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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 33–38, discuss the validity of each statement about linear systems. If the statement is always true, explain why. If not, give a counterexample. The number of equations is less than or
Solve Problems 43–46 using augmented matrix methods. Graph each solution set. Discuss the differences between the graph of an equation in the system and the graph of the system’s solution set.
In Problems 33–38, discuss the validity of each statement about linear systems. If the statement is always true, explain why. If not, give a counterexample. The number of leftmost ones is less
Solve Problems 43–46 using augmented matrix methods. Graph each solution set. Discuss the differences between the graph of an equation in the system and the graph of the system’s solution set.
Use row operations to change each matrix in Problems 39–46 to reduced form. 1 0 0 23 3 -1 -2 -6 Na 2 1 3
Solve Problems 43–46 using augmented matrix methods. Graph each solution set. Discuss the differences between the graph of an equation in the system and the graph of the system’s solution set.
Solve Problems 47 and 48 using augmented matrix methods. Write the linear system represented by each augmented matrix in your solution, and solve each of these systems graphically. Discuss the
Solve Problems 47–62 using Gauss–Jordan elimination. 2x₁ + 4x2 3x1 + 9x221x3 = + 5x2 10x3 = -2 0 1 X1 12x3 = ||
Solve Problems 47–62 using Gauss–Jordan elimination. 3x1 + 5x2 X1 + X2 + 2x1 + X3 = x3 = -1 7 = −7 11x3
Solve Problems 47–62 using Gauss–Jordan elimination. 3x1 + 8x2 - x3 = -18 2x1 + x2 + 5x3 = 8 -4 2x1 + 4x2 + 2х3 - ||
Solve Problems 47–62 using Gauss–Jordan elimination. 2x1 + 6х2 + 15x3 = -12 4x1 + 7x2 + 13x3 = -10 3x1 + 6x2 + 12x3 = -9
Solve Problems 47–62 using Gauss–Jordan elimination. 2x1 - Xx₁ - 2x₂ X1 x2 - 3x3 = 8 = 7
Solve Problems 47–62 using Gauss–Jordan elimination. 2x1 + 4x2 3x1 + 3x2 I 6х3 = 10 3x3 6 ||
Solve Problems 47–62 using Gauss–Jordan elimination. 2x1 3x1 + 2x2 - X₁ X] X2= || X₂ = X2 0 7 −1 -1
Solve Problems 47–62 using Gauss–Jordan elimination. 3x1 - 4x2 - 2x1 - 3x2 + x1 - 2x2 + 3x3 x3 = 1 x3 = 1 2
Solve Problems 47–62 using Gauss–Jordan elimination. 2x1 0 7 3x1 + 2x2 X1 - X2 = -2 X2 =
Solve Problems 47–62 using Gauss–Jordan elimination. 3x1 + 7x2 x3 = 11 3 x1 + 2х2 - x3 = 2x1 + 4x2 - 2x3 = 10 =
Solve Problems 47–62 using Gauss–Jordan elimination. 3x1 - 2x2 + x3 = -7 2xi + x2 - 4х3 X2 0 x1 + x2 - 3x3 1 = ||
Solve Problems 47–62 using Gauss–Jordan elimination. 2x1 + 3x2 + 5x3 = 21 + = -2 X1 - X2-5х3 2x1 + X2 - x3 = 11
Solve Problems 47–62 using Gauss–Jordan elimination. 2x1 + 4х2 - 2х3 2 -3x1 - 6x2 + 3x3 = -3
Solve Problems 47–62 using Gauss–Jordan elimination. 3.x - 9.x2 + 12.x3 6 -2x+6.x2 - 8.x3 = -4 ||
Solve Problems 47–62 using Gauss–Jordan elimination. 4x1 - x2 + 2х3 -4x₁ + x₂ 3x3 X2 8x1 2x2 + 9х3 = = 3 -10 -1
Solve Problems 55–74 using augmented matrix methods. x1 + 2x2 = 4 2x1 + 4x2 = -8
Solve Problems 47–62 using Gauss–Jordan elimination. 5 3x3 = -2 4 4x1 - 2x₂ + 2x3 = -6x₁ + 3x₂ 10x₁5x₂ + 9x3
Consider a consistent system of three linear equations in three variables. Discuss the nature of the system and its solution set if the reduced form of the augmented coefficient matrix has (A) One
Solve Problems 65–70 using Gauss–Jordan elimination. X₁ -2x₁ + 4x₂ - 3x1 4x1 - x₂ + 3x3 - 2x4 1 3x3 + x4 = 0.5 X₂ + 10x3 4x4 = 2.9 3x28x32x4 = 0.6
Solve Problems 65–70 using Gauss–Jordan elimination. X2 + X2 - X1 + 4х3 + Х4 X3 -X1 + 2x1 + X3 + 3x4 2x1 + 5x2 + 11x3 + 3x4 1.3 1.1 = -4.4 5.6
Solve Problems 65–70 using Gauss–Jordan elimination. x₁ - 2x₂ + x3 + x₂ + 2x5 = 2 -2x₁ + 4x₂ + 2x3 + 2x4 - 2x5 = 0 3x₁ 6x₂ + x3 + - -X₁ + 2x₂ + 3x3 + x4 + 5x5 = 4 x₁ + x₂ = 3
Solve Problems 65–70 using Gauss–Jordan elimination. x₁3x₂ + x3 + x4 + 2x5 --x₁ + 5x₂ + 2x3 + 2x4 - 2x5 2x1 6x2 + 2x3 + 2x4 + 4x5 -X₁ + 3X₂ X3 - = + X5 = 2 0 4 = -3
Solve Problems 81–84 using augmented matrix methods. Use a graphing calculator to perform the row operations. 0.8x₁ + 2.88x2 1.25x₁ +4.34x₂ = 4 = 5 =
