Prealgebra plus MyLab Math/MyLab Statistics -- Access Card Package (6th Edition) (Tobey Developmental Math Paperback Series)
6th Edition
ISBN: 9780134266336
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Textbook Question
Chapter 6, Problem 29RP
Geometry The width of a field is 22 feet shorter than the length. Define variable expressions for the length and width of the field.
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Chapter 6 Solutions
Prealgebra plus MyLab Math/MyLab Statistics -- Access Card Package (6th Edition) (Tobey Developmental Math Paperback Series)
Ch. 6.1 - Fill in the blanks. To subtract two polynomials,...Ch. 6.1 - Fill in the blanks. To add two polynomials, we...Ch. 6.1 - Identify the terms of each polynomial. 5a26a+2b4+1Ch. 6.1 - Identify the terms of each polynomial....Ch. 6.1 - Identify the terms of each polynomial. 6x63x33y1Ch. 6.1 - Identify the terms of each polynomial. 2y33x24z38Ch. 6.1 - Perform the operations indicated. (7y3)+(4y+9)Ch. 6.1 - Perform the operations indicated. (2x3)+(7x+6)Ch. 6.1 - Perform the operations indicated. (2a23a+6)+(4a2)Ch. 6.1 - Perform the operations indicated. (3c26c+3)+(2c7)
Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Simplify. (5x+2y)Ch. 6.1 - Simplify. (8x+5y)Ch. 6.1 - Simplify. (8x+4)Ch. 6.1 - Simplify. (5a+3)Ch. 6.1 - Simplify. (3x+6z5y)Ch. 6.1 - Simplify. (3x+4y8z)Ch. 6.1 - Perform the operations indicated. (10x+7)(3x+5)Ch. 6.1 - Perform the operations indicated. (8x+7)(3a+2)Ch. 6.1 - Perform the operations indicated. (7x3)(4x+6)Ch. 6.1 - Perform the operations indicated. (5y+2)(7y8)Ch. 6.1 - Perform the operations indicated. (8a+5)(4a3)Ch. 6.1 - Perform the operations indicated. (5c+2)(3c6)Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated. (4x2+7x+1)(x25)Ch. 6.1 - Perform the operations indicated. (3x2+7x+2)(x22)Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Determine the value of a if x0....Ch. 6.1 - Determine the value of a if x0....Ch. 6.1 - Determine the values of a and b if x0....Ch. 6.1 - Determine the values of a and b if x0....Ch. 6.1 - Perform the operation indicated. [4.4.1] 6x82x2Ch. 6.1 - Perform the operation indicated. [4.4.1]...Ch. 6.1 - Perform the operation indicated. [3.4.2] (4x)(2x2)Ch. 6.1 - Perform the operation indicated. [3.4.2]...Ch. 6.1 - [5.6.1]Miles Walked Maria walked 227 miles and...Ch. 6.1 - [5.6.1]Recipe Mixture A cook mixed 37 cup of brown...Ch. 6.1 - Perform the operations indicated. a. (3x+1)+(5x2)...Ch. 6.1 - Perform the operations indicated. a. (6a4)(3a2) b....Ch. 6.1 - Perform the operations indicated. a....Ch. 6.1 - Concept Check Mitchell subtracted two polynomials...Ch. 6.2 - Erin multiplied (4)(x2+2x+1) and obtained this...Ch. 6.2 - Write in words the multiplication that the word...Ch. 6.2 - Fill in the blanks and boxes to complete each...Ch. 6.2 - Fill in the blanks and boxes to complete each...Ch. 6.2 - Multiply. 3(3y24y+2) First term of the product is:...Ch. 6.2 - Multiply. 2(3y26y+1) First term of the product is:...Ch. 6.2 - To multiply (x1)(x2+3x+1): We multiply x times the...Ch. 6.2 - To multiply (y2)(y2+4y+3): We multiply the...Ch. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply. 3x2(x2)Ch. 6.2 - Use the distributive property to multiply. 