Determine which system below will produce infinitely many solutions. (2 points) select one: a. 2x + 5y = 24 2x + 5y = 42 b. 3x − 2y = 15 6x + 5y = 11 c. 4x − 3y = 9 −8x + 6y = −18 d. 5x − 3y = 16 −2x + 3y = −7

Logan wants to know how many skateboards have defective parts. he inspects 20,000 skateboards and keeps track of the number of defects per board. use his probability distribution table to find the expected value for defects on a skateboard.

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.

You draw a card at random from a deck that contains 33 black cards and 77 red cards.