Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 2.CR, Problem 30CR
To determine
(a)
To find:
The number of permutations of letters in given word.
To determine
(b)
To find:
The number of permutations of letters in given word.
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9. An elementary single period market model contains a risk-free asset with interest rate
r = 5% and a risky asset S which has price 30 at time t = 0 and will have either price
10 or 60 at time t = 1. Find a replicating strategy for a contingent claim with payoff
h(S₁) = max(20 - S₁, 0) + max(S₁ — 50, 0).
Total [8 Marks]
8. An elementary single period market model has a risky asset with price So = 20 at the
beginning and a money market account with interest rate r = 0.04 compounded only
once at the end of the investment period.
=
=
In market model A, S₁ 10 with 15% probability and S₁
21 with 85% probability.
In market model B, S₁ = 25 with 10% probability and S₁ = 30 with 90% probability.
For each market model A, B, determine if the model is arbitrage-free. If not, construct
an arbitrage.
Total [9 Marks]
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau, and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize ₁ - 2x2+x34x4
subject to 2x1+x22x3x41,
5x1 + x2-x3-×4 ≤ −1,
2x1+x2-x3-34
2,
1, 2, 3, 40.
Chapter 2 Solutions
Mathematics: A Practical Odyssey
Ch. 2.1 - Prob. 1ECh. 2.1 - Suppose A={2,5,7,9,13,25,26}. a. Find n(A) b. True...Ch. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Suppose n(U)=150, n(A)=37, and n(B)=84. a. If...Ch. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.1 - Prob. 52ECh. 2.1 - Prob. 53ECh. 2.1 - Prove the Cardinal Number Rule for the Complement...Ch. 2.1 - Prob. 55ECh. 2.1 - Prob. 56ECh. 2.1 - Answer the following questions using complete...Ch. 2.1 - Prob. 58ECh. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - Prob. 64ECh. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - The following questions are modeled after those...Ch. 2.2 - A survey of 200 people yielded the following...Ch. 2.2 - A survey of 300 workers yielded the following...Ch. 2.2 - The records of 1,492 high school graduates were...Ch. 2.2 - A department store surveyed 428 shoppers, and the...Ch. 2.2 - In a survey, 674 adults were asked what television...Ch. 2.2 - A survey asked 816 college freshmen whether they...Ch. 2.2 - A local 4-H club surveyed its members, and the...Ch. 2.2 - A local anime fan club surveyed its members...Ch. 2.2 - A recent survey of w shoppers that is, n(U)=w...Ch. 2.2 - A recent transportation survey of w urban...Ch. 2.2 - A consumer survey was conducted to examine...Ch. 2.2 - In a recent survey of monetary donations made by...Ch. 2.2 - Recently, Lady Gaga, Arcade Fire, and Skrillex had...Ch. 2.2 - Dr. Hawk works in an allergy clinic, and his...Ch. 2.2 - When the member of the Eye and I photo club...Ch. 2.2 - After leaving the polls, many people are asked how...Ch. 2.2 - In a recent survey consumer were asked where they...Ch. 2.2 - A company that specializes in language tutorial...Ch. 2.2 - In a recent survey, people were asked which radio...Ch. 2.2 - In a recent health insurance survey, employee at...Ch. 2.2 - A survey of 136 pet owners yielded the following...Ch. 2.2 - An exit poll of 300 votes yielded the following...Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Using Venn diagrams, prove De Morgans law (AB)=AB.Ch. 2.2 - Prob. 34ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 40ECh. 2.2 - If a person has type B blood, what blood types may...Ch. 2.2 - Prob. 42ECh. 2.2 - If a person has type O blood, what blood types may...Ch. 2.2 - Answer the following questions using complete...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Exercises 4652 refer to the following: A nonprofit...Ch. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Jamie has decided to buy either a Mega or a Better...Ch. 2.3 - Prob. 4ECh. 2.3 - If you buy three pairs of jeans, four sweaters,...Ch. 2.3 - A certain model of automobiles is available in six...Ch. 2.3 - To fulfill certain requirements for a degree, a...Ch. 2.3 - To fulfill a requirement for a literature class, a...Ch. 2.3 - A sporting goods store has fourteen lines of snow...Ch. 2.3 - An audio equipment store has ten different...Ch. 2.3 - A cafeteria offers a complete dinner that includes...Ch. 2.3 - A sandwich shop offers a U-Chooz special...Ch. 2.3 - How many different Social Security numbers are...Ch. 2.3 - To use an automated teller machine ATM, a customer...Ch. 2.3 - Every book published has an International Standard...Ch. 2.3 - How many different Zip Codes are possible using a...Ch. 2.3 - Telephone area codes are three-digit numbers of...Ch. 2.3 - Major credit cards such as VISA and MasterCard...Ch. 2.3 - The serial number on a dollar bill consists of a...Ch. 2.3 - The serial number on a new twenty-dollar bill...Ch. 2.3 - Each student at State University has a student ID...Ch. 2.3 - Each student at State College has a student ID...Ch. 2.3 - In Exercises 2338, find the indicated value. 