Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 1.1, Problem 8TFQ
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It is thought that prehistoric Native Americans did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:
x
5.50
6.00
6.75
7.00
7.75
y
37
38
92
70
99
Find the equation of the least squares line . Round a and b to three decimal places.
A fitness trainer wants to estimate the effect of fitness activities on muscle mass for different weight categories of club members. They choose the most popular fitness classes at the gym: yoga, circuit training, and high-intensity interval training (HIIT). Suppose that the weights of club members are separated into three levels: under 155 pounds, 155 – 200 pounds, and over 200 pounds. Draw a flow chart showing the design of this experiment.
The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x1, x2, and x3, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals.
Descriptive Statistics
Variable
N
Mean
Median
TrMean
StDev
SE Mean
x 1
15
154.14
154.34
154.14
3.842
0.992000
x 2
15
59.69
60.19
59.69
1.462
0.377487
x 3
15
205.55
204.75
205.55
4.558
1.176871
Variable
Minimum
Maximum
Q1
Q3
x 1
125
178
141.803
167.244
x 2
41
80
47.754
78.415
x 3
126
240
140.395
224.008
Correlations (Pearson)
x 1
x 2
x 2
0.892
x 3
0.839
0.567
Regression Analysis
The regression equation is
x 1 = 0.883 + 1.257x2 + 0.871x3
Predictor
Coef
StDev
T
P
Constant
0.883
0.635
1.39
0.095
x 2
1.257
0.635
1.98
0.036
x 3
0.871
0.419
2.08
0.030
S = 0.428
R-sq = 92.7 %…
Chapter 1 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 1.1 - True/False Questions
“” means “”
Ch. 1.1 - A truth table based on four simple statements...Ch. 1.1 - True/False Questions
2. If is true, then is also...Ch. 1.1 - If p and q are both false, the truth value of...Ch. 1.1 - If pq is false, the truth value of (pq)(pq) is...Ch. 1.1 - pq andqp are logically equivalent.Ch. 1.1 - True/False Questions
7. A statement and its...Ch. 1.1 - (pq)(pq) is a tautology.Ch. 1.1 - True/False Questions
9. If B is a tautology and A...Ch. 1.1 - True/False Questions
10. If A and B are both...
Ch. 1.1 - Construct a truth table for each of the following...Ch. 1.1 - (a) If pq is false, determine the truth value of...Ch. 1.1 - 3. Determine the truth value for
when are all...Ch. 1.1 - 4. Repeat Exercise 3 in the case where are all...Ch. 1.1 - 5. (a) Show that is a tautology.
(b) Show that ...Ch. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - 10. (a) Show that the statement is not logically...Ch. 1.1 - 11. If and are statements, then the compound...Ch. 1.2 - True/False Questions
Two statements A and B are...Ch. 1.2 - True/False Questions
2. “A B” and “A B” mean the...Ch. 1.2 - True/False Questions
3. () () for any statement ....Ch. 1.2 - True/False Questions
4. for any statements
Ch. 1.2 - (p(qr))((pq)(pr)) for any statements p,q,r.Ch. 1.2 - ((pq))((p)(q)) for any statements p,q.Ch. 1.2 - If A Band C is any statement, then (A C) (B ...Ch. 1.2 - True/False Questions
8. is in disjunctive normal...Ch. 1.2 - (pq(r))((p)(q)(r)) is in disjunctive normal form.Ch. 1.2 - True/False Questions
10. Disjunctive normal form...Ch. 1.2 - Prob. 1ECh. 1.2 - (a) Show that p[(pq)] is a tautology. (b) What is...Ch. 1.2 - Simplify each of the following statements. (a)...Ch. 1.2 - 4. Using truth tables, verify the following...Ch. 1.2 - 5. Using the properties in the text together with...Ch. 1.2 - Prove that the statements (p(q))q and (p(q))p are...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Express each of the following statements in...Ch. 1.2 - Find out what you can about Augustus De Morgan and...Ch. 1.3 - True/False Questions
An argument is valid if,...Ch. 1.3 - Prob. 2TFQCh. 1.3 - Prob. 3TFQCh. 1.3 - True/False Questions
4. De Morgan’s laws are two...Ch. 1.3 - The chain rule has pq and qr as its premises.Ch. 1.3 - Prob. 6TFQCh. 1.3 - Prob. 7TFQCh. 1.3 - Prob. 8TFQCh. 1.3 - Prob. 9TFQCh. 1.3 - Prob. 10TFQCh. 1.3 - Determine whether or not each of the following...Ch. 1.3 - 2. Verify that each of the five rules of inference...Ch. 1.3 - Verify that each of the following arguments is...Ch. 1.3 - Test the validity of each of the following...Ch. 1.3 - 5. Determine the validity of each of the following...Ch. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - 10. What language is being used when we say “modus...Ch. 1 - Construct a truth table for the compound statement...Ch. 1 - Determine the truth value of [p(q((r)s))](rt),...Ch. 1 - 3. Determine whether each statement is a...Ch. 1 - Two compound statements A and B have the property...Ch. 1 - 5. (a) Suppose A, B, and C are compound statements...Ch. 1 - Establish the logical equivalence of each of the...Ch. 1 - 7. Express each of the following statements in...Ch. 1 - Determine whether each of the following arguments...Ch. 1 - Discuss the validity of the argument pq(p)r Purple...Ch. 1 - 10. Determine the validity of each of the...
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