Which of these are recursive definitions that correctly define f(n) = n! for all natural numbers n? hint: proofread them carefully. you're looking for serious structural problems, e. g. the equations don't define the right value (or any value) for some of the possible inputs. you're not looking for subtle style issues. select one or more: a. f(0) = 1, f(1) = 1, f(n) = n. f(n − 1) for n > 2 b. f(0) = 1, f(n) = n. f(n − 1) for n > 1 cf(0) = 1, f(n) = n · f(n) for n > 1 d. f(0) = 1, f(1) = 1, f(n) = f(n − 1). f(n - 2) e. f(1) = 1, f(n) = n. f(n − 1) for n > 2 f. f(0) = 1, f(n) = n · (n − 1) · (n − 2) 2.1 0 g. f(0) = 1, f(n + 1) = (n +1). f(n) for n > 1 h . f(0) = 1, f(n + 1) = (n + 1). f(n) for n > 0

(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.