Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
8th Edition
ISBN: 9781259731709
Author: ROSEN
Publisher: MCG
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Textbook Question
Chapter 6.1, Problem 1E
There are 18 mathematics majors and 325 computer science majors at a college,
- In how many ways can two representatives he picked so that one is a mathematics major and the other is a computer science major?
- Inhowmanywayscanonerepresentativebepickedwhoiseitheramathematicsmajororacomputersciencemajor?
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A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.01
significance level, test the claim that injuries are independent of helmet color.
Color of Helmet
Black
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Red
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Controls (not injured)
499
373
32
159
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Cases (injured
221
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Click here to view the chi-square distribution table.
Chi-square distribution table
Area to the Right of the Critical Value
Degrees of
Freedom
0.995
0.99
0.975
0.95
0.90
0.10
0.05
0.025
0.01
0.005
C. Ho: Injuries and neimet color are dependent
H₁: Injuries and helmet color are independent
D. Ho: Whether a crash occurs and helmet color are dependent
1
0.001
0.004
0.016
2.706
3.841
5.024
6.635
7.879
2
0.010
0.020
0.051
0.103
0.211
4.605
5.991
7.378
9.210
10.597
3
0.072
0.115
0.216
0.352
0.584
6.251
7.815
9.348
11.345
12.838
4
0.207
0.297…
Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion.
A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 28, 32, 46, 39, 29, 26. Use a 0.025 significance level to test the
claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?
Click here to view the chi-square distribution table.
The test statistic is
(Round to three decimal places as needed.)
Chi-square distribution table
Area to the Right of the Critical Value
Degrees of
Freedom
0.995
0.99
0.975
0.95
0.90
0.10
0.05
0.025
0.01
0.005
1
0.001
0.004
0.016
2.706
3.841
5.024
6.635
2
0.010
0.020
0.051
0.103
0.211
4.605
5.991
7.378
9.210
7.879
10.597
3
0.072
0.115
0.216
0.352
0.584
6.251
7.815
9.348
11.345 12.838
4
0.207
0.297
0.484
0.711
1.064
7.779
9.488
11.143
13.277 14.860
5…
The online clothing retailer e-Parel is conducting a study to estimate the average size of the orders placed by visitors to its website. The project manager desires a $60 bound on the error of estimation at 90% confidence. The population standard deviation is unknown, and a “best guess” of $175 is used as the planning value for σ.
Use the Distributions tool to help you answer the questions that follow.
0123
Select a Distribution
The z-value for a 90% confidence interval of the population mean is .
In order to satisfy the requirement of a $60 bound on the error of estimation, a sample size no smaller than is needed.
Chapter 6 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Ch. 6.1 - There are 18 mathematics majors and 325 computer...Ch. 6.1 - An office building contains 27 floors and has 37...Ch. 6.1 - A multiple-choice test contains 10 questions....Ch. 6.1 - A particular of shirt comes in 12 colors, has a...Ch. 6.1 - Six different fly from New York to Denver and...Ch. 6.1 - There are four major auto routes from Boston to...Ch. 6.1 - How many different three-letter initials can...Ch. 6.1 - How many different three-letter initials with none...Ch. 6.1 - How many different three-letter initials are there...Ch. 6.1 - How many bit strings are there of length eight?
