Looks like your function is

Rewrite it as

Recall that for
, we have

If we replace
with
, we get

By the ratio test, the series converges if

Solving for
gives the interval of convergence,

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.
Using the z-distribution, as we are working with a proportion, the 95% confidence interval for the proportion of consumers who would buy the product at it's proposed price is (0.3016, 0.3830).
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:

In which:
is the sample proportion.
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
179 out of 523 members indicated they would buy the new product at the proposed price, hence:

Then the bounds of the interval are found as follows:


More can be learned about the z-distribution at brainly.com/question/25890103
9/20 because if you count the red and blue out of the 20, theres 9. So you have a 9/20 chance it will hit red or blue.
Answer:
Step-by-step explanation:
10x - 15y = 21
15y = 10x - 21
y = ⅔x - 7/5
slope of line is ⅔
slope of any perpendicular to line is -3/2
y = kx + k
slope of line is k
k = -3/2