Suppose there are 100 lockers in a school hallway and they are all closed. Only 25 students come through the hallway and start opening and closing the lockers. The first student opened
all the lockers. The second student closed every second locker and so forth. The Third student changes the state
of every 3rd locker. The fourth student changes the state of every 4th locker, the fifth student changes the state
of every 5th locker and so on, until the 25th student.
1. What is the state of the following locker numbers: #23, #55, #81, #100?

Solve each quadratic equation by factoring and using the zero product property. 14x - 49 = x^2

Select the correct answer from each drop-down menu. let c(g) be the total cost, including shoe rental, for bowling g games at pin town lanes. c(g) = 5g+3 so, c(6) = 8? 33? 30? or 14? this means that for a $6 shoe rental? for $6 per game? for 6 games? for a total cost of $6? , the games are $8 each? total cost is $33? number of games is 14? or total cost is $30? reset next

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.