COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)
14th Edition
ISBN: 9780135998083
Author: Barnett
Publisher: PEARSON
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Chapter 4.6, Problem 3E
To determine
To solve: The equation
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Exercises: Find all the whole number
solutions of the congruence equation.
1. 3x 8 mod 11
2. 2x+3= 8 mod 12
3. 3x+12= 7 mod 10
4. 4x+6= 5 mod 8
5. 5x+3= 8 mod 12
Determine whether it's true or false and the reasoning is needed
Chapter 4 Solutions
COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)
Ch. 4.1 - Solve by graphing and check:
2x − y = −3
x + 2y =...Ch. 4.1 - Solve each of the following systems by graphing:
x...Ch. 4.1 - Prob. 3MPCh. 4.1 - Prob. 4MPCh. 4.1 - Prob. 5MPCh. 4.1 - Prob. 6MPCh. 4.1 - Prob. 7MPCh. 4.1 - Prob. 1EDCh. 4.1 - Prob. 2EDCh. 4.1 - In Problems 1–6, find the x and y coordinates of...
Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - In Problems 1–6, find the x and y coordinates of...Ch. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Match each system in Problems 9–12 with one of the...Ch. 4.1 - Solve Problems 13–16 by graphing.
13.
Ch. 4.1 - Solve Problems 13–16 by graphing.
14.
Ch. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - In a free competitive market, if the demand for a...Ch. 4.1 - Problems 45−48 are concerned with the linear...Ch. 4.1 -
Problems 45−48 are concerned with the linear...Ch. 4.1 - Problems 45−48 are concerned with the linear...Ch. 4.1 - Problems 45–48 are concerned with the linear...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - In Problems 57−62, graph the equations in the same...Ch. 4.1 - In Problems 57−62, graph the equations in the same...Ch. 4.1 -
In Problems 57−62, graph the equations in the...Ch. 4.1 - 63. The coefficients of the three systems given...Ch. 4.1 - Repeat problem 63 for the following systems:
...Ch. 4.1 - Supply and demand for T-shirts. Suppose that the...Ch. 4.1 - Supply and demand for baseball caps. Suppose that...Ch. 4.1 - Supply and demand for soybeans. At $4.80 per...Ch. 4.1 - Supply and demand for corn. At $2.13 per bushel,...Ch. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Delivery charges. United Express, a national...Ch. 4.1 - Delivery charges. Refer to Problem 73. Federated...Ch. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Animal diet. Animals in an experiment are to be...Ch. 4.1 - Prob. 78ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 81ECh. 4.1 - Prob. 82ECh. 4.1 - Prob. 83ECh. 4.1 - Prob. 84ECh. 4.1 - Prob. 85ECh. 4.2 - Solve using augmented matrix methods:
2x1 − x2 =...Ch. 4.2 - Prob. 2MPCh. 4.2 - Prob. 3MPCh. 4.2 - Prob. 4MPCh. 4.2 - Prob. 1EDCh. 4.2 - Prob. 2EDCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 13ECh. 4.2 - Problems 1–14 refer to the following matrices: (If...Ch. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Perform the row operations indicated in problems...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Perform the row operations indicated in problem...Ch. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Each of the matrices in Problems 35–42 is the...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Solve Problems 47 and 48 using augmented matrix...Ch. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 64ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 66ECh. 4.2 - Solve Problems 55– 74 using augmented, matrix...Ch. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Solve Problems 55-74 using augmented, matrix...Ch. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - Solve Problems 55-74 using augmented, matrix...Ch. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Prob. 77ECh. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.2 - Prob. 80ECh. 4.2 - Prob. 81ECh. 4.2 - Prob. 82ECh. 4.2 - Prob. 83ECh. 4.2 - Prob. 84ECh. 4.3 - The matrices below are not in reduced form....Ch. 4.3 - Solve by Gauss–Jordan elimination:
3x1 + x2 − 2x3...Ch. 4.3 - Solve by Gauss-Jordan elimination:
2x1 − 4x2 − x3...Ch. 4.3 - Solve by Gauss–Jordan elimination:
Ch. 4.3 - Prob. 5MPCh. 4.3 - Prob. 6MPCh. 4.3 - Prob. 1EDCh. 4.3 - Prob. 2EDCh. 4.3 - In Problems 1–4, write the augmented matrix of the...Ch. 4.3 - Prob. 2ECh. 4.3 - In Problems 1–4, write the augmented matrix of the...Ch. 4.3 - Prob. 4ECh. 4.3 - In Problems 5−8, write the system of linear...Ch. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 14ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 16ECh. 4.3 - In Problems 9–18, if a matrix is in reduced form,...Ch. 4.3 - Prob. 18ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 20ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 22ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 24ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 26ECh. 4.3 - In Problems 19–28, write the solution of the...Ch. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - In which of Problems 19, 21, 23, 25, and 27 is the...Ch. 4.3 - Prob. 32ECh. 4.3 - In Problems 33–38, discuss the validity of each...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Use row operations to change each matrix in...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 52ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 54ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Consider a consistent system of three linear...Ch. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Solve Problems 47–62 using Gauss–Jordan...Ch. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Find a, b, and c so that the graph of the...Ch. 4.3 - Prob. 72ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 74ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Construct a mathematical model for each of the...Ch. 4.3 - Prob. 78ECh. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Taxable income. Repeat Problem 81 if tax law is...Ch. 4.3 - Construct a mathematical model for each the...Ch. 4.3 - Prob. 84ECh. 4.3 - Prob. 85ECh. 4.3 - Prob. 86ECh. 4.3 - Construct a mathematical model for each of the...Ch. 4.3 - Prob. 88ECh. 4.3 - Population growth. The U.S. population was...Ch. 4.3 - Prob. 90ECh. 4.3 - Prob. 91ECh. 4.3 - Prob. 92ECh. 4.3 - Prob. 93ECh. 4.3 - Prob. 94ECh. 4.3 - Sociology. Two sociologists have grant money to...Ch. 4.3 - Prob. 96ECh. 4.3 - Prob. 97ECh. 4.3 - Traffic flow. Refer to Problem 97. Closing...Ch. 4.4 - Add:
Ch. 4.4 - Prob. 2MPCh. 4.4 - Prob. 3MPCh. 4.4 - Prob. 4MPCh. 4.4 - Prob. 5MPCh. 4.4 - Prob. 6MPCh. 4.4 - Prob. 7MPCh. 4.4 - Find each product, if it is...Ch. 4.4 - Prob. 9MPCh. 4.4 - Prob. 10MPCh. 4.4 - Prob. 1EDCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - In Problems 1–14, perform the indicated operation,...Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - In Problems 1–14, perform the indicated operation,...Ch. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - In Problems 15–22, find the matrix product. Note...Ch. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - In Problems 15–22, find the matrix product. Note...Ch. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - B Find the products in Problems 23–30.
25.
Ch. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 -
Find the products in problems 23–30.
29.
