Finite Mathematics (11th Edition)
11th Edition
ISBN: 9780321979438
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 5, Problem 8RE
To determine
To write: True or false for the given statement.
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In this exercise, we will investigate a technique to prove that a language is notregular. This tool is called the pumping lemma.The pumping lemma says that if M = (S, I, f, s0, F ) is a DFA with p states (i.e., p = |S|) and if the wordw is in L(M ) (the language generated by M ) and w has length greater than or equal to p, then w may bedivided into three pieces, w = xyz, satisfying the following conditions:1. For each i ∈ N, xy^i z ∈ L(M ).2. |y| > 0 (i.e., y contains at least one character).3. |xy| ≤ p (i.e., the string xy has at most p characters).
Use the pumping lemma to show the following language is not regular (HINT: Use proof by contradictionto assume the language is regular and apply the pumping lemma to the language):L = {0^k1^k | k ∈ N}
A prefix of length ℓ of some word w are the first ℓ characters (in order) of w.1. Construct a context-free grammar for the language: L = {w ∈ {a, b}∗ | every prefix of w has at least as many a’s as b’s}2. Explain why every word generated by your context-free grammar (in Part 1) is contained in L. Then,prove via induction that every w ∈ L is produced by your context-free grammar.
Chapter 5 Solutions
Finite Mathematics (11th Edition)
Ch. 5.1 -
1. What factors determine the amount of interest...Ch. 5.1 - In your own words, describe the maturity value of...Ch. 5.1 -
3. What is meant by the present value of...Ch. 5.1 - We calculated the loan in Example 2(b) assuming...Ch. 5.1 - Find the simple interest. $25,000 at 3% for 9...Ch. 5.1 -
Find the simple interest.
6. $4289 at 4.5% for...Ch. 5.1 -
Find the simple interest.
7. $1974 at 6.3% for...Ch. 5.1 -
Find the simple interest.
8. $6125 at 1.25% for...Ch. 5.1 - Find the simple interest. Assume a 360-day year....Ch. 5.1 -
Find the simple interest. Assume a 360-day...
Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 -
Find the maturity value and the amount of...Ch. 5.1 -
15. Explain the difference between simple...Ch. 5.1 - Prob. 16ECh. 5.1 -
17. What is the difference between t and n?
Ch. 5.1 - In Figure 2, one line is straight and the other is...Ch. 5.1 - Find the compound amount for each deposit and the...Ch. 5.1 -
Find the compound amount for each deposit and...Ch. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Find the compound amount for each deposit and the...Ch. 5.1 - Find the interest rate for each deposit and...Ch. 5.1 - Prob. 26ECh. 5.1 -
Find the interest rate for each deposit and...Ch. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Find the effective rate corresponding to each...Ch. 5.1 -
Find the effective rate corresponding to each...Ch. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Find the present value (the amount that should be...Ch. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 -
Find the present value (the amount that should...Ch. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 -
Find the doubling time for each of the...Ch. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 -
50. Delinquent Taxes An accountant for a...Ch. 5.1 - Savings A $1500 certificate of deposit held for 75...Ch. 5.1 - Prob. 52ECh. 5.1 - Cash Advance Fees According to an advertisement,...Ch. 5.1 - Prob. 54ECh. 5.1 - Investments Suppose $10,000 is invested at an...Ch. 5.1 -
56. Investments In Exercise 55, notice that as...Ch. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Student Loan Upon graduation from college, Warren...Ch. 5.1 - Comparing Investments Two partners agree to invest...Ch. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Negative Interest Under certain conditions, Swiss...Ch. 5.1 -
Negative Interest Under certain conditions,...Ch. 5.1 - Savings On January 1, 2010, Jack deposited $1000...Ch. 5.1 - Prob. 66ECh. 5.1 - Prob. 67ECh. 5.1 - Prob. 68ECh. 5.1 - Prob. 69ECh. 5.1 -
70. Effective Rate Determine the effective...Ch. 5.1 - Prob. 71ECh. 5.1 - Prob. 72ECh. 5.1 - Buying a House Cara Tilley wants to have $30,000...Ch. 5.1 - Prob. 74ECh. 5.1 -
Doubling Time Use the ideas from Example 11 to...Ch. 5.1 - Prob. 76ECh. 5.1 - Prob. 77ECh. 5.1 - Prob. 78ECh. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.2 - Find the fifth term of each geometric sequence. a...Ch. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Find the fifth term of each geometric sequence. a...Ch. 5.2 -
Find the fifth term of each geometric...Ch. 5.2 -
Find the fifth term of each geometric...Ch. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 -
Find the sum of the first four terms for each...Ch. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Find the sum of the first four terms for each...Ch. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Find the future value of each ordinary annuity....Ch. 5.2 - Prob. 21ECh. 5.2 -
Find the future value of each ordinary annuity,...Ch. 5.2 -
Find the future value of each ordinary annuity,...Ch. 5.2 - Prob. 24ECh. 5.2 - Find the future value of each ordinary annuity, if...Ch. 5.2 - Prob. 26ECh. 5.2 -
Find the future value of each ordinary annuity,...Ch. 5.2 - Prob. 28ECh. 5.2 - Determine the interest rate needed to accumulate...Ch. 5.2 - Determine the interest rate needed to accumulate...Ch. 5.2 -
Find the periodic payment that will amount to...Ch. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 -
Find the amount of each payment to be made into...Ch. 5.2 - Find the amount of each payment to be made into a...Ch. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 -
Find the future value of each annuity due....Ch. 5.2 - Find the future value of each annuity due. Assume...Ch. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Find the future value of each annuity due. Then...Ch. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 -
50. Retirement Planning A 45-year-old man puts...Ch. 5.2 -
51. Retirement Planning At the end of each...Ch. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Individual Retirement Accounts Suppose a...Ch. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Savings A father opened a savings account for his...Ch. 5.2 - Prob. 61ECh. 5.2 - Savings Nic Daubenmire deposits $10,000 at the...Ch. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Lottery In a 1992 Virginia lottery, the jackpot...Ch. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.3 - Explain the difference between the present value...Ch. 5.3 -
