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Aufmann - Quantitative Reasoning 2/e (Homework)

James Finch

Math - Developmental, section A, Fall 2019

Instructor: Dr. Friendly

Current Score : 27 / 62

Due : Monday, December 30, 2030 23:59 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10 11 12
3/3 –/3 0/1 0/1 1/1 9/16 –/7 –/11 0/1 –/4 9/9 5/5
Total
27/62 (43.5%)

  • Instructions

    Aufmann's Discovering Mathematics: A Quantitative Reasoning Approach 2nd edition with WebAssign, written by Richard Aufmann and published by Cengage Learning, is designed for today's Quantitative Reasoning course. By focusing on topics relevant to students and helping them develop critical-thinking skills they can apply beyond the course, this solution provides students with exactly what they need, in an approachable, engaging, and streamlined format. Customizable for use in all teaching models—from lecture, hybrid, or fully online to flipped and active learning environments—Discovering Mathematics: A Quantitative Reasoning Approach will empower you to accomplish all your course objectives.

    This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    WebAssign provides a wide range of exercises that enable you to:

    • Build Student Confidence and Growth Mindset (#1-5: College Success, Math Mindset, Read It, Watch It, Preliminary Question)
    • Engage Students in the Learning Process (#6-8: Responsive Labs, Project, Math in Practice)
    • Develop Conceptual Understanding (#9-13: Learn It, Master It Tutorial, Master It Tutorial Standalone, Expanded Problem, Investigation)

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 3/3 points  |  Previous Answers mathsuccess1 3.9.003.defective My Notes
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1/1 1/1 1/1
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  • This exercise will build student confidence and growth mindset.
  • College Success Modules help students practice key foundational skills for effective learning by introducing a topic followed by a set of reflective questions to help students understand the concept and how it applies to their education.

The Process of Decision Making
Imagine that you are choosing your college major. It is unlikely that you would make such a big decision by randomly choosing the first subject that you come across. Rather, you would probably determine your interests and life goals, take a diverse set of classes, and meet with a college guidance counselor to weigh your options before arriving at a decision. Effective critical thinkers identify problems and make decisions by following a series of steps. These steps guide you through the decision-making process and enable you to see all sides of an issue before you arrive at a final decision.
The following table outlines the five steps that critical thinkers follow when identifying a problem and making a decision. It also presents scenarios about Maria, a nursing student who is considering buying a car. As you go through the steps and scenarios, notice how Maria uses critical thinking skills to identify the problem and arrive at a decision that solves the problem.
  • What is the problem that needs to be solved? Consider the issue in the following scenario.
    Maria is a nursing student. She does not own a car and relies on public transportation to get to and from campus. However, the bus does not always arrive on time, which makes her late for class. Sometimes she misses class entirely.
    What is the problem? Maria's mode of transportation is unreliable.
  • Ask yourself questions to gather the information necessary to make an informed decision. Consider the questions that Maria came up with.
    • What alternatives are there to public transportation?
    • Can I borrow my parents' car?
    • Can I invest in my own car?
    • Can I bike or walk to campus?
    • Can I ask a classmate for a ride?
  • Determine the options that are available to you. Take a look at the options that Maria came up with.
    • Option 1: Borrow my parents' car. They are willing to lend me the car two days a week. But I will still have to find alternative transportation for the other three days of class.
    • Option 2: Invest in my own car. I can use my savings as a down payment. But I will have to determine whether I can afford monthly payments.
    • Option 3: Get a ride from my classmate three days a week. But I will still have to find alternative transportation for the other two days of class.
  • When you take action, you make your choice. Review your options, and make a decision based on the information you have gathered from the previous steps in the decision-making process. Take a look at the decision Maria made.
    I can combine Options 1 and 3. I will borrow my parents' car two days a week and ride with a classmate for the other three.
  • Finally, review your decision and examine the consequences. Did you make the right decision? Or do you need to begin the process all over again? Let's look at Maria's review of her decision.
    I feel like I made the right decision. I am able to get to campus much more quickly. As a result, I am no longer late to class. I have not missed any classes, either.
Read about Felix, and help him in identifying the problem, gathering information by asking questions, identifying his options, and choosing the best option to address his problem
Halfway through the semester, Felix's car broke down. This made it much harder for him to commute to an off-campus work location and back to school.
In addition, Felix's roommate has been a major distraction. When Felix asks his roommate to try to be more quiet, the request is met with anger, and the two argue, sometimes late into the night. Normally he could handle the distractions, but this semester he is struggling in a calculus course, and there's a major midterm approaching that promises to be the most difficult exam he has ever taken. Furthermore, Felix must keep up his grades, or he risks losing his scholarship, and Felix's parents cannot afford to help him out financially.
What is the problem that needs to be solved?
     Correct: Your answer is correct.
Which of the following questions would best help Felix gather information related to his problem? Select all that apply.
Correct: Your answer is correct.

