each month the police department hosts a hot dog. This month 56 people attend the hot dog feed. this was 10 more than twice as many peopl then were at the hot dog feed last month. write and solve an equation to determaine how many people atteneded last months hot dog feed.

Solve the following inequalities and show the solution on a number line. 2x+3< 3(4x+5)

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.

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.