Home work 7.3 Name: Due June 03

Practice 7.3 problems1-27 odd, 18, 22, 28, 30, 35, 37, 39-41, 49-53, 56-58, 60, 61, 63

1. Solve for x: 12(x + 5) = (x + 122) - 29

2. An entertainment guide recommends 6 restaurants and 3 plays that appeal to a couple. (A) If the couple goes to dinner or a play, but not both, how many selections are possible? (B) If the couple goes to dinner and then to a play, how many combined selections are possible? 3. A college offers 2 introductory courses in history, 3 in science, 2 in mathematics, 2 in philosophy, and 1 in English. (A) If a freshman takes one course in each area during her first semester, how many course selections are possible? (B) If a part-time student can afford to take only one introductory course, how many selections are possible? 4. The 14 colleges of interest to a high school senior include 6 that are expensive (tuition more than $30,000 per year), 7 that are far from home (more than 200 miles away), and 2 that are both expensive and far from home. (A) If the student decides to select a college that is not expensive and within 200 miles of home, how many selections are possible? (B) If the student decides to attend a college that is not expensive and within 200 miles from home during his first two years of college, and then will transfer to a college that is not expensive but is far from home, how many selections of two colleges are possible? 5. Complete the venn diagram and table

n(A) = 80, n(B) = 50, n(A ∩B) = 20, n(U) =200

n(A’) = 35, n(B’) = 75, n(A’ U B’) = 95, n(U) = 120

6. Using the English alphabet, how many 5-character case-sensitive passwords are possible? 7. A combination lock has 5 wheels, each labeled with the 10 digits from 0 to 9. How many 5-digit opening combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different? 8. A class of 30 music students includes 13 who play the piano, 16 who play the guitar, and 5 who play both the piano and the guitar. How many students in the class play neither instrument? 9. A cable company offers its 10,000 customers two special services: high-speed internet and digital phone. If 3,770 customers use high-speed internet, 3,250 use digital phone, and 4,530 do not use either of these services, how many customers use both high-speed internet and digital phone?

Home work 7.4 Name: Due on June 03

Practice 7.4 problems 1-15 odd, 21, 27, 31, 33, 37, 39, 41, 44, 46, 48, 50-53, 63-64, 71-79odd

1. Permutation, a combination, or neither? Explain your reasoning. a. A student checked out 4 novels from the library. b. A student bought 4 books: 1 for his father, 1 for his mother, 1 for his younger sister, and 1 for his older brother. c. A father ordered an ice cream cone (chocolate, vanilla, or strawberry) for each of his 4 children. 2. How many ways can a 3-person subcommittee be selected from a committee of 7 people? How many ways can a president, vice-president, and secretary be chosen from a committee of 7 people? 3. From a standard 52-card deck, how many 6-card hands consist entirely of clubs? 4. From a standard 52-card deck, how many 7-card hands consist of 3 hearts and 4 diamonds? 5. A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet committee selects 3 appetizers, 4 main courses, and 2 desserts. How many ways can this be done? 6. In how many ways can 4 people sit in a row of 6 chairs? 7. A basketball team has 5 distinct positions. Out of 8 players, how many starting teams are possible if (A) The distinct positions are taken into consideration? (B) The distinct positions are not taken into consideration? (C) The distinct positions are not taken into consideration, but either Mike or Ken (but not both) must start? 8. How many 4-person committees are possible from a group of 9 people if (A) There are no restrictions? (B) Both Jim and Mary must be on the committee? (C) Either Jim or Mary (but not both) must be on the committee? 9. An electronics store receives a shipment of 30 graphing calculators, including 6 that are defective. Four of these calculators are selected for a local high school. (A) How many selections can be made? (B) How many of these selections will contain no defective calculators? 10. A real estate company with 14 employees in their central office, 8 in their north office, and 6 in their south office is planning to lay off 12 employees. (A) How many ways can this be done? (B) The company decides to lay off 5 employees from the central office, 4 from the north office, and 3 from the south office. In how many ways can this be done?

