EBK MATHEMATICS WITH APPLICATIONS IN TH
12th Edition
ISBN: 9780134773285
Author: MULLINS
Publisher: YUZU
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Chapter 6.5, Problem 17E
To determine
To calculate: The product of the matrices,
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9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
x
(a) Show that Qx+b (h) = Qx(h).
(b) Is it true that Qx(ah) =aQx(h)?
(c) Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qy (h)).
To put the concept in perspective, if X1, X2, X, are independent, identically
distributed random variables, and S₁ = Z=1Xk, then there exists an absolute
constant, A, such that
A
Qs, (h) ≤
√n
Some references: [79, 80, 162, 222], and [204], Sect. 1.5.
29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
91002 175/1
3
2,3,
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and
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the
28 Suppose that a mound-shaped data set has a
mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 8 and 12?
b. About what percentage of the data should
lie above 10?
c. About what percentage of the data should
lie above 12?
Chapter 6 Solutions
EBK MATHEMATICS WITH APPLICATIONS IN TH
Ch. 6.1 - Checkpoint1 Use the substitution method tosolve...Ch. 6.1 - Checkpoint 2
Use the elimination method to solve...Ch. 6.1 - Checkpoint 3
Solve the system of equations .
Draw...Ch. 6.1 - Checkpoint 4
Solve the following system:
Ch. 6.1 - Checkpoint 5
Solve the system
Draw the graph of...Ch. 6.1 - Prob. 6CPCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Use substitution to solve each system. (See...Ch. 6.1 - Use substitution to solve each system. (See...
Ch. 6.1 - Use substitution to solve each system. (See...Ch. 6.1 - Use substitution to solve each system. (See...Ch. 6.1 - Use elimination to solve each system. (See...Ch. 6.1 - Use elimination to solve each system. (See...Ch. 6.1 - Use elimination to solve each system. (See...Ch. 6.1 - Use elimination to solve each system. (See...Ch. 6.1 - Use elimination to solve each system. (See...Ch. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Use elimination to solve each system. (See...Ch. 6.1 - Use elimination to solve each system. (See...Ch. 6.1 - Prob. 16ECh. 6.1 - In Exercises 17 and 18, multiply both sides of...Ch. 6.1 - In Exercises 17 and 18, multiply both sides of...Ch. 6.1 - Millennials The number of baby boomers has been...Ch. 6.1 - Prob. 20ECh. 6.1 - Slow Midwestern Growth According to US. Census...Ch. 6.1 - Booming Florida At the start of the millennium,...Ch. 6.1 - Google Trends According to Google Trends, popular...Ch. 6.1 -
24. Heart Disease and Cancer Deaths The number of...Ch. 6.1 - Workforce Participation for Women and Men On the...Ch. 6.1 - Prob. 26ECh. 6.1 - Theater Tickets A 200-seat theater charges $8 for...Ch. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.2 - Checkpoint 1
Use the elimination method to solve...Ch. 6.2 - Prob. 2CPCh. 6.2 - Checkpoint 3 Perform the given row operations on...Ch. 6.2 - Prob. 4CPCh. 6.2 - Prob. 5CPCh. 6.2 - Prob. 6CPCh. 6.2 - Prob. 7CPCh. 6.2 - Checkpoint 8
Solve each system.
(a)
(b)
Ch. 6.2 - Prob. 9CPCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Obtain an equivalent system by performing the...Ch. 6.2 - Obtain an equivalent system by performing the...Ch. 6.2 - Obtain an equivalent system by performing the...Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Obtain an equivalent system by performing the...Ch. 6.2 - Prob. 13ECh. 6.2 - Write the augmented matrix of each of the given...Ch. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 21ECh. 6.2 - Use the indicated row operation to transform each...Ch. 6.2 - Prob. 20ECh. 6.2 - In Exercises 21-24, the reduced row echelon form...Ch. 6.2 - In Exercises 21-24, the reduced row echelon form...Ch. 6.2 - In Exercises 21-24, the reduced row echelon form...Ch. 6.2 - In Exercises 21-24, the reduced row echelon form...Ch. 6.2 - Prob. 25ECh. 6.2 - Prob. 28ECh. 6.2 - In Exercises 25-30, perform row operations on the...Ch. 6.2 - In Exercises 25-30, perform row operations on the...Ch. 6.2 - In Exercises 25-30, perform row operations on the...Ch. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Write the augmented matrix of the system and use...Ch. 6.2 - Write the augmented matrix of the system and use...Ch. 6.2 - Write the augmented matrix of the system and use...Ch. 6.2 - Write the augmented matrix of the system and use...Ch. 6.2 - Write the augmented matrix of the system and use...Ch. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Write the augmented matrix of the system and use...Ch. 6.2 - Use the Gauss-Jordan method to solve each of the...Ch. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Solve the system by any method.
