A Survey of Mathematics with Applications (10th Edition) - Standalone book
10th Edition
ISBN: 9780134112107
Author: Allen R. Angel, Christine D. Abbott, Dennis Runde
Publisher: PEARSON
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Chapter 7, Problem 1T
To determine
To convert: The given quantity into kiloliters.
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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.
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Chapter 7 Solutions
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Ch. 7.1 - In Exercises 110, fill in the blanks with an...Ch. 7.1 - Prob. 2ECh. 7.1 - In Exercises 110, fill in the blanks with an...Ch. 7.1 - Prob. 4ECh. 7.1 - In Exercises 110, fill in the blanks with an...Ch. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - Complete the following. a. 1 hectogram = ________...Ch. 7.1 - Complete the following. a. 1 centiliter =...Ch. 7.1 - In Exercises 1923, without referring to any of the...Ch. 7.1 - Prob. 20ECh. 7.1 - In Exercises 1923, without referring to any of the...Ch. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Maximum Mass In Exercises 25 and 26, use the photo...Ch. 7.1 - Prob. 26ECh. 7.1 - In Exercises 2732, fill in the missing values. 27....Ch. 7.1 - Prob. 28ECh. 7.1 - In Exercises 2732, fill in the missing values. 29....Ch. 7.1 - Prob. 30ECh. 7.1 - In Exercises 2732, fill in the missing values. 31....Ch. 7.1 - In Exercises 2732, fill in the missing values. 32....Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - Prob. 40ECh. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - Walking Would you be walking faster if you walked...Ch. 7.1 - Who Ran Faster Jim ran 100 m, and Bob ran 100 yd...Ch. 7.1 - Water Removal One pump removes 1 da of water in 1...Ch. 7.1 - Balance If 5 kg ate placed on one side of a...Ch. 7.1 - Mount Fuji and Pikes Peak The most visited...Ch. 7.1 - 2014 Ford Mustang The 2014 Ford Mustang gets about...Ch. 7.1 - Calcium Tablets Sean lakes two 250-mg chewable...Ch. 7.1 - Framing a Painting A painting, including the...Ch. 7.1 - Liters of Soda A bottle of soda contains 360 m. a....Ch. 7.1 - Track and Field A high school has a 400-m oval...Ch. 7.1 - A Home Run A baseball diamond is a square whose...Ch. 7.1 - Prob. 64ECh. 7.1 - In Exercises 6568, fill in the blank to make a...Ch. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Prob. 70ECh. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - Prob. 10ECh. 7.2 - In Exercises 1118, indicate the metric unit of...Ch. 7.2 - Prob. 12ECh. 7.2 - In Exercises 1118, indicate the metric unit of...Ch. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - In Exercises 1118, indicate the metric unit of...Ch. 7.2 - Prob. 18ECh. 7.2 - In Exercises 1924, choose the best answer. 19. The...Ch. 7.2 - In Exercises 1924, choose the best answer. 20. A...Ch. 7.2 - In Exercises 1924, choose the best answer. 21. The...Ch. 7.2 - Prob. 22ECh. 7.2 - In Exercises 1924, choose the best answer. 23. The...Ch. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - In Exercises 2530, (a) estimate the item in metric...Ch. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - In Exercises 3136, indicate the metric unit of...Ch. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - In Exercises 3742, choose the best answer. 37. A...Ch. 7.2 - In Exercises 3742, choose the best answer. 38. The...Ch. 7.2 - In Exercises 3742, choose the best answer 39. The...Ch. 7.2 - In Exercises 3742, choose the best answer. 40. The...Ch. 7.2 - In Exercises 3742, choose the best answer 41. The...Ch. 7.2 - In Exercises 3742, choose the best answer 42. The...Ch. 7.2 - Prob. 43ECh. 7.2 - In Exercises 4348, (a) estimate the area of the...Ch. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - In Exercises 4348, (a) estimate the area of the...Ch. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - In Exercises 4956, determine the metric unit that...Ch. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - In Exercises 4956, determine the metric unit that...Ch. 7.2 - In Exercises 4956, determine the metric unit that...