machine a can fill a bucket from a pipe in 4 minutes. however, machine b can empty the bucket in 6 minutes. starting from empty, if the machines are going at the same time, how long will it take to fill the tank?

Let the closed interval [a , b] be the domain of function f. the domain of f(x - 3) is given by (a) the open interval (a , b) (b) the closed interval [a , b] (c) the closed interval [a - 3 , b - 3] (d) the closed interval [a + 3 , b + 3]

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

Precalculus question, image attached.