Home work 8.1 name: Due Date: June 05

Practice 8.1 Problems 3-21 odd, 26-27, 29-31, 33, 36-38, 39-57 odd, 77, 79, 82, 83, 86, 91, 93

# A circular spinner is divided into 12 sectors of equal area: 5 red, 4 blue, 2 yellow, and 1 green. Consider the experiment of spinning the spinner once. Find the probability that the spinner lands on: a. Blue b. Yellow c. Yellow or green d. Red or blue e. Orange f. Yellow, red, or green # A combination lock has 5 wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 5 digits with no repeats, what is the probability of a person guessing the right combination? # Suppose that 5 thank-you notes are written and 5 envelopes are addressed. Accidentally, the notes are randomly inserted into the envelopes and mailed without checking the addresses. What is the probability that all the notes will be inserted into the correct envelopes? # A town council has 9 members: 5 Democrats and 4 Republicans. A 3-person zoning committee is selected at random. (A) What is the probability that all zoning committee members are Democrats? (B) What is the probability that a majority of zoning committee members are Democrats? # Two fair dice are rolled and the dots on the two sides facing up are added. Find the probability of the sum of the dots

a. Sum is 6. g. Sum is 8.

b. Sum is less than 5. h. Sum is greater than 8.

c. Sum is not 7 or 11. i. Sum is not 2, 4, or 6.

d. Sum is 1. j. Sum is 13.

e. Sum is divisible by 3. K. Sum is divisible by 4.

f. Sum is 7 or 11 (a “natural”). l. Sum is 2, 3, or 12

#Find the probability of being dealt the given hand from a standard 52-card deck.

a. A 5-card hand that consists entirely of red cards

b. A 5-card hand that consists entirely of face cards

c. A 6-card hand that contains exactly two face cards

d. A 6-card hand that contains exactly two clubs

e. A 4-card hand that contains no aces

f. A 4-card hand that contains no face cards

g. A 7-card hand that contains exactly 2 diamonds and exactly 2 spades

h. A 7-card hand that contains exactly 1 king and exactly 2 jacks

Home work 8.2 name: Due Date: June 05

Practice 8.2 Problems 1-33 odd, 36, 40-41, 50, 53-55, 57, 61, 63, 65, 79, 81, 83, 84

# Compute the probability of the following events for rolling 2 die: a. A sum that is less than or equal to 5 b. A sum that is greater than 9 c. The number on the first die is a 6 or the number on the second die is a 3. d. The number on the first die is even or the number on the second die is even. # Given the following probabilities for an event E, find the odds for and against E: (A) 3/8 (B) ¼ (C) 0.4 (D) 0.55 # What are the odds for rolling a sum of 5 in a single roll of two fair dice? # If you bet $1 that a sum of 5 will turn up, what should the house pay (plus returning your $1 bet) if a sum of 5 turns up in order for the game to be fair? # An assembly plant produces 40 outboard motors, including 7 that are defective. The quality control department selects 10 at random (from the 40 produced) for testing and will shut down the plant for trouble shooting if 1 or more in the sample are found to be defective. What is the probability that the plant will be shut down? # From a survey involving 1,000 university students, a market research company found that 750 students owned laptops, 450 owned cars, and 350 owned cars and laptops. If a university student is selected at random, what is the (empirical) probability that (A) The student owns either a car or a laptop? (B) The student owns neither a car nor a laptop? (c) The student does not own a car? (d) The student owns a car but not a laptop? #A shipment of 60 game players, including 9 that are defective, is sent to a retail store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found to be defective. What is the probability that the shipment will be rejected?

