Solve the system of equations graphically. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. y =1/2 x + 4 2y = x + 8
> y = 2x - 1 y = 3x - 4 Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.
> 2. When one quantity increases while the other quantity decreases, it is an example of________ variation. 4. In the equation y = ox, k is called the constant of___________.
> Fill in the blanks with an appropriate word, phrase, or symbol(s). 2. In a right triangle, the side that is opposite the right angleis called the _________. 4. (a) A line segment from the center of a circle to any point on the circle is called the ______
> Fill in the blank with an appropriate word, phrase, or symbol(s). (a) a ( b means that a is________ than b. (b) a ( b means that a is_________ than b. 4. When solving an inequality, if you obtain a statement that is always false, such as 3 ( 5, the answe
> x varies inversely as y. Determine x when y = 15 and k = 45. (a)Write the variation equation an (b) determine the quantity indicated.
> 2. The amount of money that is present in an ordinary annuity after t years is known as the accumulated amount or the _____value of the annuity. 4. A variable annuity is an annuity that is invested in stocks, bonds, mutual funds, or other investments th
> Prime Interest Rate Nick borrowed $600 for 3 months. The banker said that Nick must repay the loan at the rate of $200 per month plus interest. The bank was charging a rate of 2 percentage points above the prime interest rate. The prime interest rate is
> U.S. Treasury Bills On December 3, 2014, Trinity purchased a 364-day, $6000 U.S. Treasury bill at a 0.12% discount. (See Exercise 55.) (a) What is the date of maturity of the Treasury bill? (b) How much did Trinity actually pay for the Treasury bill? (c)
> Flag Company Loan On April 3, the Mears Flag Company borrowed $15,000 to pay for start-up costs for its new showroom. The loan had a simple interest rate of 8.25% and was for 270 days. The company was able to make partial payments of $6000 on May 28 and
> A partial payment is made on the date(s) indicated. Use the United States rule to determine the balance due on the note at the date of maturity. The Effective Date is the date the note was written. Assume the year is not a leap year. Where appropriate, r
> A partial payment is made on the date(s) indicated. Use the United States rule to determine the balance due on the note at the date of maturity. The Effective Date is the date the note was written. Assume the year is not a leap year. Where appropriate, r
> Change the number given as a percent to a decimal number. 0.75%
> Change the number to a percent. Express your answer to the nearest tenth of a percent. 39%
> Change the number to a percent. Express your answer to the nearest tenth of a percent. 13.678
> Change the number to a percent. Express your answer to the nearest tenth of a percent. 0.5688
> Determine the shaded area. When appropriate, use the key on your calculator and round your answer to the nearest hundredth.
> Change the number to a percent. Express your answer to the nearest tenth of a percent.
> Change the number to a percent. Express your answer to the nearest tenth of a percent.
> Selling Ties The Tie Shoppe paid $5901.79 for a shipment of 500 ties and wants to make a profit of 40% of the cost on the whole shipment. The store is having two special sales. At the first sale it plans to sell 100 ties for $9.00 each, and at the second
> Furniture Sale Kane’s Furniture Store advertised a table at a 15% discount. The original selling price was $115, and the sale price was $100. Was the sale price consistent with the ad? Explain.
> Restaurant Markup The cost of a fish dinner to the owner of the Golden Wharf restaurant is $7.95. The fish dinner is sold for $11.95. Determine the percent markup. Where appropriate, round your answer to the nearest tenth of percent.
> Weight Loss On January 1, Juan weighed 235 pounds and decided to diet and exercise. On June 30, Juan weighed 210 pounds. Determine the percent decrease in Juan’s weight from January 1 to June 30. Where appropriate, round your answer to
> Where appropriate, round your answer to the nearest tenth of percent. Vacuum Cleaner Markup If the Kirby dealership in Exercise 61 pays $320 for each unit and sells a unit for $699, what is the percent markup in the price of each unit?
> Where appropriate, round your answer to the nearest tenth of percent. Salary Increase Maya’s present salary is $42,500. As part of a promotion her salary will increase by 4% next year. What will Maya’s new salary be?
> Where appropriate, round your answer to the nearest tenth of percent. Employee Increase The Fastlock Company hired 57 new employees, which increased its staff by 30%. What was the original number of employees?