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - Prob. 64ECh. 7.2 - Prob. 65ECh. 7.2 - Prob. 66ECh. 7.2 - Prob. 67ECh. 7.2 - In Exercises 6568, (a) estimate the volume in...Ch. 7.2 - In Exercises 6972, select the best answer. 69. One...Ch. 7.2 - In Exercises 6972, select the best answer. 70. One...Ch. 7.2 - In Exercises 6972, select the best answer. 71. One...Ch. 7.2 - Prob. 72ECh. 7.2 - Prob. 75ECh. 7.2 - Prob. 76ECh. 7.2 - Prob. 77ECh. 7.2 - Prob. 78ECh. 7.2 - Prob. 79ECh. 7.2 - Prob. 80ECh. 7.2 - In Exercises 7386, when appropriate, use the key...Ch. 7.2 - Prob. 82ECh. 7.2 - Prob. 83ECh. 7.2 - Prob. 84ECh. 7.2 - Prob. 85ECh. 7.2 - Prob. 86ECh. 7.2 - Prob. 87ECh. 7.2 - Prob. 88ECh. 7.2 - Prob. 89ECh. 7.2 - Prob. 90ECh. 7.2 - Prob. 91ECh. 7.2 - Prob. 92ECh. 7.2 - In Exercises 9396, fill in the blank. 93. 501 cm3...Ch. 7.2 - In Exercises 9396, fill in the blank. 94. 435 cm3...Ch. 7.2 - In Exercises 9396, fill in the blank. 95. 263 k =...Ch. 7.2 - In Exercises 9396, fill in the blank. 96. 4.2 =...Ch. 7.2 - Glacier In Exercises 97 and 98, assume that a part...Ch. 7.2 - Glacier In Exercises 97 and 98, assume that a part...Ch. 7.2 - Challenge Problems/Group Activities In Exercises...Ch. 7.2 - Challenge Problems/Group Activities In Exercises...Ch. 7.2 - Prob. 101ECh. 7.2 - Prob. 102ECh. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 1924, select the best answer. 19. The...Ch. 7.3 - In Exercises 1924, select the best answer. 20. The...Ch. 7.3 - In Exercises 1924, select the best answer. 21. The...Ch. 7.3 - In Exercises 1924, select the best answer. 22. The...Ch. 7.3 - In Exercises 1924, select the best answer. 23. The...Ch. 7.3 - In Exercises 1924, select the best answer. 24. The...Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Curry As shown in the photo, curry being sold at...Ch. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Prob. 66ECh. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Fish Tank A rectangular fish tank is 1 yd long by...Ch. 7.3 - Prob. 71ECh. 7.3 - Prob. 72ECh. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with aft...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 32ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 50ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 13 and 14, arrange the quantities...Ch. 7 - In Exercises 13 and 14, arrange the quantities...Ch. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - A square kilometer is a square with length and...Ch. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - Prob. 50RECh. 7 - Prob. 51RECh. 7 - Prob. 52RECh. 7 - Prob. 53RECh. 7 - Prob. 54RECh. 7 - Prob. 55RECh. 7 - Prob. 56RECh. 7 - Prob. 57RECh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - Prob. 10TCh. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Prob. 13TCh. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - Prob. 16TCh. 7 - Prob. 17TCh. 7 - At the Aquarium A rectangular fish tank at an...Ch. 7 - Cost of Paint The first coat of paint for the...Ch. 7 - Prob. 20T
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- 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…arrow_forwardUse the method of undetermined coefficients to solve the given nonhomogeneous system. dx dt = 2x + 3y − 8 dy dt = −x − 2y + 6 X(t) =arrow_forwardAs discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk. (a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let ds ≥ R − Rs with ds ≥ 0. Then make the objective function: Min 1 5 5 s = 1 ds2. Let FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund…arrow_forward
- Calculus lll May I please have the blank lines completed, and final statement defined as a result? Thank you for the support!arrow_forwardFor 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_forward
- Problem 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_forwardThe Course Name Real Analysis please Solve questions by Real Analysisarrow_forwardWe consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forward
- Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_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_forward3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forward
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