Let & be integrable on an interval [a,b]. It's true that: (a) there exists no E (a,b) such that f'(xo) (b-a) = f (b) -f(a) (b) is continuous in [a,b] (b) f (c) there exists CE [a,b] such that f(c) (b-a) = f(x)dn →f is continuous in [a,b] 1 (d) inf f(x) = (flarda ≤ sup f(x) 2E[a,b] b-a nt (a,bJ (e) there exists c € [a,b] such that f(c)(b-a) = 1 f(x)dx

A math teacher asks each student to create a password to gain access to her website. The password has 5 digits. She makes up some rules for the students to follow in their password selection. The first digit must be a multiple of 1. The second digit must be a multiple of 2. The third digit must be a multiple of 3, and so on. How many possible passwords are there?

A farmer is raising chickens and cows. There are 42 total chickens and cows on his farm, in which there are a total of 140 legs. Assuming that all the chickens have 2 legs and all the cows have 4 legs, how many cows are on the farm?

The sum of an integer and 4 less than that integer is even.