g Prove that ∀n ∈ N, Pn i=0 2 i = 2n+1−1 (in other words, 1+2+4+8+· · ·+ 2 n = 2n+1 − 1). Use the following proof strategy: Proof by contradiction. Take the set of all n for which this statement is false. Use the fact that every set of non-negative integers has a minimum. Call that minimum k. Either k = 0 or the statement is true for k − 1. Get a contradiction from here.

Amanager recorded the number of bicycles sold by his company each quarter. his projected sales after t years is given by the expression below. which of the following statements best describes the expression? a. the initial sales of 575 bicycles increases at the rate of 4% over 4 quarters. b. the initial sales of 575 bicycles increases at the rate of 18% over 4 years. c. the initial sales of 575 bicycles increases at the rate of 4% over t quarters. d. the initial sales of 575 bicycles increases at the rate of 18% over t years.

Complete the solution of the equation. find the value of y when x equals to 6 4x+y=20

The diagram shows corresponding lengths in two similar figures. find the area of the smaller figure. a. 14.4 yd2 b. 24 yd2 c. 26.4 yd2 d. 28