Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 4.5, Problem 5E
| Find the z-number associated with a
|
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
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Chapter 4 Solutions
Mathematics: A Practical Odyssey
Ch. 4.1 - To study the library habits of students at a local...Ch. 4.1 - To study the eating habits of students at a local...Ch. 4.1 - To study the composition of families in Manistee,...Ch. 4.1 - To study the spending habits of shoppers in...Ch. 4.1 - The speeds, in miles per hour, of forty randomly...Ch. 4.1 - The weight, in pounds, of thirty-five packages of...Ch. 4.1 - To examine the effects of a new registration...Ch. 4.1 - The frequency distribution shown in Figure 4.21...Ch. 4.1 - The frequency distribution shown in Figure 4.22...Ch. 4.1 - To study the output of a machine that fills boxes...
Ch. 4.1 - The ages of the nearly 4 million women who gave...Ch. 4.1 - The age composition of the population of the...Ch. 4.1 - Using the data in Figure 4.26, replace the...Ch. 4.1 - Using the data in Figure 4.26, replace the...Ch. 4.1 - The frequency distribution shown in Figure 4.27...Ch. 4.1 - The frequency distribution shown in Figure 4.28...Ch. 4.1 - Figure 4.29 lists the top five reasons given by...Ch. 4.1 - Figure 4.30 lists the worlds top six countries as...Ch. 4.1 - Figure 4.31 lists the race of new AIDS cases in...Ch. 4.1 - Figure 4.32 lists the types of accidental deaths...Ch. 4.1 - Figure 4.33 lists some common specialities of...Ch. 4.1 - Figure 4.34 lists the major metropolitan areas on...Ch. 4.1 - Answer the following questions using complete...Ch. 4.1 - Answer the following questions using complete...Ch. 4.1 - Answer the following questions using complete...Ch. 4.1 - Answer the following questions using complete...Ch. 4.1 - Answer the following questions using complete...Ch. 4.1 - Prob. 28ECh. 4.1 - Use a graphing calculator or Excel on the...Ch. 4.1 - Prob. 30ECh. 4.2 - Exercises 1-4, find mean, median, and mode of the...Ch. 4.2 - In Exercises 1-4, find mean, median, and mode of...Ch. 4.2 - Exercises 1-4, find mean, median, and mode of the...Ch. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Find the mean, median, and mode of each set of...Ch. 4.2 - Find the mean, median, and mode of each set of...Ch. 4.2 - Prob. 8ECh. 4.2 - Kaitlin Mowry is a member of local 4-H club and...Ch. 4.2 - Prob. 10ECh. 4.2 - Jerry Rice holds the all-time record in...Ch. 4.2 - Wayne Gretzky, known as The Great One, holds the...Ch. 4.2 - Relief pitcher Mariano Rivera New York Yankees...Ch. 4.2 - Michael Jordan has been recognized as an...Ch. 4.2 - The frequency distribution in Figure 4.61 lists...Ch. 4.2 - Todd booth, an avid jogger, kept detailed records...Ch. 4.2 - To study the output of a machine that fills boxes...Ch. 4.2 - To study the efficiency of its new price-scanning...Ch. 4.2 - Katrina must take five exams in a math class. If...Ch. 4.2 - Eugene must take four exams in a geography class....Ch. 4.2 - The mean salary of twelve men is 58,000, and the...Ch. 4.2 - The mean salary of twelve men is 52,000, and the...Ch. 4.2 - Maria drove from Chicago, Illinois, to Milwaukee,...Ch. 4.2 - Sully drove from Atlanta, Georgia, to Birmingham,...Ch. 4.2 - The mean age of a class of twenty-five students is...Ch. 4.2 - The mean age of a class of fifteen students is...Ch. 4.2 - The mean salary of eight employees is 40.000, and...Ch. 4.2 - The mean salary of ten employees is 32,000, and...Ch. 4.2 - The number of civilians