> Where appropriate, round your answer to the nearest tenth of percent. Tax and Tip The Brants’ dinner (see Exercise 55) cost $68.00 before tax, and the tax rate was 7.5%. a) What is the tax on the Brants’ dinner? b) If the Brants decide to tip 20% of the
> -x + 2y < 2 Draw the graph of the inequality.
> Where appropriate, round your answer to the nearest tenth of percent. Determine the answer to the question. Forty-eight is 60% of what number?
> Where appropriate, round your answer to the nearest tenth of percent. Determine the answer to the question. Ten percent of what number is 75?
> Use the ordinary annuity formula to determine the accumulated amount in each annuity. Round all answers to the nearest cent. $200 invested monthly for 40 years at a 6% interest rate compounded monthly
> Where appropriate, round your answer to the nearest tenth of percent. Determine the answer to the question. Sixty-five is what percent of 104?
> $1000 invested semiannually for 20 years at a 5% interest rate compounded semiannually Use the ordinary annuity formula to determine the accumulated amount in each annuity. Round all answers to the nearest cent.
> Where appropriate, round your answer to the nearest tenth of percent. Determine the answer to the question. What percent of 75 is 15?
> Repaying a Debt The city of St. Louis wishes to repay a debt of $25,000,000 in 50 years. How much should the city invest semiannually in a sinking fund paying a 7.5% interest rate compounded semiannually to accumulate $25,000,000 in 50 years? Round all a
> Thirty-two percent of 50 is what number? Where appropriate, round your answer to the nearest tenth of percent. Determine the answer to the question.
> Campaign Fund-Raising Ashley would like to run for Congress in 10 years and would like to have $500,000 to spend on campaign expenses. How much should she invest monthly in a sinking fund with a 6% interest rate compounded monthly to accumulate $500,000
> What is 6.5% of $150.00? Where appropriate, round your answer to the nearest tenth of percent. Determine the answer to the question.
> Plot all the points on the same axes. (0, -1)
> Fill in the blanks with an appropriate word,phrase, or symbol(s). 2. In a fixed investment the interest is computed at a fixed rate and the amount invested as principal may be______ . 4. Interest that is computed on the principal and any accumulated inte
> Grandchild’s College Expenses To save for their grandchildren’s college expenses, Ken and Laura invest $500 each month in an ordinary annuity with a 6% interest rate compounded monthly. Determine the accumulated amount
> Presidential Salary The following graph shows the annual salary for the president of the United States for selected years from 1789 to 2001. a) Determine the percent increase in annual salary from 1789 to 1873. b) Determine the percent increase in annua
> Starting a Business To save money to start a new business, Sandra invests $200 each quarter in an ordinary annuity with a 5% interest rate compounded quarterly.Determine the accumulated amount in Sandra’s annuityafter 20 years. Round all answers to the n
> U.S. Population Unlike the population of Russia (see Exercise 39), the population of the United States has been increasing since 1990. In 1990, the population of the United States was about 249 million people. In 2014, the population of the United States
> Use the sinking fund formula to determine the payment needed to reach the accumulated amount. To ensure that enough is invested each period, round each answer up to the next cent. Quarterly payments with a 10% interest rate compounded quarterly for 40 ye
> Use the circle graph to answer the questions. Students at Bayshore High School were polled to determine the type of music they preferred. There were 1960 students who completed the poll. Their responses are represented in the circle graph below. Round yo
> Use the sinking fund formula to determine the payment needed to reach the accumulated amount. To ensure that enough is invested each period, round each answer up to the next cent. Weekly payment with a 7.8% interest rate compounded weekly for 25 years to
> Use the circle graph to answer the questions. Students at Bayshore High School were polled to determine the type of music they preferred. There were 1960 students who completed the poll. Their responses are represented in the circle graph below. Round yo
> Determine the monthly principal and interest payment for the mortgage. Unless told otherwise by your instructor, you may use either Table 10.4 or the principal and interest payment formula (See Examples 2 and 3).
> Use the table to answer the questions. The elements that compose seawater, along with the corresponding percents, are shown in the table below. Where appropriate, round your answers to two decimal places. Mr. Kimball collects a 6000-mâ„“
> Determine the monthly principal and interest payment for the mortgage. Unless told otherwise by your instructor, you may use either Table 10.4 or the principal and interest payment formula (See Examples 2 and 3).
