Extra Comprehensive Practice Problems MATH 1332 1. At a Christmas party some of the guests brought cookies, drinks, or candy 5 guest brought cookies, candy and drinks 19 guests brought exactly 2 items 21 guests brought drinks 20 guests did not bring cookies 8 guests brought only candy 2 guests did not bring a drink or candy 5 guests brought only cookies and drinks 11 guests brought drinks and candy (a) How many total guests when to the party? (b) How many guests didn t bring anything? Let the Universal set U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with subsets: A = {1, 3, 5, 7} B = {3, 7, 9, 10} C = {1, 7, 10} D = {4, 8} 2. Is D A? 3. Is C C? 4. Is D a proper subset of A? 5. Is D a subset of C 6. Find B D 7. Find A B 8. Find C D 9. Find A C 10. Find A D 11. Find (A B) C 12. How many subsets does B have? 13. How many proper subsets does C have? 14. Find D D 15. Find (B C) A 16. A survey was conducted on 100 people who visited the local health clinic today. Fill in the Venn diagram completely, based upon the following results. (NOTE: 2 numbers have been filled in for you) 44 did not have a cough 35 had a sore throat and runny nose 57 had a runny nose 31 had a cough and runny nose 22 did not have a sore throat or runny nose (a) how many students had a sore throat?
17. ReAnna has a rare coin collection made up of 8 silver dollars, 9 quarters, and 7 dimes. ReAnna plans to sell 5 of her coins to finance part of a car. If she selects the coins at random, what is the probability all five coins are quarters? 18. Conditional Statement: If you go for a run, you will be late for dinner. What is the inverse statement? 19. The data below shows the number of fires that occurred in the city of Metropolis during the following years. What was the average number of fires occurring during these years? Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 Number of Fires 7 4 9 2 10 13 6 8 5 20. John earned $108.74 in interest after depositing $3250 into an account earning simple interest for 11 months. What was the interest rate on the account? 21. For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be more than 62 hours. 22. Is the following syllogism valid or invalid? All dachshunds are mean. Sport is a mean Sport is a dachshund 23. Researchers asked students in grades 4 through 6 in three school districts in Michigan about what they thought was the most important thing in school. The results are below. Based on these results, what is the probability a person randomly selected from this group: (a) Thinks grades are most important? (b) Is from a Suburban area? (c) Is from an Urban area, given they think Sports is most important? (d) Thinks being Popular is most important, given they are from a Rural area? 24. An animal shelter has 15 cats and 12 dogs available for adoption. The shelter wants to select 6 cats and 4 dogs to feature in the adoption newspaper. In how many ways can this be done? 25. Twelve students are competing for 4 writing scholarships of varying amounts. In how many ways can the scholarships be awarded? 26. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last less than 7 months.
27. Use the graph to the right to determine (a) which month had the most rainfall in 1994? (b) How much rainfall occurred in August 1993? (c) Which month had the least amount of rainfall in 1993? 28. Ninety-five people were surveyed to see which characters they liked from the TV show FRIENDS. Based upon the following results, how many people said they liked ONLY liked Ross? 42 people did NOT like Ross 38 people liked Joey and Ross 71 people liked Monica 10 people like Monica and Ross, but not Joey 16 people liked ONLY Monica 21 people liked Joey, Monica, and Ross 1 person did not like any of them 29. If p is false, q is false, and r is true, decide if each of the following are TRUE or FALSE. (a) (p q) ~ r p ~ q p q (b) (c) ~p (q ~r) (d) p q r q 30. The data below shows the amount of ice cream sales over the course of 8 days as they related to the temperature that day. (a) Determine the correlation coefficient. Does a correlation exist at α = 0.01? (b) What is the line of best fit? (to 2 decimals) (c) Using the line of best fit, determine what the ice cream sales would be on a day the temperature is 93. 31. Is the following syllogism valid or invalid? Some kids love balloons. All kids who love balloons love clowns. Some kids love clowns. 32. Leslie wants to have $75,000 in 20 years to give as a gift to her dear friend Patrice. How much should she deposit today into an account earning annual interest rate of 2.25% compounded daily in order to reach her goal?
