A) find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the following.

(i) 4 to 5

(ii) 4 to 4.5

(iii) 4 to 4.1

(b) find the instantaneous rate of change when r = 4.

a'(4) =

The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). the mean maximum oxygen uptake for elite athletes has been found to be 60 with a standard deviation of 7.2. assume that the distribution is approximately normal.

In the diagram below? p is circumscribed about quadrilateral abcd. what is the value of x

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).