Nursing Shifts A nurse’s work pattern at Community Hospital consists of working the 7 a.m. –3 p.m. shift for 3 weeks and then the 3 p.m. –11 p.m. shift for 2 weeks. a) If it is the third week of the pattern, what shift will the nurse be working 6 weeks from now? b) If it is the fourth week of the pattern, what shift will the nurse be working 7 weeks from now? c) If it is the first week of the pattern, what shift will the nurse be working 11 weeks from now?
> 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
> Determine A + B and A * B. If an operation cannot be performed, explain why.
> If necessary, round all dollar figures to the nearest cent and round percents to the nearest hundredth of a percent. Contest Winnings Mary wins $2500 in a singing contest and invests the money in a 4-year CD that pays 3% interest compounded monthly. How
> Determine A + B and A * B. If an operation cannot be performed, explain why.
> x + y = 4 -x + y = 4 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.
> The desired accumulated amount is $15,000 after 30 years invested in an account with 3% interest compounded monthly. Use the present value formula to determine the amount to be invested now, or the present value needed.
> Determine A + B and A * B. If an operation cannot be performed, explain why.
> The desired accumulated amount is $75,000 after 5 years invested in an account with 4% interest compounded semiannually. Use the present value formula to determine the amount to be invested now, or the present value needed.
> Determine A + B and A * B. If an operation cannot be performed, explain why.
> $5600 for 7 years at 2.7% compounded daily Use the compound interest formula to compute the total amount accumulated and the interest earned. Round all answers to the nearest cent.
> Determine A ( B.
> $2500 for 4 years at 1.2% compounded monthly Use the compound interest formula to compute the total amount accumulated and the interest earned. Round all answers to the nearest cent.
> Determine A ( B.
> $7500 for 5 years at 1.6% compounded quarterly Use the compound interest formula to compute the total amount accumulated and the interest earned. Round all answers to the nearest cent.
> Determine A ( B.
> The percent of light that filters through water and the depth of the water Use your intuition to determine whether the variation between the indicated quantities is direct or inverse.
> Determine the simple interest. Unless noted otherwise, assume the rate is an annual rate. Assume 360 days in a year. Round answers to the nearest cent. p = $465, r = 2.75%, t = 1.25 years
> Determine the following. 3B - 2C
> 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
> Determine the following. -3B
> 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
> Determine A - B.
> 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
> Assume that Sunday is represented as day 0, Monday is represented as day 1, and so on. If today is Thursday (day 4), determine the day of the week it will be in the specified number of days. Assume no leap years. 61 days
> Determine the due date of the loan, using the exact time, if the loan is made on the given date for the given number of days. July 5 for 210 days
> Rolling Wheel The wheel shown is to be rolled. Before the wheel is rolled, it is resting on number 0. The wheel will be rolled at a uniform rate of one complete roll every 4 minutes. In exactly 1 year (not a leap year), what number will be at the bottom
> (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.
> Determine the due date of the loan, using the exact time, if the loan is made on the given date for the given number of days. May 11 for 120 days
> More Birthday Questions During a certain leap year, Josephine’s birthday is on Tuesday, May 18. What is the minimum number of years in which Josephine’s birthday will fall on a a) Friday? b) Saturday?
> Determine the exact time from the first date to the second date. Use Table 10.1. Assume the year is not a leap year unless otherwise indicated. December 21 to April 28
> Determine the smallest positive number divisible by 5 to which 2 is congruent in modulo 6.
> Determine the exact time from the first date to the second date. Use Table 10.1. Assume the year is not a leap year unless otherwise indicated. June 14 to January 24
> Solve for x where k is any counting number. 7k + 1 ( x (mod 7)
> Determine the exact time from the first date to the second date. Use Table 10.1. Assume the year is not a leap year unless otherwise indicated. February 14 to December 25
> 1 ÷ 2 ( ? (mod 5)
> If necessary round all dollar figures to the nearest cent and round percents to the nearest hundredth of a percent. A Pawn Loan Jeffrey wants to take his mother out for dinner on her birthday, so he pawns his watch. The pawnbroker loans Jeffrey $75. Four
> 3 ÷ 4 ( ? (mod 7)
> x + 2y > 4 Draw the graph of the inequality.
> Bank Discount Note Kwame borrowed $2500 for 5 months from a bank using a 3% discount note. (a) How much interest did Kwame pay the bank for the use of its money? (b) How much did he receive from the bank? (c) What was the actual rate of interest he paid?
> Construct a modulo 7 multiplication table. Repeat parts (b)–(g) in Exercise 67.
> Personal Note Aidan runs a car repair garage and needs $6000 to install a new car lift. He borrows the money on a 30-month personal bank note with his mother cosigning the loan. The simple interest rate charged is 5.75%. (a) How much interest does Aidan
> Construct a modulo 8 addition table. Repeat parts (b)–(h) in Exercise 65.
> Business Loan The city of Bradenton is offering simple interest loans to start-up businesses at a rate of 3.5%. Mr. Cannata obtains one of these loans of $6000 for 3 years to help pay for start-up costs of his restaurant, Ortygia. Determine the amount of
> p = $1650.00, r = ?, t = 6.5 years, i = $343.20 Use the simple interest formula to determine the missing value. If necessary, round all dollar figures to the nearest cent.
