A pseudo-complete binary tree is a binary tree that becomes a perfect tree when the bottom level is removed. Consider the OBST problem for the sorted array aa1 < aa2 < ⋯< aann where all the qqii’s are equal to 0 and all the ppii’s are equal to 1 nn. Prove that the optimal binary search trees in this case are the pseudo-complete binary search trees.

Barney & noblet customers can choose to purchase a membership for $25 per year members receive 10% off all store purchases 1. how much would a member pay per year if he bought $50 worth of items each year? 2. write a slope-intercept equation that expresses how much a member pays per year using x to represent his purchases per year 3. how much would a member have to spend per year to pay off his membership fee?