Prealgebra (6th Edition)
6th Edition
ISBN: 9780134179018
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Chapter 3.4, Problem 2QQ
Simplify.
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b.
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Chapter 3 Solutions
Prealgebra (6th Edition)
Ch. 3.1 - Fill in the blanks. The sum of a number and its...Ch. 3.1 - Fill in the blanks. The sum of two supplementary...Ch. 3.1 - Fill in the blanks. To Solve x6=3, we __________ 6...Ch. 3.1 - Fill in the blanks. To Solve x+6=2, we __________...Ch. 3.1 - Fill in each with the number that gives the...Ch. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Fill in each with the number that gives the...Ch. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Fill in each with the number that gives the...Ch. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Fill in each with the number that gives the...Ch. 3.1 - Fill in each with the correct number to solve the...Ch. 3.1 - Prob. 18ECh. 3.1 - Fill in each with the correct number to solve the...Ch. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Solve and check your solution. a. 18=x+2 b. 18=x2Ch. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Simplify and then solve. Check Solution. 4x3x3=8Ch. 3.1 - Prob. 42ECh. 3.1 - Simplify and then solve. Check Solution. 5y4y+1=5Ch. 3.1 - Simplify and then solve. Check Solution. 3y2y+3=1Ch. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Simplify each side of the equation, then solve the...Ch. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Simplify each side of the equation, then solve the...Ch. 3.1 - Simplify each side of the equation, then solve the...Ch. 3.1 - Prob. 52ECh. 3.1 - Simplify each side of the equation, then solve the...Ch. 3.1 - Prob. 54ECh. 3.1 - Simplify each side of the equation, then solve the...Ch. 3.1 - Simplify each side of the equation, then solve the...Ch. 3.1 - Find the measure of the unknown angle for each...Ch. 3.1 - Find the measure of the unknown angle for each...Ch. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Simplify each side of each equation, then solve...Ch. 3.1 - Prob. 72ECh. 3.1 - Prob. 73ECh. 3.1 - Simplify each side of each equation, then solve...Ch. 3.1 - Prob. 75ECh. 3.1 - Prob. 76ECh. 3.1 - Prob. 77ECh. 3.1 - Translate into symbols. [1.4.2] The product of...Ch. 3.1 - Prob. 79ECh. 3.1 - Translate into symbols. [1.8.4] Double what number...Ch. 3.1 - Prob. 81ECh. 3.1 - Translate into symbols. Replace the ? with the...Ch. 3.1 - Fantasy Basketball Fantasy basketball is a game...Ch. 3.1 - Prob. 84ECh. 3.1 - Prob. 1QQCh. 3.1 - Prob. 2QQCh. 3.1 - a. Translate into symbols. The measure of ais35...Ch. 3.1 - Concept Check To solve the equation 9+x=15, Damien...Ch. 3.2 - Fill in the blanks. To solve the equation 22x=66,...Ch. 3.2 - Fill in the blanks. To solve the equation 16x=64,...Ch. 3.2 - Prob. 3ECh. 3.2 - Fill in each with the number that gives the...Ch. 3.2 - Prob. 5ECh. 3.2 - Fill in each with the number that gives the...Ch. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Fill in each with the number that gives the...Ch. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Solve and check your solution. 6x=66Ch. 3.2 - Solve and check your solution. 10x=40Ch. 3.2 - Solve and check your solution. 6y=88Ch. 3.2 - Solve and check your solution. 6y=18Ch. 3.2 - Solve and check your solution. 4a=48Ch. 3.2 - Solve and check your solution. 5m=35Ch. 3.2 - Solve and check your solution. 7y=42Ch. 3.2 - Solve and check your solution. 3y=15Ch. 3.2 - Solve and check your solution. 4x=12Ch. 3.2 - Solve and check your solution. 7a=49Ch. 3.2 - Solve and check your solution. 6y=36Ch. 3.2 - Solve and check your solution. 48=6xCh. 3.2 - Solve and check your solution. 30=3yCh. 3.2 - Solve and check your solution. 