2. What does it mean to amortize a loan?
Ch. 5.3 - Prob. 3ECh. 5.3 - Find the present value of each ordinary annuity....Ch. 5.3 -
Find the present value of each ordinary...Ch. 5.3 -
Find the present value of each ordinary...Ch. 5.3 - Find the present value of each ordinary annuity....Ch. 5.3 -
Find the present value of each ordinary...Ch. 5.3 - Find the lump sum deposited today that will yield...Ch. 5.3 - Find the lump sum deposited today that will yield...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 -
Suppose that in the loans described in Exercises...Ch. 5.3 -
Suppose that in the loans described in Exercises...Ch. 5.3 - Suppose that in the loans described in Exercises...Ch. 5.3 -
Suppose that in the loans described in Exercises...Ch. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - What sum deposited today at 5% compounded annually...Ch. 5.3 - What lump sum deposited today at 8% compounded...Ch. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Find the monthly house payments necessary to...Ch. 5.3 - Prob. 31ECh. 5.3 -
Suppose that in the loans described in Exercise...Ch. 5.3 -
Suppose that in the loans described in Exercise...Ch. 5.3 - Prob. 34ECh. 5.3 - House Payments Calculate the monthly payment and...Ch. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 -
40. New Car Financing In 2014, some dealers...Ch. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Installment Buying In Exercises 44-46, prepare an...Ch. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - House Payments Jason Hoffa buys a house for...Ch. 5.3 -
50. House Payments The Chavara family buys a...Ch. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5 - Lorri Morgan received $50 on her 16th birthday,...Ch. 5 - At the beginning of the year, Yvette Virgil...Ch. 5 - Prob. 3EACh. 5 - Prob. 4EACh. 5 - People often lose money on investments. Karen...Ch. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Find the simple interest for each loan. $4902 at...Ch. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 -
Find the compound amount in each loan.
18....Ch. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 -
Find the amount of interest earned by each...Ch. 5 - Find the amount of interest earned by each...Ch. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Find the present value of each amount. $17,650 in...Ch. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Find the future value of each annuity and the...Ch. 5 -
Find the future value of each annuity and the...Ch. 5 - Prob. 41RECh. 5 - Prob. 42RECh. 5 - Prob. 43RECh. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 -
Find the amount of each payment that must be...Ch. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - Prob. 49RECh. 5 -
Find the present value of each ordinary...Ch. 5 - Prob. 51RECh. 5 - Prob. 52RECh. 5 - Find the present value of each ordinary annuity....Ch. 5 - Prob. 54RECh. 5 - Find the amount of the payment necessary to...Ch. 5 - Prob. 56RECh. 5 - Prob. 57RECh. 5 - Prob. 58RECh. 5 - Prob. 59RECh. 5 - Prob. 60RECh. 5 - Prob. 61RECh. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Personal Finance Carla Truss owes $5800 to her...Ch. 5 - Business Financing Candice Cotton needs to borrow...Ch. 5 - Prob. 66RECh. 5 - Business Investment A developer deposits $84,720...Ch. 5 - Prob. 68RECh. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Prob. 72RECh. 5 - Business Financing The owner of Eastside Hallmark...Ch. 5 - Personal Finance To buy a new computer, David Berg...Ch. 5 - Prob. 75RECh. 5 - Prob. 76RECh. 5 - Prob. 77RECh. 5 -
78. New Car In Spring 2014, some dealers...Ch. 5 - Buying and Selling a House The Bahary family...Ch. 5 - Prob. 80RECh. 5 - Prob. 81RE
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