DISCRETE MATHEMATICS WITH APPLICATION (
5th Edition
ISBN: 9780357097717
Author: EPP
Publisher: CENGAGE L
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Chapter 8.3, Problem 32ES
To determine
Describe the equivalence classes of the given relation.
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I need some assistance solving Part B of this question. Refer to the excel data in the image provided to answer Part B. SoftBus Company sells PC equipment and customized software to small companies to help them manage their day-to-day business activities. Although SoftBus spends time with all customers to understand their needs, the customers are eventually on their own to use the equipment and software intelligently. To understand its customers better, SoftBus recently sent questionnaires to a large number of prospective customers. Key personnel—those who would be using the software—were asked to fill out the questionnaire. SoftBus received 82 usable responses, as shown in the file. You can assume that these employees represent a random sample of all of SoftBus's prospective customers. SoftBus believes it can afford to spend much less time with customers who own PCs and score at least 4 on PC Knowledge. Let's call these the "PC-savvy" customers. On the other hand, SoftBus believes it…
(12 points) Let
E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}.
(a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such
that
(x, y, z) (psin cos 0, psin sin 0, p cos) € E.
(b) (8 points) Calculate the integral
E
xyz dV using spherical coordinates.
Let us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a
university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when
examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both
sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force
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Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null
hypothesis, 40 0. What level of type II error would you recommend here?
=
Round your answer to four decimal places (e.g. 98.7654). Use α = 0.05.
β
= 0.0594
What sample size would be required?
Assume the sample sizes are to be…
Chapter 8 Solutions
DISCRETE MATHEMATICS WITH APPLICATION (
Ch. 8.1 - If R is a relation from A to B, xA , and yB , the...Ch. 8.1 - Prob. 2TYCh. 8.1 - Prob. 3TYCh. 8.1 - Prob. 4TYCh. 8.1 - If R is a relation on a set A, the directed graph...Ch. 8.1 - As in Example 8.1.2, the congruence modulo 2...Ch. 8.1 - Prove that for all integers m and n,m-n is even...Ch. 8.1 - The congruence modulo 3 relation, T, is defined...Ch. 8.1 - Define a relation P on Z as follows: For every...Ch. 8.1 - Prob. 5ES
Ch. 8.1 - Let X={a,b,c}. Define a relation J on P(X) as...Ch. 8.1 - Define a relation R on Z as follows: For all...Ch. 8.1 - Prob. 8ESCh. 8.1 - Let A be the set of all strings of 0’s, 1’s, and...Ch. 8.1 - Let A={3,4,5} and B={4,5,6} and let R be the “less...Ch. 8.1 - Let A={3,4,5} and B={4,5,6} and let S be the...Ch. 8.1 - Prob. 12ESCh. 8.1 - Prob. 13ESCh. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Prob. 16ESCh. 8.1 - Prob. 17ESCh. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Exercises 19-20 refer to unions and intersections...Ch. 8.1 - Prob. 20ESCh. 8.1 - Define relation R and S on R as follows:...Ch. 8.1 - Prob. 22ESCh. 8.1 - Prob. 23ESCh. 8.1 - Prob. 24ESCh. 8.2 - For a relation R on a set A to be reflexive means...Ch. 8.2 - For a relation R on a set A to be symmetric means...Ch. 8.2 - For a relation R on a set A to be transitive means...Ch. 8.2 - Prob. 4TYCh. 8.2 - Prob. 5TYCh. 8.2 - Prob. 6TYCh. 8.2 - Prob. 7TYCh. 8.2 - Prob. 8TYCh. 8.2 - Prob. 9TYCh. 8.2 - Prob. 10TYCh. 8.2 - Prob. 1ESCh. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - Prob. 3ESCh. 8.2 - Prob. 4ESCh. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9—33, determine whether the given relation is...Ch. 8.2 - In 9—33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - Prob. 15ESCh. 8.2 - Prob. 16ESCh. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - Prob. 18ESCh. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - Prob. 20ESCh. 8.2 - Prob. 21ESCh. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - Prob. 24ESCh. 8.2 - In 9-33, determine whether the given is reflexive...Ch. 8.2 - Prob. 26ESCh. 8.2 - Prob. 27ESCh. 8.2 - Prob. 28ESCh. 8.2 - Prob. 29ESCh. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - Prob. 31ESCh. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 34-36, assume that R is a relation on a et A....Ch. 8.2 - Prob. 35ESCh. 8.2 - Prob. 36ESCh. 8.2 - Prob. 37ESCh. 8.2 - Prob. 38ESCh. 8.2 - Prob. 39ESCh. 8.2 - Prob. 40ESCh. 8.2 - Prob. 41ESCh. 8.2 - In 37-42, assume that R and S are relations on a...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - Prob. 44ESCh. 8.2 - Prob. 45ESCh. 8.2 - Prob. 46ESCh. 8.2 - Prob. 47ESCh. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - Prob. 49ESCh. 8.2 - Prob. 50ESCh. 8.2 - Prob. 51ESCh. 8.2 - In 51—53, R, S, and T are relations defined on...Ch. 8.2 - Prob. 53ESCh. 8.2 - Prob. 54ESCh. 8.2 - Prob. 55ESCh. 8.2 - Prob. 56ESCh. 8.3 - For a relation on a set to be an equivalence...Ch. 8.3 - The notation m=n(modd) is...Ch. 8.3 - Prob. 3TYCh. 8.3 - Prob. 4TYCh. 8.3 - Prob. 5TYCh. 8.3 - Prob. 6TYCh. 8.3 - Prob. 1ESCh. 8.3 - Prob. 2ESCh. 8.3 - Prob. 3ESCh. 8.3 - In each of 3—6, the relation R is an equivalence...Ch. 8.3 - Prob. 5ESCh. 8.3 - In each of 3-6, the relation R is an equivalence...Ch. 8.3 - Prob. 7ESCh. 8.3 - Prob. 8ESCh. 8.3 - Prob. 9ESCh. 8.3 - In each of 7-14, relation R is an equivalence...Ch. 8.3 - Prob. 11ESCh. 8.3 - In each of 7-14, relation R is an equivalence...Ch. 8.3 - In each of 7-14, the relation R is an equivalence...Ch. 8.3 - In each of 7—14, the relation R is an equivalence...Ch. 8.3 - Determine which of the following congruence...Ch. 8.3 - Let R be the relation of congruence modulo 3....Ch. 8.3 - Prob. 17ESCh. 8.3 - Prob. 18ESCh. 8.3 - In 19-31, (1) prove that the relation is an...Ch. 8.3 - Prob. 20ESCh. 8.3 - Prob. 21ESCh. 8.3 - Prob. 22ESCh. 8.3 - Prob. 23ESCh. 8.3 - In 19-31. (1) prove that the relation is an...Ch. 8.3 - In 19-31,(1) prove that the relation is an...Ch. 8.3 - Prob. 26ESCh. 8.3 - Prob. 27ESCh. 8.3 - Prob. 28ESCh. 8.3 - Prob. 29ESCh. 8.3 - Prob. 30ESCh. 8.3 - In 19—31, (1) prove that the relation is an...Ch. 8.3 - Prob. 32ESCh. 8.3 - Prob. 33ESCh. 8.3 - Prob. 34ESCh. 8.3 - Prob. 35ESCh. 8.3 - Prob. 36ESCh. 8.3 - Prob. 37ESCh. 8.3 - Prob. 38ESCh. 8.3 - Prob. 39ESCh. 8.3 - Prob. 40ESCh. 8.3 - Prob. 41ESCh. 8.3 - Prob. 42ESCh. 8.3 - Prob. 43ESCh. 8.3 - Let A=Z+Z+ . Define a relation R on A as follows:...Ch. 8.3 - Prob. 45ESCh. 8.3 - Let R be a relation on a set A and suppose R is...Ch. 8.3 - Refer to the quote at the beginning of this...Ch. 8.4 - When letters of the alphabet are encrypted using...Ch. 8.4 - Prob. 2TYCh. 8.4 - Prob. 3TYCh. 8.4 - Prob. 4TYCh. 8.4 - Prob. 5TYCh. 8.4 - Prob. 6TYCh. 8.4 - Prob. 7TYCh. 8.4 - Prob. 8TYCh. 8.4 - Fermat’s little theorem says that if p is any...Ch. 8.4 - Prob. 10TYCh. 8.4 - Prob. 1ESCh. 8.4 - Use the Caesar cipher to encrypt the message AN...Ch. 8.4 - Prob. 3ESCh. 8.4 - Let a=68, b=33, and n=7. Verify that 7|(68-33)....Ch. 8.4 - Prove the transitivity of modular congruence. That...Ch. 8.4 - Prob. 6ESCh. 8.4 - Verify the following statements. 