Document 2400028

Name: __________________________________________________ Math 139: Study Guide Questions Round all answers to 2 decimal places when necessary. 1. Find the simple interest paid to borrow $3700 for 3 years at 9%. 𝐼 = 𝑃𝑟𝑡 2. Billy deposits $2000 into a savings account that pays 5.25% interest compounded annually. How much will Billy have after 5 years? 𝐴 = 𝑃 1 +
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3. Sharon wants to have $10,000 as a down payment for her house in 5 years. How much money must she invest at 9% compounded quarterly to have enough for the down payment? 𝐴 = 𝑃 1 +
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4. The average 5 oz. cup of frozen yogurt costs $5.79 in 2012. Inflation since 2005 has been 5%, what was the average cost a 5 oz. cup of frozen yogurt in 2005? 𝐴 = 𝑃𝑒 !" 5. The average cost of the Toyota Camry in 2012 is $23,000. Inflation is at 7%, what will the cost of a Toyota Camry be in 30 years? 𝐴 = 𝑃𝑒 !" 6. Megan is buying new SUV that costs $25,000. She pays $2500 down at 3% add-­‐on interest for 6 years. a. How much needs to be financed? b. What is the total amount of interest paid over the course of the loan? 𝐼 = 𝑃𝑟𝑡 c.
What is the total amount to be repaid? 𝐴 = 𝑃 + 𝑃𝑟𝑡 d. What is the monthly payment? e. What is the total cost of Megan’s car? 7. John takes out a loan for $175,000 to buy a house. The current mortgage rates are 3.25% for 30 years. !
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a. Calculate the monthly payment. 𝑅 =
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b. How much interest will he pay over the life of the 30-­‐year loan? c. Complete the first two months of his Amortization Schedule. Payment # Interest Payment 𝐼 = 𝑃
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Principal Payment Balance of Principal $175,000 1 2 8. Four members are running for President of the Greater New Orleans Stamp Club: Andy (a), Brett (b), Carol (c), and Denise (d). The voter profile is summarized in the table. a. Use the plurality method to determine the winner. b. Use the pairwise comparison method to determine the winner. c.
Use the Borda method to determine the winner. d. Use the Hare method to determine the winner. 9. The table below represents a pairwise comparisons method election.
What is the missing number of pairwise comparisons won?
Candidate
Number of pairwise comparisons won
A
3
10. (3 pts.) The given table represents a Borda method election.
Find the missing number of Borda points.
Total number of voters: 26
Candidate
Number of Borda points
A B C D
54 49 57 ?
E
38
B
1
C
5
D
3
E F
1 ?
9.8 Fractals 1. Understand deductive reasoning. 2. Understand inductive reasoning. 3. Label each of the following as inductive or deductive: a. If the mechanic says it will take seven days to repair your car, then it will actually take 10 days. The mechanic says, “I figure it will take a week to fix it, ma’am.” Then you can expect it to be ready ten days from now. b. It has rained every day for the past six days, and it is raining today as well. So it will also rain tomorrow. c. Carrie’s first three children were boys. If she has another baby, it will be a boy. d. If the same number is subtracted from both sides of a true equation, the new equation is also true. I know that 9 + 18 = 27. Therefore, (9 + 18) – 13 = 27 – 13. e. If you build it, they will come. You build it. Therefore, they will come. f. All men are mortal. Socrates is a man. Therefore, Socrates is a mortal. 4. Determine the most probable next term in each of the following lists of numbers. a. 6, 9, 12, 15, 18 b. 13, 18, 23, 28, 33 c. 3, 12, 48, 192, 768 d. 3, 6, 9, 15, 24, 39 e.