Once Felix has defined the problem and gathered information, it is time to generate possible options for solving the problem. Consider the three lists of options, and pick the best list.
List 1 List 2 List 3
  1. Call the towing company, and get the car fixed.
  2. Find public transportation to and from work.
  3. Make a schedule that accounts for extra time on public transit.
  4. Visit calculus instructor during office hours with questions about the midterm.
  5. Make a study schedule to prepare for the midterm.
  6. Try once more to reason with roommate; if discussion does not go well, research options for finding a new place to live, considering dorm policy and moving costs.
  1. Sell the car for extra cash.
  2. Get a friend to drive you around.
  3. Do calculus homework while at off-campus job
  4. Tell your boss you might be late a few times because of the car.
  5. Tell the roommate to shape up or move out.
  1. Try to fix the car yourself.
  2. Find public transportation to and from work.
  3. Make a schedule that accounts for extra time on public transit.
  4. Visit calculus instructor during office hours to explain why you're not doing well.
  5. Study calculus at work.
  6. Leave notes for roommate so you don't have to talk.
Correct: Your answer is correct. seenKey

List 1
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2. –/3 points mathsuccess1 1.1.001.defective My Notes
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–/3
 
  • This exercise will build student confidence and growth mindset.
  • Math Mindset Modules prepare students for challenging math topics with interactive and reflective exercises on relevant topics.

What Is Growth Mindset?

Watch the following video about Growth Mindset vs. Fixed Mindset.
Passion Over Approval
One of the key differences between the two mindsets is the idea of seeking approval. Those with a fixed mindset compare themselves against others when it comes to their ability and intelligence. They put high value on their grades because, to them, grades prove their intelligence. Being at the top of the class makes them feel smart, and they see good grades as a result of their natural intelligence. On the other hand, having others perform better than them causes them to feel inferior. In addition, if they try their hardest and still do not perform as well as others, they are more likely to give up.
If someone with a growth mindset is outperformed by their peers, they understand that it was likely because they need to put more work into their studies. They ask themselves how they can do better next time. There is nothing hard work cannot fix when it comes to their ability and knowledge. If they perform well, they know it reflects their effort, not their intelligence.
Comparing Growth and Fixed Mindsets in Math and Stats Class
The following accordion sections describe how you can approach challenges in your math and stats classes with a fixed mindset and growth mindset.
  • Scenario: You are working through an exam prep test and you encounter a word problem. You attempt the problem and it takes you a good chunk of time. You check an answer key and discover you got it wrong.
    Fixed Mindset: You give up on the problem or ask a classmate for their solution to see how they got their answer. You also put the question in a search engine and find the full solution online.
    Growth Mindset: You review your work and compare your steps with similar problems from class. You move on to other questions and return to the word problem later. You cover up your previous attempt and try again. If you are still stuck, you consult a classmate on a step, but not the entire process.
  • Scenario: Your instructor is presenting a concept, and halfway through the lecture, you find that you are completely lost.
    Fixed Mindset: You shut down and give up on the lecture. Your immediate thought is that the instructor is not explaining it well, but you do not ask questions. You may ask a classmate for their notes after class, but for the rest of your lecture, you sit there and let your attention drift.
    Growth Mindset: You immediately ask your instructor questions about what confused you. You keep working through the lecture in hopes that something is explained in a different way later on. If you end up being lost at the end of the lecture, you make an appointment to go to your instructor's office hours.
  • Scenario: You get your exam back and you see that you got a 60%. You thought you knew—really, really knew—the material going into it. Many questions have red Xs, and there are comments written next to the incorrect questions.
    Fixed Mindset: You figure you thought you knew it and it is clear you were not smart enough. You put the test in your desk drawer and never speak of it again.
    Growth Mindset: You bring your exam home and rework the questions you got incorrect. For questions you are stumped on, you make an appointment with your instructor during their office hours and ask clarifying questions about where you went wrong.
If you are worried that you have a fixed mindset, remember that the most important lesson is that mindsets can change. Approaching challenges and criticism from a different angle can help you learn from mistakes and reach higher levels of success.
📖 Journal Questions
Answer the following questions honestly to get yourself thinking about your own mindsets.
How would you describe your mindset about math? Is it a growth mindset or a fixed mindset? Do you have different mindsets for different types of math?