> Physical Therapy A man has an Achilles’ tendon injury and is receiving physical therapy. He must have physical therapy twice a day for 5 days, physical therapy once a day for 3 days, and then 2 days off; then the cycle begins again. If he is in his secon
> p = +800.00, r = 4%, t = ?, i = $64.00 Use the simple interest formula to determine the missing value. If necessary, round all dollar figures to the nearest cent.
> Flight Schedules A pilot is scheduled to fly for 5 consecutive days and rest for 3 consecutive days. If today is the second day of her rest shift, determine whether she will be flying or resting a) 60 days from today. b) 90 days from today. c) 240 days
> Graph the solution set of the inequality, where x is a real number, on the number line.
> (2). To change a fraction to a percent, first divide the numerator by the denominator to obtain a decimal number. Then multiply the decimal number by 100 and add a(n) _______ sign. (4). To change a percent to a decimal number, divide the number by 100 an
> p = ?, r = 2.1%, t = 135 days, i = $37.80 Use the simple interest formula to determine the missing value. If necessary, round all dollar figures to the nearest cent.
> Governors’ Elections Wisconsin gubernatorial elections (elections for governor) have been held every four years starting in 1970. Each of these years is congruent to 2 in modulo 4. a) List the first five Wisconsin gubernatorial election years held after
> p =$41,864, r = 0.0375% per day, t = 60 days Determine the simple interest. Unless noted otherwise, assume the rate is an annual rate. Assume 360 days in a year. Round answers to the nearest cent.
> Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. ? - 3 = 4 (mod 8)
> Determine the simple interest. Unless noted otherwise, assume the rate is an annual rate. Assume 360 days in a year. Round answers to the nearest cent. p = $550.31, r = 8.9%, t = 67 days
> Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 3 • ? = 3 (mod 12)
> Determine the simple interest. Unless noted otherwise, assume the rate is an annual rate. Assume 360 days in a year. Round answers to the nearest cent.
> Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 3 • ? = 5 (mod 6)
> p = $6742.75, r = 6.05%, t = 90 days Determine the simple interest. Unless noted otherwise, assume the rate is an annual rate. Assume 360 days in a year. Round answers to the nearest cent.
> Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 4 • ? = 3 (mod 7)
> y = x + 3 y = -1 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.
> The identity element is C. Determine the inverse, if it exists, of (a) A, (b) B, and (c) C.
> Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 3 - ? = 7 (mod 9)
> Determine if the system has an identity element. If so, list the identity element. Explain how you determined your answer.
> Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. 4 + ? = 3 (mod 6)
> Determine if the system is closed. Explain how you determined your answer.
> Determine all positive number replacements (less than the modulus) for the question mark that make the statement true. ? + 3 = 2 (mod 5)
> In Exercises 67 and 68 the tables shown below and on the next page are examples of noncommutative, or nonabelian, groups. For each exercise, do the following.
> Find the modulo class to which each number belongs for the indicated modulo system. -39, mod 7
> (a) Let E and O represent even numbers and odd numbers, respectively, as in Exercise 65. Complete the table for the operation of multiplication. (b) Determine whether this mathematical system forms a commutative group under the operation of multiplicatio
> Find the modulo class to which each number belongs for the indicated modulo system. -7, mod 4
> The time it takes an ice cube to melt in water and the temperature of the water Use your intuition to determine whether the variation between the indicated quantities is direct or inverse.
> For the mathematical system given, determine which of the five properties of a commutative group do not hold.
> Find the modulo class to which each number belongs for the indicated modulo system. 75, mod 8
> For the mathematical system given, determine which of the five properties of a commutative group do not hold.
> Find the modulo class to which each number belongs for the indicated modulo system. 43, mod 6
> For the mathematical system given, determine which of the five properties of a commutative group do not hold.
> Find the modulo class to which each number belongs for the indicated modulo system. 38, mod 9
> Consider the mathematical system defined by the following table. (a) Is the system closed? Explain. (b) Is there an identity element in the set? If so, what is it? c) For each element in the set, give the corresponding inverse element, if it exists. (d)
> Determine what number the sum, difference, or product is congruent to in modulo 5. (4 – 9) • 7
> Repeat parts (a)–(h) of Exercise 53 for the mathematical system defined by the given table. Assume that the associative property holds for the given operation.
> Determine what number the sum, difference, or product is congruent to in modulo 5. 2 - 4
> Determine (a) the area and (b) the circumference of the circle. Use the key on your calculator and round your answer to the nearest hundredth.
> Repeat parts (a)–(h) of Exercise 53 for the mathematical system defined by the given table. Assume that the associative property holds for the given operation.
> Determine what number the sum, difference, or product is congruent to in modulo 5. 8 . 7
> A mathematical system is defined by a three-element by three-element table where every element in the set appears in each row and each column. Must the mathematical system be a commutative group? Explain.
> Determine what number the sum, difference, or product is congruent to in modulo 5. 12 - 5
> Determine the sum or difference in clock 7 arithmetic. 3 – (2 – 6)
> Determine what number the sum, difference, or product is congruent to in modulo 5. 2 + 3
> Determine the sum or difference in clock 7 arithmetic. 2 – 3
> Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months. 5 years, 9 months
> Determine the sum or difference in clock 7 arithmetic. 6 + 7
> Consider the 12 months to be a modulo 12 system with January being month 0. If it is currently October, determine the month it will be in the specified number of months. 7 years
> y < -2x + 2 Draw the graph of the inequality.
> Determine the sum or difference in clock 7 arithmetic. 2 + 6