62.
Ch. 6.2 - Prob. 63ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - Prob. 70ECh. 6.2 - Prob. 71ECh. 6.2 - 72. Explain why a system with more variables than...Ch. 6.3 - Checkpoint 1 In Example 1, suppose that the...Ch. 6.3 - Checkpoint 2 Write the augmented matrix of the...Ch. 6.3 - Prob. 3CPCh. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Prob. 3ECh. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Prob. 10ECh. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Prob. 16ECh. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - Use systems of equations to work these applied...Ch. 6.3 - A graphing calculator or other technology is...Ch. 6.3 - A graphing calculator or other technology is...Ch. 6.3 - 25. Social Science The table shows Census Bureau...Ch. 6.3 - 26. Social Science The table shows Census Bureau...Ch. 6.3 - 27. Business At a pottery factory, fuel...Ch. 6.3 - Prob. 28ECh. 6.4 - Checkpoint 1
Rewrite matrix M in Example 1 in a...Ch. 6.4 - Prob. 2CPCh. 6.4 - Prob. 3CPCh. 6.4 - Prob. 4CPCh. 6.4 - Prob. 5CPCh. 6.4 - Prob. 6CPCh. 6.4 - Prob. 7CPCh. 6.4 - Prob. 8CPCh. 6.4 - Prob. 9CPCh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Find the size of each of the given matrices....Ch. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Perform the indicated operations where possible....Ch. 6.4 - Prob. 14ECh. 6.4 - Perform the indicated operations where possible....Ch. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Let and . Find each of the following. (See...Ch. 6.4 - Prob. 19ECh. 6.4 - Let and . Find each of the following. (See...Ch. 6.4 - Prob. 21ECh. 6.4 - Let and . Find each of the following. (See...Ch. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Using matrices
verify that the statements in...Ch. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Work the following exercises. (See Example...Ch. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.5 - Prob. 1CPCh. 6.5 - Prob. 2CPCh. 6.5 - Prob. 3CPCh. 6.5 - Prob. 4CPCh. 6.5 - Prob. 5CPCh. 6.5 - Prob. 6CPCh. 6.5 - Prob. 7CPCh. 6.5 - Prob. 8CPCh. 6.5 - Prob. 9CPCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - In Exercises 1-6, the sizes of two matrices A and...Ch. 6.5 - In Exercises 1-6, the sizes of two matrices A and...Ch. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Find each of the following matrix products, if...Ch. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Find each of the following matrix products, if...Ch. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Find each of the following matrix products, if...Ch. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Given matrices
verify that the statements in...Ch. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Prob. 28ECh. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Prob. 31ECh. 6.5 - Determine whether the given matrices are inverses...Ch. 6.5 - Prob. 37ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - Find the inverse, if it exists, for each of the...Ch. 6.5 - Prob. 33ECh. 6.5 - Find the inverse, if it exists, for each of the...Ch. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Find the inverse, if it exists, for each of the...Ch. 6.5 - Find the inverse, if it exists, for each of the...Ch. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - Prob. 49ECh. 6.5 - Work these exercises. (See Example 4.)
50. Bulk...Ch. 6.5 - Prob. 56ECh. 6.5 - A graphing calculator or other technology is...Ch. 6.5 - Prob. 55ECh. 6.5 - Prob. 52ECh. 6.5 - Prob. 53ECh. 6.5 - Prob. 54ECh. 6.6 - Prob. 1CPCh. 6.6 - Prob. 2CPCh. 6.6 - Prob. 3CPCh. 6.6 - Prob. 4CPCh. 6.6 - Prob. 5CPCh. 6.6 - Prob. 6CPCh. 6.6 - Prob. 7CPCh. 6.6 - Checkpoint 8
Use the following matrix to find the ...Ch. 6.6 - Prob. 9CPCh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Use the inverse of the coefficient matrix to solve...Ch. 6.6 - Prob. 9ECh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Use the inverse of the coefficient matrix to solve...Ch. 6.6 - Prob. 13ECh. 6.6 - Prob. 14ECh. 6.6 - Prob. 15ECh. 6.6 - Prob. 16ECh. 6.6 - Write a system of equations, and use the inverse...Ch. 6.6 - Prob. 18ECh. 6.6 - Prob. 20ECh. 6.6 - Prob. 19ECh. 6.6 - Write a system of equations, and use the inverse...Ch. 6.6 - 22. Health A 100-bed nursing home provides two...Ch. 6.6 - Find the production matrix for the given...Ch. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - Exercises 25 and 26 refer to Example 6.
