Aformal description of the problems: the input is a set x of n points: x = {x1 < x2 < . . < xn}, where each xi (1 ≤ i ≤ n) represents a house. we need to select a subset y ⊆ x such that: (1) for every point xi ∈ x, there is a point xj ∈ y with |xi − xj | ≤ 5, and (2) the 2 size of y is minimum, subject to condition (1). describe a polynomial time greedy algorithm for solving this problem. you need to prove the correctness of the algorithm.

Aretha wanted to gather data about the cost of local bowling leagues in her area. she plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20. identify and interpret the y-intercept in this model. the y-intercept is 20. this is the cost per month. the y-intercept is 20. this is the cost of registration. the y-intercept is 15. this is the cost of registration. the y-intercept is 15. this is the cost per month.