Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Chapter 8.1, Problem 47ES
Perform the modular arithmetic.
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You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below.
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship.
Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size).
Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model.
Interpret the…
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots.
Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars)
are as follows.
From
To
Hamilton Butler
Clermont
Southern Gas
10
20
15
Northwest Gas
12
15
18
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
Assignment 3 graph.docx
Score: 1 out of 1
Comment:
(b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs (in thousands of…
Chapter 8 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 8.1 - Determine the day of the week on which you were...Ch. 8.1 - Determine the day of the week on which Abraham...Ch. 8.1 - Determine the day of the week on which January 1,...Ch. 8.1 - Determine the day of the week on which Valentines...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 4ESCh. 8.1 - Prob. 5ESCh. 8.1 - Prob. 6ES
Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 8ESCh. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 10ESCh. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 14ESCh. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 16ESCh. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Prob. 22ESCh. 8.1 - Prob. 23ESCh. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Evaluate each expression, where + and indicate...Ch. 8.1 - Prob. 26ESCh. 8.1 - Evaluate each expression, where + and indicate...Ch. 8.1 - Prob. 28ESCh. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Prob. 32ESCh. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Prob. 38ESCh. 8.1 - List five different natural numbers that are...Ch. 8.1 - List five different natural numbers that are...Ch. 8.1 - Perform the modular arithmetic. (9+15)mod7Ch. 8.1 - Prob. 42ESCh. 8.1 - Perform the modular arithmetic. (5+22)mod8Ch. 8.1 - Prob. 44ESCh. 8.1 - Perform the modular arithmetic. (42+35)mod3Ch. 8.1 - Prob. 46ESCh. 8.1 - Perform the modular arithmetic. (37+45)mod12Ch. 8.1 - Prob. 48ESCh. 8.1 - Prob. 49ESCh. 8.1 - Perform the modular arithmetic. (2510)mod4Ch. 8.1 - Prob. 51ESCh. 8.1 - Prob. 52ESCh. 8.1 - Prob. 53ESCh. 8.1 - Prob. 54ESCh. 8.1 - Perform the modular arithmetic. (1532)mod7Ch. 8.1 - Prob. 56ESCh. 8.1 - Perform the modular arithmetic. (68)mod9Ch. 8.1 - Prob. 58ESCh. 8.1 - Prob. 59ESCh. 8.1 - Prob. 60ESCh. 8.1 - Perform the modular arithmetic. (1418)mod5Ch. 8.1 - Prob. 62ESCh. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Prob. 66ESCh. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Prob. 71ESCh. 8.1 - Prob. 72ESCh. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Prob. 75ESCh. 8.1 - Prob. 76ESCh. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Prob. 79ESCh. 8.1 - Prob. 80ESCh. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Prob. 83ESCh. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Prob. 86ESCh. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Modular division can be performed by considering...Ch. 8.1 - Prob. 90ESCh. 8.1 - Prob. 91ESCh. 8.1 - Prob. 92ESCh. 8.1 - Prob. 93ESCh. 8.1 - Modular division can be performed by considering...Ch. 8.1 - Prob. 95ESCh. 8.1 - Prob. 96ESCh. 8.1 - Prob. 97ESCh. 8.1 - Prob. 98ESCh. 8.1 - Prob. 99ESCh. 8.1 - Many people consider the 13th of the month an...Ch. 8.2 - What is the ciphertext for the word CODE?Ch. 8.2 - Prob. 2EECh. 8.2 - Prob. 3EECh. 8.2 - Prob. 4EECh. 8.2 - Prob. 5EECh. 8.2 - ISBN Numbers. Determine whether the given number...Ch. 8.2 - ISBN Numbers. Determine whether the given number...Ch. 8.2 - Prob. 3ESCh. 8.2 - Prob. 4ESCh. 8.2 - Prob. 5ESCh. 8.2 - ISBN Numbers. Determine whether the given number...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - Prob. 10ESCh. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - Prob. 23ESCh. 8.2 - Prob. 24ESCh. 8.2 - Money Orders Some money orders have serial numbers...Ch. 8.2 - Money Orders Some money orders have serial numbers...Ch. 8.2 - Air Travel Many printed airline tickets contain a...Ch. 8.2 - Air Travel Many printed airline tickets contain a...Ch. 8.2 - Air Travel Many printed airline tickets contain a...Ch. 8.2 - Prob. 30ESCh. