the radius of a sphere is increased by 2 and a half % find the percentage increase in the volume using differentiation​

Find the product. type your answer in the space provided. use / for a fraction bar (example: 1/2) and ^ for an exponent (example: x^5). do not put spaces in your answer. (x -1 y 5)^2 · (2xy -2)^5

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. complete parts (a) through (c) below. a. if 1 adult female is randomly selected, find the probability that her pulse rate is between 65 beats per minute and 79 beats per minute. the probability is? b. if 16 adult females are randomly selected, find the probability that they have pulse rates with a mean between 65 beats per minute and 79 beats per minute. the probability is? c. why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

What is the true solution to the logarithmic equation below?