Problem 2.2 If a hypothesis set H cannot produce all dichotomies on any set of k points, then k is said to be a break point. (a) Give an example of a hypothesis set H that has a break point of one, i. e., a hypothesis set that cannot generate all dichotomies on one point. (b) Give an example of a hypothesis set H that has a break point of two. (c) Given an example of a hypothesis set H that has a break point of ten. (d) Given an example of a hypothesis set H that does not have a break point.

On the way home from visiting his family, vincent’s plane cruised at an altitude of 3.2 × 104 feet. he had heard that a man named felix baumgartner skydived from an altitude of 1.28 × 105 feet. vincent wants to know how much higher felix went on his skydiving trip. question 1 you have already seen how adding numbers works in either scientific notation or standard notation. but can you subtract numbers in scientific notation and get the same results as subtracting in standard notation? to find out, first solve vincent’s problem in standard notation. part a write the cruising altitude of vincent’s plane in standard notation.

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate is the height of the pile changing when the pile is 12 feet high? (hint: the formula for the volume of a cone is v = 1 3 πr2h.)

Handsome jack is buying a pony made of diamonds. the price of the pony is p dollars, and jack also has to pay a 25% diamond pony tax. which of the following expressions could represent how much jack pays in total for the pony?