1 3 5 7 9
, , , , 2 4 6 8 10
f. 1, 4, 9, 16, 25 g. 2, 6, 12, 20, 30, 42 h. -­‐1, 2, -­‐3, 4, -­‐5, 6 5. What is the next term in the list? O, T, T, F, F, S, S, E, N, T (Hint: Think about words and their relationship to numbers) 6. If you ask Becca how many dogs she has, she answers with a riddle: “Four-­‐fifths of my dogs plus 8.” How many dogs does she have? 7. You have brought two unmarked buckets to a stream. The buckets hold 7 gallons and 3 gallons of water, respectively. How can you obtain exactly 5 gallons of water to take home? 8. How many squares are in the figure? 9. A day is divided into 24 hours. Each hour has 60 minutes, and each minute has 60 seconds. In another system of measurement, each day has 250 naps and each nap has 5000 winks. How many winks are in a second? 10. True or False: a. Every natural number is divisible by 1. b. There are no even prime numbers. c. If n is a natural number and 9 n , then 3 n . d. If n is a natural number and 5 n , then 10 n . e. 1 is the least prime number. f. Every natural number is both a factor and a multiple of itself. g. If 16 divides a natural number, then 2, 4 and 8 must also divide the natural number. h. The prime number 53 has exactly two natural number factors. i.
Every natural number is positive. j.
Every whole number is positive. k. Every integer is a rational number. l.
Every rational number is a real number. 11. Use divisibility tests to decide whether the given number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, 10, 12 a. 321 b. 540 c. 36,360 d. 123,456,789 12. List two primes that are consecutive natural numbers. 13. For a natural number to be divisible by both 2 and 5, what must be true about the last digit? 14. Find the prime factorization of each composite number. a. 168 b. 300 c. 468 d. 931 15. F22 = 17, 711 and F24 = 46, 368 . What is the value of F23 ? 16. A pattern is established involving the Fibonacci sequence. Use deductive reasoning to make a conjecture concerning the next equation in the pattern. a. b. 17. Express each as a sum of Fibonacci numbers where no number is used more than once. a. 37 b. 40 c. 52 d. 175 18. Give a number that satisfies the given condition. a. An integer between 4.5 and 5.5 b. A rational number between 2.8 and 2.9 c. A whole number that is not positive and is less than 1 d. A whole number greater than 4.5 e. A irrational number that is between 13 and 15 f. A real number that is neither negative nor positive. "
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1 3
19. List all numbers from the set #−9, − 7, −1 , − , 0, 5, 3, 5.9, 7& that are: $
'
4 5
a. natural numbers b. whole numbers c. integers d. rational numbers e. irrational numbers f. real numbers 20. Give one number between -­‐6 and 6 that satisfies each given condition. a. Positive real number that is not an integer. b. Real number that is not positive. c. Real number that is not whole. d. Rational number that is not an integer. e. Real number that is not rational. f. Rational number that is not negative. 21. Label each as rational or irrational. !"
a. ! b. 3.14159 c. 𝜋 d. 0.2626262626 … e. 0.28228222822228 … 22. Simplify each expression. a.
441 b. 252 c.
240 23. For each of the following sets give the cardinal numbers.
a. {m, a, t, h}
b. {3, 6, 9, 12, 15, . . . }
c. 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟
d. {January, February, March, …, November, December}
e. 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟
24. Show that the set{4, 8, 12, 16, 20, . . .} has a cardinal number
by setting up a one-to-one correspondence
between the given set and the set of natural (counting) numbers.
