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 7.5, Problem 5E
a)
To determine
The number of ways bunches of a half-dozen roses can be formed.
b)
To determine
The number of ways bunches of a half-dozen can be formed if each bunch must contain at least one rose of each color.
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5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
1. Consider the following preference ballots:
Number of voters
Rankings 6 5 4 2
1st choice A DCB
DC
2nd choice B B D
3rd choice DCBD
4th choice CA
AAA
For each of the four voting systems we have studied, determine who would win the election
in each case. (Remember: For plurality with runoff, all but the top two vote-getters are
simultaneously eliminated at the end of round 1.)
Practice
k Help
ises
A
96
Anewer The probability that you get a sum of at least 10 is
Determine the number of ways that the specified event can occur when
two number cubes are rolled.
1. Getting a sum of 9 or 10
3. Getting a sum less than 5
2. Getting a sum of 6 or 7
4. Getting a sum that is odd
Tell whether you would use the addition principle or the multiplication
principle to determine the total number of possible outcomes for the
situation described.
5. Rolling three number cubes
6. Getting a sum of 10 or 12 after rolling three number cubes
A set of playing cards contains four groups of cards designated by color
(black, red, yellow, and green) with cards numbered from 1 to 14 in each
group. Determine the number of ways that the specified event can occur
when a card is drawn from the set.
7. Drawing a 13 or 14
9. Drawing a number less than 4
8. Drawing a yellow or green card
10. Drawing a black, red, or green car
The spinner is divided into equal parts.
Find the specified…
Chapter 7 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 7.1 - True/False Questions 5!=120Ch. 7.1 - Prob. 2TFQCh. 7.1 - Prob. 3TFQCh. 7.1 - Prob. 4TFQCh. 7.1 - Prob. 5TFQCh. 7.1 - Prob. 6TFQCh. 7.1 - True/False Questions
7. An r-permutation of n...Ch. 7.1 - Prob. 8TFQCh. 7.1 - Prob. 9TFQCh. 7.1 - True/False Questions There are 4!=24 ways in which...
Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - In how many ways can ten boys and four girls sit...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - [BB] In how many ways can two couples, the...Ch. 7.1 - Repeat Exercise 12, assuming, in each part, that a...Ch. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - 17. (a) In how many numbers with seven distinct...Ch. 7.1 - Prob. 18ECh. 7.2 - True/False Questions
Ch. 7.2 - Prob. 2TFQCh. 7.2 - Prob. 3TFQCh. 7.2 - Prob. 4TFQCh. 7.2 - Prob. 5TFQCh. 7.2 - Prob. 6TFQCh. 7.2 - Prob. 7TFQCh. 7.2 - Prob. 8TFQCh. 7.2 - Prob. 9TFQCh. 7.2 - Prob. 1ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 3ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - [BB] In how many ways can Tom, Billie, and Peter...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - 7. In a popular lottery known as Lotto 6/49, a...Ch. 7.2 - Prob. 8ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - 16. The head of the Department of Mathematical...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.3 - Prob. 1TFQCh. 7.3 - Prob. 2TFQCh. 7.3 - Prob. 3TFQCh. 7.3 - Prob. 4TFQCh. 7.3 - Prob. 5TFQCh. 7.3 - Prob. 6TFQCh. 7.3 - Prob. 7TFQCh. 7.3 - Prob. 8TFQCh. 7.3 - Prob. 9TFQCh. 7.3 - Prob. 10TFQCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - [BB] A fair coin is tossed six times. Find the...Ch. 7.3 - Prob. 6ECh. 7.3 - The next two exercises refer to Lotto 6/49, a...Ch. 7.3 - 8. In Lotto 6/49, find the probability of...Ch. 7.3 - 9. [BB] A basket contains five red balls, four...Ch. 7.3 - Prob. 10ECh. 7.3 - [BB] Repeat Exercise 9 assuming the first ball...Ch. 7.3 - 12. Repeat Exercise 10 assuming the two balls are...Ch. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Find the probability that an integer selected at...Ch. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - (See Exercise 11 of Section 7.1), find the...Ch. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.4 - Prob. 1TFQCh. 7.4 - Prob. 2TFQCh. 7.4 - Prob. 3TFQCh. 7.4 - Prob. 4TFQCh. 7.4 - Prob. 5TFQCh. 7.4 - Prob. 6TFQCh. 7.4 - Prob. 7TFQCh. 7.4 - Prob. 8TFQCh. 7.4 - Prob. 9TFQCh. 7.4 - Prob. 10TFQCh. 7.4 - Prob. 1ECh. 7.4 - 2. If the die in Exercise 1 is tossed twice, find...Ch. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - [BB] A coin has P(H)=14. If it is tossed six times...Ch. 7.4 - The answers to exercises marked [BB] can be found...Ch. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - 15. A fair coin is tossed n times. Let A be the...Ch. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - 22. (a) Find the probability that everyone in a...Ch. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - [BB] Given 70P20=.3,40P50=.5, and 10P40=.9, find...Ch. 7.4 - [BB] The probability that two persons aged 20 and...Ch. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - 29. [BB] Consumers in the town of Trout River have...Ch. 7.4 - Prob. 30ECh. 7.4 - 31. A new three- screen cinema has just opened in...Ch. 7.5 - Prob. 1TFQCh. 7.5 - (Answers can be found in the back of the book.)
