DISCRETE MATH
8th Edition
ISBN: 9781266712326
Author: ROSEN
Publisher: MCG CUSTOM
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Chapter 6, Problem 54SE
Suppose that when an enzyme that breaks RXA chains after each G linkis applied to a 12-link chain, the fragments obtained areAC, UG, and ACG and when an enzyme that breaks RXA chains after each C or Ulinkis applied, the fragments obtained are U, GAC, and GAC. Can you determine the entire RXA chain from these two sets of fragments? If so, what is this RNA chain-
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The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation. While these are all great books, our only interest for this project is how often each letter is used.
Identify those letters whose Cls do not overlap with any the CIs of any of the other letters. (For example the CI [0.042, 0.052] overlaps with [0.050, 0.060] because the upper bound of the first CI is greater than the lower bound of the second CI.) List the letters with the non-overlapping Cis and specify how many such letters there are.
The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation. While these are all great books, our only interest for this project is how often each letter is used.
3) Identify those letters whose Cls do not overlap with any the CIs of any of the other letters. (For example the CI [0.042, 0.052] overlaps with [0.050, 0.060] because the upper bound of the first CI is greater than the lower bound of the second CI.) List the letters with the non-overlapping Cis and specify how many such letters there are
Question 3 answers:
Letters
Lower bound
Upper bound
L
0.037072109
0.042042
D
0.043728076
0.049092
E
0.11621383
0.12451
4) The previous analysis could be useful if our goal was to decipher an encrypted message, where each letter is scrambled (for example, each “a” might become a “g”, while each “b” might become an “o” and so forth).
a) Assume that the letter “z” in encrypted message has a relative frequency of 0.06…
Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than 15 from w.
Chapter 6 Solutions
DISCRETE MATH
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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}. The...Ch. 6.6 - Find the Cantor digits an ti2,that correspond to...Ch. 6.6 - Prob. 15ECh. 6.6 - i6,Find the permutations of {1,2,3,4,5} that...Ch. 6.6 - Prob. 17ECh. 6 - Explain how the sum and product rules can be used...Ch. 6 - Explain how to find the number of bit strings of...Ch. 6 - Prob. 3RQCh. 6 - How can yon find the number of possible outcomes...Ch. 6 - How can you find the number of bit strings...Ch. 6 - State the pigeonhole principle, Explain how the...Ch. 6 - State the generalized pigeonhole principle....Ch. 6 - ft What is the difference between an r-combination...Ch. 6 - What i s Pas cal's tri angle? How can arow of...Ch. 6 - What is meant by a combinatorial proof of an...Ch. 6 - ii. Explain how to prove Pascal's identity using a...Ch. 6 - Stateth e bin omial th eor em. Explain how to pr o...Ch. 6 - Explain how to find a formula for the number of...Ch. 6 - Letnand r be positive integers. Explain why the...Ch. 6 - Prob. 15RQCh. 6 - Prob. 16RQCh. 6 - a) How many ways are there to deal hands of five...Ch. 6 - Describe an algorithm for generating all the...Ch. 6 - i. How many ways are there to choose 6 items from...Ch. 6 - a.H 01 v many ways ar e ther e to ch o o se1o...Ch. 6 - Prob. 3SECh. 6 - How many strings of length10either start with ooo...Ch. 6 - Prob. 5SECh. 6 - Prob. 6SECh. 6 - Prob. 7SECh. 6 - Hoi v many positive integers less than iqoo have...Ch. 6 - Prob. 9SECh. 6 - Prob. 10SECh. 6 - Prob. 11SECh. 6 - How many people are needed to guarantee that at...Ch. 6 - Show that given anv set of 10 positive integers...Ch. 6 - Prob. 14SECh. 6 - Prob. 15SECh. 6 - Prob. 16SECh. 6 - Show that in a sequence ofmintegers there exists...Ch. 6 - Prob. 18SECh. 6 - Show that the decimal expansion of a rational...Ch. 6 - Once a computer worm infects a personal computer...Ch. 6 - si.How many ways are there to choose a dozen...Ch. 6 - ss.Findn if P(n,2] = 110. J\?i, n] = 5040....Ch. 6 - Prob. 23SECh. 6 - Show that ifnandrare nonnegative integers and n >...Ch. 6 - Prob. 25SECh. 6 - Give a combinatorial proof ofCorollary 2ofSection...Ch. 6 - Prob. 27SECh. 6 - a8. Prove using mathematical induction that O>• 2)...Ch. 6 - Prob. 29SECh. 6 - Show that V7' XIt. I = (’) if nis an integer withCh. 6 - Prob. 31SECh. 6 - Prob. 32SECh. 6 - How many bit strings of length n, where n > 4,...Ch. 6 - Prob. 34SECh. 6 - Prob. 35SECh. 6 - Prob. 36SECh. 6 - How many ways are there to assign 24 students to...Ch. 6 - Prob. 38SECh. 6 - - How many solutions are there to the equation xt...Ch. 6 - How many different strings can be made from the...Ch. 6 - How many subsets of a set with ten el e m ents...Ch. 6 - Prob. 42SECh. 6 - Prob. 43SECh. 6 - How many ways are. there to seat six boys and...Ch. 6 - How many ways are there to distribute six objects...Ch. 6 - How many ways are there to distribute five obj...Ch. 6 - Find these signless Stirling numb er s of the...Ch. 6 - Show that ifnis a positive integer, then ,Ch. 6 - Prob. 49SECh. 6 - Prob. 50SECh. 6 - Prob. 51SECh. 6 - j2, How many n-element RXA sequences consist of 4...Ch. 6 - *53. Suppose that when an enzyme that breaks RXA...Ch. 6 - Suppose that when an enzyme that breaks RXA chains...Ch. 6 - Devise an algorithm for generating all the...Ch. 6 - Devise an algorithm for generating all the...Ch. 6 - Prob. 57SECh. 6 - Prob. 58SECh. 6 - Prob. 1CPCh. 6 - Prob. 2CPCh. 6 - Prob. 3CPCh. 6 - Prob. 4CPCh. 6 - Given a positive integern,listallthe permutations...Ch. 6 - Prob. 6CPCh. 6 - Prob. 7CPCh. 6 - Prob. 8CPCh. 6 - Prob. 9CPCh. 6 - Prob. 10CPCh. 6 - Prob. 1CAECh. 6 - Prob. 2CAECh. 6 - Prob. 3CAECh. 6 - Prob. 4CAECh. 6 - Prob. 5CAECh. 6 - Prob. 6CAECh. 6 - Prob. 7CAECh. 6 - Prob. 8CAECh. 6 - Prob. 9CAECh. 6 - Describe some of the earliest uses of the...Ch. 6 - Prob. 2WPCh. 6 - Discuss the importance of combinatorial reasoning...Ch. 6 - Jlanv combinatonal identities are described in...Ch. 6 - Prob. 5WPCh. 6 - Prob. 6WPCh. 6 - Prob. 7WPCh. 6 - Describe the latest discoveries of values and...Ch. 6 - Prob. 9WPCh. 6 - Prob. 10WP
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