This answer has not been graded yet.

Describe a time when you put in effort to learn something difficult.

This answer has not been graded yet.

Identify at least one aspect of a growth mindset (i.e., approaching challenges, taking criticism, etc.) that you are going to focus on this semester.

This answer has not been graded yet.

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3. 0/1 points  |  Previous Answers AufQR2 2.1.022. My Notes
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  • This exercise will build student confidence and growth mindset.
  • Read It links are available as a learning tool under each question so students can quickly jump to the corresponding section of the eTextbook.

Find the complement of the set given that
U = {0, 1, 2, 3, 4, 5, 6}.
 (Use the roster method to write the set. Enter EMPTY or ∅ for the empty set.)
{composite numbers}
{1,2,3,5}
Incorrect: Your answer is incorrect. \{$ans\}
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  • This exercise will build student confidence and growth mindset.
  • Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.

Find the complement of the set given that
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
 (Use the roster method to write the set. Enter EMPTY or ∅ for the empty set.)
{prime numbers}
{4,6,8,9}
Incorrect: Your answer is incorrect. \{$ans\}

Need Help? Watch It

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5. 1/1 points  |  Previous Answers AufQR2 1.3.P.007. My Notes
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  • This exercise will build student confidence and growth mindset.
  • Preliminary Questions test students' understanding of concepts by providing an opportunity to work an exercise closely related to an example in the section.

Two U.S. coins have a total value of 30¢. One of the coins is not a quarter. What are the two coins? (Select all that apply. See Example 7 in this section.)
Correct: Your answer is correct.

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6. 9/16 points  |  Previous Answers AufQR2 4.Lab.001. My Notes
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1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
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9/16
 
  • This exercise will engage students in the learning process.
  • Responsive Labs provide learners with opportunities to think about and use the mathematics they are learning in various ways outside of the classroom by providing a real-life application that adapts to the data that students have provided.

Dream vs. Reality: Financing a Car

  • Overview

    We all have a dream car, but just how practical is it to own? For this project, you will find the monthly payments and interest on a dream car and those on a more practical choice. You will then compare your results to see which option best fits your budget.

  • Materials

    • Calculator (scientific or graphing)
    • Car advertisements (optional)

  • Procedure Part 1

    Think of your dream car. Think big, think luxury, and don't skimp on the features. If you can't think of one, ask a friend or family member if they have one in mind. Once you decide on a make and model, research the cost of it (with all desirable features included, i.e., stereo, leather interior, etc.). Don't worry about finding the most affordable option for your dream car. Splurge away!
    What is the Make and Model of your dream car?

    Key: Answers may vary.

    Score: 1 out of 1

    Comment:

    What is the price of your dream car? If your dream car price is less than $85,000, enter 85,000. If you dream car price is more than $150,000, enter 150,000. Otherwise, enter the exact price of your dream car rounded to the nearest dollar. (This value will be used to make later calculations.)
    $ Correct: Your answer is correct. seenKey

    150000

         Your value is acceptable.

  • Procedure Part 2

    Now, think of a more practical car choice. Consider new vehicles that cost between $10,000 and $45,000. Have or plan to have a family? Choose one that will accommodate them. Have or plan to have a pet? Figure that into your decision. Keep in mind what you'll need this car for (e.g., groceries, traveling, mileage). Once you decide on one, research three different options for costs from three different car dealerships.
    What is the Make and Model of your practical car choice?

    Key: Answers may vary.

    Score: 1 out of 1

    Comment:

    Rounding to the nearest dollar, enter three prices from three different car dealerships for this car. (All prices must be between $10,000 and $45,000. These values will be used to make later calculations.)
    Price 1 $ Correct: Your answer is correct. seenKey

    45000

         Your value is acceptable.     Price 2 $ Correct: Your answer is correct. seenKey

    37000

         Your value is acceptable.     Price 3 $ Correct: Your answer is correct. seenKey

    39000

         Your value is acceptable.

  • Procedure Part 3

    Find the average cost using the three car prices found in Part 2. (If necessary, round your value to the nearest cent.)
    $ Correct: Your answer is correct. seenKey

    40333.33
    For the duration of this project, the values you enter for your sample calculations should exactly match the corresponding values you entered above for the price of the dream car and the practical car average. If necessary, round your answers to the nearest cent.