Solve Problems 75–80 using augmented matrix methods.3x1 - X2 = 7 2x1 + 3x2 = 1
Match each system in Problems 9–12 with one of the following graphs, and use the graph to solve the system. 5 (A) X 5 (B) X
Solve Problems 13–16 by graphing. = 3x - y = 2 x + 2y = 10
Solve Problems 13–16 by graphing. 3x 2y = 12 7x + 2y = 8
Solve Problems 13–16 by graphing. m + 2n = 2m + 4n 4 -8
Solve Problems 13–16 by graphing. Зи 3и + 5v = 15 би + 10г -30 ||
Solve Problems 17–20 using substitution. y = 2x - 3 x + 2y = 14
Solve Problems 17–20 using substitution. У y=x - 4 x + 3у = 12
Solve Problems 17–20 using substitution. 2x + y = 6 x=y=-3
Solve Problems 17–20 using substitution. 3x - y = 7 2х + 3у = 1
Solve Problems 21–24 using elimination by addition. Зи - 2v = 12 7u + 2 = 8
Solve Problems 21–24 using elimination by addition. 2x - 3y = -8 5x + 3y = 1
Solve Problems 21–24 using elimination by addition. 2m - n = 10 m2n = -4
Solve Problems 21–24 using elimination by addition. 2х + 3y = 1 3x - y = 7
Solve Problems 25–34 using substitution or elimination by addition. 9x - 3y = 24 11x +2y = 1
Solve Problems 25–34 using substitution or elimination by addition. 4х + 3у = 26 3x-11y 11y = -7
In Problems 7 and 8, find an equation in point–slope form, y - y1 = m(x - x1), of the line through the given points.(2, 7) and (4, -5).
Solve Problems 25–34 using substitution or elimination by addition. 2x - 3y = -2 -4x+6y= 7
Solve Problems 25–34 using substitution or elimination by addition. 3x - бу = -9 -2x + 4y = 12
Solve Problems 25–34 using substitution or elimination by addition. 3x + 8y = 4 15x + 10y = -10
Solve Problems 25–34 using substitution or elimination by addition. 7m + 12n = 5m 3n -1 7
Solve Problems 25–34 using substitution or elimination by addition. -6х 3x + 10y = -30 + бу = 15
Solve Problems 25–34 using substitution or elimination by addition. 2x + 4y = x + 2y = -8 4
Solve Problems 25–34 using substitution or elimination by addition. x + 0.3x y = 1 0.4y = 0
Solve Problems 25–34 using substitution or elimination by addition. x + y = 1 0.5x – 0.4y = 0
In Problems 35–42, solve the system. Note that each solution can be found mentally, without the use of a calculator or penciland-paper calculation; try to visualize the graphs of both lines. x + Oy
In Problems 35–42, solve the system. Note that each solution can be found mentally, without the use of a calculator or penciland-paper calculation; try to visualize the graphs of both lines. 5x +
In Problems 35–42, solve the system. Note that each solution can be found mentally, without the use of a calculator or penciland-paper calculation; try to visualize the graphs of both lines. 6x +
In Problems 35–42, solve the system. Note that each solution can be found mentally, without the use of a calculator or penciland-paper calculation; try to visualize the graphs of both lines. x 2y =
In Problems 35–42, solve the system. Note that each solution can be found mentally, without the use of a calculator or penciland-paper calculation; try to visualize the graphs of both lines. x + 3y
In Problems 49–56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. y = 2x - 9 y = 3x + 5
In Problems 49–56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. y = -3x + 3 y = 5x + 8
In Problems 49–56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. y = 2x + 1 y = 2x + 7
In Problems 57–62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect and discuss the nature of the solution set. x - 2y
In Problems 57–62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect and discuss the nature of the solution set. x+y= 1 x -
In Problems 57–62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect and discuss the nature of the solution set. 4x - 3у 4х
In Problems 1–4, find the indicated quantity, given A = P(1 + rt).A = ?; P = $200; r = 9%; t = 8 months
In Problems 1–4, find the indicated quantity, given A = P(1 + rt).A = $900; P = ?; r = 14%; t = 3 months
In Problems 1–4, find the indicated quantity, given A = P(1 + rt).A = $312; P = $250; r = 7%; t = ?
