
Introductory Combinatorics
5th Edition
ISBN: 9780136020400
Author: Richard A. Brualdi
Publisher: Prentice Hall
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Chapter 6, Problem 20E
To determine
To prove: That the
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The manager of a fleet of automobiles is testing
two brands of radial tires and assigns one tire of
each brand at random to the two rear wheels of
eight cars and runs the cars until the tires wear
out. The data (in kilometers) follow.
CAR BRAND1
BRAND2
DIFFERENCE = (BRAND1 - BF
1
36,925 33,018
3,907
2
45,300 43,280
2,020
3
36,240
35,500
740
4
32,100
31,200
900
5
37,210
37,015
195
6
48,360
46,800
1,560
7
38,200
37,810
390
8
33,500
33,215
285
Diabetes and obesity are serious health concerns in the United States and much of the
developed world. Measuring the amount of body fat a person carries is one way to monitor
weight control progress, but measuring it accurately involves either expensive X-ray
equipment or a pool in which to dunk the subject. Instead body mass index (BMI) is often
used as a proxy for body fat because it is easy to measure: BMI = mass(kg)/(height(m))² = 703
mass(lb)/(height(in))².
In a study of 15 men at TXST, both BMI and body fat were measured. Researchers imported
the data into statistical software for analysis.
A few values are missing from the output. Complete the table by filling in the missing values.
Model Summary
S
R-sq
%
(three decimal places)
(two decimal places. e.g. 12.3456%, enter 12.35)
Analysis of Variance
Source
Model
Error
Total
DF
SS
MS
F
P
17.600
0.001
DF: whole numbers
SS or MS; three decimal places
34.810
Does a simple linear regression model seem reasonable in this situation?…
The use of electromyostimulation (EMS) as a
method to train healthy skeletal muscle is
studied. EMS sessions consisted of 30
contractions (4-second duration, 85 Hz) and
were carried out three times per week for three
weeks on 17 ice hockey players. The 10-meter
skating performance test showed a standard
deviation of 0.90 seconds. Is there strong
evidence to conclude that the standard deviation
of performance time exceeds the historical value
of 0.75 seconds? Use a = 0.05.
Chapter 6 Solutions
Introductory Combinatorics
Ch. 6 - Prob. 1ECh. 6 - Find the number of integers between 1 and 10,000...Ch. 6 - Find the number of integers between 1 and 10,000...Ch. 6 - Prob. 4ECh. 6 - Determine the number of 10-combinations of the...Ch. 6 - A bakery sells chocolate, cinnamon, and plain...Ch. 6 - Determine the number of solutions of the equation...Ch. 6 - Determine the number of solutions of the equation...Ch. 6 - Determine the number of integral solutions of the...Ch. 6 - Let S be a multiset with k distinct objects with...
Ch. 6 - Determine the number of permutations of {1, 2, …,...Ch. 6 - Determine the number of permutations of {1, 2, ⋯,...Ch. 6 - Determine the number of permutations of {1, 2, …,...Ch. 6 - Determine a general formula for the number of...Ch. 6 - At a party, seven gentlemen check their hats. In...Ch. 6 - Use combinatorial reasoning to derive the...Ch. 6 - Determine the number of permutations of the...Ch. 6 - Verify the factorial formula
Ch. 6 - Using the evaluation of the derangement numbers as...Ch. 6 - Prob. 20ECh. 6 - Prove that Dn is an even number if and only if n...Ch. 6 - Show that the numbers Qn of Section 6.5 can be...Ch. 6 - (Continuation of Exercise 22.) Use the...Ch. 6 - What is the number of ways to place six...Ch. 6 - Prob. 25ECh. 6 - Count the permutations i1i2i3i4i5i6 of {1, 2, 3,...Ch. 6 - Prob. 27ECh. 6 - Prob. 28ECh. 6 - Prob. 29ECh. 6 - Prob. 30ECh. 6 - Prob. 31ECh. 6 - Prob. 32ECh. 6 - Prob. 33ECh. 6 - Prob. 34ECh. 6 - Consider the board with forbidden positions as...Ch. 6 - Prob. 38ECh. 6 - Prob. 39ECh. 6 - Consider the multiset X = {n1 · a1, n2 · a2, …, nk...
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- One-Sample Z Test Test of М = 45 vs not === 45 The assumed standard deviation = 2.8 VARIABLE N MEAN STDEV SE MEAN X Instructions: 46.377 2.500 0.626 95% CI (,) Fill in the missing values. N: Round the answer to the nearest whole number. Cl: Round to three decimal places. Z: Round to two decimal places. P: Round to three decimal places.arrow_forwardNeed detailed report solution without AI and Chatgpt,arrow_forwardBased on the software output, write the fitted simple linear regression equation. Coefficients Term Coef SE Coef T-Value P-Value Constant 3.20 1.92 1.67 0.237 [Select] y= 0.600 0.566 1.06 0.400 +[Select] x Does a simple linear regression model seem reasonable in this situation? [Select]arrow_forward
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- 538 Chapter 13 12. Given: Points E(-4, 1), F(2, 3), G(4, 9), and H(-2, 7) a. Show that EFGH is a rhombus. b. Use slopes to verify that the diagonals are perpendicular. 13. Given: Points R(-4, 5), S(-1, 9), T(7, 3) and U(4, -1) a. Show that RSTU is a rectangle. b. Use the distance formula to verify that the diagonals are congruent. 14. Given: Points N(-1, -5), O(0, 0), P(3, 2), and 2(8, 1) a. Show that NOPQ is an isosceles trapezoid. b. Show that the diagonals are congruent. Decide what special type of quadrilateral HIJK is. Then prove that your answer is correct. 15. H(0, 0) 16. H(0, 1) 17. H(7, 5) 18. H(-3, -3) I(5, 0) I(2,-3) 1(8, 3) I(-5, -6) J(7, 9) K(1, 9) J(-2, -1) K(-4, 3) J(0, -1) K(-1, 1) J(4, -5) K(6,-2) 19. Point N(3, - 4) lies on the circle x² + y² = 25. What is the slope of the (Hint: Recall Theorem 9-1.) - line that is tangent to the circle at N? 20. Point P(6, 7) lies on the circle (x + 2)² + (y − 1)² = 100. What is the slope of the line that is tangent to the circle at…arrow_forwardConsider a set of data ...arrow_forwardFor each graph in Figure 16, determine whether f (1) is larger or smaller than the slope of the secant line between x = 1 and x = 1 + h for h > 0. Explain your reasoningarrow_forward
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