4!Ch. 2.3 - In Exercises 2338, find the indicated value. 5!Ch. 2.3 - In Exercises 2338, find the indicated value. 10!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!Ch. 2.3 - In Exercises 2338, find the indicated value. 20!Ch. 2.3 - In Exercises 2338, find the indicated value. 25!Ch. 2.3 - In Exercises 2338, find the indicated value. 6!4!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!6!Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - Find the value of n!(nr)!, when n=16 and r=14.Ch. 2.3 - Find the value of n!(nr)!, when n=19 and r=16.Ch. 2.3 - Find the value of n!(nr)!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!, when n=r.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=3.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=4.Ch. 2.3 - Find the value of n!(nr)!r!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!r!, when n=r.Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 51ECh. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.4 - In Exercises 112, find the indicated value: a. 7P3...Ch. 2.4 - In Exercises 112, find the indicated value: a. 8P4...Ch. 2.4 - In Exercises 112, find the indicated value: a. 5P5...Ch. 2.4 - In Exercises 112, find the indicated value: a. 9P0...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a. xP1...Ch. 2.4 - In Exercises 112, find the indicated value: a. xP2...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - a. Find 3P2. b. List all of the permutations of...Ch. 2.4 - a. Find 3C2. b. List all of the combinations of...Ch. 2.4 - Prob. 15ECh. 2.4 - a. Find 4P2. b. List all of the permutations of...Ch. 2.4 - Prob. 17ECh. 2.4 - An English class consists of twenty-three students...Ch. 2.4 - In how many ways can the letters in the word...Ch. 2.4 - A committee of four is to be selected from a group...Ch. 2.4 - A softball league has thirteen teams. If every...Ch. 2.4 - In a group of eighteen people, each person shakes...Ch. 2.4 - A softball league has thirteen teams. How many...Ch. 2.4 - Three hundred people buy raffle tickets. Three...Ch. 2.4 - A group of nine women and six men must select a...Ch. 2.4 - A group of ten seniors, eight juniors, six...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - How many five-card poker hands containing two pair...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - A 5/36 lottery requires choosing five of the...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Over forty states participate in Powerball, a...Ch. 2.4 - Over forty states participate in Mega Millions, a...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - a. Find the sum of the entries in the first row of...Ch. 2.4 - a. Add adjacent entries of the sixth row of...Ch. 2.4 - Use Pascals Triangle to answer the following. a....Ch. 2.4 - Given the set S={a, b, c, d}, answer the...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutations...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Exercise 6367 refer to the following: A baseball...Ch. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.5 - Prob. 1ECh. 2.5 - In Exercises 1-10, find the cardinal numbers of...Ch. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Consider the following one-to-one correspondence...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.CR - Prob. 1CRCh. 2.CR - Prob. 2CRCh. 2.CR - Prob. 3CRCh. 2.CR - Prob. 4CRCh. 2.CR - Prob. 5CRCh. 2.CR - Prob. 6CRCh. 2.CR - Prob. 7CRCh. 2.CR - Prob. 8CRCh. 2.CR - Prob. 9CRCh. 2.CR - A survey of 1,000 college seniors yielded the...Ch. 2.CR - A survey of recent college graduates yielded the...Ch. 2.CR - A local anime fan club surveyed 67 of its members...Ch. 2.CR - An exit poll yielded following information...Ch. 2.CR - Prob. 14CRCh. 2.CR - Prob. 15CRCh. 2.CR - Prob. 16CRCh. 2.CR - Prob. 17CRCh. 2.CR - A certain model of pickup truck is available in...Ch. 2.CR - Each student at State University has a student ID...Ch. 2.CR - Prob. 20CRCh. 2.CR - Prob. 21CRCh. 2.CR - Prob. 22CRCh. 2.CR - A group of ten women and twelve men must select a...Ch. 2.CR - Prob. 24CRCh. 2.CR - Prob. 25CRCh. 2.CR - Using a standard deck of fifty-two cards no...Ch. 2.CR - Prob. 27CRCh. 2.CR - A 6/42 lottery requires choosing six of the...Ch. 2.CR - Prob. 29CRCh. 2.CR - Prob. 30CRCh. 2.CR - Prob. 31CRCh. 2.CR - Prob. 32CRCh. 2.CR - Prob. 33CRCh. 2.CR - Prob. 34CRCh. 2.CR - Prob. 35CRCh. 2.CR - Prob. 36CRCh. 2.CR - Prob. 37CRCh. 2.CR - Consider the following one to one correspondence...Ch. 2.CR - Prob. 39CRCh. 2.CR - Prob. 40CRCh. 2.CR - Prob. 41CRCh. 2.CR - Prob. 42CRCh. 2.CR - Prob. 43CRCh. 2.CR - Prob. 44CRCh. 2.CR - Prob. 45CRCh. 2.CR - Prob. 46CRCh. 2.CR - Prob. 47CRCh. 2.CR - Prob. 48CR
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