4x3(x3)Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use FOIL to multiply. (x+6)(x+7)Ch. 6.2 - Use FOIL to multiply. (a+2)(a+1)Ch. 6.2 - Use FOIL to multiply. (x+3)(x+9)Ch. 6.2 - Use FOIL to multiply. (y+2)(y+5)Ch. 6.2 - Use FOIL to multiply. (a+6)(a+2)Ch. 6.2 - Use FOIL to multiply. (x+4)(x+1)Ch. 6.2 - Use FOIL to multiply. (y+4)(y8)Ch. 6.2 - Use FOIL to multiply. (a+7)(a4)Ch. 6.2 - Use FOIL to multiply. (x+2)(x4)Ch. 6.2 - Use FOIL to multiply. (x+3)(x5)Ch. 6.2 - Use FOIL to multiply. (x4)(x+2)Ch. 6.2 - Use FOIL to multiply. (m3)(m+5)Ch. 6.2 - Use FOIL to multiply. (2x+1)(x+2)Ch. 6.2 - Use FOIL to multiply. (3x+1)(x+2)Ch. 6.2 - Use FOIL to multiply. (3x3)(x1)Ch. 6.2 - Use FOIL to multiply. (4x3)(x1)Ch. 6.2 - Use FOIL to multiply. (2y1)(y+2)Ch. 6.2 - Use FOIL to multiply. (4y2)(y+1)Ch. 6.2 - Use FOIL to multiply. (2y+1)(y2)Ch. 6.2 - Use FOIL to multiply. (4y+2)(y1)Ch. 6.2 - Multiply. 5a(2a4b6)Ch. 6.2 - Multiply. 4x(3x+5y7)Ch. 6.2 - Multiply. 7x3(x3)Ch. 6.2 - Multiply. 8x3(x5)Ch. 6.2 - Prob. 51ECh. 6.2 - Multiply. (x4)(x2+x2)Ch. 6.2 - Multiply. (z+2)(z5)Ch. 6.2 - Multiply. (b+1)(b3)Ch. 6.2 - Multiply. (2x+1)(4x2+2x8)Ch. 6.2 - Multiply. (3x+1)(2x2+3x2)Ch. 6.2 - Multiply. (y7)(y+2)Ch. 6.2 - Multiply. (y8)(y+5)Ch. 6.2 - Prob. 59ECh. 6.2 - Multiply. a. (z+2)(z+4) b. (z2)(z4)Ch. 6.2 - Multiply. a. (x5)(x+3) b. (x+5)(x3)Ch. 6.2 - Prob. 62ECh. 6.2 - Simplify. (x+2)(x1)+2(3x+3)Ch. 6.2 - Simplify. (x3)(x+1)+4(2x+1)Ch. 6.2 - Simplify. 2x(x2+3x1)+(x2)(x3)Ch. 6.2 - Simplify. 3x(x2+x2)+(x1)(x2)Ch. 6.2 - If a(2x3)=14x+21, what is the value of a?Ch. 6.2 - If b(3xx+4)=15x20, what is the value of b?Ch. 6.2 - Perform the operations indicated. [3.2.3]Coin...Ch. 6.2 - Prob. 70ECh. 6.2 - Perform the operations indicated. [4.6.3]Calories...Ch. 6.2 - Perform the operations indicated. [4.5.3]Earnings...Ch. 6.2 - Prob. 1QQCh. 6.2 - Multiply. (x1)(4x22x+8)Ch. 6.2 - Prob. 3QQCh. 6.2 - Concept Check Multiply each of the following. 1....Ch. 6.3 - Fill in the blanks. Age Comparison Juan is two...Ch. 6.3 - Fill in the blanks. Age Comparison Rhonda is three...Ch. 6.3 - Fill in the blanks. Miles Run Alice can run 1 mile...Ch. 6.3 - Fill in the blanks. Home Runs Last season Jose...Ch. 6.3 - Prob. 5ECh. 6.3 - Write an applied problem using the following...Ch. 6.3 - Geometry The second angle of a triangle is 20...Ch. 6.3 - Wage Comparison Victors monthly salary is $95 less...Ch. 6.3 - Company Profit A companys profit for the fourth...Ch. 6.3 - Fundraiser Andrew walked 4 miles more than Dave...Ch. 6.3 - Height Comparison The height of a pole is one-half...Ch. 6.3 - Enrollment The number of students enrolled in Eden...Ch. 6.3 - Geometry The length of a rectangle is double the...Ch. 6.3 - Prob. 14ECh. 6.3 - Geometry The width of a rectangle is 13 inches...Ch. 6.3 - Geometry The width of a rectangle is 25 inches...Ch. 6.3 - Music DVDs The number of music DVDs that Carl has...Ch. 6.3 - Company Profit A companys profit for the second...Ch. 6.3 - Geometry The length of a rectangular box is double...Ch. 6.3 - Geometry The width of a rectangular box is double...Ch. 6.3 - Model Car Collection Jim has sixteen more blue...Ch. 6.3 - Height Comparison Sion is 3 inches taller than...Ch. 6.3 - Geometry The second side of a triangle is 4 inches...Ch. 6.3 - Geometry The second side of a triangle is 3 inches...Ch. 6.3 - Height Comparison The height