Math 139 Final Exam Review

Math 139 Final Exam Review
1. Joe’s parents want to have $100,000 in a savings account when he turns 20 (Joe was just born). How
much do they need to deposit in a savings account that offers them 2% compounded semi-annually?
Round to two decimal places.
! !
𝐴=𝑃 1+!
2. In 2003 a car cost $15,000. Find the 2009 price with 5% inflation.
𝐴 = 𝑃𝑒 !"
3. Joe is buying a new car that costs $20,000. He has $2000 from selling his old car to put as a down
payment. Answer the following questions, rounding your answers to two decimal places.
a. How much does he need to finance?
b. The dealer says the interest rate is 7% add-on interest for four years. Find the amount to be
repaid.
𝐴 = 𝑃 + 𝑃𝑟𝑡
c. What is the monthly payment?
d. What is the total amount of interest paid over the course of the loan?
4. Complete the first two months of the following amortization schedule. The mortgage is $100,000 at
5% interest over 15 years. Round your answers to two decimal places.
𝑟
𝑃 12
𝑅=
12
1 − 12 + 𝑟
Payment # Interest Payment !r $
I = P # & " 12 %
Principal Payment !"!
Balance of Principal $100,000 1 2 5. Thirty-five people vote for their favorite board game with these three choices given:
Clue (C), Monopoly (M), and Scrabble (S). The votes are summarized below.
Number of Votes
10
12
13
Ranking
C>M>S
M>S>C
S>M>C
a. Use the plurality method to determine a winner.
b. Use the pairwise comparison method to determine a winner.
c. Use the Borda method to determine a winner.
d. Use the Hare method to determine a winner.
6. What type of reasoning is used in each of the following scenarios?
Please write “inductive” or “deductive” on the blank.
a. The sum of an odd number and an even number is always odd.
Thus, 7 + 2 = an odd number.
________________________
b. Every morning over the last two months Jill drank a cup of coffee and ate a piece of toast.
So, tomorrow morning Jill will drink a cup of coffee and eat a piece of toast.
________________________
7. Identify a pattern in the given list of numbers.
Then, use this pattern to find the next number in the pattern.
a. 81, 27, 9, _______
b.
1 1 1 1
, , , , _______
2 4 8 16
8. You have a 6 oz. cup and a 10 oz. cup. How do you get exactly 8 oz. of water in the 10 oz. cup?
9. Someone asked me how many pairs of shoes I have in my closet, and I responded,
“Two-thirds of my shoes plus 8.” How many pairs of shoes do I have? Show all work.
10. Use the rules of divisibility to determine whether 6,876,648 is divisible by the following numbers.
State “yes” or “no” for each, and explain your answers. (You MUST use the divisibility tests and
explain your answers for credit.)
a. 2
b. 3
c. 4
d. 5
e. 6
f. 8
g. 9
h. 10
i. 12
11. Find the prime factorization for each of the following numbers:
a. 90
_____________________
b. 24
_____________________
c. 55
_____________________
12. List the first twelve numbers in the Fibonacci sequence.
13. Express the following as a sum of distinct Fibonacci numbers:
a.
40
_____________________
b.
72
_____________________
14. Simplify the following expressions.
a.
50 =
_____________________
b.
9
=
49
_____________________
15. Find numbers between -3 and 3 that meet the following criteria:
a. A whole number that is not a natural number
__________________
b. A positive irrational number
__________________
c. A negative rational number that is not an integer
__________________
16. Label each of the following as “rational” or “irrational”.
a. 2.56
__________________
b. 5.12121212121212... __________________
c.
3
7
d.
17
e. e
__________________
__________________
__________________
17. True or False?
a. Every natural number is positive.
_____________________
b. Every rational number is a real number.
_____________________
c. There is a largest prime number.
_____________________
d. Every integer is a rational number.
_____________________
e. Every rational number is an integer.
_____________________
18. List the cardinality of each of these sets:
a. the set of rational numbers
_______
b. {apple, pear, banana, orange} _______
c. the set of irrational numbers _______
d. {2, 5, 8, 13, 24, 29, 35}
_______
19. Show that the following set has cardinal number ℵ! by setting up a one-to-one correspondence
between the given set and the set of counting numbers.
Show all work.
{4, 8, 12, 16, ...}
20. Draw Stages 1 and 2 of the Sierpinski triangle.
Stage 0
Stage 1
Stage 2
21. Draw Stages 1 and 2 of the Koch Snowflake.
______________
Stage 0
Stage 1
a. If the old size = 1, what is the new size of the Koch Snowflake?
b. What is the scale factor of the Koch Snowflake?
Stage 2
22. Use the graph to answer the following:
a. In what years was the gross domestic product above
14,000 billion dollars?
b. In what years was the gross domestic product
between 12,000 and 14,000 billion dollars?
c. What was the gross domestic product in 2005?
(approximately)
23. The weights of 10 different people were recorded as follows. Find each of the following for this set of
data.
Weights: 131, 145, 178, 203, 134, 165, 121, 145, 198, 154
a. Mean:
b. Median:
c. Mode:
24. Find the grade point average for a student with the following grades.
Assume A = 4, B = 3, C = 2, D = 1, and F = 0.