Home work 8.3 name: Due Date: June 10

8.3 7-17 odd, 21, 25, 27, 29, 33, 35, 49, 54, 60, 62, 71, 74, 81, 82, 84, 86

# If 37% of high school students said that they exercise regularly. find the probability that 5 randomly selected high school students will say that they exercise regularly. #Sixty-nine percent of U.S. heads of households play video or computer games. Choose 4 heads of households at random. Find the probability that a. None play video or computer games b. All four do # In 2006, 86% of U.S. households had cable TV. Choose 3 households at random. Find the probability that

a. None of the 3 households had cable TV

b. All 3 households had cable TV c. At least 1 of the 3 households had cable TV

# It is reported that 72% of working women use computers at work. Choose 5 working women at random. Find a. The probability that at least 1 doesn’t use a computer at work b. The probability that all 5 use a computer in their jobs # College Courses At a large university, the probability that a student takes calculus and is on the dean’s list is 0.042. The probability that a student is on the dean’s list is 0.21. Find the probability that the student is taking calculus, given that he or she is on the dean’s list. # Reading to Children Fifty-eight percent of American children (ages 3 to 5) are read to every day by someone at home. Suppose 5 children are randomly selected. What is the probability that at least 1 is read to everyday by someone at home? # Doctoral Assistantships Of Ph.D. students, 60% have paid assistantships. If 3 students are selected at random, find the probabilities

a. All have assistantships b. None have assistantships c. At least 1 has an assistantship

#An urn contains 2 one-dollar bills, 1 five-dollar bill, and 1 ten-dollar bill. A player draws bills one at a time without

replacement from the urn until a ten-dollar bill is drawn. Then the game stops. All bills are kept by the player.

(A) What is the probability of winning $16?

(B) What is the probability of winning all bills in the urn?

(C) What is the probability of the game stopping at the second draw?

Home work 8.5 name: Due Date: June 10

Practice 8.5 problems 7-17, 19-33 odd, 42, 49, 51, 53

# Two coins are flipped. You win $2 if either 2 heads or 2 tails turn up; you lose $3 if a head and a tail turn up. What is the expected value of the game? # A game has an expected value to you of $100. It costs $100 to play, but if you win, you receive $100,000 (including your $100 bet) for a net gain of $99,900. What is the probability of winning? Would you play this game? Discuss the factors that would influence your decision. # A box of 8 flashbulbs contains 3 defective bulbs. A random sample of 2 is selected and tested. Let X be the random variable associated with the number of defective bulbs in a sample. (A) Find the probability distribution of X. (B) Find the expected number of defective bulbs in a sample. # One thousand raffle tickets are sold at $1 each. Three tickets will be drawn at random (without replacement), and each will pay $200. Suppose you buy 5 tickets. (A) Create a payoff table for 0, 1, 2, and 3 winning tickets among the 5 tickets you purchased. (If you do not have any winning tickets, you lose $5; if you have 1 winning ticket, you net $195 since your initial $5 will not be returned to you; and so on.) (B) What is the expected value of the raffle to you? # After paying $4 to play, a single fair die is rolled, and you are paid back the number of dollars corresponding to the number of dots facing up. For example, if a 5 turns up, $5 is returned to you for a net gain, or payoff, of $1; if a 1 turns up, $1 is returned for a net gain of -$3; and so on. What is the expected value of the game? Is the game fair?

Home work 10.2/10.3 name: Due Date: June 12

Practice 10.2 problems 11, 13, 21-27

Practice 10.3 problems 21, 22, 25, 27

1. High Temperatures The reported high temperatures (in degrees Fahrenheit) for selected world cities on an October day are shown below.

62 72 66 79 83 61 62 85 72 64 74

Find the followings for the highest temperature on that day:

A. Range:

B. Mid-Range:

C. Median:

D. Mode:

Number x x-mean (x-mean)2

Sum= Sum=

E. N = total number of data: ______________

F. Mean:_______________

G. variance = Sum of (x - Mean)2 divided by (n – 1 ): = _______________.

H. D. Standard deviation = square root of variance = _______________.

2. Net Worth of Corporations These data represent the net worth (in millions of dollars) of 45 national corporations.

Class limits Frequency 10–20 2 21–31 8 32–42 15 43–53 7 54–64 10 65–75 3

Formula for sample standard deviation is 2( )

1

midx x fs

n

− =

−

Complete the table:

Class Frequency ( f ) Midpoint (xmid) xmid * f (xmid – mean)2 * f

sum= sum= sum= Find: N = total no of cities: the median (class): The modal (class): Mean = Variance: Standard deviation:

Home work 10.4 name: Due Date: June 17

10.4 Practice #1-13 odd, 14, 20-21, 23, 26, 28-30, 43-44, 47-50, 54

1. A student takes a 10-question, true/false exam and guesses on each question. Find the probability of scoring

I.exactly 70%.

ii.70% or better.

iii.Find the mean, variance and standard deviation 2. A student takes a 10-question, 4 multiple choice exam and guesses on each question. Find the probability of passing if the lowest passing grade is 70%. Also, find the mean, variance and standard deviation. 3. Average rate of completing a course at ACC is 70%. Out of 7 students, what is the probability that

i.exactly 5 complete the course?

ii.5 or more complete the course?

iii.Also, Find the mean, variance and standard deviation

4. In a box of 100 new calculator on average 5 are defective. To control quality each day a random sample of 6 is selected and inspected.

i.write the probability distribution function

ii.construct a table

iii.draw a histogram

iv.Compute the mean, variance and standard deviation.

Home work 10.5 name: Due Date: June 17

10.5 Practice #1-33 odd, 65-75 odd

1. Students SAT score is normally distributed with a mean score 500 and standard deviation 100. a. Find the approximate probability of scoring 790. b. Find the approximate probability of scoring between 400 and 750 c. What percent of students score 700 and more. 2. The average healing time of a certain type of incision is 240 hours, with standard deviation of 20 hours. a. What percent of people having the incision would heal in 8 days. b. Find the approximate probability of healing between 7 to 12 days. c. What percent of people having the incision would heal in more than 14 days

Home work 5.1/ 5.2/ 5/3 name: Due Date: June 24

5.1 practice 1-9 odd, 21, 23, 33, 39, 55, 61

5.2 practice1-9 odd, 13, 15, 17, 20, 27, 30, 35, 37, 41, 44, 46, 51, 52

5.3 practice 13, 15, 19, 22, 23, 28, 31, 32, 49, 51

Submit 1. The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 40 students, requires 3 chaperones, and costs $1,200 to rent. Each van can transport 8 students, requires 1 chaperone, and costs $100 to rent. Since there are 400 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 400 students. Since only 36 parents have volunteered to serve as chaperones, the officers must plan to use at most 36 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?

2. An investor has $60,000 to invest in a CD and a mutual fund. The CD yields 5% and the mutual fund yields an average

of 9%. The mutual fund requires a minimum investment of $10,000, and the investor requires that at least twice as much

should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund

to maximize the return? What is the maximum return?

Home work 6.1 / 5.3 name: Due Date: June 26

6.1 Practice 1, 2, 5-9 odds, 14-18, 41, 43, 45, 61, 63, 65

Submit: Solve the given problems using table method then check your answer by solving using graphing method.

a. No of problem constraints m = b. Numbers of rows on the table = (m+2)(m+1)/2 = c. Numbers of columns on the table = (m+2) = d. Number of variables in the original problem= (to put __ 0’s on the rows)

e. Draw and complete your table to find maximum value of P = 35x1 + 25 x2 f. Solve using graphing method to check answer:

a. No of problem constraints m = b. Numbers of rows on the table = (m+2)(m+1)/2 = c. Numbers of columns on the table = (m+2) =

d. Number of variables in the original problem= (to put that number of 0’s on the rows of table) e. Draw and complete your table to find maximum value of P = 35x1 + 25 x2

f. Solve using graphing method to check answer:

g. No of problem constraints m = h. Numbers of rows on the table = (m+2)(m+1)/2 = i. Numbers of columns on the table = (m+2) =

j. Number of variables in the original problem= (to put that number of 0’s on the rows of table) k. Draw and complete your table to find maximum value of P = 35x1 + 25 x2

l. Solve using graphing method to check answer:

Home work 1.2 / 2.1 name: Due Date: July 01

Practice only (don’t need to submit)

section 1.2 problem 1-4, 7, 9, 11, 15, 17, 19, 23, 27, 31, 45, 51, 57, 61, 73, 77, 85

Section 2.1 5, 9-19 odd, 31, 47, 49, 54, 63, 67, 77, 79, 87, 89, 90

Submit:

1. A plant can manufacture 80 golf clubs per day for a total daily cost of $7,647 and 100 golf clubs per day for a total daily cost of $9,147. (A) Assuming that daily cost and production are linearly related, find the total daily cost of producing x golf clubs. (B) Graph the total daily cost for 0 ≤ x ≤ 200. Interpret the slope and y intercept of this cost equation.