of a building is four...Ch. 6.3 - Geometry The length of a yard is triple the length...Ch. 6.3 - School Election In a school election for class...Ch. 6.3 - Cookie Sales Betty-Jo sold 20 fewer boxes of Girl...Ch. 6.3 - Wage Comparison Vus salary is $125 more than Sams...Ch. 6.3 - Computer Game Scores Lena earned 120 points less...Ch. 6.3 - Investment Jerry invested $3000 more in stocks...Ch. 6.3 - Music Downloads The number of songs Arnold...Ch. 6.3 - Answer true or false. We can solve 3x+6.Ch. 6.3 - Answer true or false. We can solve 3x+6=12.Ch. 6.3 - Solve [3.2.1] 11x=44Ch. 6.3 - Solve [3.2.1] y+77=6Ch. 6.3 - Solve [5.7.1] m7=5Ch. 6.3 - Solve [3.1.2] 4x3x+8=62Ch. 6.3 - [3.3.2] Find the area of a rectangle with...Ch. 6.3 - [3.3.2] Find the volume of a rectangle with...Ch. 6.3 - Tinas monthly salary is triple Mais monthly...Ch. 6.3 - Dixie is 4 years older than Sugar. Pumpkin is 3...Ch. 6.3 - Phoebe purchased a watch, ring, and bracelet at...Ch. 6.3 - Concept Check The width of a box is triple the...Ch. 6.4 - Jessie incorrectly factored 6x12 as follows:...Ch. 6.4 - Explain why the following polynomial is not...Ch. 6.4 - For 9 and 27: a. State the common factors. b....Ch. 6.4 - For 4 and 24: a. State the common factors. b....Ch. 6.4 - Find the GCF for each set of numbers. 4, 16Ch. 6.4 - Find the GCF for each set of numbers. 5, 20Ch. 6.4 - Find the GCF for each set of numbers. 18, 27Ch. 6.4 - Find the GCF for each set of numbers. 14, 21Ch. 6.4 - Find the GCF for each set of numbers. 6, 9, 15Ch. 6.4 - Find the GCF for each set of numbers. 8, 10, 12Ch. 6.4 - Find the GCF for each set of numbers. 10, 15, 20Ch. 6.4 - Find the GCF for each set of numbers. 12, 18, 24Ch. 6.4 - For the polynomial a3bc+a6c: a. What variables are...Ch. 6.4 - For the polynomial x4yzx2z: a. What variables are...Ch. 6.4 - Find the GCF for each expression. xy2+xy3Ch. 6.4 - Find the GCF for each expression. mn3+mn4Ch. 6.4 - Find the GCF for each expression. a2b5+a3b4Ch. 6.4 - Find the GCF for each expression. x3y4+x2y5Ch. 6.4 - Find the GCF for each expression. a3bc2+ac3Ch. 6.4 - Find the GCF for each expression. x2yz3+xz2Ch. 6.4 - Find the GCF for each expression. x3yz3+xy4Ch. 6.4 - Find the GCF for each expression. a2bc3+ab3Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing + or sign. a. b.Ch. 6.4 - Fill in the missing + or sign. a. b.Ch. 6.4 - Factor. Check by multiplying. 3a6Ch. 6.4 - Factor. Check by multiplying. 7x14Ch. 6.4 - Factor. Check by multiplying. 5y+5Ch. 6.4 - Factor. Check by multiplying. 9x+9Ch. 6.4 - Factor. Check by multiplying. 10a+4bCh. 6.4 - Factor. Check by multiplying. 6x+10yCh. 6.4 - Factor. Check by multiplying. 15m+3nCh. 6.4 - Factor. Check by multiplying. 5a+25bCh. 6.4 - Factor. Check by multiplying. 7x+14y+21Ch. 6.4 - Factor. Check by multiplying. 6a+42b+30Ch. 6.4 - Factor. Check by multiplying. 8a+18b6Ch. 6.4 - Factor. Check by multiplying. 15x+20y10Ch. 6.4 - Factor. Check by multiplying. 2a24aCh. 6.4 - Factor. Check by multiplying. 15y23yCh. 6.4 - Factor. Check by multiplying. 4abb2Ch. 6.4 - Factor. Check by multiplying. 5xyy2Ch. 6.4 - Factor. Check by multiplying. 5x+10xyCh. 6.4 - Factor. Check by multiplying. 9x+18xyCh. 6.4 - Factor. Check by multiplying. 7x2y14xyCh. 6.4 - Factor. Check by multiplying. 8a2b16abCh. 6.4 - Factor. Check by multiplying. 