let s be a semigroup. prove that s is a group if and only if the following conditions hold:
1. s has a left identity—there exists an element e ∈ s such that ea = a for all a ∈ s;
2. each element of s has a left inverse—for each a ∈ s, there exists an element a -1 ∈ s such that a -1a = e.

For which of the following counts would a binomial probability model not be reasonable? a)the number of people in a classroom born in januaryb) the number of people in a classroom with red hair c) the number of people admitted to a hospital in a day with a particular disease d) the number of heart beats in a one-minute perio.

What is the solution to the equation in the & show work i’m very

Which expression do you get when you eliminate the negative exponents of 4a^2 b^216a^-3 b