A winery has a barrel to hold chardonnay. An inlet pipe can fill the barrel in 15 hours, while an outlet pipe can empty the barrel in 20 hours. How many hours would it take to fill the barrel if both the inlet and outlet pipes are open? Express your answer as a fraction reduced to lowest terms, if needed.

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.

If the square of a positive integer is added to 2 times the integer the result is 48. find the integer.

Hannah has 5 more than twice the number of baseball cards that leo has. if leo has x cards, which expression shows the number of baseball cards hannah has?