Suppose that f : x → y is a function and that a is a σ-algebra of subsets of x. show that the following collection of subsets of y is also a σ-algebra: b : = {b ⊂ y : f −1 (b) ∈ a}

Mason and christian go to the movie theater and purchase refreshments for their friends. mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. using these equations, determine and state the price of a drink, to the nearest cent.