1. Use the graph to the right to answer the following: a. Of the period 2001-­‐2011, list all years when receipts exceeded outlays b. Identify the greatest one-­‐year drop in receipts c. Identify the greatest one-­‐year rise in outlays 2. Use the graphs below to answer the following: a. About what was the gross domestic product in 2008? b. Over the six-­‐year period, about what was the highest consumer price index, and when did it occur? c. What was the greatest year-­‐to-­‐year change in unemployment rate, and when did it occur? 3. Use the graph below to answer the following: a. What is the greatest single expense category? b. What percentage is spent on Social Security and Defense? 4. Use the graph below to answer the following: a. Assuming Claire can maintain an average annual return of 9%, how old will she be when her money runs out? b. If she could earn an average of 12% annually, what maximum net worth would Claire achieve? At about what age would the maximum occur? 5. The following data represent the daily high temperatures (in degrees Fahrenheit) for the month of June in a southeastern U.S. city 79 84 88 96 102 104 99 97 92 94 85 92 100 99 101 104 110 108 106 106 90 82 74 72 83 107 111 102 97 94 Use six classes with uniform width of seven. a. Construct a frequency and relative frequency distribution table. b. Construct a histogram. 6. Use the table to below to find the following: a. Find the mean, median and mode (if any) for departures. b. Find the mean, median and mode (if any) for fatal accidents. c. Find the mean, median and mode (if any) for fatalities. 7. Find the grade point average. A = 4, B = 3, C = 2, D = 1, F = 0. 8. You Math 139 grade consists of homework, labs, four exams and a final exam. You grade is weighted as follows: Homework: 10% Labs: 10% Each Exam: 12.5% Final Exam: 30% At the end of the semester you are trying to calculate your average. You have a 100% for homework, an 88% on labs, and you scored a 70, 62, 54 and a 58 on the four exams. Then you scored a 66 on the final exam. What is your final average in the class? Will you pass the class with at least a C average? 9. The following are the numbers of dinner customers served by a restaurant on 40 consecutive days. 46 51 52 55 56 56 58 59 59 59 61 61 62 62 63 63 64 64 64 65 66 66 66 67 67 67 68 68 69 69 70 70 71 71 72 75 79 79 83 88 a. Find the fifteenth percentile b. Find the seventy-­‐fifth percentile \ 10. The lifetimes of Brand A tires are distributed with mean 45,000 miles and standard deviation 4500 miles, while brand B tires last for only 38,000 miles on the average (mean) with standard deviation 2080 miles. Nicole’s Brand A tires lasted 37,000 miles and Matt’s Brand B tires lasted 35,000 miles. Relatively speaking, within their own brands, which driver got the better wear? 11. Construct box plots for both exports and imports, one above the other in the same drawing. 12. On standard IQ tests, the mean is 100, with a standard deviation of 15. The results come very close to fitting a normal curve. Suppose the IQ test is given to a very large group of people. Find the percent of people whose IQ scores fall into each category. a. Less than 100 b. Greater than 115 c. Between 70 and 130 d. More than 145 e. Less than 70 13. Raymond rolls a die and flips a coin. a. List all he possible outcomes. b. How many ways are there to get an even number and a “head”? 14. Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}. a. List the different ways of choosing three representatives. b. How many different ways are there to choose three representatives if two must be male and one must be female? 15. Paul is making a CD of his 16 favorite songs to listen to on his drive to work. 10 of the songs are from Mumford and Sons and 6 of the songs are from The Avett Brothers. a. How many ways can he order the songs on the CD if there are no restrictions? b. How many ways can he create his CD if he wants all of the Avett Brothers songs first? 16. At a lumber company, shelves are sold in four different types of wood, three different widths and three different lengths. How many different types of shelves could be ordered? 17. Cassie’s 30th birthday is coming up and she wants to rent a limo. The limo only holds 11 other people besides her. She has 17 close friends to choose to take in the limo with her for her birthday celebration. How many different ways can 11 of her friends be chosen to be in the limo for the celebration? 18. The CCU math department needs to select a chairperson for each of five different committees. There are 15 professors to choose from. How many different ways can five chairpersons be selected? 19. Determine the number of distinguishable arrangements of the letters in the word SCIENTIFIC. 20. Consider each of the following scenarios and decide if order matters or doesn’t matter. a. Ordering a pizza with 3 different toppings from a restaurant that offers 22 toppings. b. A professor choosing 5 specific problems to grade on a homework assignment out of 15 problems that were assigned. c. Your phone number. d. Being called up to the counter at the DMV. 1.
The table below shows the outcomes from rolling a six-sided die 30 times.
a.
b.
What is the empirical probability that I rolled a three?
What is the theoretic probability I rolled a three?
2.
