MATH 191 EXAM 2 NAME

There are 17 problems on this exam. Only those problems that say “explain” require explanations. Answers that require explanations will be given at most half credit without the required explana- tion. Be sure to follow all directions.

In problems 1-2 use the three set Venn diagram with sections numbered 1-8 to determine the specified information.

U 1 A B

2 3 4

6

5 7

C 8

1. Use sets A, B, and/or C together with the operations of union, intersection, set difference, and/or complements to identify the set that includes the specified sections. (3 points each)

(a) Section8 (b) Sections3,4,and7

2. Identify by number the section(s) included in each of the following sets. (3 points each)

(a) A ∩ C (b) (B ∪ C) ∩ A 3. There are 40 families living in a large neighborhood in Carville. For a school project one of the neighborhood children surveyed each family about the colors of their cars. Use the following clues to sort the families by the colors of their cars among the eight sections in the Venn diagram below. In set B put the number of families that have a blue car, in set R put the number of families that have a red car, and in set W put the number of families that have a white car. (8 points)

None of the families have only a blue car.

2 families have a blue car but not a red car.

9 families have a red car but not a white car.

3 families have a blue car and a red car but not a white car.

10 families have a blue car.

22 families have a red car.

23 families have a white car.

U

B R

W

4. Use the completed Venn diagram in problem 3 to determine the following. (3 points each)

(a) n(R ∪ W ) (b) n((B ∪ R) ∪ W ) In problems 5-9 indicate what operation is needed to solve the problem and indicate by name the model/interpretation that should be used to solve the problem. DO NOT SOLVE THE PROB- LEMS. (4 points each)

5. On each of the past three days Bugs Bunny has pick four carrots from Elmer Fudd’s garden. How many carrots did Bugs Bunny pick during the last three days?

6. Last month Marvin the Martian made three trips from Mars to the Earth. If each trip covers four margons (a margon is a Martian unit of length), what was the total distance traveled by Marvin?

7. Porky Pig bought eight chocolate cupcakes for his beloved Petunia. If Porky gets hungry and eats two of the cupcakes, how many will he have left to give to Petunia?

8. Bugs Bunny is nibbling on one of Elmer Fudd’s prize carrots that is eight inches long. If Bugs Bunny has eaten three inches of the carrot, how much of the carrot remains to be eaten?

9. Yosemite Sam is bagging his gold nuggets to take to the assay office. If he has fifteen gold nuggets and is placing them equally in three bags, how many nuggets will be in each bag? In problems 10-14 use an appropriate model/interpretation to solve the problems. Explain your model in the context of the problem and be sure to answer the question(s) posed by the problem. (8 points each)

10. Marvin the Martian is traveling eight margons (a margon is a Martian unit of length) to visit his friend on Venus. If Marvin has already traveled three margons, how much farther does he need to travel to reach his destination?

11. Granny has seventeen cat treats for Sylvester. If she gives Sylvester three treats a day, how many days will it be before she needs to buy more treats? 12. Pepe le Pew is going to buy a bouquet for his beloved Penelope. At the flower shop he can choose one of four colors of roses (red, yellow, pink, or purple) bound with one of three colors of ribbon (white, red, or green). How many different choices of a bouquet does Pepe have?

13. Marvin the Martian is changing the carpet on the flight deck in his spaceship. The flight deck has a rectangular shape that is three feet by five feet. How many one foot by one foot carpet squares will he need to complete the project? 14. Porky Pig is on a diet. His goal is to lose six inches off his waistline. If he loses two inches per week, how many weeks will it take for him to reach his goal?

15. Start at 423 and count by ones in Base Six. Record your counting in the boxes below. (5 points)

423 16. A box contains the following Base Six blocks: 5six flats, 22six rods, and 14six cubes. Draw a picture of these blocks and determine what Base Six number they represent. Show any necessary trades. (8 points)

17. What property can be used to justify each of the following equations? Give the full name of the property and be sure the spelling is correct. (3 points each)

(a) 5 · 3+2=2+5 · 3

(b) (5+3)+2=5+(3+2)