Some members of the track team are practicing running along a marathon course. Their position along the course is given by the variable d, in miles. The variable t represents the amount of time after 9:00 a. m., in hours. Some runners started running before 9:00 a. m. The position of runner Cheng is given by d=8(t+0.5). The position of runner Antonelli is given by d=4+8t. Which is true?

Runner Antonelli will catch and pass runner Cheng.

Runner Cheng is running at a fixed distance behind runner Antonelli.

Runner Cheng and runner Antonelli are at the same point along the course.

The runners started together, but now runner Antonelli is ahead.
(gives 15 points)

Players on the school soccer team are selling candles to raise money for an upcoming trip. each player has 24 candles to sell. if a player sells 4 candles a profit of$30 is made. if he sells 12 candles a profit of $70 is made

Two times a number plus three times another number equals 4. three times the first number plus four times the other number is 7. find the numbers

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.