circular. In this case, the exterior of the shape will become circular when we rotate about line m.

A 3D shape with the above description is a cylinder. So, cross off C, D, and E. Now, when we rotate this figure to get the cylinder, the top is a circle. Since the figure is simply being rotated, the radius is not lengthened or shortened; it stays the same.

Therefore, the radius of the cylinder is still 5.

Thus, the answer is A.

Hope this helps!

We fail to reject the null hypothesis that the average content of containers of the lubricant is 10 liters, this at the significance level of 0.01

Step-by-step explanation:

Let X be the random variable that represents the content of a container of the lubricant. We have observed n = 10 values, = 10.06 and s = 0.2459. We assume that X is normally distributed.

We have the following null and alternative hypothesis

vs (two-tailed alternative)

We will use the test statistic  

because we have a small sample size. And the observed value is

if is true, then T has a t distribution with n-1 = 9 degrees of freedom.

The rejection region for a two-tailed alternative and a significance level of 0.01 is given by RR = {t | t < -3.2498 or t > 3.2498}, where 3.2498 is the value such that there is an area of 0.005 above this number and under the density of the t distribution with 9 df.

Because the observed value 0.7716 does not fall inside RR, we fail to reject the null hypothesis.