Math 1001 Exam 1 Name: Date: 1 2 3 4 5 6 7 8 9 10 11 12 Score (1) (12 points) A survey revealed the following results about the news sources that a sample of 130 people use: TV/radio only 20 TV/radio and Internet only 12 Internet only 29 TV/radio and Newspapers only 18 Newspapers only 15 Internet and Newspapers only 22 None 6 All three sources 8 Draw a three-circle Venn diagram that summarizes the results of the survey. How many people use TV/radio or Internet? (c) How many people use TV/radio but not newspapers?
2 (2) (8 points) Write the converse and contrapositive of the following propositions. Clearly label which is the converse and which is the contrapositive statement. If the patient is alive, then the patient is breathing. If the polar ice caps melt, then the oceans will rise.
3 (3) (12 points) State the truth value of the following statements. Cucumbers are vegetables and apples are not fruit. France is a country or Paris is a continent. (c) If pigs can fly, then fish can brush their teeth. (d) If 2 3 = 6, then 2 + 3 = 6.
4 (4) (8 points) You are deciding whether to buy a car for $18000 or to accept a lease agreement. The lease entails a $1000 initiation fee plus monthly payments of $240 for 36 months. Under the lease agreement, you are responsible for service on the car and insurance. At the end of the lease, you may purchase the car for $9000. Should the cost of service and insurance determine which option you choose? Does the total cost of purchasing the car at the end of the lease agreement exceed the cost of purchasing the car at the outset?
5 (5) (8 points) A new sidewalk will be 4 feet wide, 200 feet long, and filled to a depth of 6 inches (0.5 foot) with concrete. How many cubic yards of concrete are needed? (6) (8 points) Two cars, 360 kilometers apart, begin driving toward each other on a long, straight highway. One car travels 80 kilometers per hour and the other 100 kilometers per hour. At the same time, a canary, starting on one car, flies back and forth between the two cars as they approach each other. If the canary flies 120 kilometers per hour and spends no time to turn around at each car, how far has it flown when cars collide?
6 (7) (8 points) Clint s salary increased from $20000 to $28000 over a three year period. Helen s salary increase from $25000 to $35000 over the same period. Whose salary had the largest percent increase? Justify your answer. (8) (8 points) The 2410 women undergraduates at the college comprise 54% of all undergraduates. How many undergraduates attend the college?
7 (9) (12 points) Jordan and Amari run a 200-meter race, and Jordan wins by 10 meters. They decide to run the 200 meter race again with Jordan starting 10 meters behind the starting line. Assuming both runners run at the same pace as they did in the first race, who wins the second race? How far behind the starting line must Jordan start so the second race is a tie?
8 (10) (12 points) Gas mileage actually varies slightly with driving speed of a car. Suppose your car averages 38 miles per gallon on the highway if your average speed is 55 miles per hour, and it averages 32 miles per gallon on the highway if your average speed is 70 miles per hour. What is the driving time for a 2000-mile trip if you drive at an average speed of 55 miles per hour? What is the driving time at 70 miles per hour? Assume a gasoline price of $3.90 per gallon. What is the gasoline cost for a 2000 mile trip if you drive at an average speed of 55 miles per hour? What is the gasoline cost at 70 miles per hour?
9 (11) (8 points) The following rules are among many provisions of a particular credit card agreement. For the regular plan, the minimum payment due is the greater of $10 or 5% of the new balance shown on your statement (rounded to the nearest dollar)) plus any unpaid late fees and returned check fees, and any amounts shown as past due on your statement. If you make a purchase under a regular plan, no finance charges will be imposed in any billing period in which (i) there is no previous balance or (ii) payments received and credits issued by the payment due date, which is 25 days after the statement closing date shown on your last statement, equal or exceed the previous balance. If the new balance is not satisfied in full by the payment due date shown on your last statement, there will be a finance charge on each purchase from the date of purchase If the new balance in your account is $8 and you have $35 in unpaid late fees, what is your minimum payment due? Suppose you have a previous balance of $150 and you pay $200 one month after the statement closing date. Will you be assessed a finance charge?
10 (12) (6 points) A human heart beats about 70 times per minute. If an average human being lives to the age of 80 years old, how many times does the average heart beat in a lifetime?