Exercise 1.5.1. Finish the following proof for Theorem 1.5.7. Assume B is a countable set. Thus, there exists f : N → B, which is 1–1 and onto. Let A ⊆ B be an infinite subset of B. We must show that A is countable. Let n1 = min{n ∈ N : f(n) ∈ A}. As a start to a definition of g : N → A, set g(1) = f(n1). Show how to inductively continue this process to produce a 1–1 function g from N onto A.

In a graph with several intervals o data how does a constant interval appear? what type of scenario produces a constant interval?

Find the ratios of the corresponding sides

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.