2....Ch. 7.5 - (Answers can be found in the back of the book.)...Ch. 7.5 - Prob. 4TFQCh. 7.5 - Prob. 5TFQCh. 7.5 - Prob. 6TFQCh. 7.5 - Prob. 7TFQCh. 7.5 - Prob. 8TFQCh. 7.5 - Prob. 9TFQCh. 7.5 - Prob. 10TFQCh. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - 6. Twenty varieties of chocolates are available...Ch. 7.5 - Prob. 7ECh. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 10ECh. 7.5 - 11. (a) [BB] In how many ways can ten red balls,...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 13ECh. 7.5 - Find the number of arrangements of the letters of...Ch. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Show that there is a one-to-one correspondence...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 19ECh. 7.6 - (Answers can be found in the back of the book.)
1....Ch. 7.6 - Prob. 2TFQCh. 7.6 - Prob. 3TFQCh. 7.6 - Prob. 4TFQCh. 7.6 - Prob. 5TFQCh. 7.6 - Prob. 6TFQCh. 7.6 - (Answers can be found in the back of the book.)
7....Ch. 7.6 - Prob. 8TFQCh. 7.6 - Prob. 9TFQCh. 7.6 - Prob. 10TFQCh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - [BB] In how many ways can the integers 1 through 9...Ch. 7.6 - Without any calculation, prove that...Ch. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.7 - (Answers can be found in the back of the book.)
1....Ch. 7.7 - Prob. 2TFQCh. 7.7 - Prob. 3TFQCh. 7.7 - Prob. 4TFQCh. 7.7 - Prob. 5TFQCh. 7.7 - Prob. 6TFQCh. 7.7 - Prob. 7TFQCh. 7.7 - Prob. 8TFQCh. 7.7 - Prob. 9TFQCh. 7.7 - Prob. 10TFQCh. 7.7 - Prob. 1ECh. 7.7 - The answers to exercises marked [BB] can be found...Ch. 7.7 - Prob. 3ECh. 7.7 - Prob. 4ECh. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Sequences of integers, {xn},{yn},n0, are defined...Ch. 7.7 - Prob. 15ECh. 7.7 - The answers to exercises marked [BB] can be found...Ch. 7.7 - Prob. 17ECh. 7.7 - 18. Prove the Binominal Theorem by mathematical...Ch. 7.7 - Prob. 19ECh. 7.7 - Prob. 20ECh. 7.7 - Prob. 21ECh. 7.7 - Prob. 22ECh. 7.7 - Prob. 23ECh. 7.7 - 24. There are n books in a line on a shelf and...Ch. 7.7 - Prob. 25ECh. 7 - Prove that 2nP(2n,n) for all integers n1.Ch. 7 - In how many ways can seven boys and six girls...Ch. 7 - Do Exercise 2 again with circle instead of row.Ch. 7 - How many permutations of the letters a, b, c, d,...Ch. 7 - 5. (a) In how many permutations of the 26...Ch. 7 - 6. Find an expression for the number of five-card...Ch. 7 - A committee of seven is to be chosen from eight...Ch. 7 - In how many ways can 12 people from four groups of...Ch. 7 - A car manufacturer is forced to admit that the...Ch. 7 - 10. Ten students find themselves in an...Ch. 7 - 11. For Christmas, Gail wants to buy each of her...Ch. 7 - 12. A Middle East peace conference will be...Ch. 7 - Prob. 13RECh. 7 - Frank wants to buy 12 muffins and finds seven...Ch. 7 - Twelve ships enter the St. Johns harbor one after...Ch. 7 - 16. A candy merchant carries bubble gum balls in...Ch. 7 - 17. In how many ways can the letters of the word...Ch. 7 - 18. In how many ways can five rings be put onto...Ch. 7 - Find the coefficient of x6 in (16x212x)12....Ch. 7 - Find the coefficient of x6 in (16x212x)12....Ch. 7 - 21. Prove that for any .
Ch. 7 - Give a verbal argument for the truth of the...Ch. 7 - 23. Find a simple expression for .
Ch. 7 - Show that (2nn) is even for all n1.Ch. 7 - On the day before midterm break, 20 of the 32...Ch. 7 - 26. A fair coin is tossed n times. Prove that...
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