Example 6...Ch. 6.6 - Work these problems. (See Examples 3-6.)
28....Ch. 6.6 - Prob. 27ECh. 6.6 - Prob. 29ECh. 6.6 - Work these problems. (See Examples...Ch. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - Prob. 33ECh. 6.6 - Prob. 34ECh. 6.6 - Prob. 35ECh. 6.6 - Prob. 36ECh. 6.6 - Work these coding exercises. (See Example 7 and...Ch. 6.6 - Prob. 38ECh. 6.6 - Prob. 39ECh. 6.6 - Prob. 40ECh. 6.6 - Prob. 41ECh. 6.6 - Prob. 42ECh. 6.6 - Prob. 43ECh. 6.6 - 44. Business The figure shows four southern cities...Ch. 6 - Prob. 1RECh. 6 - Solve each of the following systems.
2.
Ch. 6 - Solve each of the following systems.
3.
Ch. 6 - Solve each of the following systems.
4.
Ch. 6 - 5. Business Abigail Henderson plans to buy shares...Ch. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RECh. 6 - Prob. 69RECh. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 72RECh. 6 - Prob. 73RECh. 6 - Prob. 74RECh. 6 - Prob. 75RECh. 6 - Prob. 76RECh. 6 - Prob. 77RECh. 6 - Prob. 78RECh. 6 - Prob. 79RECh. 6 - Prob. 80RECh. 6 - Prob. 81RECh. 6 - Prob. 82RECh. 6 - Prob. 83RECh. 6 - Prob. 84RECh. 6 - Prob. 85RECh. 6 - Solve each of the following problems by any...Ch. 6 - Prob. 87RECh. 6 - Prob. 88RECh. 6 - Prob. 89RECh. 6 - Use technology to do Exercises 89-91.
90. Business...Ch. 6 - Prob. 91RECh. 6 - Prob. 92RECh. 6 - Prob. 93RECh. 6 - Prob. 94RECh. 6 - Prob. 95RECh. 6 - Prob. 96RECh. 6 - Prob. 1CECh. 6 - 2. It was shown previously that there are four...Ch. 6 - 3. Which trips in the Stampede Air network take...Ch. 6 - Prob. 4CECh. 6 - Prob. 5CECh. 6 - Prob. 6CE
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- 27 Suppose that you have a data set of 1, 2, 2, 3, 3, 3, 4, 4, 5, and you assume that this sample represents a population. The mean is 3 and g the standard deviation is 1.225.10 a. Explain why you can apply the empirical rule to this data set. b. Where would "most of the values" in the population fall, based on this data set?arrow_forward30 Explain how you can use the empirical rule to find out whether a data set is mound- shaped, using only the values of the data themselves (no histogram available).arrow_forward5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward
- 6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows: P(X=-x) = P(X = x)=p. P(X=0)= 1-2p. Show that there is equality in Chebyshev's inequality for X. This means that Chebyshev's inequality, in spite of being rather crude, cannot be improved without additional assumptions.arrow_forward4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).arrow_forward
- 2. Derive the component transformation equations for tensors shown be- low where [C] = [BA] is the direction cosine matrix from frame A to B. B[T] = [C]^[T][C]T 3. The transport theorem for vectors shows that the time derivative can be constructed from two parts: the first is an explicit frame-dependent change of the vector whereas the second is an active rotational change of the vector. The same holds true for tensors. Starting from the previous result, derive a version of transport theorem for tensors. [C] (^[T])[C] = dt d B dt B [T] + [WB/A]B[T] – TWB/A] (10 pt) (7pt)arrow_forwardUse the graph of the function y = f (x) to find the value, if possible. f(x) 8 7 6 Q5 y 3 2 1 x -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6 -7 -8+ Olim f(z) x-1+ O Limit does not exist.arrow_forward3. Prove that, for any random variable X, the minimum of E(X - a)² is attained for a = EX. Provedarrow_forward
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