Ch. 6.1 - How many bit strings of length ten both begin and...Ch. 6.1 - How many bit strings are there of length six or...Ch. 6.1 - How many bit strings with length not exceeding n,...Ch. 6.1 - How many bit strings of lengthn,wherenis a...Ch. 6.1 - How many strings are there of lowercase letters of...Ch. 6.1 - How many strings are there of four lowercase...Ch. 6.1 - How many strings of five ASCII characters @ (“at”...Ch. 6.1 - How many 5-element DNA sequences end with A? start...Ch. 6.1 - lg.How many 6-element RNA sequences Do not contain...Ch. 6.1 - How many positive integers between 5 and 31 are...Ch. 6.1 - How many positive integers between 50 and 100 are...Ch. 6.1 - How many positive integers less than 1000 are...Ch. 6.1 - How many positive integers between 100 and 999...Ch. 6.1 - How many positive integers between 1000 and 9999...Ch. 6.1 - How many strings of three decimal digits do not...Ch. 6.1 - How many strings of four decimal digits do not...Ch. 6.1 - Prob. 27ECh. 6.1 - How many license, plates can be made using either...Ch. 6.1 - How many license plates can be made using either...Ch. 6.1 - How many license plates can be made using either...Ch. 6.1 - How many license plates can be made using either...Ch. 6.1 - How many strings of eight uppercase English...Ch. 6.1 - How many strings of eight English letters are...Ch. 6.1 - Prob. 34ECh. 6.1 - How many one-to-one functions are there from a set...Ch. 6.1 - How many functions are there from the set {1,2,n},...Ch. 6.1 - Prob. 37ECh. 6.1 - How many partial functions (seeSection 2.3)are...Ch. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - How many 4-element DNA sequences do not contain...Ch. 6.1 - How many 4-eJement RNA sequenoes contain the base...Ch. 6.1 - On each of the 22 work days in a particular month,...Ch. 6.1 - At a large university, 434 freshman, 883...Ch. 6.1 - Prob. 46ECh. 6.1 - How many ways are there to seat six people around...Ch. 6.1 - In how many ways can a photographer at a wedding...Ch. 6.1 - In how many ways can a photographer at a wedding...Ch. 6.1 - How many bit strings of length seven either begin...Ch. 6.1 - Prob. 51ECh. 6.1 - How many bit strings of length 10 contain either...Ch. 6.1 - How many bit strings of length eight contain...Ch. 6.1 - ...Ch. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Suppose that a password for a computer system must...Ch. 6.1 - The name, of a variable in the C programming...Ch. 6.1 - The name of a variable in the JAVA programming...Ch. 6.1 - 6o, The International Telecommunications Union...Ch. 6.1 - Prob. 61ECh. 6.1 - A key in the Vigenere cryptosystem is a string of...Ch. 6.1 - Prob. 63ECh. 6.1 - Suppose that P and q are prime numbers and than n...Ch. 6.1 - Use the principle of inclusion-exclusion to find...Ch. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - Prob. 71ECh. 6.1 - Determine the number of matches played in a...Ch. 6.1 - Prob. 73ECh. 6.1 - *74-Use the product rule to show that there are 22...Ch. 6.1 - Prob. 75ECh. 6.1 - Use mathematical induction to prove the product...Ch. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.2 - Prob. 1ECh. 6.2 - Show that if there are 30 students in a class,...Ch. 6.2 - A drawer contains a dozen brown socks and a dozen...Ch. 6.2 - Abowl contains 10 red balls and 10 blue balls....Ch. 6.2 - Undergraduate students at a college belong to one...Ch. 6.2 - 6,There are six professors teaching the...Ch. 6.2 - group of five (not necessarily consecutive)...Ch. 6.2 - 8,Let d be a positive integer, Show that among anv...Ch. 6.2 - Letnbe a positive integer. Show that in any set...Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Show that if five integers are selected from the...Ch. 6.2 - i6. Show that if seven integers are selected from...Ch. 6.2 - How many numbers must be selected from the set...Ch. 6.2 - Howmany numbers must be selected from the set...Ch. 6.2 - A company stores products in a warehouse. Storage...Ch. 6.2 - Suppose that there are nine students in a discrete...Ch. 6.2 - i. Suppose that every student in a discrete...Ch. 6.2 - Prob. 22ECh. 6.2 - Construct a sequenceof16 positive integers that...Ch. 6.2 - Prob. 24ECh. 6.2 - Show that whenever 25 girl? and 25 boys are seated...Ch. 6.2 - Prob. 26ECh. 6.2 - Descnbe an algorithm in pseudocode for producing...Ch. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - In the 17th century, there were more than 800,000...Ch. