u are on a 4-week vacation, you will play at least one set of tennis matches each day, but you wouldn’t play more than forty sets total during this time. Prove that no matter how you distribute your games during the four weeks, there is a span of consecutive days during which you

u are on a 4-week vacation, you will play at least one set of tennis matches each day, but you wouldn’t play more than forty sets total during this time. Prove that no matter how you distribute your games during the four weeks, there is a span of consecutive days during which you

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that your schedule for next semester must consist of one natural science class, one liberal arts class, one humanities class, and one physical science class. How many ways can you make up your schedule if you can choose from 3 natural science classes, 4 liberal arts classes, 6 humanities classes and 3 physical science classes?
a store can stock a maximumof 210 of tires, hubs and car seats. they know from past experience that they should stock twice as many tires as hubs and at least 30 seats.. each tire sells for $450, each hub sells for $2000 and each seat sell for $750,how many of each should be stocked and sold for maximum revenue? what is the maxiumum revenue?
Juan Hernandez, a Cuban athlete who visits the Unite States and Europe frequently, is allowed to return with a limited number of consumer items not generally available in Cuba. The items, which are carried in a duffle bag, cannot exceed a weight of 5 pounds. Once Juan is in Cuba, he sells the items at highly inflated prices. The three most popular items in Cuba are denim jeans, CD players, and CDs of U.S. rock groups. The weight and profit (in U.S. dollars) of each items are as follows. Items Weight (lb) Profit ($)1. Denim jeans 2 902. CD players 3 1503. Compact discs 2 30 Juan wants to determine the combination of items he should pack in his duffel bag that will maximize his profit. The problem is an example of a type of integer programming known as a "knapsack" problem. Formulate and solve this problem.
Last year Matthia's uncle worked for the ducks. therefore, matthias attended more home ducks games than paco. In fact, mattias went to one more than twice the home games paco did. If the two of them attended a total of at least 58 home games, how many games might paco and matthias actually have attended last year?
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Alphonse donates a fair amount of money to various charities each year. He wants to know that his money is actually going to do the charity work, though. Suppose that 90% of the charities that he donates to are probably reputable and 10% are probably not. Also, suppose that 80% of the money that goes to the real charities ends up actually being used for the charity work, while 20% goes to administrative costs. If he donates the same amount to each charity, then what percent probably goes to actual charity work? 72| % SUBMIT ANSWER O ASK FOR HELP TURN IT IN to search 344 111 80 Y U D H. V
Three friends, Pedro, Juan, and Jose, can do a certain work alone in 10 hours, 15 hours, and 18 hours, respectively. Suppose that after Pedro and Juan work together for 2 hours, Pedro left and Jose took his place until the work is finish. How long did it take Pedro and Juan to finish the work?
A company produces widgets at plants 1 and 2. It costs 125x1y2 dollars to produce x units at plant 1 and 235x1y3 dollars to produce x units at plant 2.Each plant can produce up to 500 units. Each unit produced can be sold for $10. At most 800 widgets can be sold. Determine how -the company canmaximize its profit.
You have a bag of poker chips, containing 2 white, 1 red, and 3 blue chips. White chips are worth $5, red chips are worth $10 and blue chips are worth $20. You need $20 worth of chips in order to see someone's raise, so you take chips out of the bag one at a time, noting the color of each one as it's removed, and stop when the total value of the chips removed is at least $20. How many sequences of chip colors are possible when you do this? (A) 0 (В) 9 (С) 5 (D) 10 (E) 3 (F) 11 (G) 8 (Н) 7
Students at Upscale University are required to take at least 3 humanities and 4 science courses. The maximum allowable number of science courses is 12. Each humanities course carries 4 credits and each science course 5 credits. The total number of credits in science and humanities cannot exceed 88. Quality points for each course are assigned in the usual way: the number of credit hours times 4 for an A grade, times 3 for a B grade, and times 2 for a C grade. Susan Katz expects to get B's in all her science courses. She expects to get C's in half of her humanities courses, B's in one-fourth of them, and A's in the rest. Under these assumptions, how many courses of each kind should she take in order to earn the maximum possible number of quality points? Susan Katz should take science courses and humanities courses in order to maximize her quality points.