72=9xCh. 3.2 - Solve and check your solution. 56=14yCh. 3.2 - Solve and check your solution. 8x=104Ch. 3.2 - Solve and check your solution. 9y=135Ch. 3.2 - Solve and check your solution. 19x=76Ch. 3.2 - Solve and check your solution. 22y=132Ch. 3.2 - Solve and check your solution. 2(3x)=54Ch. 3.2 - Solve and check your solution. 5(2x)=80Ch. 3.2 - Solve and check your solution. 5(4x)=40Ch. 3.2 - Solve and check your solution. 3(2x)=30Ch. 3.2 - Solve and check your solution. 5(x2)=402Ch. 3.2 - Solve and check your solution. 3(x5)=602Ch. 3.2 - Solve and check your solution. 4(x2)=963Ch. 3.2 - Solve and check your solution. 6(x5)=1202Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Simplify each side of the equation, then solve....Ch. 3.2 - Solve and check your solution. 15y=165Ch. 3.2 - Solve and check your solution. 14x=168Ch. 3.2 - Solve and check your solution. 4x=323Ch. 3.2 - Solve and check your solution. 3a=413Ch. 3.2 - Solve and check your solution. 12x4x=56Ch. 3.2 - Solve and check your solution. 15x10=95Ch. 3.2 - Solve and check your solution. 55=5aCh. 3.2 - Solve and check your solution. 44=4yCh. 3.2 - Solve and check your solution. (3x)2=363Ch. 3.2 - Solve and check your solution. (8x)3=482Ch. 3.2 - Solve and check your solution. 9x+3x=120Ch. 3.2 - Solve and check your solution. 7x+3x=90Ch. 3.2 - Dimensions of a building The length (L) of a...Ch. 3.2 - Comparing weights The weight of a steel beam (B)...Ch. 3.2 - Prob. 61ECh. 3.2 - The width (W) of a yard is triple the length (L)....Ch. 3.2 - Cost of Race Boat The cost of a new race boat (R)...Ch. 3.2 - Dimensions of Wood The length of the larger piece...Ch. 3.2 - Tickets sold There were three times as many child...Ch. 3.2 - Write vs. Res Cars There are two times as many...Ch. 3.2 - Soccer Goals The total number of soccer goals...Ch. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Distance Traveled On Monday Leah drove x miles on...Ch. 3.2 - Prob. 72ECh. 3.2 - Solve. a. 13x=26 b. 13x=26 c. x+13=26 d. x13=26Ch. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Solve. a. 9y=72 b. 9y=72 c. y+9=72 d. y9=72Ch. 3.2 - Prob. 77ECh. 3.2 - Prob. 78ECh. 3.2 - Find the value of x for each pair of supplementary...Ch. 3.2 - Prob. 80ECh. 3.2 - Find the value of x for each pair of supplementary...Ch. 3.2 - Prob. 82ECh. 3.2 - [1.2.5] Find the perimeter of a rectangle with a...Ch. 3.2 - Prob. 84ECh. 3.2 - [2.6.2] Evaluate. 2xy for x=7andy=9Ch. 3.2 - Prob. 1QQCh. 3.2 - Prob. 2QQCh. 3.2 - Prob. 3QQCh. 3.2 - Prob. 4QQCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Fill in each blank with the correct formula. a....Ch. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - For each of the following: (a) State the...Ch. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Find the length and width of each rectangle....Ch. 3.3 - Prob. 16ECh. 3.3 - Find the length and width of each rectangle. a....Ch. 3.3 - Prob. 18ECh. 3.3 - Find the length and width of each rectangle. Floor...Ch. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - For each of the following: (a) State the...Ch. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Find the unknown side of each rectangle.Ch. 3.3 - Prob. 28ECh. 3.3 - Find the unknown measure for each parallelogram.Ch. 3.3 - Prob. 30ECh. 3.3 - Find the area of each shape made of rectanglesCh. 3.3 - Prob. 32ECh. 3.3 - Find the area of each shape made of rectanglesCh. 3.3 - Find the area of each shape made of rectanglesCh. 3.3 - Solve each applied problem. a. How many cubes with...Ch. 3.3 - Prob. 36ECh. 3.3 - Solve each applied problem. Water in a fish tank A...Ch. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - For each of the following rectangular solids: (a)...Ch. 3.3 - Find the unknown side of each rectangular solid.Ch. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Find the perimeter of each shape. A rectangle with...Ch. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Find the volume of each solid. A rectangular solid...Ch. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Find the unknown side of each shape.Ch. 3.3 - Find the unknown side of each shape.Ch. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Wood Flooring Loretta has a townhome with a family...Ch. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.3 - Chest Lining One roll of felt material at the...Ch. 3.3 - Painting a Room The walls of Anitas family room...Ch. 3.3 - Painting a Room The walls of Anitas family room...Ch. 3.3 - Find the area of the shaded region.Ch. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - Find the next two figures that would appear in the...Ch. 3.3 - [2.6.3] Simplify 7(x2)Ch. 3.3 - Prob. 72ECh. 3.3 - [1.4.3] Simplify (2)(3x)(5)Ch. 3.3 - [2.3.2] Perform the indicated operations. 8314.Ch. 3.3 - The width of a rectangle is double the length. If...Ch. 3.3 - Find the area of the following shape made of...Ch. 3.3 - A storage facility claims the volume of its...Ch. 3.3 - Prob. 4QQCh. 3.4 - Is 2422=46? Why or why not?Ch. 3.4 - Prob. 2ECh. 3.4 - a. Is 2(3x2)=23+2x2=6+2x2 ? Why or why not? b. Is...Ch. 3.4 - Prob. 4ECh. 3.4 - Fill in the blank. In the algebraic expression...Ch. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Prob. 11ECh. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Prob. 13ECh. 3.4 - Write each expression as repeated multiplication...Ch. 3.4 - Write each expression as repeated multiplication...Ch. 3.4 - Write each expression as repeated multiplication...Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Multiply and write the product in exponent form....Ch. 3.4 - Simplify. (4y5)(6y7)Ch. 3.4 - Simplify. (5y3)(3y3)Ch. 3.4 - Simplify. (6a6)(9a8)Ch. 3.4 - Simplify. (6a4)(2a4)Ch. 3.4 - Simplify. (5x)(3x2)Ch. 3.4 - Simplify. (6x)(3x)Ch. 3.4 - Simplify. (4y)(3y)Ch. 3.4 - Simplify. (5y)(4y)Ch. 3.4 - Simplify. (5a)(7a3)(2a6)Ch. 3.4 - Simplify. (3x)(2x4)(4x5)Ch. 3.4 - Simplify. (x)(4x6)(7x5)Ch. 3.4 - Simplify. (4x)(x7)(9x6)Ch. 3.4 - Simplify. (5x)(3y)(2x)Ch. 3.4 - Simplify. (5x)(2y)(7x)Ch. 3.4 - Simplify. (6y)(3x)(3y)Ch. 3.4 - Simplify. (3a)(2b)(4a)Ch. 3.4 - Identify each polynomial as a monomial, binomial,...Ch. 3.4 - Identify each polynomial as a monomial, binomial,...Ch. 3.4 - Simplify. 2x(x2+5)Ch. 3.4 - Simplify. 5y(y2+6)Ch. 3.4 - Simplify. 6x2(3x31)Ch. 3.4 - Simplify. 7x3(2x22)Ch. 3.4 - Simplify. 5y3(y42y)+3y7Ch. 3.4 - Simplify. 7x2(x36x)+2x5Ch. 3.4 - Simplify. 2x3(x2+4x)+5x5Ch. 3.4 - Simplify. 3x2(x3+3x)+6x5Ch. 3.4 - Simplify. (2y5)(6y2)Ch. 3.4 - Simplify. (5x1)(3x2)Ch. 3.4 - Simplify. (2x34x)(3x)Ch. 3.4 - Prob. 66ECh. 3.4 - Write the area of each rectangle as an algebraic...Ch. 3.4 - Write the area of each rectangle as an algebraic...Ch. 3.4 - Write the area of each parallelogram as an...Ch. 3.4 - Write the area of each parallelogram as an...Ch. 3.4 - Write the volume of each rectangular solid as an...Ch. 3.4 - Write the volume of each rectangular solid as an...Ch. 3.4 - Write the perimeter of each rectangle as an...Ch. 3.4 - Write the perimeter of each rectangle as an...Ch. 3.4 - Write the perimeter of each rectangle as an...Ch. 3.4 - Write the perimeter of each rectangle as an...Ch. 3.4 - For each of the following rectangles: (a) Write...Ch. 3.4 - For each of the following rectangles: (a) Write...Ch. 3.4 - Perform the operation indicated. a. 4cd+9cd b....Ch. 3.4 - Perform the operation indicated. a. 5xz+2xz b....Ch. 3.4 - Perform the operation indicated. a. 9ab57ab5 b....Ch. 3.4 - Perform the operation indicated. a. 6y7z3y7z b....Ch. 3.4 - Write the width of each rectangle as an algebraic...Ch. 3.4 - Write the width of each rectangle as an algebraic...Ch. 3.4 - [2.4.4] Divide. 357Ch. 3.4 - [2.4.3] Evaluate. (3)3Ch. 3.4 - [1.5.4] Divide. 