In Problems 1–4, find the indicated quantity, given A = P(1 + rt).A = $3,120; P = $3,000; r = ?; t = 8 months
In Problems 7–14, find i (the rate per period) and n (the number of periods) for each annuity. Quarterly deposits of $500 are made for 20 years into an annuity that pays 8% compounded quarterly.
In Problems 7 and 8, find the indicated quantity, given A = Pert.A = ?; P = $5,400; r = 5.8%; t = 2 years
In Problems 7 and 8, find the indicated quantity, given A = Pert.A = 45,000; P = ?; r = 9.4%; t = 72 months
In Problems 9 and 10, find the indicated quantity, given FV = $10,000; PMT = ?; i = 0.016; n = 54 FV = PMT (1 + i)" - 1 i
In Problems 9–12, use compound interest formula (1) to find each of the indicated values. P = $5,000; i = 0.005; n = 36; A = ?
In Problems 9 and 10, find the indicated quantity, given FV = ?; PMT = $1,200; i = 0.004; n = 72 FV = PMT (1 + i)" - 1 i
In Problems 11 and 12, find the indicated quantity, givenFV = ?; PMT = $3,500; i = 0.03; n = 14 PV = PMT 1- (1 + i)" i
In Problems 9–12, use compound interest formula (1) to find each of the indicated values.A = $8,000; i = 0.02; n = 32; P = ?
In Problems 11 and 12, find the indicated quantity, given FV = $9,000; PMT = ?; i = 0.0065; n = 16 1 - (1 + i)"¹ i PV = PMT-
In Problems 7–14, find i (the rate per period) and n (the number of periods) for each annuity. Annual deposits of $3,100 are made for 12 years into an annuity that pays 5.95% compounded annually.
In Problems 15–22, use the future value formula (6) to find each of the indicated values. n = 20; i = 0.03; PMT = $500; FV = ?
You need to borrow $4,000 for 9 months. The local bank is willing to supply the money at 9% simple interest. Calculate the amount of interest that will be paid on the loan for the stated period and
In Problems 15–22, use the future value formula (6) to find each of the indicated values.FV = $5,000; n = 15; i = 0.01; PMT = ?
In Problems 15–22, use the future value formula (6) to find each of the indicated values.FV = $4,000; i = 0.02; PMT = 200; n = ?
One investment pays 13% simple interest and another 9% compounded annually. Which investment would you choose? Why?
In Problems 21–26, use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.9% compounded monthly
Which is the better investment and why: 9% compounded quarterly or 9.25% compounded annually?
In Problems 21–26, use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.14.6% compounded daily.
A credit card company charges a 22% annual rate for overdue accounts. How much interest will be owed on a $635 account 1 month overdue?
In Problems 21–26, use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.15% compounded monthly.
In Problems 21–26, use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.4.8% compounded quarterly.
In Problems 21–26, use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period.3.2% compounded semiannually.
A loan of $2,500 was repaid at the end of 10 months with a check for $2,812.50. What annual rate of interest was charged?
Guaranty Income Life offered an annuity that pays 6.65% compounded monthly. If $500 is deposited into this annuity every month, how much is in the account after 10 years? How much of this is interest?
American General offers a 10-year ordinary annuity with a guaranteed rate of 6.65% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $5,000
In Problems 27–32, use the given interest rate i per compounding period to find r, the annual rate. 0.395% per month.
You want to purchase an automobile for $21,600. The dealer offers you 0% financing for 48 months or a $3,000 rebate. You can obtain 4.8% financing for 48 months at the local bank. Which option should
In Problems 27–32, use the given interest rate i per compounding period to find r, the annual rate. 0.012% per day.
In Problems 27–32, use the given interest rate i per compounding period to find r, the annual rate.0.9% per quarter.
In Problems 27–32, use the given interest rate i per compounding period to find r, the annual rate. 0.175% per month.

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