Determine whether the samples are independent or dependent. upper a data set includes the weight of 140 students before and after their first year of college. choose the correct answer below. a. the samples are independent because there is a natural pairing between the two samples. b. the samples are dependent because there is not a natural pairing between the two samples. c. the samples are dependent because there is a natural pairing between the two samples. d. the samples are independent because there is not a natural pairing between the two samples

Option C)

Step-by-step explanation:

The samples are dependant.  There should be a relation between the weights of the students, even though there could be changes, as any value can go up or down. A student with a weight around of 30 has a higher chance of getting a weight around of 35 after the firts year than a student with weight around of 55. This means that the probability a student has for getting certain amount of weight after the first year may change depending on the weight the student had at the start of the year. You can therefore naturally relate the weight a student had before the first year with the weight the student had after the first year.

So, the samples are dependant because there is a natural pairing between the to samples, as option C says.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).