12a2b6a2Ch. 6.4 - Factor. Check by multiplying. 15ab35b3Ch. 6.4 - Factor. Check by multiplying. 3x29x+18Ch. 6.4 - Factor. Check by multiplying. 2x28x+12Ch. 6.4 - Factor and check your answer. 4x2+8x3Ch. 6.4 - Factor and check your answer. 3y3+9y2Ch. 6.4 - Factor and check your answer. 2x2y+4xyCh. 6.4 - Factor and check your answer. 3a2b+6abCh. 6.4 - Factor and check your answer. 4y+2Ch. 6.4 - Factor and check your answer. 10x+5Ch. 6.4 - Factor and check your answer. 15a20Ch. 6.4 - Factor and check your answer. 9b15Ch. 6.4 - Factor and check your answer. 5x10xyCh. 6.4 - Factor and check your answer. 9x18xyCh. 6.4 - Factor and check your answer. 9xy33xyCh. 6.4 - Factor and check your answer. 4xy22xyCh. 6.4 - Factor and check your answer. 6x3y+12Ch. 6.4 - Factor and check your answer. 10a+20b+25Ch. 6.4 - Factor and check your answer. 4x2+8x4Ch. 6.4 - Factor and check your answer. 9x2+18x9Ch. 6.4 - Factor and check your answer. 2x3y38x2y2Ch. 6.4 - Factor and check your answer. 5x3y310x2y2Ch. 6.4 - Factor and check your answer. 4a2b+6ab+8aCh. 6.4 - Factor and check your answer. 12xy2+4xy+8yCh. 6.4 - When factoring a polynomial whose first...Ch. 6.4 - When factoring a polynomial whose first...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - [5.6.1]Rainfall Measured A rain gauge collected...Ch. 6.4 - [4.6.4]Potato Salad Servings Louise ordered 45...Ch. 6.4 - Find the GCF. a. 12, 20, 36 b. x2yz2x2y2Ch. 6.4 - Factor. 4x210y+2Ch. 6.4 - Factor. 5ab215abCh. 6.4 - Concept Check For the expression 12xy+16x a. Is xy...Ch. 6 - Prob. 1RPCh. 6 - Identify the terms of each polynomial. a42b23b4Ch. 6 - Simplify.Ch. 6 - Simplify. (6x+4y2)Ch. 6 - Perform the operations indicated. (3x9)+(5x2)Ch. 6 - Perform the operations indicated. (4x+8)(8x+2)Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Multiply. 4(6x28x+5)Ch. 6 - Prob. 12RPCh. 6 - Multiply. 3x(9x3y+2)Ch. 6 - Multiply. 5n(4n9m7)Ch. 6 - Multiply. 4x2(x44)Ch. 6 - Multiply. x4(x52x3)Ch. 6 - Multiply. (z+4)(5z)Ch. 6 - Multiply. (y+10)(6y)Ch. 6 - Multiply. (x36x)(4x2)Ch. 6 - Multiply. (x2)(2x2+3x1)Ch. 6 - Prob. 21RPCh. 6 - Multiply. (y1)(3y2+4y+5)Ch. 6 - Multiply. (2x+3)(x2+3x1)Ch. 6 - Use the FOIL method to multiply. (x2)(x+4)Ch. 6 - Use the FOIL method to multiply. (y+4)(y7)Ch. 6 - Use the FOIL method to multiply. (x2)(3x+4)Ch. 6 - Use the FOIL method to multiply. (x3)(5x6)Ch. 6 - Company Profit A companys profit for the third...Ch. 6 - Geometry The width of a field is 22 feet shorter...Ch. 6 - Geometry The measure of a is 30 more than the...Ch. 6 - Floral Bouquet A floral shop puts three times as...Ch. 6 - Wage Comparison Phoebes salary is $145 more than...Ch. 6 - Eye Color In a first-period history class at a...Ch. 6 - Geometry The length of the second side of a...Ch. 6 - Geometry The length of a box is 7 inches longer...Ch. 6 - Find the GCF for each of the following. 14, 21Ch. 6 - Find the GCF for each of the following. 6, 21Ch. 6 - Find the GCF for each of the following. 25, 45Ch. 6 - Find the GCF for each of the following. 18, 36Ch. 6 - Find the GCF for each of the following. 8, 14, 18Ch. 6 - Find the GCF for each of the following. 12, 16, 20Ch. 6 - Find the GCF for each of the following. a2bc+ab3Ch. 6 - Find the GCF for each of the following. xy3z+x2y2Ch. 6 - Factor. 6x14Ch. 6 - Factor. 