> Use the table to answer the questions. The elements that compose seawater, along with the corresponding percents, are shown in the table below. Where appropriate, round your answers to two decimal places. If a saltwater aquarium contains 55 gallons of se
> Comparing Payment Frequency Janet is purchasing a new house for $315,000. Her credit union requires her to make a 20% down payment, and the current mortgage rate is 6%. Janet is exploring different 10-year mortgage payment options. Use the principal and
> Use the circle graph to answer the questions. The Lafayette County Library classifies its DVDs into one of the categories shown below. The library owns 1743 DVDs. Round your answers to the nearest whole number. Determine the number of foreign DVDs.
> An Adjustable Rate Mortgage The Pourans purchased a new home for $378,000 with a down payment of $127,000. They obtained a 10-year adjustable rate mortgage with the following terms. The interest rate is based on the one-year Treasury bill rate, which is
> Use the circle graph to answer the questions. The Lafayette County Library classifies its DVDs into one of the categories shown below. The library owns 1743 DVDs. Round your answers to the nearest whole number. Determine the number of romance DVDs.
> Comparing Loans Paul is negotiating with two credit unions for a mortgage to buy a condominium selling for $525,000. The terms at Grant County Teacher’s Credit Union are a 20% down payment, an interest rate of 7.5%, a 15-year mortgage, and 1 point to be
> Where appropriate, round answers to the nearest tenth of a percent unless specified otherwise . Reduced-Fat Triscuits One serving of Original Triscuit crackers contains 4 grams of fat. Reduced-Fat Triscuit crackers contain 37.5% less fat per serving than
> Evaluating a Loan Request Kathy wants to buy a condominium selling for $95,000. The taxes on the property are $1500 per year, and homeowners’ insurance is $336 per year. Kathy’s gross monthly income is $4000. She has 15 monthly payments of $135 remaining
> Where appropriate, round answers to the nearest tenth of a percent unless specified otherwise. Potassium The U.S. Department of Agriculture’s recommended daily allowance (USRDA) of potassium for adults is 3500 mg. One serving of Cheerios provides 95 mg o
> -2(x – 3) ( 4x + 6 Graph the solution set of the inequality, where x is a real number, on the number line.
> A 25-Year Conventional Mortgage The Bells obtain a 25-year, $110,000 conventional mortgage at a 10.5% rate on a house selling for $160,000. Their monthly mortgage payment, including principal and interest, is $1038.60. They also pay 2 points at closing.
> Change the number given as a percent to a decimal number. 298.7%
> Qualifying for a Mortgage The Zhengs’ gross monthly income is $4100. They have 18 remaining boat payments of $505. The Zhengs are applying for a 20-year, $275,000 mortgage at a 9% interest rate to buy a new house. The taxes and insurance on the house are
> Change the number given as a percent to a decimal number.
> Down Payment and Points The Nicols are buying a house selling for $245,000. They pay a down payment of $45,000 from the sale of their current house. To obtain a 15-year mortgage at a 4.5% interest rate, the Nicols must pay 1.5 points at the time of closi
> Determine A - B.
> Buying a First House The Firszts are purchasing their first home for $199,900. They are obtaining an FHA mortgage through their credit union and are required to make a 3% down payment. They obtain a 30-year mortgage with an interest rate of 4.5%. (a) Det
> Determine A + B.
> Buying a Condominium Toni is buying a condominium selling for $135,000. To obtain the mortgage, Toni is required to make a 20% down payment. Toni obtains a 15-year mortgage with an interest rate of 3.0%. (a) Determine the amount of the required down paym
> Determine A + B.
> (a) Use the Pythagorean theorem to determine the length of the unknown side of the triangle, (b) Determine the perimeter of the triangle, and (c) determine the area of the triangle.
> $4000 for 2 years at 6% compounded semiannually Use the compound interest formula to compute the total amount accumulated and the interest earned. Round all answers to the nearest cent.
> Two 2 ( 2 matrices, A and B, whose product is the multiplicative identity matrix (See Exercise 63) are said to be multiplicative inverses. That is, if A ( B = B ( A = I, then A and B are multiplicative inverses. In parts (a) and (b) below, show that matr
> Rule of 72 A simple formula can help you estimate the number of years required to double your money. It’s called the rule of 72. You simply divide 72 by the interest rate (without the percent sign). For example, with an interest rate of 4%, your money wo
> Consider the mathematical system consisting of the set of all 2 ( 4 matrices under the operation of matrix addition. (a) Is the system closed? (b) Is there an additive identity matrix? If so, what is it? (c) Does each matrix in the set have an additive i
> Inflation The average cost for a loaf of bread in 2014 was $2.27. Assuming an annual inflation rate of 0.5% per year, what will be the cost for a loaf of bread in 2019?
