Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 8.3, Problem 19E
To determine
To find: The number of different subsets of {1, 2, ... , 10} contain exactly six elements.
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Calculs Insights
πT
| cos x |³ dx
59
2
2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)
Chapter 8 Solutions
Discrete Mathematics
Ch. 8.1 - Evaluate the numbers in Exercises 1-12.
C(5, 3)
Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Evaluate the numbers in Exercises 1-12.
C(12, 7)
Ch. 8.1 - Prob. 5ECh. 8.1 - Evaluate the numbers in Exercises 1-12.
the...Ch. 8.1 - Prob. 7ECh. 8.1 - Evaluate the numbers in Exercises 1-12.
the...Ch. 8.1 - Prob. 9ECh. 8.1 - Evaluate the numbers in Exercises 1-12.
the...
Ch. 8.1 - Evaluate the numbers in Exercises 1-12.
the...Ch. 8.1 - Evaluate the numbers in Exercises 1-12.
the...Ch. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.2 - How many people must there be in order to assure...Ch. 8.2 - If a committee varies its meeting days, how many...Ch. 8.2 - Prob. 3ECh. 8.2 - How many words must be chosen in order to assure...Ch. 8.2 - Prob. 5ECh. 8.2 - If there are 6 sections of Discrete Math with a...Ch. 8.2 - Prob. 7ECh. 8.2 - A sociologist intends to send a questionnaire to...Ch. 8.2 - Prob. 9ECh. 8.2 - How many different pizzas can be ordered if a...Ch. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - A restaurant offers a choice of 3 green vegetables...Ch. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - How many 8-bit strings begin with 010 or end with...Ch. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prove that in any nonempty list of n integers (not...Ch. 8.2 - Prob. 35ECh. 8.2 - Suppose that there are 15 identical copies of The...Ch. 8.3 - Evaluate the numbers in Exercises 1-12.
1. C(6,...Ch. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Evaluate the numbers in Exercises 1-12.
4. C(8,...Ch. 8.3 - Evaluate the numbers in Exercises 1-12.
5. P(4,...Ch. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Evaluate the numbers in Exercises 1-12.
8. P(12,...Ch. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Evaluate the numbers in Exercises 1-12.
12. P(n,...Ch. 8.3 - Prob. 13ECh. 8.3 - How many different arrangements are there of the...Ch. 8.3 - Prob. 15ECh. 8.3 - How many different ways are there of selecting...Ch. 8.3 - Prob. 17ECh. 8.3 - How many different 16-bit strings contain exactly...Ch. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.4 - How many distinct arrangements of the letters in...Ch. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - How many different assortments of 6 boxes of...Ch. 8.4 - Prob. 7ECh. 8.4 - How many different boxes containing 10 wedges of...Ch. 8.4 - Prob. 9ECh. 8.4 - In how many different ways can 15 distinct books...Ch. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - In how many different ways can 6 identical sticks...Ch. 8.4 - A father has 10 identical life insurance policies....Ch. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - In how many different ways can 8 identical...Ch. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 26ECh. 8.4 - How many positive integers less than 10,000 are...Ch. 8.4 - How many distinct arrangements are there of two...Ch. 8.4 - How many positive integers less than 1,000,000 are...Ch. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - What is the probability that a randomly chosen...Ch. 8.5 - Prob. 20ECh. 8.5 - Three $ 10 bills, four $5 bills, and six $1 bills...Ch. 8.5 - If a 5-member committee is selected at random from...Ch. 8.5 - Suppose that we randomly distribute 5 distinct...Ch. 8.5 - If 10 quarters are distributed at random to 4...Ch. 8.5 - Exactly 4 of 20 microcomputer diskettes are...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - A file contains 25 accounts numbered 1–25. If 5 of...Ch. 8.5 - In the Illinois State Lotto game, 6 of the...Ch. 8.6 - In a survey of moviegoers it was found that 33...Ch. 8.6 - Among a group of children, 88 liked pizza and 27...Ch. 8.6 - Among the 318 members of a local union, 127 liked...Ch. 8.6 - In a particular dormitory, there are 350 college...Ch. 8.6 - From a group of 650 residents of a city, the...Ch. 8.6 - In tabulating the 5681 responses to a...Ch. 8.6 - The following data were obtained from the...Ch. 8.6 - The following information was found about the...Ch. 8.6 - Eight married couples came to a bridge party. Each...Ch. 8.6 - List all the derangements of 1, 2, 3, 4.