5x+15Ch. 6 - Factor. 4a+12bCh. 6 - Factor. 3y9zCh. 6 - Factor. 6xy212xyCh. 6 - Factor. 8a2b16abCh. 6 - Factor. 10x3y+5x2yCh. 6 - Factor. 4y36y2+2yCh. 6 - Factor. 3a6b+12Ch. 6 - Factor. 2x+4y10Ch. 6 - Write the answers. Identify the terms of the...Ch. 6 - Write the answers. Simplify. (4x2y6)Ch. 6 - Perform the operations indicated. (5x+3)+(2x+4)Ch. 6 - Perform the operations indicated. (4y+5)(2y3)Ch. 6 - Perform the operations indicated. (7p2)(3p+4)Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Prob. 9TCh. 6 - Multiply. 7a(2a+3b4)Ch. 6 - Multiply. 2x3(4x23)Ch. 6 - Multiply. (x+5)(x+9)Ch. 6 - Multiply. (x+3)(x2)Ch. 6 - Multiply. (2x+1)(x3)Ch. 6 - Multiply. (3x31)(4x4)Ch. 6 - Prob. 16TCh. 6 - The width of a piece of wood is three inches...Ch. 6 - The second side of a triangle is 6 inches longer...Ch. 6 - Jason received 3000 fewer votes than Lena in an...Ch. 6 - Find the GCF. 9, 21Ch. 6 - Find the GCF. 8, 16, 20Ch. 6 - Find the GCF. x2yz+x3zCh. 6 - Factor. 3x+12Ch. 6 - Factor. 7x214x+21Ch. 6 - Factor. 2x2y6xy2
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- The following ordered data list shows the data speeds for cell phones used by a telephone company at an airport: A. Calculate the Measures of Central Tendency from the ungrouped data list. B. Group the data in an appropriate frequency table. C. Calculate the Measures of Central Tendency using the table in point B. D. Are there differences in the measurements obtained in A and C? Why (give at least one justified reason)? I leave the answers to A and B to resolve the remaining two. 0.8 1.4 1.8 1.9 3.2 3.6 4.5 4.5 4.6 6.2 6.5 7.7 7.9 9.9 10.2 10.3 10.9 11.1 11.1 11.6 11.8 12.0 13.1 13.5 13.7 14.1 14.2 14.7 15.0 15.1 15.5 15.8 16.0 17.5 18.2 20.2 21.1 21.5 22.2 22.4 23.1 24.5 25.7 28.5 34.6 38.5 43.0 55.6 71.3 77.8 A. Measures of Central Tendency We are to calculate: Mean, Median, Mode The data (already ordered) is: 0.8, 1.4, 1.8, 1.9, 3.2, 3.6, 4.5, 4.5, 4.6, 6.2, 6.5, 7.7, 7.9, 9.9, 10.2, 10.3, 10.9, 11.1, 11.1, 11.6, 11.8, 12.0, 13.1, 13.5, 13.7, 14.1, 14.2, 14.7, 15.0, 15.1, 15.5,…arrow_forwardA tournament is a complete directed graph, for each pair of vertices x, y either (x, y) is an arc or (y, x) is an arc. One can think of this as a round robin tournament, where the vertices represent teams, each pair plays exactly once, with the direction of the arc indicating which team wins. (a) Prove that every tournament has a direct Hamiltonian path. That is a labeling of the teams V1, V2,..., Un so that vi beats Vi+1. That is a labeling so that team 1 beats team 2, team 2 beats team 3, etc. (b) A digraph is strongly connected if there is a directed path from any vertex to any other vertex. Equivalently, there is no partition of the teams into groups A, B so that every team in A beats every team in B. Prove that every strongly connected tournament has a directed Hamiltonian cycle. Use this to show that for any team there is an ordering as in part (a) for which the given team is first. (c) A king in a tournament is a vertex such that there is a direct path of length at most 2 to any…arrow_forwardUse a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.) y = 100e0.01x (x, y) = y = 11,250 ×arrow_forward
