Test #3 - Covers 5.2, 5.3, 5.4, 6.1 and 6.2

No note cards!

Scratch paper is provided.

Use of calculators is encouraged.

This test is 9 pages and includes 12 problems and one extra credit problem.

Instructions:

To receive credit, you must show all work and explain all your reasoning. If you use you calculator, tell me how. If you guess-and-check, tell me how.

Honor Statement:

By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam. This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor. Furthermore, you agree not to discuss this exam with anyone until the exam testing period is over. In addition, your calculator’s program memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor.

Signature Date

1. True and False. [2 pts each]

a) . T F

b) If x and y are integers then . T F

c) 30% of 70 = 70% of 30. T F

d) is a rational number. T F

e) T F T F

1. Find three fractions that are between . Show your work and explain your reasoning. [6 pts]

2. Study the array below:

mmmmmmm

a) Circle 2/3 of the m's [ 2 pts]

b) How many m's did you circle? Explain [2 pts]

c) Draw a picture that represents fraction equivalent to the one in part (a) and explain your reasoning. [2 pts]

3. A certain antibiotic kills approximately ½ the germs on the first day you take it, ½ of those left on the second day, ½ of those left on the third day, etc.

After 10 days, what fraction of germs remains? [4 pts]

If you had 20 million germs in your body, how many of them remain after 10 days of taking the antibiotic? [4 pts]

4. Bristol Staple Manufacturing uses 4.2 centimeters of steel wire for each roofing staple they manufacture.

a) If the plant uses 3,549000 cm of wire in a day, how many staples did they make? Show your work and explain your reasoning. [4 pt]

b) If the wire cost 3.4¢ per meter (100 cm), what is the cost per day of the wire? Show your work and explain your reasoning [4 pt]

5. Sean has quiches. He figures one serving should be about of a quiche.

a) How many people can he serve? [4 pts]

b) How much quiche does he have left over? [3 pts]

c) What percent of a serving is the amount you found in part b? [3 pts]

6. Using either an array model or a paper-folding model solve and give a brief description of why it works. [8 pts]

7. If of the members of a committee show up at the meeting, and there are only enough chairs for of those present.

a) What fraction of the committee can be seated on chairs? [4 pts]

b) If there are 18 members on the committee, how many chairs are there? [4 pts]

8. Find the product by

a) Changing the numbers into fractions, performing the multiplication, and changing back into decimal form. [2 pts]

b) Multiplying the two decimals together. [2 pts]

c) Are your answers the same? Why or why not. [2 pt]

9. The ratio of women to men in Phil’s class is 3:2 (not MTE 180J). The ratio of women to men in Tracey’s class is 2:1. Phil has 30 students enrolled in her class, and Tracey has 39 students enrolled. Who has more men enrolled? Explain your reasoning. [6 pts]

10. Lance makes $52,000 per year, and Stan makes $45,000. Lance just got a $2000 raise. If Stan got a raise that was proportional to Lance's, how much is Stan's raise? [8 pt]

11. Stock in Bristol Manufacturing started out the week selling at $50 per share. Tuesday it lost 5% of its value, on Wednesday it's price went down another 10% and Thursday it went down another 5% of its value. Friday, however, the stock rallied, and the price increased 20%. What is the selling price of the stock (to the nearest cent) on Friday? Show your work and explain your reasoning. [8 pt]

12. A 3-ounce portion of chicken has 130 calories. Your portion weighs 5 ounces. How many calories does it have? [8 pt]

Extra Credit

Me and three other people were stuck in a cave and one person was injured and would need to go to the hospital. Since we had no supplies left except for one flashlight, we had to get everyone out of the cave before we could go to the hospital. Now the tunnel out of the cave was only large enough for only 2 people to go through it at a time. The two people need to take the flashlight with them and then one of the 2 people has to return the flashlight to the other people in the cave. Now, I can crawl through the tunnel in 1 hour, Jen can crawl through in 2 hours, Mary takes 4 hours, and John (who is injured) takes 7 hours. When two people are traveling out together, they must stick together so they can only go as fast as the slowest person. Also, it takes a person the same amount of time to return to where everyone is stuck as it takes he or she to get out of the cave. What is the absolute fastest time everyone can get out of the cave so we can get John to the hospital? What order should we go in to achieve this time? [4 pts]