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Prob. 33ESCh. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Prob. 35ESCh. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Prob. 38ESCh. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Encryption Julius Caesar supposedly used an...Ch. 8.2 - Decoding Julius Caesar supposedly used an...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Decoding Decode the message LOFT JGMK LBS MNWMK...Ch. 8.2 - Decoding Decode the message BTYW SCRBKN UCYN that...Ch. 8.2 - Prob. 61ESCh. 8.2 - Decoding Decode the message GBBZ OJQBWJ TBR GJHI...Ch. 8.2 - Money Orders Explain why the method used to...Ch. 8.2 - Prob. 64ESCh. 8.2 - Banking. When banks process an electronic funds...Ch. 8.3 - Prob. 1EECh. 8.3 - Prob. 2EECh. 8.3 - Prob. 3EECh. 8.3 - Prob. 4EECh. 8.3 - Prob. 5EECh. 8.3 - Prob. 1ESCh. 8.3 - Prob. 2ESCh. 8.3 - Prob. 3ESCh. 8.3 - Prob. 4ESCh. 8.3 - Prob. 5ESCh. 8.3 - Prob. 6ESCh. 8.3 - Prob. 7ESCh. 8.3 - Prob. 8ESCh. 8.3 - Prob. 9ESCh. 8.3 - Prob. 10ESCh. 8.3 - Prob. 11ESCh. 8.3 - Prob. 12ESCh. 8.3 - Prob. 13ESCh. 8.3 - Prob. 14ESCh. 8.3 - Prob. 15ESCh. 8.3 - Prob. 16ESCh. 8.3 - Prob. 17ESCh. 8.3 - Prob. 18ESCh. 8.3 - Prob. 19ESCh. 8.3 - Prob. 20ESCh. 8.3 - Prob. 21ESCh. 8.3 - Prob. 22ESCh. 8.3 - Prob. 23ESCh. 8.3 - Prob. 24ESCh. 8.3 - Prob. 25ESCh. 8.3 - Prob. 26ESCh. 8.3 - Prob. 27ESCh. 8.3 - Prob. 28ESCh. 8.3 - Prob. 29ESCh. 8.3 - Prob. 30ESCh. 8.3 - Prob. 31ESCh. 8.3 - Prob. 32ESCh. 8.3 - Prob. 33ESCh. 8.3 - Prob. 34ESCh. 8.3 - Refer to the group of permutations of the numbers...Ch. 8.3 - Prob. 36ESCh. 8.3 - Prob. 37ESCh. 8.3 - Prob. 38ESCh. 8.3 - Prob. 39ESCh. 8.3 - Prob. 40ESCh. 8.3 - Prob. 41ESCh. 8.3 - Prob. 42ESCh. 8.3 - Prob. 43ESCh. 8.3 - Prob. 44ESCh. 8.3 - Prob. 45ESCh. 8.3 - Prob. 46ESCh. 8.3 - Prob. 47ESCh. 8.3 - Prob. 48ESCh. 8.3 - Prob. 49ESCh. 8.3 - Prob. 50ESCh. 8.3 - Prob. 51ESCh. 8.3 - Prob. 52ESCh. 8.3 - Prob. 53ESCh. 8.3 - Prob. 54ESCh. 8.3 - Prob. 55ESCh. 8.3 - Consider the set of elements a,b,c,d with the...Ch. 8.3 - Prob. 57ESCh. 8.3 - Prob. 58ESCh. 8.3 - Prob. 59ESCh. 8.3 - Prob. 60ESCh. 8.3 - Prob. 61ESCh. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression. Where + and indicate...Ch. 8 - Evaluate each expression. Where + and indicate...Ch. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Clocks and Calendars. Use modular arithmetic to...Ch. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Find all whole number solutions of the congruence...Ch. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - ISBN Numbers. Determine the correct check digit...Ch. 8 - ISBN Numbers. Determine the correct check digit...Ch. 8 - UPC Codes. Determine the correct check digit for...Ch. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Encryption. Encode the message using a cyclical...Ch. 8 - Encryption. Encode the message using a cyclical...Ch. 8 - Encryption. Use a cyclical alphabetic encrypting...Ch. 8 - Prob. 44RECh. 8 - Encryption Use the encrypting congruence...Ch. 8 - Encryption Decode the message WEU LKGGMF NHM NMGN,...Ch. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Use symbolic notation, shown below, for the...Ch. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Evaluate each expression, where and indicate...Ch. 8 - January 1, 2017, was a Sunday. What day of the...Ch. 8 - Determine whether the congruence is true or false....Ch. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 6TCh. 8 - Scheduling Disregarding A.M. or P.M., if it is now...Ch. 8 - Prob. 8TCh. 8 - Prob. 9TCh. 8 - Find the additive inverse and the multiplicative...Ch. 8 - ISBN Number Determine the correct check digit for...Ch. 8 - UPC Codes Determine the correct check digit for...Ch. 8 - Prob. 13TCh. 8 - Encryption Encrypt the plaintext message REPORT...Ch. 8 - Prob. 15TCh. 8 - Prob. 16TCh. 8 - Prob. 17TCh. 8 - Prob. 18TCh. 8 - In the permutation group of the numbers 1 2 3,...Ch. 8 - Prob. 20T
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- For each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram? A 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92 B 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91 C 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93 D 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forward
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