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - A computer network consists of six computers, Each...Ch. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Ad arm wrestler is the champion for a period of 75...Ch. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - ,There are 51 houses on a street, Each house has...Ch. 6.2 - Letibe an irrational number, Showthatfor some...Ch. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.3 - i. List all the permutations of{a, b,c}.Ch. 6.3 - How many different permutations are there of the...Ch. 6.3 - How many permutations of{a, b,c, d,e.fg]end withCh. 6.3 - LetS = {i,2, 3,4, 5}. List all the 3-permutations...Ch. 6.3 - Find the value of each of these quantities P(6,3)...Ch. 6.3 - Find the value of each of these quantities. CCs,i)...Ch. 6.3 - Find the number of 5-permutations of a set Kith...Ch. 6.3 - In how many different orders can five runners...Ch. 6.3 - Prob. 9ECh. 6.3 - There are six different candidates for governor of...Ch. 6.3 - ii.How many bit strings of length 10 contain...Ch. 6.3 - IE.How many bit strings of length12contain exactly...Ch. 6.3 - A group contains n men and n women. How many ways...Ch. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Prob. 41ECh. 6.3 - Find the number of circular 3-permutations...Ch. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - How many ways are there for a horse race with...Ch. 6.4 - Find the expansion of (r + using combinatorial...Ch. 6.4 - Find the expansion of Cr + j,)5 using...Ch. 6.4 - Find the expansionCh. 6.4 - Find the coefficient of in Cr + y)13.Ch. 6.4 - How many terms are therein the expansion of...Ch. 6.4 - What isthecoefficient of .v in (1 +1)Ch. 6.4 - What is the coefficient of i9 in (2 - 1)Ch. 6.4 - What is the coefficient ofxsy9 in the expansion of...Ch. 6.4 - What is the coefficient of xloly" in the expansion...Ch. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - IS. Use the binomial theorem to find the...Ch. 6.4 - *3-Use the binomial theorem to find the...Ch. 6.4 - Give a formula for the coefficient ofi^in the...Ch. 6.4 - Prob. 15ECh. 6.4 - The row of Pascal’s triangle containing the...Ch. 6.4 - What is the r ow of Pascal's triangle containing...Ch. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - so. Use Exercise 18 andCorollary 1to show that...Ch. 6.4 - Prob. 21ECh. 6.4 - Suppose thatbis an integer withb> 7. Use the...Ch. 6.4 - Prove Pas cal’s identity, u sing the formula for...Ch. 6.4 - Suppose that t andnare integers withi which...Ch. 6.4 - Provethatifnandfcareintegers^th i< fc using a...Ch. 6.4 - Prove the identity (")(') = (J)(Xf), whenever n,...Ch. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Letnbe a positive integer. Show thatCh. 6.4 - Prob. 30ECh. 6.4 - Prove the hockey-stick identity ('?’)...Ch. 6.4 - Show that if ra is a positive integer, then =2t" i...Ch. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prove the binomial theorem using mathematical...Ch. 6.4 - In this exercise we will count the number of paths...Ch. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - Determine a formula involving binomial...Ch. 6.5 - In how many different wavs can five elements be...Ch. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - How many different ways are there to choose a...Ch. 6.5 - A bagel shop has onion bagels, poppy seed bagels,...Ch. 6.5 - io. A croissant shop has plain croissants, cherry...Ch. 6.5 - ii. 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How many ways are there to distribute five...Ch. 6.5 - 6i. How many ways are there to distribute five...Ch. 6.5 - Suppose that a basketball league has 32 teams,...Ch. 6.5 - f 63. Suppose that a weapons inspector must...Ch. 6.5 - Howmanv dififerentterms are therein the expansion...Ch. 6.5 - Prob. 65ECh. 6.5 - Prob. 66ECh. 6.5 - Find the coefficient ofi3y2z5 in Qc + y + z)Ch. 6.5 - How many terms are there in the expansionCh. 6.6 - ...Ch. 6.6 - ...Ch. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Find the next larger permutation in lexicographic...Ch. 6.6 - Find the next larger permutation in lexicographic,...Ch. 6.6 - Use Algorithm 1 to generate the 24 permutations of...Ch. 6.6 - Prob. 8ECh. 6.6 - Use Algorithm 3 to listallthe 3-combinations of{1,...Ch. 6.6 - Show that Algorithm1produces the next larger...Ch. 6.6 - Show that Algorithm 3 produces the next larger...Ch. 6.6 - Develop an algorithm for generating the...Ch. 6.6 - List all 3-permutations of {1,2,3,4,5}. 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