In a round-robin tournament, every two distinct players play against each other just once. For a round-robin tournament with no tied games, a record of who beat whom can be described with a tournament digraph, where the vertices correspond to players and there is an edge x→yx→y iff xx beat yy in their game.

A ranking is a path that includes all the players. So in a ranking, each player won the game against the next lowest ranked player, but may very well have lost their games against much lower ranked players —whoever does the ranking may have a lot of room to play favorites.

Prove that every finite tournament digraph has a ranking. Thanks!

Larissa has also provided the following information. during the year, the company raised $36 million in new long-term debt and retired $20.52 million in long-term debt. the company also sold $22 million in new stock and repurchased $32.4 million. the company purchased $54 million in fixed assets, and sold $6,107,400 in fixed assets. larissa has asked dan to prepare the financial statement of cash flows and the accounting statement of cash flows. she has also asked you to answer the following questions: 1. how would you describe east coast yachts' cash flows? 2. which cash flows statement more accurately describes the cash flows at the company? 3. in light of your previous answers, comment on larissa's expansion plans.

Consider how health insurance affects the quantity of health care services performed. suppose that the typical medical procedure has a cost of $160, yet a person with health insurance pays only $40 out of pocket. her insurance company pays the remaining $120. (the insurance company recoups the $120 through premiums, but the premium a person pays does not depend on how many procedures that person chooses to undergo.) consider the following demand curve in the market for medical care. use the black point (plus symbol) to indicate the quantity of procedures demanded if each procedure has a price of $160. then use the grey point (star symbol) to indicate the quantity of procedures demanded if each procedure has a price of $40. q d at p=$160 q d at p=$40 0 10 20 30 40 50 60 70 80 90 100 200 180 160 140 120 100 80 60 40 20 0 price of medical procedures quantity of medical procedures demand if the cost of each procedure to society is truly $160, the quantity that maximizes total surplus is procedures. economists often blame the health insurance system for excessive use of medical care. given your analysis, the use of care might be viewed as excessive because consumers get procedures whose value is than the cost of producing them.

Jordan, inc. sells fireworks. the company’s marketing director developed the following cost of goods sold budget for april, may, june, and july. april may june july budgeted cost of goods sold $62,000 $72,000 $82,000 $88,000 jordan had a beginning inventory balance of $3,000 on april 1 and a beginning balance in accounts payable of $14,600. the company desires to maintain an ending inventory balance equal to 15 percent of the next period’s cost of goods sold. jordan makes all purchases on account. the company pays 65 percent of accounts payable in the month of purchase and the remaining 35 percent in the month following purchase. required prepare an inventory purchases budget for april, may, and june. determine the amount of ending inventory jordan will report on the end-of-quarter pro forma balance sheet. prepare a schedule of cash payments for inventory for april, may, and june. determine the balance in accounts payable jordan will report on the end-of-quarter pro forma balance sheet.