- how to construct the following same table?arrow_forwardThe following is known. The complete graph K2t on an even number of vertices has a 1- factorization (equivalently, its edges can be colored with 2t - 1 colors so that the edges incident to each vertex are distinct). This implies that the complete graph K2t+1 on an odd number of vertices has a factorization into copies of tK2 + K₁ (a matching plus an isolated vertex). A group of 10 people wants to set up a 45 week tennis schedule playing doubles, each week, the players will form 5 pairs. One of the pairs will not play, the other 4 pairs will each play one doubles match, two of the pairs playing each other and the other two pairs playing each other. Set up a schedule with the following constraints: Each pair of players is a doubles team exactly 4 times; during those 4 matches they see each other player exactly once; no two doubles teams play each other more than once. (a) Find a schedule. Hint - think about breaking the 45 weeks into 9 blocks of 5 weeks. Use factorizations of complete…arrow_forward. The two person game of slither is played on a graph. Players 1 and 2 take turns, building a path in the graph. To start, Player 1 picks a vertex. Player 2 then picks an edge incident to the vertex. Then, starting with Player 1, players alternate turns, picking a vertex not already selected that is adjacent to one of the ends of the path created so far. The first player who cannot select a vertex loses. (This happens when all neighbors of the end vertices of the path are on the path.) Prove that Player 2 has a winning strategy if the graph has a perfect matching and Player 1 has a winning strategy if the graph does not have a perfect matching. In each case describe a strategy for the winning player that guarantees that they will always be able to select a vertex. The strategy will be based on using a maximum matching to decide the next choice, and will, for one of the cases involve using the fact that maximality means no augmenting paths. Warning, the game slither is often described…arrow_forward
- Let D be a directed graph, with loops allowed, for which the indegree at each vertex is at most k and the outdegree at each vertex is at most k. Prove that the arcs of D can be colored so that the arcs entering each vertex must have distinct colors and the arcs leaving each vertex have distinct colors. An arc entering a vertex may have the same color as an arc leaving it. It is probably easiest to make use of a known result about edge coloring. Think about splitting each vertex into an ‘in’ and ‘out’ part and consider what type of graph you get.arrow_forward3:56 wust.instructure.com Page 0 Chapter 5 Test Form A of 2 - ZOOM + | Find any real numbers for which each expression is undefined. 2x 4 1. x Name: Date: 1. 3.x-5 2. 2. x²+x-12 4x-24 3. Evaluate when x=-3. 3. x Simplify each rational expression. x²-3x 4. 2x-6 5. x²+3x-18 x²-9 6. Write an equivalent rational expression with the given denominator. 2x-3 x²+2x+1(x+1)(x+2) Perform the indicated operation and simplify if possible. x²-16 x-3 7. 3x-9 x²+2x-8 x²+9x+20 5x+25 8. 4.x 2x² 9. x-5 x-5 3 5 10. 4x-3 8x-6 2 3 11. x-4 x+4 x 12. x-2x-8 x²-4 ← -> Copyright ©2020 Pearson Education, Inc. + 5 4. 5. 6. 7. 8. 9. 10. 11. 12. T-97arrow_forwardplease work out more details give the solution.arrow_forward
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