2. At a price of $2.28 per bushel, the supply of barley is 7,500 million bushels and the demand is 7,900 million bushels. At a price of $2.37 per bushel, the supply is 7,900 million bushels and the demand is 7,800 million bushels.

A. Find a price–supply equation of the form p = mx + b.

B. Find a price–demand equation of the form p = mx + b.

C. Find the equilibrium point.

D. Graph the price–supply equation, price–demand equation.

3. A company manufactures memory chips for microcomputers. Its marketing research department, using statistical techniques, collected the data shown in Table 1, where p is the wholesale price per chip at which x million chips can be sold. Using special analytical techniques (regression analysis), an analyst produced the following price–demand function to model the data: P(x) = 75 - 3x 1 ≤ x ≤ 20 Table 1: Demand -Price x (millions) p ($) 1 72 4 63 9 48 14 33 20 15

(A) Plot the data points in Table 1, and sketch a graph of the price–demand function in the same coordinate system.

(B) What would be the estimated price per chip for a demand of 7 million chips? For a demand of 11 million chips? (C) Find the company’s revenue function R(x) and indicate its domain. (E) The financial department for the company established the following cost function for producing and selling x million memory chips: C(x) = 125 + 16x (in million dollars). The fixed cost is : ____________$ variable cost per item:_________________. (F) Write a profit function for producing and selling x million memory chips and indicate its domain. (F) Graph the Cost, Revenue, and Profit function on the same plane. Indicate the region of Loss, Profit, identify the break

– even.

Home work 2.4 name: Due Date: July 05

Practice 2.4 #1, 3, 6, 11, 14, 23, 27, 33, 35, 36, 37, 39, 40, 45, 47, 57, 59, 61

Submit:

1. Given the rational function: 𝑓(𝑥) = 2𝑥2

𝑥2−𝑥−6

(A) Find the domain.

(B) Find the x and y intercepts.

(C) Find the equations of all vertical asymptotes.

(D) If there is a horizontal asymptote, find its equation.

(E) Using the information from (A)–(D) and additional points as necessary, sketch a graph of f for -10 ≤ x ≤ 10.

2. Financial analysts in a company that manufactures DVD players arrived at the following daily cost equation for

manufacturing x DVD players per day: C(x) = x2 + 2x + 2,000

The average cost per unit at a production level of x players per day is 𝐶̅ (x) = 𝐶(𝑥)

𝑥

(A) Find the rational function 𝐶̅ (x).

(B) Graph 𝐶̅ (x) on your calculator.

(C) Graph the average cost function 𝐶̅ (x) on a graphing calculator and use an appropriate command to find the daily production level (to the nearest integer) at which the average cost per player is at a minimum. What is the minimum average cost to the nearest cent?

Home work 2.5 2.6 name: Due Date:

2.5 3, 5, 11, 13, 15, 18, 20, 23, 29, 36, 41, 45, 51, 53, 55, 60

2.6 3-19 odd, 29-37 odd, 47-53, 65-69, 83-88

1) An initial investment of $12,000 is invested for 2 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period. 2) Suppose that $2200 is invested at 3% interest, compounded semiannually. Find the function for the amount of money after t years.

3) Solve for t: = 0.05 Round your answer to four decimal places.

4) Solve for x:

5) Solve for x to two decimal places (using a calculator). 700 = 500

6) Use the properties of logarithms to solve. x + (x - 2) = 24

7) If $1250 is invested at a rate of 8 % compounded monthly, what is the balance after 10 years? [A = ]

8) If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact.

