Name: 1332 Review for Final. 1. Use the given definitions to answer the following questions. 1,2,3,4,5,6,7,8,9,10

Transcription

1 1 Name: 1332 Review for Final 1. Use the given definitions to answer the following questions. U E A B C 1,2,3,4,5,6,7,8,9,10 x x is even 1,2,4,7,8 1,3, 4,5,8 2,4,8 D x x is a power of 2 and 2 x 10 a. Is a subset of E? b. Find n( C A). c. A is equal / equivalent to B. choose the correct word d. How many subsets are there of A? e. 3 is / of C. choose the correct symbol f. C is a / of A choose the correct symbol 2. Let U q, r, s, t, u, v, w, x, y, z A q, s, u, w, y B q, s, y, z C v, w, x, y, z Determine the following: a. AB C

2 2 b. C A c. B AC 3. Which of the following sets best describes the shaded part of the Venn diagram? C A B a) BC b) c) d) e) none of these AC B 4. A survey of 150 A&M students were asked which football activities they attended last weekend. Use the Venn diagram to help figure out how many students ONLY went to the game. 73 tailgated 22 went to midnight yell, tailgated, and attended the football game 48 did not attend the football game 30 went to midnight yell and the game 47 tailgated, but did not go to midnight yell 54 tailgated and went to the game 19 did none of these activities U A C B How many students ONLY went to the game? 5. Assume that p is true and that q and r are both false. Indicate whether the compound statements below are true or false: a. ~ p ~ r b. p (q ~ r) 6. Let p and q be any statements. Construct a truth table for: ( ~(p q ) q) ~p p q T T T F F T F F

3 3 7. Use a truth table to determine if these statements are equivalent: p ( q r) and ~ p ( q r). 8. Write the converse, inverse, and contrapositive of the statement: If you received a refund of over $1,000, then you cannot make a claim. 9. Determine a valid conclusion to an argument with the given premises: If it is a duck, then it does not waltz. If it is an officer, then it waltzes. If it is one of my poultry, then it is a duck. 10. Determine if the following is a valid argument: All businesses are subject to safety inspections. This restaurant is subject to safety inspections. This restaurant is a business. 11. John Lee's savings account has a balance of $4957. After 27 months, what will the amount of interest be at a 4.3% simple interest rate per year? Round to the nearest cent if needed. 12. Gilbert bought calculators for the math department. He paid $1,300 for the calculators and agreed to pay for them in 6 months at 3.5% simple interest. Find the amount of interest that he will owe. 13. A relative has decided to establish a bank account for your newborn daughter that will pay for some of her future college expenses. It is intended that the amount be worth $10,000 eighteen years from now. Assuming that the account will earn 7.6% compounded quarterly, how much money should be deposited into the account? 14. You wish to purchase a $123, home. You have enough for a 15% down payment. Furthermore, you are offered a 30 year mortgage at 6.75%. What are the monthly payments on the mortgage? 15. Eric has set up an ordinary annuity to save for his retirement in 15 years. If his monthly payments are $200 and the annuity has an annual interest rate of 6.5% compounded monthly what will be the value of the annuity when he retires?

4 4 16. George opened an IRA which earned 9% compounded monthly when he was 22, and deposited $100 every month into his account. How much money will be in this account when George retires at age 69? 17. If 81% of scheduled airline flights actually take place, and cancellations are independent events, what is the probability that 3 separate flights will take place? 18. One letter from the word MISSISSIPPI is written on each of 11 cards. What is the probability of drawing a card that shows an I? 19. Two fair die are rolled. What is the probability of rolling an even sum or a sum that is greater than 5? 20. If the probability that an event will not occur is 0.37, what are the odds that the event will occur? 21. The table shows the number of college students who prefer a given pizza topping. Toppings Freshman Sophomore Junior Senior Cheese Meat Veggie If a junior is selected at random, determine the probability a student prefers meat topping. 22. If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a "double". 23. How many ways can first, second, and third place be filled if 7 women are running in a race?

5 5 24.A signal is made by placing flags, one above the other, on a flag pole. a. If your signal uses 3 flags, how many possible signals can be flown if there are 8 different flags available? b. If your signal uses 7 flags, how many possible signals can be flown if there are 26 different flags available? 25. Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 10 shirts and 11 pairs of pants to choose from, in how many different ways can this be done? 26. Find the number of ways to arrange the letters in BASEBALL. 27. A class has 10 boys and 12 girls. In how many ways can a committee of 6 students be selected if: a. the committee can have at most two girls? b. the committee must have at least two girls? 28. A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. a. Find the probability that you have 1 lemon candy. b.find the probability that you have 2 orange candies and 1 lemon candy.

6 6 29. a. How many students attended 2 games? b. How many games were attended by the students in the survey? 30. A survey of the 4032 vehicles on the campus of State University yielded the following circle graph. a. What percent of the vehicles are hatchbacks? b. Find the number of motorcycles. Round your result to the nearest whole number. 31. Find the mean, median, mode and range, in that order, of the following data: 42, 64, 75, 82, 96, 93, 77, 82, 67, 78, 88, 90, 80, 72, 71, 80, 81, 98, 61, 75.

7 7 32. The following table shows the possible scores in a competition and the number of people who received each score. Find the mean, range, and standard deviation, in that order. Score Number of people A survey of white-collar workers found that the workers had a mean of years of experience, with a standard deviation of years. Assuming that the experience level is normally distributed what is the percentage of workers that had between 19 and 24 years of experience? 34. The table below shows the number of Mad about Math magazine subscribers (in millions) on December 31 st of the given years. Year Subscribers a. Find the linear equation of best fit (the least-squares regression line) for this data. Express the number of subscribers (in millions) as a function of the number of years since Round the slope and y-intercept of the line to 3 decimal places. b. If the trend continues, estimate the number of subscribers the magazine will have in c. When would you expect the number of magazine subscribers to reach 12,000,000? 35. The following table shows the July electric bill of selected homes in Cincinnati along with the number of rooms in each home. Determine the linear correlation coefficient for the data rounded to the nearest thousandth, and also determine whether there is significant linear correlation between the variables at 0.05 Number of Rooms March Electric Bill 4 $87 5 $102 5 $115 6 $112 7 $125 7 $135 8 $138