PLEASE ANSWER WHENEVER POSSIBLE This high school stadium contains a track that surrounds a soccer field. The soccer field is 100 yards long and 70 yards wide.

1. What is the area of one of the semicircles at either side of the track?

2. The school decided to cover the semicircles with grass to create a space for stretching and other activities. How many square yards of grass will the school need to cover the entire circle?

3. What is the distance around one of the semicircles at either end of the soccer field?

4. What is the distance around the inner lane of the track (i. e., the lane closest to the soccer field?

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.