[A = ]

9) Assume that a savings account earns interest at the rate of 2% compounded monthly. If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made?

1) $12,994.28 2) A = 2200 3) 42.7962 4) 1 5) 8.58 6) 6 7) $2844.31

8) 6 years 9) 417 months

HW 3.1-3.4 Name: Date:

Practice 3.1 # 25-40, 49-64

3.2 #1-5, 13-19odd, 43-50, 55, 58, 62, 65-75 odd, 79

3.3 #3-21 odd, 27-42, 45-46

3.4 #27-35 odd, 40, 41, 45-55 odd

Submit:

Future Value of simple Interest A = P + Pr t = P(1 + r t) where A = amount, or future value P = principal, or present

value r = annual simple interest rate(written as a decimal) ; t = time in years

1. A. Find the total amount due on a loan of $1000 at 4.5% simple interest at the end of 6 months.

B. Find the total amount due on a loan of $1500 at 6% simple interest at the end of 42 months.

Future value of Compound Interest A = P(1 + 𝑟

𝑚)m t

where A = amount (future value) at the end of n periods; P = principal (present value); r = annual nominal rate, m =

number of compounding periods per year; r = rate m = number of compounding periods per year

Continuous Compound Interest Formula If a principal P is invested at an annual rate r (expressed as a decimal)

compounded continuously, then the amount A in the account at the end of t years is given by A = Pert

2. If $1,000 is invested in an account that earns 8% compounded annually for 6 years, find the interest earned during

each year and the amount in the account at the end of each year. Organize your results in a table.

3.How long will it take $10,000 to grow to $12,000 if it is invested at 9% compounded monthly?

Future Value of an Ordinary Annuity 𝐹𝑉 = 𝑃𝑀𝑇 (1+

𝑟

𝑚)

𝑚𝑡−1

𝑟

𝑚

= 𝑃𝑀𝑇 (1+𝑖)𝑛−1

𝑖

Periodic payments 𝑃𝑀𝑇 = 𝐹𝑉 𝑟

𝑚

(1+𝑟

𝑚)

𝑚𝑡−1

= 𝐹𝑉 𝑖

(1+𝑖)𝑛−1

where FV = future value, PMT = periodic payment, r = rate, m = no of compounding in a year, i = r/m = rate per

period, n = mt = total number of payments. Note: Payments are made at the end of each period.

4.. You invest $1,000 at the end of each year in your retirement account that pays 6% interest compounded annually. A) How much will you have in the account after 5 years?

B) How much did you pay into the account?

C) How much is interest for the whole 5 years?

5. You deposit $150 per month in a retirement account that pays 6% compounded monthly. a) How much money will you have after 25 years?

b) How much interest you will get for only the 25th year?

Step 1. FV(after 25 years) =

FV(after 24 years) =

Step 2. Growth in 25th year = FV(after 25 years) - FV(after 24 years)

Step 3. How much you are paying on 25th year =

Step 4. interest you will get for only the 25th year = Growth in 25th year - How much you are paying on 25th year =

6. A person makes annual deposits of $1,000 into an ordinary annuity. After 20 years, the annuity is worth $55,000. What annual compound rate has this annuity earned during this 20-year period? Express the answer as a percentage, correct to two decimal places.

Amortizing a debt means that the debt is retired in a given length of time by equal periodic payments that include

compound interest. Present Value of an Amortization 𝒊𝒔 𝑃𝑉 = 𝑃𝑀𝑇 1−(1+

𝑟

𝑚)

−𝑚𝑡

𝑟

𝑚

= 𝑃𝑀𝑇 1−(1+𝑖)−𝑛

𝑖

Periodic payments 𝑃𝑀𝑇 = 𝑃𝑉 𝑟

𝑚

1−(1+𝑟

𝑚)

−𝑚𝑡 = 𝑃𝑉 𝑖

1−(1+𝑖)−𝑛

7. A couple purchased a home 20 years ago for $65,000. The home was financed by paying 20% down and signing a 30-year mortgage at 8% on the unpaid balance. The net market value of the house is now $130,000, and the couple wishes to sell the house. How much equity (to the nearest dollar) does the couple have in the house now after making 240 monthly payments?