20,566312Ch. 3.4 - [1.4.4] Multiply 31,42328Ch. 3.4 - Golf Scores In golf, par is the number of strokes...Ch. 3.4 - Golf Scores In golf, par is the number of strokes...Ch. 3.4 - Multiply. Leave your answer in exponent form. a....Ch. 3.4 - Simplify. a. 6a(a3+8a) b. (x53)(2x2)Ch. 3.4 - Write the area of the following rectangle as an...Ch. 3.4 - Concept Check Explain in words the steps to...Ch. 3 - Write the definition for each word. (3.1) Adjacent...Ch. 3 - Write the definition for each word. (3.1)...Ch. 3 - Write the definition for each word. (3.3) Parallel...Ch. 3 - Write the definition for each word. (3.4)...Ch. 3 - Write the definition for each word. (3.4)...Ch. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - Write the definition for each word. (3.4)...Ch. 3 - Prob. 9RPCh. 3 - Prob. 10RPCh. 3 - Prob. 11RPCh. 3 - Prob. 12RPCh. 3 - Prob. 13RPCh. 3 - Prob. 14RPCh. 3 - Prob. 15RPCh. 3 - Prob. 16RPCh. 3 - Prob. 17RPCh. 3 - Prob. 18RPCh. 3 - Prob. 19RPCh. 3 - Prob. 20RPCh. 3 - Prob. 21RPCh. 3 - Prob. 22RPCh. 3 - Prob. 23RPCh. 3 - Prob. 24RPCh. 3 - Prob. 25RPCh. 3 - Prob. 26RPCh. 3 - Prob. 27RPCh. 3 - Prob. 28RPCh. 3 - Prob. 29RPCh. 3 - Blue vs. White Cars There are twice as many white...Ch. 3 - Prob. 31RPCh. 3 - Miles Jogged On Friday Leo jogged x miles for his...Ch. 3 - The perimeter of a triangle is the sum of the...Ch. 3 - Prob. 34RPCh. 3 - Find the area of the square garden.Ch. 3 - Prob. 36RPCh. 3 - Prob. 37RPCh. 3 - Prob. 38RPCh. 3 - Prob. 39RPCh. 3 - Prob. 40RPCh. 3 - Find the length of the unknown side of each...Ch. 3 - Prob. 42RPCh. 3 - Prob. 43RPCh. 3 - Prob. 44RPCh. 3 - Buying Weed Killer The McBeths front yard measures...Ch. 3 - Prob. 46RPCh. 3 - Prob. 47RPCh. 3 - Multiply and leave your answer in exponent form....Ch. 3 - Prob. 49RPCh. 3 - Prob. 50RPCh. 3 - Multiply and leave your answer in exponent form....Ch. 3 - Prob. 52RPCh. 3 - Prob. 53RPCh. 3 - Multiply and leave your answer in exponent form....Ch. 3 - Prob. 55RPCh. 3 - Prob. 56RPCh. 3 - Multiply and leave your answer in exponent form....Ch. 3 - Multiply and leave your answer in exponent form....Ch. 3 - Prob. 59RPCh. 3 - Identify each polynomial as a monomial, binomial,...Ch. 3 - Identify each polynomial as a monomial, binomial,...Ch. 3 - Use the distributive property to simplify. x(x2+3)Ch. 3 - Use the distributive property to simplify....Ch. 3 - Write the area of the rectangle as algebraic...Ch. 3 - Write the volume of the rectangular solid as an...Ch. 3 - Solve each equation and check your solution. x2=8Ch. 3 - Solve each equation and check your solution....Ch. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Solve each equation and check your solution....Ch. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - a. Translate into symbols. Angle x measures 10...Ch. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Find the area of a rectangle with length 5 ft and...Ch. 3 - Prob. 14TCh. 3 - Prob. 15TCh. 3 - Find the length of the unknown side.Ch. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 22TCh. 3 - Prob. 23TCh. 3 - Prob. 24TCh. 3 - Prob. 25TCh. 3 - Prob. 26T
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- As 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_forwardCalculus 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_forward
- In 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_forwardThe Course Name Real Analysis please Solve questions by Real Analysisarrow_forward
- We 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_forwardQuestion 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_forward
- 3. 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_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…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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