Community Gym charges a $60 membership fee and a $70 monthly fee. Workout Gym charges a $180 membership fee and a $60 monthly fee.

1. Let m represent the number of months that the monthly fee is paid.

2. Solve the equation you created above to find out after how many months would the total amount paid to both gyms is the same.

3. Use the value of m you found above to determine the amount she would pay to the gyms.

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.