> MODELING—Food Prices To raise money for a local charity,the Spanish Club at Montclair High School sold hot dogs, soft drinks, and candy bars for 3 days in the student lounge. The sales for the 3 days are summarized in matrix A. The cost
> Doubling the Principal Compute the total amount and the interest paid at 12% compounde monthly for 2 years for the following principals. (a) $100 (b) $200 (c) $400 (d) Is there a predictable outcome in the interest when the principal is doubled? Explai
> Cookie Orders (a) Express these orders as a 1 * 4 matrix. (b) Use matrix multiplication to determine the amount of each ingredient needed to fill the day’s order.
> After seeing its neighboring village obtain a new water tower (see Exercise 39), the city board of East Dubuque begins planning to replace its water towers. The board estimates that it will need $1,750,000 to build the new water towers in 20 years. At th
> Hollister sells two types of t-shirts—male and female. Matrix A indicates the stock on hand of each type and size of t-shirt at the beginning of a given day. Matrix B indicates the stock on hand of each type and size of t-shirt at the e
> 4y - 3x ( 8 Draw the graph of the inequality.
> A New Roof Rebecca will need to replace the roof of her house in 5 years. How much should Rebecca invest now in a money market account that pays 2.1% interest compounded quarterly in order to have $6000 in 5 years? If necessary, round all dollar figures
> Show that the associative property of multiplication, 1A ( B2 ( C = A ( 1B ( C 2, holds for matrices A, B, and C.
> Starting a New Business Mr. Fink’s goal is to have $26,000 to start a new lawn mower repair business when he retires in 15 years. How much should he invest now in a CD that pays 2% interest compounded quarterly to reach his goal? If ne
> Show that the associative property of multiplication, 1A ( B2 ( C = A ( 1B ( C 2, holds for matrices A, B, and C.
> Verifying APY Suppose you saw an advertisement in the newspaper for a financial planner who was recommending a certificate of deposit that paid 4.5% interest compounded quarterly. In the fine print at the bottom of the advertisement, it stated that the A
> Determine whether the commutative property of multiplication, A ( B = B ( A, holds for matrices A and B.
> If necessary, round all dollar figures to the nearest cent and round percents to the nearest hundredth of a percent. Investment Choice Confiance Bank advertises a 1-year CD that pays 1.75% compounded semiannually. Firme Bank advertises a 1-year CD that p
> Determine whether the commutative property of multiplication, A ( B = B ( A, holds for matrices A and B.
> Determining Effective Annual Yield Determine the effective annual yield for $1 invested for 1 year at 4.75% compounded monthly. If necessary, round all dollar figures to the nearest cent and round percents to the nearest hundredth of a percent.
> Show that the associative property of addition, (A + B) + C = A + (B + C), holds for matrices A, B, and C.
> Graph the solution set of the inequality, where x is a real number, on the number line. 3x + 12 ( 5x + 14
> Little League Braden River Little League held various fund raisers and received the following amounts of money: $450 from a car wash, $278 from a bake sale, and $327 from a used equipment sale. The league decides to invest the total of these amounts in a
> Show that the associative property of addition, (A + B) + C = A + (B + C), holds for matrices A, B, and C.
> Forgoing Interest Rikki borrowed $6000 from her daughter, Lynette. She repaid the $6000 at the end of 2 years. If Lynette had left the money in a bank account that paid an interest rate If necessary, round all dollar figures to the nearest cent and round
> Show the commutative property of addition, A + B = B + A, holds for matrices A and B.
> Investing a Signing Bonus Joe just started a new job and has received a $5000 signing bonus. Joe decides to invest this money now so that he can buy a new motor scooter in 5 years. If Joe invests in a 5-year CD paying 3.35% interest compounded quarterly,
> Show the commutative property of addition, A + B = B + A, holds for matrices A and B.
> Investing Prize Winnings Marcella wins third prize in the Clearinghouse Sweepstakes and receives a check for $250,000. After spending $10,000 on a vacation, she decides to invest the rest in a money market account that pays 1.5% interest compounded month
