Identify the mistakes, if any, with the following "proof" by strong induction. "theorem" for every nonnegative integer n, 5n = 0. basis step: 5 ⋅ 0 = 0. inductive step: suppose that 5j = 0 for all nonnegative integers j with 0 ≤ j ≤ k. write k + 1 = i + j, where i and j are natural numbers less than k + 1. by the inductive hypothesis, 5(k + 1) = 5(i + j) = 5i + 5j = 0 + 0 = 0.

The number of branches on a tree demonstrates the fibonacci sequence. how many branches would there be on the next two levels of this tree? 13 | | | m branches

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size.it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?

How do your peer relationships affect your overall health status? what can you do to improve your peer relationships?