33. Make a truth table to find the truth values for: (a) (q p) ~q (b) (p ~q) ~p (c) ~p (q p) (d) (~p q) p 34. Let the conditional statement be: If we have pecans, then we can make a pie. What is the contrapositive statement? 35. If p is true, q is false, and r is false, decide if each of the following are TRUE or FALSE. (a) p (q ~r) (b) ~(q ~p) r (c) ~q (p r) 36. Tanner buys a house costing $284,000. He makes a down payment of 25% and finances the rest at an annual interest rate of 4.92% compounded monthly over the next 15 years. (a) What are his minimum monthly payments? (b) How much interest will he end up paying on this house? 37. A committee of 5 is to be chosen from among 10 women and 6 men. In how many ways can this be done if 3 women and 2 men must be on the committee? 38. Conditional Statement: If the radio is playing, then I am singing. What is the converse statement? 39. Is the following syllogism valid or invalid? All marigolds are annuals. Some tulips are annuals. Some tulips are marigolds. 40. Cooper invested $950 in an account earning simple interest at 4.2% for 9 months. How much interest did he earn? 41. Mason wants to have $15000 in 6 years to buy himself a car. What should his quarterly payments be if he invests his money in an account earning an annual interest rate of 3.15% compounded quarterly? 42. Pyper has a list of 15 people she needs to call on the phone. If she only has time to call 9 of them, in how many ways could these phone calls be made? 43. Conditional Statements: If you do not like basketball, then we cannot be friends. (a) What s the inverse? (b) What s the converse? (c) What s the contrapositive?
44. Is the following syllogism valid or invalid? No scarecrows are tin men. No tin men are lions. No scarecrows are lions. 45. A group of runners were asked how many miles they ran over the course of the past week. Based on the data to the right, (a) How many runners ran over 30 miles? (b) How many runners ran less than 15 miles? (c) How many runners ran 18 miles exactly? 46. Determine TRUE or FALSE for each of the following: (a) {penny} {penny, nickel, dime, quarter} (b) {a,b,c} {b,c,a} (c) {3, 4} {1, 2, 3, 4} (d) {3, 4} {1, 2, 3, 4} (e) {$,@,#} {@,#,$} 47. A bag contains five batteries, all the same size. Each battery is a different brand. You select three batteries at random, one at a time, from the bag. In how many ways could the batteries be selected if they are chosen (a) with replacement (b) without replacement 48. Cheryl goes grocery shopping. The probability she has a cracked egg when she gets home is 0.19. The probability she has a popped bag of chips when she gets home is 0.08. The probability the milk she bought is outdated is 0.0025. The probability she forgot the ice is 0.13. What s the probability (a) She forgot the ice and has a popped bag of chips. (b) She has a cracked egg or the milk is outdated. (c) The milk is outdated and she forgot the ice and the bag of chips is popped. (d) She has a cracked egg or she forgot the ice or the bag of chips is popped. 49. Mason has a bucket of sidewalk chalk. In the bucket, there are 2 blue, 8 green, 2 pink, 4 yellow, and 5 pieces of white chalk. If he randomly pulls out 4 pieces of chalk, what is the probability all four pieces are green?
50. Based on the table below, what is the probability that a randomly selected person (a) is an 8 th grader? (b) is a 7 th grader who like Math/Science best? (c) prefers history, given that the person is an 8th grader? (d) is a 7th grader given that the person prefers English? 51. The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $17,000. What percentage of employees make a salary of more than $42,500? 52. The height (in inches) and weight (in pounds) of ten different people were recorded in the table to the right. (a) Determine the correlation coefficient. (b) Is there a significant correlation at α = 0.05? (c) What is the line of best fit (to 2 decimal places)? (d) Use the equation to estimate the weight of a person who is 67 inches tall. 53. Let the universal set be U={a, b, c, d, e, f, g, h, i} with subsets: A = {x x vowels}, B = {c, d, f, g}, C = {a, b, c, d}, D = {e, f, g, h, i} (a) Find C D (b) Find A C (c) Find B D (d) Find A D (e) Is B a subset of A? (f) Is B a proper subset of A? (g) How many subsets does D have? 54. Julie buys a car for $28,500. She pays 15% down and finances the rest for 5 years at an annual percentage rate of 6.8% compounded monthly. (a) What are her minimum monthly payments? (b) How much interest does she end up paying on the car?