Pathways To Math Literacy (looseleaf)
2nd Edition
ISBN: 9781259985607
Author: David Sobecki Professor, Brian A. Mercer
Publisher: McGraw-Hill Education
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Chapter 2.6, Problem 3PSQ
Using only the fact that
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find the value of each variable
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Chapter 2 Solutions
Pathways To Math Literacy (looseleaf)
Ch. 2.1 - Fill in each blank. a. 120isof500. b. 11isof20. c....Ch. 2.1 - Perform each calculation. Convert fractions to...Ch. 2.1 - Put this list in order from least to greatest....Ch. 2.1 - There are three different measures that well study...Ch. 2.1 - There are three different measures that well study...Ch. 2.1 - There are three different measures that well study...Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - The spreadsheet summarizes the results for one...
Ch. 2.1 - The spreadsheet summarizes the results for one...Ch. 2.1 - Compute the other two measures of average, then...Ch. 2.1 - Find the other two measures of average, and...Ch. 2.1 - How many total points can be earned in the course?Ch. 2.1 - What percentage of the total score is accounted...Ch. 2.1 - If you dont show up for the first exam and take a...Ch. 2.1 - What would your final percentage be if you score...Ch. 2.1 - Try this problem to see if you understand the...Ch. 2.1 - Suppose that the instructor who wrote the test in...Ch. 2.1 - Suppose that the instructor who wrote the test in...Ch. 2.1 - Type a short answer to each question. Describe the...Ch. 2.1 - Name...Ch. 2.1 - Name...Ch. 2.1 - Name...Ch. 2.1 - Name...Ch. 2.2 - Perform each operation a. 35 b. (2)6 c....Ch. 2.2 - Perform each operation a. 12+202 b. (4)(6)7 c....Ch. 2.2 - Perform each operation a. 20+2(94)2 b. 33242 c....Ch. 2.2 - Perform each operation a. ((801)3)2 b....Ch. 2.2 - Provide a couple more examples of where an input...Ch. 2.2 - What is a variable?Ch. 2.2 - Prob. 2CCh. 2.2 - Consider the following relationships, where one...Ch. 2.2 - If we wanted to know the cost of a 7-mile cab...Ch. 2.2 - Evaluate the cost formula for m=4, then attach...Ch. 2.2 - When using the formula A=P+Prt in a given...Ch. 2.2 - Now forget about formulas for a second, and...Ch. 2.2 - Now substitute the values provided in Question 5...Ch. 2.2 - Complete the table of values for your shiny new...Ch. 2.2 - Whats the value of the account after 2 years?Ch. 2.2 - How long does it take for the account to reach a...Ch. 2.2 - Evaluate this formula for P=10,000,t=40,andr=0.06....Ch. 2.2 - Write a formula that describes the value of an...Ch. 2.2 - Use a calculator or spreadsheet to complete this...Ch. 2.2 - Whats the value of this account after 20 years?Ch. 2.2 - To the nearest year, how long does it take the...Ch. 2.2 - Try this problem to see if you understand the...Ch. 2.2 - Try this problem to see if you understand the...Ch. 2.2 - Try this problem to see if you understand the...Ch. 2.2 - Name...Ch. 2.2 - Type a short answer to each question. What is a...Ch. 2.2 - Type a short answer to each question. When two...Ch. 2.2 - Type a short answer to each question. Describe the...Ch. 2.2 - Type a short answer to each question. How do the...Ch. 2.2 - If we were to find a formula that relates the...Ch. 2.2 - The formula D=R+0.05R2 describes the total...Ch. 2.2 - If youre driving at 25 miles per hour through a...Ch. 2.2 - How slow would you have to go in order to decrease...Ch. 2.2 - At the scene of an accident, a traffic...Ch. 2.2 - According to the U.S. Department of...Ch. 2.2 - What are some factors that would affect stopping...Ch. 2.3 - Add the quantities if possible, or describe why...Ch. 2.3 - If possible, rewrite the quantities so they can be...Ch. 2.3 - Perform each multiplication. a. 4y6y b. (4km)(6km)...Ch. 2.3 - To find the amount of simple interest earned,...Ch. 2.3 - The temperature in degrees Fahrenheit can be...Ch. 2.3 - Notice that each of the small boxes in the figure...Ch. 2.3 - When length is measured in inches, the correct...Ch. 2.3 - Use your answer from Question 1 to write a formula...Ch. 2.3 - This time, we have a three-dimensional figure made...Ch. 2.3 - When length is measured in centimeters, the...Ch. 2.3 - Use your answer from Question 4 to write a formula...Ch. 2.3 - My friend David Najar is an acclaimed artist. The...Ch. 2.3 - The volume of a cylindrical oil storage tank can...