Anthony’s math class has 15 girls and 10 boys. Anthony randomly selects a student to put a problem on the board, with event E =
{selecting a girl}, give each of the following:
a. the number of favorable outcomes
b. the number of unfavorable outcomes
c. the total number of possible outcomes
d. the probability of an selecting a girl
e. the odds in favor of selecting a girl
3.
Three fair coins are tossed.
a. Write out the sample space
b. Determine the probability of no heads
c. Determine the probability of exactly one head
d. Determine the probability of exactly two heads
e. Determine the odds in favor of three heads.
4.
An urn has 8 red marbles, 5 blue marbles and 6 yellow marbles. Find each of the following:
a. P(Red)
b. Odds in favor of Yellow
c. P(not Blue)
d. Probability of blue and then red without replacement
e. Probability of blue and then red with replacement.
5.
In an essay contest, a teacher finds that seven students have written excellent essays. Three of these students are Alicia, Pat, and David.
If the teacher chooses the first place winner, second place winner, and third place winner from these seven students, what is the
probability that Alicia will win first prize, Pat will win second prize and David will win third prize?
6.
The Gray Stone Rock Band will give 10 performances this season. Four of these will be only songs from the 70s. If Tony gets to pick
two tickets at random, what is the probability that he will get both 70s tickets?
7.
For the experiment of drawing a single card from a standard 52-car deck
a. Find the probability of a king or queen
b. Find the probability of a club or heart
c. The card is an ace or not a club
d. Find the probability of not a heart
e. Find the probability of a spade or face card
f. Find the odds in favor of not an ace
g. Find the odds in favor of a heart.
h. Find the probability of a heart or a seven.
i. Find the probability of neither a heart nor a seven.
8.
Decide whether the following events are mutually exclusive or not:
a. Being a male and being a nurse
b. Drawing a face card and a two in one draw.
c. Drawing a face card and a space in one draw.
d. Wearing a coat and wearing a sweater.
Decide whether the following events are independent or not.
a. A die is rolled twice. The events are “the sum is eight” and “the first roll is a 3.”
b. Two marbles are drawn without replacement. The first marble is red and the second marble is green.
9.
10. Using the chart, find the probability that a customer is:
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
11. The table shows the distribution of family size in a certain U.S. city. If a family is selected at
find each of the following probabilities:
a. The family size is less than 5
b. The family size is not 3
c. The family size is at least 6
random,
12. An urn contains 8 balls identical in every aspect except color. There is 1 red ball, 2 green balls, and 5 blue balls. You draw two balls
from the urn, but do not replace the first ball before drawing the second. Find the probability that the first ball is blue and the second is
green.
13. An urn contains 8 balls identical in every aspect except color. There is 1 red ball, 2 green balls, and 5 blue balls. You draw two balls
from the urn, but replace the first ball before drawing the second. Find the probability that the first ball is blue and the second is green.
14. If two fair dice are rolled, find the probability that the sum is six, given that the roll is a “double.”
15. For the experiment of drawing 2 cards from a deck without replacement:
a. Find the probability that both cards are black
b. Find the probability of getting a heart on the first card and a diamond on the second.
c. Find the probability of drawing Two face cards (aces are not face cards)
d. Find the probability of drawing a queen of heart given you drew a seven of heart first.
16. A game consists of rolling a single fair die and pays off as follows: $3 for a 6, $2 for a 5, $1 for a 4, and no payoff otherwise.
a. Find the expected winnings for this game.
b. What is a fair price to pay to play this game?
17. Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What are your
expected net winnings?
18. An insurance company will insure a $220,000 home for its total value for an annual premium of $510. If the company spends $30 per
year to service such a policy, the probability of total loss is 0.001 and you assume either total loss or no loss will occur, what is the
company’s expected annual gain (or profit) on such a policy?
19. Ten thousand raffle tickets are sold. One first prize of $2000, four second prizes of $700 each, and eight third prizes of $300 each are to
be awarded, with all winners selected randomly. If you purchase one ticket, what are your expected earnings?
20. Know how to play and answer questions about Corudo.