Ch. 8.6 - While taking a 6-week summer math class, Alison...Ch. 8.6 - How many sequences of five digits (0–9) contain at...Ch. 8.6 - For the following graph, determine the number of...Ch. 8.6 - If three married couples are seated randomly in...Ch. 8.6 - How many positive integers less than 101 are...Ch. 8.6 - How many sequences of six digits (0–9) contain at...Ch. 8.6 - At Brokaw Hospital, six babies were born to six...Ch. 8.6 - In how many ways can four married couples be...Ch. 8.6 - How many arrangements of the numbers 1, 1, 2, 2,...Ch. 8.6 - How many five-card poker hands contain at least...Ch. 8.6 - How many of the functions with domain {5, 6, 7, 8,...Ch. 8.6 - How many nonnegative integer solutions of x1 + x2...Ch. 8.6 - Suppose that five balls numbered 1, 2, 3, 4, and 5...Ch. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - Prob. 28ECh. 8.6 - For nonnegative integers n and m, define S(n, m)...Ch. 8.6 - Prob. 30ECh. 8.6 - Prob. 31ECh. 8.6 - Prob. 32ECh. 8.6 - Prob. 35ECh. 8.6 - Prob. 36ECh. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - In Exercises 7-18, determine the successor of...Ch. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - Prob. 15ECh. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - Prob. 18ECh. 8.7 - Prob. 19ECh. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - Prob. 22ECh. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.7 - Prob. 28ECh. 8.7 - Prob. 29ECh. 8.7 - Prob. 30ECh. 8.7 - Prob. 31ECh. 8.7 - Prob. 32ECh. 8 - Prob. 1SECh. 8 - Prob. 2SECh. 8 - Prob. 3SECh. 8 - Prob. 4SECh. 8 - Prob. 5SECh. 8 - Prob. 6SECh. 8 - Prob. 7SECh. 8 - Prob. 8SECh. 8 - Prob. 9SECh. 8 - Prob. 10SECh. 8 - Prob. 11SECh. 8 - Prob. 12SECh. 8 - Prob. 13SECh. 8 - Prob. 14SECh. 8 - Prob. 15SECh. 8 - Prob. 16SECh. 8 - Prob. 17SECh. 8 - How many integers between 1500 and 8000...Ch. 8 - Prob. 19SECh. 8 - Prob. 20SECh. 8 - Prob. 21SECh. 8 - Prob. 22SECh. 8 - Prob. 23SECh. 8 - Prob. 24SECh. 8 - Prob. 25SECh. 8 - Prob. 26SECh. 8 - Prob. 27SECh. 8 - Prob. 28SECh. 8 - Prob. 29SECh. 8 - Prob. 30SECh. 8 - Prob. 31SECh. 8 - Prob. 32SECh. 8 - Prob. 33SECh. 8 - Prob. 34SECh. 8 - Prob. 35SECh. 8 - Prob. 36SECh. 8 - Prob. 37SECh. 8 - Prob. 38SECh. 8 - Prob. 39SECh. 8 - Prob. 41SECh. 8 - Prob. 42SECh. 8 - Prob. 43SECh. 8 - Prob. 44SECh. 8 - Prob. 45SECh. 8 - Prob. 46SECh. 8 - Prob. 47SECh. 8 - Prob. 49SECh. 8 - Prob. 50SECh. 8 - Prob. 51SECh. 8 - Prob. 52SECh. 8 - Prob. 53SECh. 8 - Prob. 56SECh. 8 - Prob. 57SECh. 8 - Prob. 3CPCh. 8 - Prob. 4CP
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