  • Procedure Part 4

    Some annual simple interest rates for a car loan are listed in the table below.
    36 Months 48 Months 60 Months 72 Months
    Bank 1 3.28% 3.28% 3.26% 3.36%
    Bank 2 2.71% 2.71% 2.71% 3.34%
    Pick a bank and rate from the table above. The bank rate you choose will be used for the duration of this project.
    The loan will be from Correct: Your answer is correct. with a duration of Correct: Your answer is correct. months.
    Use the loan information and the interest rate formula to determine the total interest for each car.
    Dream Car $ Practical Car $

  • Procedure Part 5

    Using the total price and the total interest calculated in part 4, determine the monthly payment for each car.
    Dream Car $ Practical Car $

  • Procedure Part 6

    Assume you have a yearly income of $55,000. Determine what your remaining monthly income would be in both scenarios: after paying for your dream car and your real car.
    Dream Car $ Practical Car $

  • Procedure Part 7

    Is your remaining monthly income enough to live off of and cover your other monthly expenses? Considering food, rent, and other necessary expenses, use complete sentences to examine both car choices.

    This answer has not been graded yet.

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7. –/7 points AufQR2 7.PJT.001. My Notes
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  • This exercise will engage students in the learning process.
  • Short Projects and Investigations (PJT) are activities taken from the text that provide good opportunities for group work and class discussion. These activities guide students on how to navigate and organize their work.

Keno

The casino game keno is played by choosing numbers from 1 to 80 with hopes that the casino will draw balls with the same numbers. A player can choose exactly 1 number or as many as 20. The casino will then pick 20 numbered balls from the 80 possible. If enough of the player's numbers match the lucky numbers the casino chooses, the player wins money. The amount won varies according to how many numbers were chosen and how many are "lucky." (Round your answers to the eight decimal places.)
(a)
A gambler playing keno randomly chooses five numbers. What is the probability that the gambler will match at least one lucky number?
(b)
If five numbers are chosen, compute the probability of matching fewer than five lucky numbers.
(c)
Suppose if the keno player chooses 15 numbers, bets $1, and matches 11 of the lucky numbers, the gambler will be paid $12,000. What is the probability of this occurring?
(d)
Suppose if the keno player chooses 15 numbers and matches 6 or 7 of the lucky numbers, the gambler gets the bet back but is not paid any extra. What is the probability of this occurring?
(e)
Some casinos will let you choose up to 20 numbers. In this case, if you don't match any of the lucky numbers, the casino pays you! Although this may seem unusual, it is actually more difficult not to match any of the lucky numbers than it is to match a few of them. Compute the probability of not matching any of the lucky numbers at all, and compare it to the probability of matching five lucky numbers.
not matching any lucky numbers matching five lucky numbers
(f)
If 20 numbers are chosen, find the probability of matching at least one lucky number.
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8. –/11 points AufQR2 5.MIP.001. My Notes
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0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/11
 
  • This exercise will engage students in the learning process.
  • Math in Practice exercises expand on chapter learning objectives with real-world, applicable situations students can relate to in their daily lives, or their intended career tracks.

In medicine, it seems like common sense that the amount of medication a child requires is much smaller than the amount of medication an adult requires. In fact, the value for a child's dose of medication is based on their body surface area, BSA, which is given in square meters. Some nurses are given the responsibility of calculating a child's dose of medication. The formula for finding the body surface area is based on height and weight, which are measured by a nurse at a medical appointment.

  • Part 1

    The formula for body surface area, BSA, for a child weighing 101 pounds is
    BSA = 
    h
    31
    ,
    where h is the child's height in inches. Suppose a child weighing 101 pounds is 56 inches tall. What is the child's BSA? (Round your answer to two decimal places.)
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9. 0/1 points  |  Previous Answers AufQR2 3.2.006. My Notes
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1
0/1
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0/1
 
  • This exercise will develop conceptual understanding.
  • Learn It modules address your students' knowledge gaps with just-in-time instruction. Learn Its provide targeted instruction and practice on that topic using narrative, videos, and tutorials all in one place. If the topic is still too challenging, students can choose to continue learning through associated prerequisite Learn Its.

Convert between the two measurements.
7,000 lb = _____ tons
Incorrect: Your answer is incorrect. seenKey

3.5

 tons
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10. –/4 points AufQR2 8.5.003.MI. My Notes
Question Part
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1 2 3 4
–/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100
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–/4
 
  • This exercise will develop conceptual understanding.
  • Master It tutorials are an optional student-help tool available within select questions for just-in-time support. Students can use the tutorial to guide them through the problem-solving process step-by-step using different numbers.

