Solve for each variable.

a =

b =

c =

how did you find these answers?

A= 38

B= 54

C= 54

Step-by-step explanation:

To find a, you just have to subtract 180 and 142 since 142 and a make a straight line. so 180-142= 38

To find b, you just have to do 180-38+88=b. Since angle a has a vertical partner its the same inside. To make a triangle you need 3 angles that make 180 so since you have the vertical angle 38 and you have the given angle 88 you add them and subtract them to 180 which gives you54.

To find c is much simpler because it equals the same as b. It equals the same because of AIA. Which is Alternate Interior Angles. when an 2 angles make a z shape its AIA meaning they are congruent so they are equal.

We need a sample of at least 1797 if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 2.3% of the population percentage.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

In this problem, we have that:

How large a sample is needed if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 2.3% of the population percentage?

We have to find n for which . So

We need a sample of at least 1797 if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 2.3% of the population percentage.