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. \\ \\

Health insurance protects you if you experience any of the following except: a: if you have to be hospitalized b: if you damage someone's property c: if you need to visit a clinic d: if you can't work because of illness

Win goods inc. is a large multinational conglomerate. as a single business unit, the company's stock price is estimated to be $200. however, by adding the actual market stock prices of each of its individual business units, the stock price of the company as one unit would be $300. what is win goods experiencing in this scenario? a. diversification discount b. learning-curveeffects c. experience-curveeffects d. economies of scale

Juan's investment portfolio was valued at $125,640 at the beginning of the year. during the year, juan received $603 in interest income and $298 in dividend income. juan also sold shares of stock and realized $1,459 in capital gains. juan's portfolio is valued at $142,608 at the end of the year. all income and realized gains were reinvested. no funds were contributed or withdrawn during the year. what is the amount of income juan must declare this year for income tax purposes?