Harry's competitive math team has been ranked the number one team for the past 40 days. His team competes in a math competition at least once per day and competes in no more than 60 competitions in these 40 days. Show that there is some day $i$ and some day $j$ such that between $i$ and $j$, exactly 19 matches have been played. \\ \\

Guardian inc. is trying to develop an asset-financing plan. the firm has $450,000 in temporary current assets and $350,000 in permanent current assets. guardian also has $550,000 in fixed assets. assume a tax rate of 40 percent. a. construct two alternative financing plans for guardian. one of the plans should be conservative, with 70 percent of assets financed by long-term sources, and the other should be aggressive, with only 56.25 percent of assets financed by long-term sources. the current interest rate is 12 percent on long-term funds and 7 percent on short-term financing. compute the annual interest payments under each plan.

Shelby company produces three products: product x, product y, and product z. data concerning the three products follow (per unit): product x product y product z selling price $ 85 $ 65 $ 75 variable expenses: direct materials 25.50 19.50 5.25 labor and overhead 25.50 29.25 47.25 total variable expenses 51.00 48.75 52.50 contribution margin $ 34.00 $ 16.25 $ 22.50 contribution margin ratio 40 % 25 % 30 % demand for the company’s products is very strong, with far more orders each month than the company can produce with the available raw materials. the same material is used in each product. the material costs $8 per pound, with a maximum of 4,400 pounds available each month. required: a. compute contribution margin per pound of materials used. (round your intermediate calculations and final answers to 2 decimal places.) contribution margin per pound product x $ product y $ product z $ b. which orders would you advise the company to accept first, those for product x, for product y, or for product z? which orders second? third? product x product y product z

Which of the following statements is true regarding the reporting of outside interests and the management of conflicts? investigators are responsible for developing their own management plans for significant financial interests. the institution must report identified financial conflicts of interest to the u. s. office of research integrity. investigators must disclose their significant financial interests related to their institutional responsibilities and not just those related to a particular project. investigators must disclose all of their financial interests regardless of whether they are related to a research project.