Units
3
12
6
3
Grade
A
B
C
D
25. Draw each of the following:
a. A normal distribution
b. A uniform distribution
c. A bimodal distribution
d. A skewed left distribution
e. A skewed right distribution
26. Consider a set of test scores with a mean of 75 and standard deviation 3. The test scores are normally
distributed.
a. What percentage of students scored over 75?
b. What percentage of students scored under 72?
c. What percentage of students scored between 72 and 78?
27. Denise decided to take the SAT to gain entrance into college and scored a 1920. The average SAT
score is a 1500 with a standard deviation of 240. Sharon on the other hand took the ACT and scored a
29. The average ACT score is a 21 with a standard deviation of 6.
a. Find the z-score for Denise
b. Find the z-score for Sharon
c. Relatively speaking, who did better?
28. The following scores on the midterm exam in Math 139 were recorded.
59
60
61
67
68
69
71
72
76
77
78
81
82
82
83
84
88
89
91
94
95
96
Complete the grouped frequency and relative frequency distribution table.
Class Limits
Frequency f
Relative Frequency f/n
59-66
3
13.6%
67-74
75-82
6
83-90
91-98
18.2%
4
29. John took the SAT and scored in the 75th percentile.
a. What percentage of scores were above his score?
b. What percentage of scores were at or below his score?
30. Joe flips a coin 3 times.
a. Draw a tree diagram and list all possible outcomes.
b. Based on your diagram, how many ways are there to get exactly 1 tails?
c. Based on your diagram, how many ways are there to get at least 2 heads?
31. Jill is choosing an outfit. The outfit must consist of shoes, pants, and a shirt. She has 5 pairs of shoes,
3 pairs of pants, and 8 shirts. Assuming that all of the pieces match, how many different outfits can
she make?
32. There are 10 people to be seated on stage, 3 women and 7 men.
a. How many ways are there to seat the 10 people if all 3 women must be seated first?
b. How many ways if there are no restrictions on who is seated first?
33. There are 20 horses in a race, and Bob much choose a 1st place, 2nd place, and 3rd place winner on
which to bet. How many different bets can he make?
34. There are 25 people in a class, and 10 people are selected to present their projects on the first day of
presentations. How many different ways can this group of 10 people be selected?
35. Permutation or combination? (Simply write P or C. You do not need to compute.)
a. Ways of choosing a committee of 3 people out of 15
b. Possible outcomes in a beauty pageant with 1st, 2nd, and 3rd places
c. Telephone number possibilities
36. I rolled a die 50 times with the following results:
# on die # of rolls 1 2 3 4 5 6 11 7 8 10 6 8 What is the empirical probability for rolling a 4? 37. There are 45 marbles in a box. 7 are blue, 24 are green, and 14 are red. A marble is randomly selected
from the box.
a. What is the probability that the marble chosen is blue? b. What is the probability that the marble chosen is not blue? c. What are the odds in favor of a blue marble being chosen? d. What are odds in favor of a blue marble not being chosen? 38. One card is drawn from a well-shuffled deck of 52 cards. Find each of the following:
a. P(club or spade) = _____
b. P(not a club) = _____
c. P(club or king) = _____
d. P(not a club nor a king) = _____
39. A group of 20 people were surveyed to see how many ounces of water they drink on average each day.
Ounces # of people Less than 16 3 16-­‐32 7 33-­‐48 5 49-­‐64 3 65 or more 2 If a person is select at random: a. What is the probability that the person drinks more than 32 ounces per day on average?
b. What is the probability that the person drinks between 16 and 64 ounces per day on average?
40. You draw a card from a standard 52-card deck. What is the probability that the card is a three given
that the card is a club?
P( three | club ) = 41. Label the following as “independent” or “dependent” events.
a. Flipping a coin twice
____________
b.
____________
Choosing 3 animals from a pet store without replacement
c. Choosing 3 marbles from a box with replacement
____________
42. A coin is flipped twice. What is the probability that you flip heads and then flip tails?
43. Two cards are selected from a standard 52-card deck without replacement. What is the probability of
selecting a jack and then a face card?
44. There are 15 marbles in a box, 7 blue and 8 red. You randomly choose two marbles with replacement.
What is the probability that you select two red marbles? 45. Using the chart, find the probability that a customer is: (DO NOT REDUCE!)
a. Not satisfied
b. Not satisfied and walk-in
c. Not satisfied, given referred
d. Very satisfied
e. Very satisfied, given referred
f. Very satisfied and TV ad
46. You participate in a raffle to win $1000. There are 400 tickets sold, and each ticket costs $1. Find the
expected value if you buy one ticket. Round to the nearest cent.
47. You are playing a game in which you roll a die. If you roll a 2 you win $6, if you roll a 6 you win $10,
and otherwise you lose.
a. To be a fair game, what must be true of the expected value?
b. How much should be charged to be a fair game? Round to the nearest cent.
48. Three people are playing Corudo. Player #1 bids “eight sixes”.
Player #2 calls Corudo. Who wins the round? Player #1’s dice: Player #2's dice: Player #3's dice: 49. Suppose during a round of Corudo, the person before you bids 11 sixes. If there are currently 33 dice
in the game (including yours), and under your cup you have:
Number Expected 40% 25% 16% of dice value confidence confidence confidence 27 9 1 2 2 30 10 1 2 3 33 11 1 2 3 36 12 1 2 3 Should you challenge him/her? (“Challenge” means call Corudo). Explain your answer. 50. The person before you bids “six fives.” What is a legal bid for you to make on your turn (if you aren’t
calling corudo)?