128=2(mod7) and...Ch. 8.4 - Verify the following statements. 45=3 (mod 6) and...Ch. 8.4 - Prob. 9ESCh. 8.4 - In 9-11, prove each of the given statements,...Ch. 8.4 - In 9-11, prove each of the given statements,...Ch. 8.4 - Prove that for every integer n0,10n=1(mod9) . Use...Ch. 8.4 - Prob. 13ESCh. 8.4 - Prob. 14ESCh. 8.4 - Prob. 15ESCh. 8.4 - In 16-18, use the techniques of Example 8.4.4 and...Ch. 8.4 - Prob. 17ESCh. 8.4 - Prob. 18ESCh. 8.4 - Prob. 19ESCh. 8.4 - Prob. 20ESCh. 8.4 - Prob. 21ESCh. 8.4 - In 19-24, use the RSA cipher from Examples 8.4.9...Ch. 8.4 - Prob. 23ESCh. 8.4 - Prob. 24ESCh. 8.4 - Prob. 25ESCh. 8.4 - Prob. 26ESCh. 8.4 - In 26 and 27, use the extended Euclidean algorithm...Ch. 8.4 - Prob. 28ESCh. 8.4 - Prob. 29ESCh. 8.4 - Prob. 30ESCh. 8.4 - Find an inverse for 210 modulo 13. Find appositive...Ch. 8.4 - Find an inverse for 41 modulo 660. Find the least...Ch. 8.4 - Prob. 33ESCh. 8.4 - Prob. 34ESCh. 8.4 - Prob. 35ESCh. 8.4 - In 36,37,39 and 40, use the RSA cipher with public...Ch. 8.4 - Prob. 37ESCh. 8.4 - Find the least positive inverse for 43 modulo 660.Ch. 8.4 - Prob. 39ESCh. 8.4 - Prob. 40ESCh. 8.4 - Prob. 41ESCh. 8.4 - Prob. 42ESCh. 8.4 - Prob. 43ESCh. 8.5 - Prob. 1TYCh. 8.5 - Prob. 2TYCh. 8.5 - Prob. 3TYCh. 8.5 - Prob. 4TYCh. 8.5 - Prob. 5TYCh. 8.5 - Prob. 6TYCh. 8.5 - Prob. 7TYCh. 8.5 - Prob. 8TYCh. 8.5 - Prob. 9TYCh. 8.5 - Prob. 10TYCh. 8.5 - Each of the following is a relation on {0,1,2,3}...Ch. 8.5 - Prob. 2ESCh. 8.5 - Let S be the set of all strings of a’s and b’s....Ch. 8.5 - Prob. 4ESCh. 8.5 - Prob. 5ESCh. 8.5 - Let P be the set of all people who have ever lived...Ch. 8.5 - Prob. 7ESCh. 8.5 - Prob. 8ESCh. 8.5 - Prob. 9ESCh. 8.5 - Suppose R and S are antisymmetric relations on a...Ch. 8.5 - Let A={a,b}, and supposeAhas the partial order...Ch. 8.5 - Prob. 12ESCh. 8.5 - Let A={a,b} . Describe all partial order relations...Ch. 8.5 - Let A={a,b,c}. Describe all partial order...Ch. 8.5 - Prob. 15ESCh. 8.5 - Consider the “divides” relation on each of the...Ch. 8.5 - Prob. 17ESCh. 8.5 - Let S={0,1} and consider the partial order...Ch. 8.5 - Let S={0,1} and consider the partial order...Ch. 8.5 - Let S={0,1} and consider the partial order...Ch. 8.5 - Consider the “divides” relation defined on the set...Ch. 8.5 - Prob. 22ESCh. 8.5 - Prob. 23ESCh. 8.5 - Prob. 24ESCh. 8.5 - Prob. 25ESCh. 8.5 - Prob. 26ESCh. 8.5 - Prob. 27ESCh. 8.5 - Prob. 28ESCh. 8.5 - Prob. 29ESCh. 8.5 - Prob. 30ESCh. 8.5 - Prob. 31ESCh. 8.5 - Prob. 32ESCh. 8.5 - Consider the set A={12,24,48,3,9} ordered by the...Ch. 8.5 - Suppose that R is a partial order relation on a...Ch. 8.5 - Prob. 35ESCh. 8.5 - The set A={2,4,3,6,12,18,24} is partially ordered...Ch. 8.5 - Find a chain of length 2 for the relation defined...Ch. 8.5 - Prob. 38ESCh. 8.5 - Prob. 39ESCh. 8.5 - Prob. 40ESCh. 8.5 - Prob. 41ESCh. 8.5 - Prob. 42ESCh. 8.5 - Prob. 43ESCh. 8.5 - Prob. 44ESCh. 8.5 - Prob. 45ESCh. 8.5 - Prob. 46ESCh. 8.5 - Prob. 47ESCh. 8.5 - Prob. 48ESCh. 8.5 - Prob. 49ESCh. 8.5 - A set S of jobs can be ordered by writing x_y to...Ch. 8.5 - Suppose the tasks described in Example 8.5.12...
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