The formula for the volume of a sphere is upper v equals four thirds pi r cubedv= 4/3πr3, where r is the radius of the sphere. the steel ball to the right is in the shape of a sphere and has a diameter of 3030 millimeters. a. find the exact volume of the sphere. b. find a 2-decimal-place approximation for the volume.

What basic trigonometric identity would you use to verify that sin x cos x tan x =1-cos^(2)x?

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Determine the mean and variance of the random variable with the following probability mass function. f(x)=( 729divided by 91) (1 divided by 9) superscript x baseline comma x equals 1,2,3 round your answers to three decimal places (e.g. 98.765).