Leona tracks her calories burned while boxing. The number of calories she burns is expressed by the function c(t) = 425t, where t is the number of hours spent boxing. To burn more calories, Leona wears heavier gloves while boxing. The number of calories she burns while wearing heavier gloves is expressed by the function b(c) = 1.1c, where c is the number of calories burned while boxing without heavy gloves.

Which of the following composite functions expresses the calories, as a function of time, that Leona burns while boxing with heavy gloves?

c[b(t)] = 467.5t
c[b(t)] = 426.1t
b[c(t)] = 467.5t
b[c(t)] = 426.1t

Determine the volume of a cylinder bucket if the diameter is 8.5 in. and the height is 11.5 in.

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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.