Tim urban, owner/manager of urban's motor court in key west, is considering outsourcing the daily room cleanup for his motel to duffy's maid service. tim rents an average of 50 rooms for each of 365 nights (365 × 50 equals the total rooms rented for the year). tim's cost to clean a room is $ 13.50. the duffy's maid service quote is $ 18.50 per room plus a fixed cost of $ 26 comma 000 for sundry items such as uniforms with the motel's name. tim's annual fixed cost for space, equipment, and supplies is $ 61 comma 000. based on the given information related to costs for each of the options, the crossover point for tim is ? .

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.