8. The annual interest rate on a credit card is 18.99%. How long will it take to pay off an unpaid balance of $847.29 if no new purchases are made and the minimum payment of $20.00 is made each month?

9. You have negotiated a price of $25,200 for a new Bison pickup truck. Now you must choose between 0% financing for 48 months or a $3,000 rebate. If you choose the rebate, you can obtain a credit union loan for the balance at 4.5% compounded monthly for 48 months. (a) Which option should you choose?

(b) Which option should you choose if your credit union raises its loan rate to 7.5% compounded monthly and all other data remain the same?

10. A person makes annual deposits of $1,000 into an ordinary annuity. After 20 years, the annuity is worth $55,000. What annual compound rate has this annuity earned during this 20-year period? Express the answer as a percentage, correct to two decimal places.

11. Find the payments needed to pay off a $9500 loan with an interest rate of 6.9% making monthly payments over 5 years.

What was the total amount paid over the 5 years? After the loan is paid off, how much interest was paid?

HW 4.1-4.4 Name: Date:

Practice 4.1 #9-17 odd, 21, 25, 35(on # 35, you’ll have to adjust window), 57, 65, 69, 71

4.2 #1, 5, 7, 43, 47, 55-77 odd

4.3 #39, 41, 43, 47, 48, 56, 57, 73, 75, 85

4.4 #3, 5, 7, 9, 11, 21, 25, 31, 35, 37, 69 a. b. and d

You can use any one of - 1. Graphing method, 2. Substitution method, 3. elimination method, 4. Gauss-Jordan elimination 5. RREF on calculator.

Show work for your equation setup and solution steps.

Submit:

1. Sam and Chad are ticket-sellers at their class play. Sam is selling student tickets for $2.00 each, and Chad selling adult tickets for $5.50 each. If their total income for 24 tickets was $83.00, how many tickets did Sam sell?

2. Suppose that the supply and demand equations for a logo sweat shirt in a week are for the demand

equation; and , for the supply equation. Find the equilibrium price and quantity.

3. Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The income from the 5% and 6% investments is the same as the income from the 8% investment. Find the amount invested at each rate.

4. There were 340 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $490. How many adults and how many children attended?

5. A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank invest in each?

Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount invested in mortgages.

6. Hurst's Feed & Seed sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $31.00. To another customer he sold 2 bushels of wheat, 3 of corn, and 5 of rye, for $27.60. To a third customer he sold 3 bushels of wheat, 5 of corn, and 2 of rye for $32.70. What was the price per bushel for each of the different grains?

Let x represent the price per bushel for wheat, y the price per bushel for corn, and z the price per bushel for rye.

7. Your screen print operation is doing extremely well at the craft shows. Last week you sold 50 tie-dyed shirts for $15 each, 40 Cheraw-Tech crew shirts for $10 each and 30 hand painted T-shirts for $12 each. Use matrix operations to calculate your total revenue for the week.

8. A chain of amusement parks pays experienced workers $240 per week and inexperienced workers $220 per week. The total number of workers and total weekly wages at three different parks are given in the table. How many experienced workers does each park employ? Set up a system of linear equations and solve using matrix inverse methods.

Park 1 Park 2 Park 3

Number of workers 120 120 120

Total weekly wages 28,400 27,200 28,000

n Suggested Problems by ACC math department

4.5 1, 7, 13, 15, 31, 39, 45, 53, 55, 65, 67

4.6 5-15 odd, 19, 23, 29, 32, 37, 46, 63, 64, 65

4.7 9-12, 21-28, 31, 35, 37

1. A retail company offers, through two different stores in a city, three models, A, B, and C, of a particular brand of camping stove. The inventory of each model on hand in each store is summarized in matrix M. Wholesale (W) and retail (R) prices of each model are summarized in matrix M. Find the product MN and label its columns and rows appropriately. What is the wholesale value of the inventory in Store 1?

M = N =