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - In Questions 9-13, perform each calculation. Then...Ch. 2.3 - Perform each multiplication. For parts a and b,...Ch. 2.3 - Use the formula P=a+b+c to find the perimeter of...Ch. 2.3 - Prob. 11CCh. 2.3 - Prob. 12CCh. 2.3 - Try this problem to see if you understand the...Ch. 2.3 - Try this problem to see if you understand the...Ch. 2.3 - Try this problem to see if you understand the...Ch. 2.3 - Type a short answer to each question. Why are...Ch. 2.3 - Type a short answer to each question. What does it...Ch. 2.3 - The calculation below is intended to find the...Ch. 2.3 - Find the fix needed to correct the mistake in the...Ch. 2.3 - Use your corrected formula to find the volume of...Ch. 2.3 - What percentage of the volume of the can is filled...Ch. 2.3 - After performing the division in Question 4, what...Ch. 2.3 - Racquetballs have a radius of about 2.8 cm. If...Ch. 2.3 - Golf balls also come in packages of three, but...Ch. 2.4 - Write each fraction in lowest terms. a. 1218 b....Ch. 2.4 - Write each fraction with the given denominator. a....Ch. 2.4 - Perform each operation, and reduce your answer if...Ch. 2.4 - Simplify each fractional expression by dividing...Ch. 2.4 - Use the table on the previous page to find an...Ch. 2.4 - Write two different conversion factors based on...Ch. 2.4 - There are two ways we could multiply our...Ch. 2.4 - What are the units for the other calculation? Do...Ch. 2.4 - So how many liters of magic potion are in the...Ch. 2.4 - According to our handy-dandy conversion chart, 1...Ch. 2.4 - Use one of the two conversion factors to convert...Ch. 2.4 - Now heres one of the great things about...Ch. 2.4 - My house is just about 15 miles from the Gulf of...Ch. 2.4 - Convert 0.44 L of love potion into dLandkL by...Ch. 2.4 - Dr. Phails potion also comes in a 0.75-gallon...Ch. 2.4 - According to the table of equivalences,...Ch. 2.4 - Use the idea from Question 11 to convert your...Ch. 2.4 - Based on what you just did, fill in the blank to...Ch. 2.4 - Explain what is meant when we say a car is...Ch. 2.4 - The entire 450mL of Dr. Phails Love Potion (from...Ch. 2.4 - Simplify the rate you wrote in Question 2 so that...Ch. 2.4 - It might seem like it would be really complicated...Ch. 2.4 - While in production, the love potion needs to be...Ch. 2.4 - Use the appropriate formula to convert 200F to...Ch. 2.4 - Use one of the two formulas provided to convert...Ch. 2.4 - Use a calculator or spreadsheet along with an...Ch. 2.4 - According to the online dosage guide for one brand...Ch. 2.4 - A dosage of 1,700 mg of cefadroxil is to be...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Try this problem to see if you understand the...Ch. 2.4 - Type a short answer to each question. Describe the...Ch. 2.4 - Type a short answer to each question. Whats a...Ch. 2.4 - Type a short answer to each question. Whats a...Ch. 2.4 - Type a short answer to each question. How can we...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - For Questions 1-5, use dimensional analysis with...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.4 - Glaciers are large masses of ice that flow like...Ch. 2.5 - Locate 40, 15, 15, 27, and 2 on the number line.Ch. 2.5 - The pie chart shows the distribution of grades on...Ch. 2.5 - The bar graph shows the number of students that...Ch. 2.5 - The scatter plot shows the final grades for all 31...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - This number line is a timeline of important...Ch. 2.5 - Now well practice estimation using a bar graph....Ch. 2.5 - Prob. 12CCh. 2.5 - Now well practice estimation using a bar graph....Ch. 2.5 - Now well practice estimation using a bar graph....Ch. 2.5 - Another type of graph that we often have to...Ch. 2.5 - Another type of graph that we often have to...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - In Questions 1922, write the statement as an...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - An isotherm is a curve on a map that connects...Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Spend some time thinking about Questions 812....Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Try this problem to see if you understand the...Ch. 2.5 - Reflections Type a short answer to each question....Ch. 2.5 - Reflections Type a short answer to each question....Ch. 2.5 - Prob. 4RCh. 2.5 - According to a survey reported by the Nielsen...Ch. 2.5 - Write the set of described numbers using the...Ch. 2.5 - Shopping provides a really good example of the...Ch. 2.5 - Shopping provides a really good example of the...Ch. 2.5 - Shopping provides a really good example of the...Ch. 2.5 - Estimation is useful for tipping when youre dining...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.5 - This graph shows the violent crime rate in 2014...Ch. 2.6 - Convert each fraction into percent form. a. 1240...Ch. 2.6 - Find the area of a building made up of three...Ch. 2.6 - Using only the fact that 1yd=3ft, convert 10 cubic...Ch. 2.6 - Using only the fact that 12in.=1ft, convert 5,000...Ch. 2.6 - Find the relative change if you win $5,000,000 and...Ch. 2.6 - Compare the relative change for the two scenarios...Ch. 2.6 - Your instructor tells you that youre going to get...Ch. 2.6 - For Questions 4 and 5, write a sentence that...Ch. 2.6 - For Questions 4 and 5, write a sentence that...Ch. 2.6 - For Questions 6 and 7, write a statement using the...Ch. 2.6 - For Questions 6 and 7, write a statement using the...Ch. 2.6 - Suppose that $435 million is spent for...Ch. 2.6 - Suppose that only $440 million is budgeted for...Ch. 2.6 - A news article reports that this program has been...Ch. 2.6 - Write a sentence or two describing the 5.4% cut...Ch. 2.6 - When youre buying carpet, do you want an...Ch. 2.6 - Find the area of the bedroom only in square...Ch. 2.6 - Find the area of the closet in square inches.Ch. 2.6 - Each of the doorways shown is 30 inches wide, and...Ch. 2.6 - What is the total carpeted area? Convert the total...Ch. 2.6 - Write a sentence or two describing how the...Ch. 2.6 - Find the percent error in the estimate. Round to...Ch. 2.6 - Not everyone realizes this, but when you buy...Ch. 2.6 - Use the actual error in the estimate to find the...Ch. 2.6 - One suggestion for estimating carpet is to measure...Ch. 2.6 - List some situations where relative change is a...Ch. 2.6 - Try this problem to see if you understand the...Ch. 2.6 - Try this problem to see if you understand the...Ch. 2.6 - Try this problem to see if you understand the...Ch. 2.6 - Type a short answers to each question. How would...Ch. 2.6 - Type a short answers to each question. Both Shawna...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.6 - Name...Ch. 2.7 - Find the mean of the numbers listed. 23 34 45 56...Ch. 2.7 - The pie chart represents the breakdown of...Ch. 2.7 - In an average year, there is at least some...Ch. 2.7 - Write a verbal description of each interval...Ch. 2.7 - Write an inequality that describes each interval....Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Two golfers were competing in a televised...Ch. 2.7 - Fill in the second column of the table below. Step...Ch. 2.7 - Fill in the third column of the table by squaring...Ch. 2.7 - Find the mean of the values in the third column of...Ch. 2.7 - Find the standard deviation by computing the...Ch. 2.7 - Describe the pattern made by the seed pods, and...Ch. 2.7 - Use the information just given about and to fill...Ch. 2.7 - Based on your diagram, about what percentage of...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Try these problems to see if you understand the...Ch. 2.7 - Type a short answers to each question. Describe...Ch. 2.7 - Type a short answers to each question. What can we...Ch. 2.7 - In Lesson 2-1, you found the mean of the exam...Ch. 2.7 - According to numerous online resources, the mean...Ch. 2.7 - Write an expression of the form P(inequality) that...Ch. 2.7 - In a group of 500 women, how many would you expect...Ch. 2.7 - On one campus, about 95% of students work between...