At the beginning of a political science class at a large university the

# At the beginning of a political science class at a

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63* At the beginning of a political science class at a large university, the students were asked which term, liberalor conservative, best described their political views. They were asked the same question at the end of the course, to see what effect the class discussions had on their views. Of those that characterized themselves as “lib eral initially, 30% held conservative views at the end. Of those who were conservative initially, 40% moved to the liberal camp. It turned out that there were justas many students with conservative views at the end as there had been liberal students at the beginning. Out of the 260 students in the class, how many held liberal and conservative views at the beginning of the course and at the end? (No students joined or dropped the class between the surveys, and they all participated in both surveys.) 64.At the beginning of a semester, 55 students have signed up for Linear Algebra; the course is offered in two sections that are taught at different times. Because of scheduling conflicts and personal preferences, 20% of the students in Section A switch to Section B in the first few weeks of class, while 30% of the students in Section B switch to A, resulting in a net loss of 4 stu dents for Section B. How large were the two sections at the beginning of the semester? No students dropped Linear Algebra (why would they?) or joined the course late. 65.Five cows and two sheep together cost ten liang12 of silver. Two cows and five sheep together cost eight liangof silver. What is the cost of a cow and a sheep, respec tively? (Nine Chapters,13 Chapter 8, Problem 7) 66. If you sell two cows and five sheep and you buy 13 pigs, you gain 1,000 coins. If you sell three cows and three pigs and buy nine sheep, you break even. If you sell six sheep and eight pigs and you buy five cows, you lose 600 coins. What is the price of a cow, a sheep, and a pig, respectively? (Nine Chapters, Chapter 8, Problem 8) 67.You place five sparrows on one of the pans of a balance and six swallows on the other pan; it turns out that the sparrows are heavier. But if you exchange one sparrow and one swallow, the weights are exactly balanced. All the birds together weigh 1jin.What is the weight of a sparrow and a swallow, respectively? [Give the answer in liang, with 1 jin =16 liang.] (Nine Chapters, Chapter 8, Problem 9)68. Consider the task of pulling a weight of 40 dan14 up a hill; we have one military horse, two ordinary horses, and three weak horses at our disposal to get the job done. It turns out that the military horse and one of the ordi nary horses, pulling together, are barely able to pull the12A liangwas about 16 grams at the time of the Han Dynasty.