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!

Aceramics manufacturer sold cups last year for $7.50 each. variable costs of manufacturing were $2.25 per unit. the company needed to sell 20,000 cups to break even. net income was $5,040. this year, the company expects the price per cup to be $9.00; variable manufacturing costs to increase 33.3%; and fixed costs to increase 10%. how many cups (rounded) does the company need to sell this year to break even?

Exercise 8-6 goods in transit [lo8-2] the kwok company's inventory balance on december 31, 2016, was $190,000 (based on a 12/31/16 physical count) before considering the following transactions: 1. goods shipped to kwok f.o.b. destination on december 20, 2016, were received on january 4, 2017. the invoice cost was $35,000. 2. goods shipped to kwok f.o.b. shipping point on december 28, 2016, were received on january 5, 2017. the invoice cost was $22,000. 3. goods shipped from kwok to a customer f.o.b. destination on december 27, 2016, were received by the customer on january 3, 2017. the sales price was $45,000 and the merchandise cost $27,000. 4. goods shipped from kwok to a customer f.o.b. destination on december 26, 2016, were received by the customer on december 30, 2016. the sales price was $25,000 and the merchandise cost $18,000. 5. goods shipped from kwok to a customer f.o.b. shipping point on december 28, 2016, were received by the customer on january 4, 2017. the sales price was $30,000 and the merchandise cost $17,000. required: determine the correct inventory amount to be reported in kwok's 2016 balance sheet.

What is an example of a good stock to buy in a recession? a) cyclical stock b) defensive stock c) income stock d) bond