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.7 - For each of the quantities in Questions 69, decide...Ch. 2.8 - There are 52 cards in a standard deck, equally...Ch. 2.8 - When you roll one six-sided die, whats the...Ch. 2.8 - Convert each percentage to decimal form: a. 87 b....Ch. 2.8 - Add the numbers across each of the 10 rows, and...Ch. 2.8 - On average, how much did you win per roll?Ch. 2.8 - Add the answers from Question 2 for every group in...Ch. 2.8 - Congratulations: Youve just found the expected...Ch. 2.8 - What is the probability of getting a 1 when...Ch. 2.8 - What is the probability of getting any individual...Ch. 2.8 - Complete the second column of this table by...Ch. 2.8 - Find the sum of the values in the third column....Ch. 2.8 - Obviously, playing this game for free would ROCK:...Ch. 2.8 - Lets say you were setting up this game somewhere...Ch. 2.8 - If you were charging $2 to play, the outcomes for...Ch. 2.8 - Using the scores provided, find the percentage of...Ch. 2.8 - Use information on the grading scale to fill in...Ch. 2.8 - The points out of 100 earned for each category is...Ch. 2.8 - The overall grade, out of 100, is the sum of all...Ch. 2.8 - What letter grade did Christine earn?Ch. 2.8 - Which category would you say had the most negative...Ch. 2.8 - So lets say that you have the following scores in...Ch. 2.8 - So lets say that you have the following scores in...Ch. 2.8 - So lets say that you have the following scores in...Ch. 2.8 - Whats the net gain if you land on blue? Write your...Ch. 2.8 - Compute and record the probability for each gain...Ch. 2.8 - Calculate and record the product for each X*P(X)....Ch. 2.8 - Whats the expected value? Record in the table,...Ch. 2.8 - A game of chance is called a fair game if the...Ch. 2.8 - A game favors the player if the players expected...Ch. 2.8 - If you played this game 100 times, how much would...Ch. 2.8 - Try these problems to see if you understand the...Ch. 2.8 - Try these problems to see if you understand the...Ch. 2.8 - Prob. 3DYGICh. 2.8 - Prob. 4DYGICh. 2.8 - For all but one bet in standard American roulette,...Ch. 2.8 - Betting on 0, 00, 1, 2, and 3 in roulette has an...Ch. 2.8 - What makes a grading system weighted?Ch. 2.8 - Name one thing you learned or discovered in this...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Below are the grades that our friend Christine...Ch. 2.8 - Next, well study a traditional carnival game that...Ch. 2.8 - Find the expected value of this game. The table,...Ch. 2.8 - Would you prefer to be the player in this game, or...Ch. 2.8 - What should the player expect to happen if he...Ch. 2.8 - The grading structure for my Calc 2 class last...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Carefully read through the list of terminology...Ch. 2 - Compute the mean, median, and mode for the lengths...Ch. 2 - A prepaid calling card starts with a value of $40....Ch. 2 - Compute the standard deviation for the lengths of...Ch. 2 - The table shows the number of points possible on...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - Consider the table showing points earned on exam 1...Ch. 2 - According to www.boeing.com/, the Boeing 747...Ch. 2 - Use your calculator or a spreadsheet to complete...Ch. 2 - How many gallons would be remaining after 1,000...Ch. 2 - How many miles were flown if there were 56,000...Ch. 2 - Write a sentence or two using the terms input,...Ch. 2 - Which is most likely the correct way to compute...Ch. 2 - The formula A=r2 can be used to find the area of a...Ch. 2 - The formula V=r2h can be used to find the volume...Ch. 2 - In Questions 15 and 16, simplify each expression....Ch. 2 - In Questions 15 and 16, simplify each expression....Ch. 2 - Determine the number of cups that are in a 2-liter...Ch. 2 - Determine the speed in inches per second of a...Ch. 2 - A 5-k race is 5 kilometers long. How long is that...Ch. 2 - Convert 68 Fahrenheit to Celsius.Ch. 2 - Write a brief summary of Polyas 4-step...Ch. 2 - If in a typical month your cell-phone bill is...Ch. 2 - A seven-passenger van can transport at most seven...Ch. 2 - On March 1, 2017, the Dow Jones Industrial Average...Ch. 2 - If a jet was fueled with 68,000 lbs of fuel and...Ch. 2 - Runners often keep a training log to keep track of...Ch. 2 - Runners often keep a training log to keep track of...Ch. 2 - Runners often keep a training log to keep track of...Ch. 2 - It has been reported that credit card debt for...Ch. 2 - Write an expression that describes the probability...Ch. 2 - Use the empirical rule to find P(2,162x5,462) and...Ch. 2 - Suppose you decide to set up a simple dice-rolling...Ch. 2 - Suppose you decide to set up a simple dice-rolling...Ch. 2 - The grading structure for a Stats course is...
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