The following table gives retail values of a 2017 Corvette for various odometer readings.
Odometer Reading Retail Value ($)
13,000 52,375
18,000 51,625
20,000 51,200
25,000 50,525
29,000 49,775
32,000 49,075
(a)
Find the equation of the least-squares line for the data. (Where odometer reading is the independent variable, x, and retail value is the dependent variable. Round your numerical values to two decimal places.)
ŷ =
(b)
Use the equation from part (a) to predict the retail price of a 2017 Corvette with an odometer reading of 28,000. Round to the nearest $100.
$
(c)
Find the linear correlation coefficient for these data. (Round your answer to four decimal places.)
r =
(d)
What is the significance of the fact that the linear correlation coefficient is negative for these data?
The variables are negatively correlated, which means that as the odometer reading goes up, the retail value goes .

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11. 9/9 points  |  Previous Answers AufQR2 5.2.013.MI.SA. My Notes
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1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
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9/9
 
  • This exercise will develop conceptual understanding.
  • Master It tutorials—Standalone are embedded, step-by-step tutorials used to help students understand each step required to solve the problem, before inputting their final answer.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
The following graph shows the relationship between the distance traveled by a motorist and the time of travel.
A line is on the x y coordinate plane. The x-axis is labeled "Time (hours)," and the y-axis is labeled "Distance (miles)." The line begins at the origin, goes up and to the right, passes through the points (3, 75) and (6, 150), and exits the right of the viewing window.
Find the slope of the line between the two points shown on the graph.
Write a sentence that states the meaning of the slope in the context of this application.
Step 1
To find the slope of the line through two points
(x1, y1)
 and
(x2, y2),
 we find the ratio of the change in the y-coordinates to the change in the x-coordinates using the following formula:
m = 
y2 − y1
x2 − x1
Using the labeled points on the graph, if we let
(x1, y1) = (3, 75),
 then
(x2, y2) = 
$$6,150
Correct: Your answer is correct. webMathematica generated answer key
.
Step 2
Use the slope formula to find the slope between
(x1, y1) = (3, 75)
 and
(x2, y2) = (6, 150).
m = 
y2 − y1
x2 − x1
 
 = 
150 − 75 Correct: Your answer is correct. seenKey

75
6 − 3
 
 = 
75 Correct: Your answer is correct. seenKey

75
3
 
 = 25 Correct: Your answer is correct. seenKey

25
Step 3
The slope of the line between the two points given in the graph is 25.
Since the slope is a ratio of two quantities, the units associated with the slope will also be a ratio.
A line is on the x y coordinate plane. The x-axis is labeled "Time (hours)," and the y-axis is labeled "Distance (miles)." The line begins at the origin, goes up and to the right, passes through the points (3, 75) and (6, 150), and exits the right of the viewing window.
The x-coordinates on the graph represent the time of travel using the unit hr Correct: Your answer is correct. seenKey

hr

 .
The y-coordinates on the graph represent the distance the motorist traveled using the unit mi Correct: Your answer is correct. seenKey

mi

 .
Therefore, this slope calculation represents the change in distance (y-coordinates) divided by the change in time (x-coordinates) of the motorist using the unit mi/hr Correct: Your answer is correct. seenKey

mi/hr

 .
The motorist was traveling at the rate of 25 Correct: Your answer is correct. seenKey

25

 mi/hr Correct: Your answer is correct. seenKey

mi/hr

 .
You have now completed the tutorial.
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12. 5/5 points  |  Previous Answers AufQR2 1.1.001.EP. My Notes
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1/100 1/100 1/100 1/100 1/100
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5/5
 
  • This exercise will develop conceptual understanding.
  • Expanded Problems enhance student understanding by going beyond a basic exercise and asking students to solve each step of the problem in addition to their final answer.

Consider the following sequence.
1, 4, 9, 16, 25, 36, 49, 64, ?
Inspect the sequence and complete the following statement.
The first two numbers differ by Correct: Your answer is correct. seenKey

3

 . The second and third numbers differ by Correct: Your answer is correct. seenKey

5

 . The third and fourth numbers differ by Correct: Your answer is correct. seenKey

7

 . The difference between any two successive numbers always seems to be Correct: Your answer is correct. seenKey

2

 more than the preceding difference.
Use inductive reasoning to predict the missing number in the sequence.
Correct: Your answer is correct. seenKey

81
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