The radius of a spherical balloon is measured as 20 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible error in calculating the following. a) Calculate the volume of the sphere. b) Calculate the surface area of the sphere. c) Calculate the relative errors in part a) and b).

An office supply company conducted a survey before marketing a new paper shredder designed for home use. in the survey, 80 % of the people who tried the shredder were satisfied with it. because of this high satisfaction rate, the company decided to market the new shredder. assume that 80 % of all people are satisfied with this shredder. during a certain month, 100 customers bought this shredder. find the probability that of these 100 customers, the number who are satisfied is 69 or fewer.