holding government jobs in...Ch. 4.2 - The ages of the nearly 4 million women who gave...Ch. 4.2 - The age composition of the population of the...Ch. 4.2 - In Exercises 32 and 33. use the age composition of...Ch. 4.2 - In Exercises 32 and 33. use the age composition of...Ch. 4.2 - Prob. 34ECh. 4.2 - Suppose the mean of Group I is A and the mean of...Ch. 4.2 - Prob. 36ECh. 4.3 - Perform each task, given the following sample...Ch. 4.3 - Perform each task, given the following sample...Ch. 4.3 - Perform each task, given the following sample...Ch. 4.3 - Find the mean and standard deviation of each set...Ch. 4.3 - Find the mean and standard deviation of each set...Ch. 4.3 - Find the mean and standard deviation of each set...Ch. 4.3 - 7.Joey and Dee Dee bowled five games at the Rock n...Ch. 4.3 - Paki surveyed the price of unleaded gasoline...Ch. 4.3 - Kaitlin Mowry is a member of the local 4H club and...Ch. 4.3 - Before Lance Armstrong admitted doping and was...Ch. 4.3 - 11.Relief pitcher Mariano RiveraNew York Yankees...Ch. 4.3 - Micheal Jordan has been recognized as an...Ch. 4.3 - The Truly Amazing Dudes are a group of comic...Ch. 4.3 - The weights in Pounds of the ten Truly Amazing...Ch. 4.3 - The normal monthly rainfall in Seattle,...Ch. 4.3 - The normal monthly rainfall in Phoenix, Arizona,...Ch. 4.3 - The frequency distribution in Figure 4.87 lists...Ch. 4.3 - Prob. 18ECh. 4.3 - To study the output of a machine that fills boxes...Ch. 4.3 - To study the efficiency of its new price-scanning...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - The ages of all employees at a specific state...Ch. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Do Double Stuff Oreos really contain twice as much...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.4 - The weight in ounces of several bags of corn chips...Ch. 4.4 - 451 435 482 449 454 451 479 448 432 423 461 475...Ch. 4.4 - The time in minutes spent waiting in line for...Ch. 4.4 - A die was rolled several times, and the results...Ch. 4.4 - What percent of the standard normal z-...Ch. 4.4 - What percent of the standard normal z-...Ch. 4.4 - What percent of the standard normal z-...Ch. 4.4 - What percent of the standard normal z-...Ch. 4.4 - A population is normally distributed with mean...Ch. 4.4 - A population is normally distributed with mean...Ch. 4.4 - Find the following probabilities. a. p(0<z<1.62)...Ch. 4.4 - Find the following probabilities. a. p(0<z<1.42)...Ch. 4.4 - Find c such that each of the following is true. a....Ch. 4.4 - Find c such that each of the following is true. a....Ch. 4.4 - A population X is normally distributed with mean...Ch. 4.4 - A population X is normally distributed with mean...Ch. 4.4 - A population is normally distributed with mean...Ch. 4.4 - A population is normally distributed with mean...Ch. 4.4 - The mean weight of a box of cereal filled by a...Ch. 4.4 - The amount of time required to assemble a...Ch. 4.4 - The time it takes an acrylic paint to dry is...Ch. 4.4 - The shrinkage in length of a certain brand of blue...Ch. 4.4 - The mean volume of a carton of milk filled by a...Ch. 4.4 - The amount of time between taking a pain reliever...Ch. 4.4 - The results of a statewide exam for assessing the...Ch. 4.4 - Professor Harde assumes that exam scores are...Ch. 4.4 - The time it takes an employee to package the...Ch. 4.4 - The time it takes an employee to package the...Ch. 4.4 - What are the characteristics of a normal...Ch. 4.4 - Are all distributions of data normal distributed?...Ch. 4.4 - Why is total area under a bell curve equal to 1?.Ch. 4.4 - Why are there no negative z-numbers in the body...Ch. 4.4 - When converting an x-number to a z-number, what...Ch. 4.4 - Is it logical to assume that the heights of all...Ch. 4.4 - Is it reasonable to assume that the ages of all...Ch. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.5 - In exercises 1-4, use the body table in Appendix F...Ch. 4.5 - In exercises 1-4, use the body table in Appendix F...Ch. 4.5 - In exercises 1-4, use the body table in Appendix F...Ch. 4.5 - In exercises 1-4, use the body table in Appendix F...Ch. 4.5 - Find the z-number associated with a 92 level of...Ch. 4.5 - Find the z-number associated with a 97 level of...Ch. 4.5 - Find the z-number associated with a 75 level of...Ch. 4.5 - Find the z-number associated with a 85 level of...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 9-22, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 9-22, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - In Exercises 922, round off your answers sample...Ch. 4.5 - A survey asked, Can you imagine a situation in...Ch. 4.5 - A survey asked, Do you think that homeless people...Ch. 4.5 - A sample consisting of 430 men and 765 women was...Ch. 4.5 - A sample consisting of 942 men and 503 women was...Ch. 4.5 - A poll pertaining to environmental concerns had...Ch. 4.5 - A poll pertaining to educational goals had the...Ch. 4.5 - A recent poll pertaining to educational reforms...Ch. 4.5 - A recent poll pertaining to educational reforms...Ch. 4.5 - In exercises 29-32, you are planning a survey for...Ch. 4.5 - In exercises 29-32, you are planning a survey for...Ch. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.6 - A set of n=6 ordered pairs has the following sums:...Ch. 4.6 - A set of n=8 ordered pairs has the following sums:...Ch. 4.6 - A set of n=5 ordered pairs has the following sums:...Ch. 4.6 - Given the ordered pairs (4,40), (6,37), (8,34) and...Ch. 4.6 - Given the ordered pairs (5,5), (7,10), (8,11),...Ch. 4.6 - 6.Given the ordered pairs (5,20), (6,15), (10,14),...Ch. 4.6 - Given the ordered pairs (2,6), (3,12), (6,15),...Ch. 4.6 - 8.The unemployment rate and the amount of...Ch. 4.6 - 9.The average hourly earnings and the average...Ch. 4.6 - Prob. 10ECh. 4.6 - The amounts of rice and tobacco grown in the...Ch. 4.6 - The median home price and average mortgage rate in...Ch. 4.6 - Prob. 13ECh. 4.6 - Prob. 14ECh. 4.6 - Prob. 15ECh. 4.6 - Prob. 16ECh. 4.6 - Prob. 17ECh. 4.6 - Throughout the twentieth century, the record time...Ch. 4.6 - 19.Heart disease is a much less problem in France...Ch. 4.CR - Find a the mean, b the median, c the mode, and d...Ch. 4.CR - To study the compositions of the families in...Ch. 4.CR - Prob. 3CRCh. 4.CR - Prob. 4CRCh. 4.CR - Prob. 5CRCh. 4.CR - The mean salary of twelve men is $37000 and the...Ch. 4.CR - Prob. 7CRCh. 4.CR - Prob. 8CRCh. 4.CR - Prob. 9CRCh. 4.CR - Classify the following types of data as discrete,...Ch. 4.CR - Prob. 11CRCh. 4.CR - Prob. 12CRCh. 4.CR - Prob. 13CRCh. 4.CR - All incoming freshmen at a major university are...Ch. 4.CR - Prob. 15CRCh. 4.CR - Prob. 16CRCh. 4.CR - Prob. 17CRCh. 4.CR - Prob. 18CRCh. 4.CR - Prob. 19CRCh. 4.CR - Prob. 20CRCh. 4.CR - Prob. 21CRCh. 4.CR - Prob. 22CRCh. 4.CR - Prob. 23CRCh. 4.CR - Prob. 24CRCh. 4.CR - Prob. 25CRCh. 4.CR - Prob. 26CRCh. 4.CR - Prob. 27CRCh. 4.CR - Prob. 28CRCh. 4.CR - Answer the following questions using complete...
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