Ch. 4.4 - Prob. 30ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 36ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Problems 31–48 refer to the following...Ch. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - If a and b are nonzero real numbers,
find AB and...Ch. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - If a, b, c, and d so that
Ch. 4.4 - Prob. 56ECh. 4.4 - If a, b, c, and d, so that
Ch. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Markup. An import car dealer sells three models of...Ch. 4.4 - Prob. 68ECh. 4.4 - Labor costs. A company with manufacturing plants...Ch. 4.4 - Inventory value. A personal computer retail...Ch. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.5 - Prob. 1MPCh. 4.5 - Prob. 2MPCh. 4.5 - Prob. 3MPCh. 4.5 - Prob. 4MPCh. 4.5 - Prob. 5MPCh. 4.5 - Prob. 1EDCh. 4.5 - Prob. 2EDCh. 4.5 - Prob. 3EDCh. 4.5 - In Problems 1-4, find the additive inverse and the...Ch. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 22ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 24ECh. 4.5 - In Problems 19–28, examine the product of the two...Ch. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Without performing any row operations, explain why...Ch. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Given M in problems 39–48, find M−1 and show that...Ch. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Given M in Problems 39–48, find M–1and show that...Ch. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Find the inverse of each matrix in Problems 49–56,...Ch. 4.5 - Prob. 50ECh. 4.5 - Find the inverse of each matrix in problem 49–56,...Ch. 4.5 - Given M in problem 39–48, find M–1 and show that...Ch. 4.5 - Find the inverse of each matrix in problems 49–56,...Ch. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - In Problems 57–60, find the inverse. Note that...Ch. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Prob. 64ECh. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Find the inverse of each matrix in problems 61–68,...Ch. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Show that (A–1)–1 = A for: A =
Ch. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Cryptography. The following message was encoded...Ch. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4.5 - Prob. 86ECh. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4.6 - Given an n × n matrix A and n × 1 column matrices...Ch. 4.6 - Prob. 2MPCh. 4.6 - Prob. 3MPCh. 4.6 - Prob. 4MPCh. 4.6 - Prob. 1EDCh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.6 - Prob. 7ECh. 4.6 - Prob. 8ECh. 4.6 - Write Problems 9–12 as systems of linear equations...Ch. 4.6 - Prob. 10ECh. 4.6 - Write problems 9–12 as system of linear equations...Ch. 4.6 - Prob. 12ECh. 4.6 - Write each system on Problems 13–16 as a matrix...Ch. 4.6 - Prob. 14ECh. 4.6 - Write each system in Problems 13–16 as a matrix...Ch. 4.6 - Prob. 16ECh. 4.6 - Find x1 and x2 in problems 17–20.
Ch. 4.6 - Prob. 18ECh. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - In Problems 21–24, find x1 and x2.
Ch. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - In Problems 21–24, find x1 and x2.
Ch. 4.6 - In Problems 25–30, solve for x1 and x2.
Ch. 4.6 - In Problems 25–30, solve for x1 and x2.
Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - In problems 25–30, solve for x1 and x2.
Ch. 4.6 - Prob. 30ECh. 4.6 - In Problems 31–38, write each system as a matrix...Ch. 4.6 - Prob. 32ECh. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - In Problems 31–38, write each system as a matrix...Ch. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - Prob. 40ECh. 4.6 - Prob. 41ECh. 4.6 - Prob. 42ECh. 4.6 - Prob. 43ECh. 4.6 - Prob. 44ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 46ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 48ECh. 4.6 - In Problems 45–50, explain why the system cannot...Ch. 4.6 - Prob. 50ECh. 4.6 - Prob. 51ECh. 4.6 - Prob. 52ECh. 4.6 - Prob. 53ECh. 4.6 - Prob. 54ECh. 4.6 - Prob. 55ECh. 4.6 - Prob. 56ECh. 4.6 - Prob. 57ECh. 4.6 - Prob. 58ECh. 4.6 - In Problems 59–62, write each system as a matrix...Ch. 4.6 - Prob. 60ECh. 4.6 - Prob. 61ECh. 4.6 - Prob. 62ECh. 4.6 - Concert tickets. A concert hall has 10,000 seats...Ch. 4.6 - Prob. 64ECh. 4.6 - Production scheduling. A supplier manufactures car...Ch. 4.6 - Prob. 66ECh. 4.6 - Prob. 67ECh. 4.6 - Prob. 68ECh. 4.6 - Prob. 69ECh. 4.6 - Prob. 70ECh. 4.7 - An economy is based on three sectors, coal, oil,...Ch. 4.7 - Prob. 1EDCh. 4.7 - Prob. 1ECh. 4.7 - Prob. 2ECh. 4.7 - Prob. 3ECh. 4.7 - Prob. 4ECh. 4.7 - Prob. 5ECh. 4.7 - Prob. 6ECh. 4.7 - Prob. 7ECh. 4.7 - Prob. 8ECh. 4.7 - Problems 9–14 pertain to the following...Ch. 4.7 - Problems 9–14 pertain to the following input-...Ch. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Prob. 18ECh. 4.7 - Prob. 19ECh. 4.7 - Problems 15–20 pertain to the following input-...Ch. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Prob. 26ECh. 4.7 - Prob. 27ECh. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - Prob. 41ECh. 4.7 - Repeat Problem 41 with the following table:
Four...Ch. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RE
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- In triangle with sides of lengths a, b and c the angle a lays opposite to a. Prove the following inequality sin a 2√bc C α b a Warrow_forward1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.arrow_forwardScenario Sales of products by color follow a peculiar, but predictable, pattern that determines how many units will sell in any given year. This pattern is shown below Product Color 1995 1996 1997 Red 28 42 21 1998 23 1999 29 2000 2001 2002 Unit Sales 2003 2004 15 8 4 2 1 2005 2006 discontinued Green 26 39 20 22 28 14 7 4 2 White 43 65 33 36 45 23 12 Brown 58 87 44 48 60 Yellow 37 56 28 31 Black 28 42 21 Orange 19 29 Purple Total 28 42 21 49 68 78 95 123 176 181 164 127 24 179 Questions A) Which color will sell the most units in 2007? B) Which color will sell the most units combined in the 2007 to 2009 period? Please show all your analysis, leave formulas in cells, and specify any assumptions you make.arrow_forward
- 5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+ f(0). (a) Find the representing matrix A of L with respect to the ordered basis {x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2. (b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect to the ordered basis {2,1-x}arrow_forwardOne hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs \[36\] \[20\] \[56\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] problem 1 Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal. \[P\left(\text{prefers dogs}\right)=\] Incorrect Check Hide explanation Preference Male Female TOTAL Prefers dogs \[\blueD{36}\] \[\blueD{20}\] \[\blueE{56}\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.arrow_forwardFor the spinner below, assume that the pointer can never lie on a borderline. Find the following probabilities. (enter the probabilities as fractions)arrow_forward
- Evaluate the following integrals as they are writtenarrow_forwardFind the values of x, y, and z. Round to the nearest tenth, if necessary. 8, 23arrow_forward11 In the Pharlemina's Favorite quilt pattern below, vega-pxe-frame describe a motion that will take part (a) green to part (b) blue. Part (a) Part (b)arrow_forward
- Business discussarrow_forward(c) Describe the distribution plan and show the total distribution cost. Optimal Solution Amount Cost $ 2000 Southern-Hamilton 200 Southern-Butler $ Southern-Clermont 300 4500 Northwest-Hamilton 200 $2400 Northwest-Butler 200 $3000 Northwest-Clermont $ Total Cost ક (d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units. (i) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier. Distribution Plan with Southern Gas Amount Southern-Hamilton $ Cost × Southern-Butler x $ Southern-Clermont 300 $ 4500 Northwest-Hamilton 64 x Northwest-Butler $ × Northwest-Clermont 0 $0 Total Cost $ (ii) Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier. Distribution Plan with Northwest Gas Southern-Hamilton Southern-Butler 0 Southern-Clermont Northwest-Hamilton Northwest-Butler Northwest-Clermont Total Cost Amount × x x +7 $0 Cost × $ × $ × +4 $ -/+ $ × ×arrow_forwardThe distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows. Warehouse Plant Capacity 1 2 1 4 7 450 2 8 5 600 3 5 6 380 Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows. Customer Warehouse 1 2 3 1 6 4 8 2 3 6 7 7 Demand 300 300 300 400 (a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Formulate a linear programming model of the problem. (Let Plant 1 be node 1, Plant 2 be node 2, Plant 3 be node 3, Warehouse 1 be node 4, Warehouse 2 be node 5, Customer 1 be node 6, Customer 2 be node 7, Customer 3 be node 8, and Customer 4 be node 9. Express your answers in the form x;;, where x,; represents the number of units shipped from node i to node j.) Min 4x14+8x24+5x34+7x15 +5x25…arrow_forward
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