The diagram shows a sphere and a solid cylinder.

The sphere has radius 6 cm.
The solid cylinder has a base radius of 3 cm and a height of h
cm.

The total surface area of the cylinder is twice the total surface area of the sphere. Work out the ratio of the volume of the sphere to the volume of the cylinder. Give your answer in its simplest form.

(5 marks)

List the elements of the set in roster notation. (enter empty or ∅ for the empty set.) {x | x is a letter in the word hippopotamus}

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.