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 6.4, Problem 26E
Fill in the missing numbers or variables needed to factor each expression.
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For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Year Month Rate (%)2009 Mar 8.72009 Apr 9.02009 May 9.42009 Jun 9.52009 Jul 9.52009 Aug 9.62009 Sep 9.82009 Oct 10.02009 Nov 9.92009 Dec 9.92010 Jan 9.82010 Feb 9.82010 Mar 9.92010 Apr 9.92010 May 9.62010 Jun 9.42010 Jul 9.52010 Aug 9.52010 Sep 9.52010 Oct 9.52010 Nov 9.82010 Dec 9.32011 Jan 9.12011 Feb 9.02011 Mar 8.92011 Apr 9.02011 May 9.02011 Jun 9.12011 Jul 9.02011 Aug 9.02011 Sep 9.02011 Oct 8.92011 Nov 8.62011 Dec 8.52012 Jan 8.32012 Feb 8.32012 Mar 8.22012 Apr 8.12012 May 8.22012 Jun 8.22012 Jul 8.22012 Aug 8.12012 Sep 7.82012 Oct…
For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Date IBM9/7/2010 $125.959/8/2010 $126.089/9/2010 $126.369/10/2010 $127.999/13/2010 $129.619/14/2010 $128.859/15/2010 $129.439/16/2010 $129.679/17/2010 $130.199/20/2010 $131.79
a. Construct a line chart of the closing stock prices data. Choose the correct chart below.
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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- 1) Express these large and small numbers from the Read and Study section in scientific notation: (a) 239,000 miles (b) 3,800,000,000,000 sheets of paper (c) 0.0000000000000000000000167 grams 2) Find all values for the variable x that make these equations true. (a) 5x = 1 (b) 3x = 1/1 9 (c) 4* = 11/ 4 (e) 4* = 64 (g) 10x = 1,000,000 (d) 3x=-3 (f) 2x = = 8 (h) 10x = 0.001arrow_forward(b) 4) Find an equation to fit each of the following graphs: (a) 20 20 18 16 14 12 10 8 6 4 2 24 22 20 18 16 14 12 10 8 16 A 2 -3 -2 -1-0 2 3 4. -1 0 1 2 3. -2 -2arrow_forward3) Which of the following are equivalent to 3? (There may be more than one that is equivalent!) -1 (a) (9)¯¹ 3. (b) (-3)-1 (c) (-3) -1 (d) -(¯3) (e) 11 3-1 (f) 3-4arrow_forward
- Y- ___b=_____ (X- )arrow_forwardFor each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical) Date IBM9/7/2010 $125.959/8/2010 $126.089/9/2010 $126.369/10/2010 $127.999/13/2010 $129.619/14/2010 $128.859/15/2010 $129.439/16/2010 $129.679/17/2010 $130.199/20/2010 $131.79arrow_forward5) State any theorems that you use in determining your solution. a) Suppose you are given a model with two explanatory variables such that: Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n Using partial differentiation derive expressions for the intercept and slope coefficients for the model above. [25 marks] b) A production function is specified as: Yi = α + B₁x1i + ẞ2x2i + Ui, i = 1, 2, ... n, u₁~N(0,σ²) where: y = log(output), x₁ = log(labor input), x2 = log(capital input) The results are as follows: x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10, = 8, Syy = 10, S2y n = 23 (individual firms) i) Compute values for the intercept, the slope coefficients and σ². [20 marks] ii) Show that SE (B₁) = 0.102. [15 marks] iii) Test the hypotheses: ẞ1 = 1 and B2 = 0, separately at the 5% significance level. You may take without calculation that SE (a) = 0.78 and SE (B2) = 0.102 [20 marks] iv) Find a 95% confidence interval for the estimate ẞ2. [20 marks]arrow_forward
- Page < 2 of 2 - ZOOM + The set of all 3 x 3 upper triangular matrices 6) Determine whether each of the following sets, together with the standard operations, is a vector space. If it is, then simply write 'Vector space'. You do not have to prove all ten vector space axioms. If it is not, then identify one of the ten vector space axioms with its number in the attached sheet that fails and also show that how it fails. a) The set of all polynomials of degree four or less. b) The set of all 2 x 2 singular matrices. c) The set {(x, y) : x ≥ 0, y is a real number}. d) C[0,1], the set of all continuous functions defined on the interval [0,1]. 7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and show that it is orthogonal to both u and v. 8) a) Find the equation of the least squares regression line for the data points below. (-2,0), (0,2), (2,2) b) Graph the points and the line that you found from a) on the same Cartesian coordinate plane.arrow_forward1. A consumer group claims that the mean annual consumption of cheddar cheese by a person in the United States is at most 10.3 pounds. A random sample of 100 people in the United States has a mean annual cheddar cheese consumption of 9.9 pounds. Assume the population standard deviation is 2.1 pounds. At a = 0.05, can you reject the claim? (Adapted from U.S. Department of Agriculture) State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): 2. The CEO of a manufacturing facility claims that the mean workday of the company's assembly line employees is less than 8.5 hours. A random sample of 25 of the company's assembly line employees has a mean workday of 8.2 hours. Assume the population standard deviation is 0.5 hour and the population is normally distributed. At a = 0.01, test the CEO's claim. State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): Statisticsarrow_forwardPage < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.arrow_forward
- Find the Laplace Transform of the function to express it in frequency domain form.arrow_forwardPlease draw a graph that represents the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?arrow_forwardGiven the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations? 7 y 6 5 4 3 2 -6-5-4-3-2-1 1+ -2 1 2 3 4 5 6 x + 2y = 8 2x + 4y = 12 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. O The slopes are the same, and the y-intercepts are the same.arrow_forward
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