Piper and her children went into a movie theater and she bought $59.50 worth of bags of popcorn and candies. Each bag of popcorn costs $8.50 and each candy costs $4.25. She bought 8 more candies than bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x, and the number of candies, ,y, that Piper bought. plot on a graph

Using the graph below, select all statements that are true. a. f(0.6)=0 b. f(-3.2)=-3 c. f(5.1)=5 d. this is the graph of the greatest integer function. e. this graph is one-to-one.

Points a, b, and c form a triangle. complete the statements to prove that the sum of the interior angles of triangle abc is 180

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.