Atrack coach claims that their new month long training program will reduce your mile time by 1 minute. you want to statistically test if the training program reduces your mile time by something other than 1 minute. you decide to randomly select 8 people and record their mile times. you then have them follow the coach’s training program for a month and record their mile times post training program. the times of the subjects are listed below.
col1 subject mile time before training 9.5 7 6.7 8.45 6.2 6.3
col2 mile time after training 7.1 5.2 6.8 6.2 4 5.5 7.3
(a) what type of test is appropriate for this experiment set up?
(b) state the appropriate hypotheses
(c) how many degrees of freedom are involved in this test?
(d) perform a test of the hypotheses from (a) using a significance level of 5%. make sure to compute the test statistic and p-value, and make a conclusion in context.

How do i put 3(x+7) in distributive property

The area of a circle is equal to 1 dm². find the radius of the circle.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)