Linear Modeling and Logic Unit


Linear Modeling and Logic Review


  1. Write a linear equation for the cost of leasing a car with a $1000 down payment and a $360 per month charge.

    2. y = 360x + 1000

  2. State and interpret the rate of change shown in the graph:
    3. A linear graph that is decreasing from left to right. The x-axis represents the hours and goes from 0 to 8 counting by 1. The y-axis represents the money in the wallet and goes from 0 to 50 counting by 10. Two points on the graph are (0,50) and (8,0).

    The money in the wallet decreases by $6.25 per hour spent at the casino

  3. Write the equation of the line shown in the graph:
    4. A linear graph that is increasing from left to right. The x-axis represents the years and goaes from 0 to 6 counting by 1. The y-axis represents the profit in dollars and goes from -15000 to 20000 counting by 5000. Two points on the line are (0,-10000) and (6,20000).

    y = 5000x - 10000

  4. The U-Haul in Knoxville charges $39.95 for a 20 foot moving truck plus $0.89 per mile that a customer drives the truck over one weekend. Write a linear equation that models the total cost of the truck for one weekend.

    5. Equation:

    y = 0.89x + 39.95

  5. Joseph spent his vacation time in Kalamazoo, Michigan, a distance of 552 miles from his home. He drives home at an average speed of 55 mph.
    1. What is the independent variable and the dependent variable in this scenario.

      2. Independent variable - time in hours

      Dependent variable - distance from home in hours

    2. Write an equation that models the distance Joseph is from home relative to the amount of time he has been driving.

      3. y = 552 - 55x

    3. How far from home is Joseph if he has been driving for 7 hours?

      4. 167 miles

    4. How long will it take Joseph to get home?

      5. approximately 10 hours

  6. A 3-month-old Australian Shepherd female puppy weighed 12 pounds. When she was 3 years old, she weighed 45 pounds. Find the average rate of change and explain its meaning within the context of this scenario.

    7. The rate of change is equal to 1. The puppy was gaining one pound per month.

  7. How many doctors who are over 35 work at the hospital?

    8. 150

    A Venn Diagram titled with two intersecting circles. One circle represents the number of doctors and the other circle represents the number of staff who are under 35. The number 20 is in the intersection of the circles. The number 150 is in the doctors circle and the number 275 is in the under 35 circle. The number 162 is outside both circles.

  8. Draw a Venn diagram to represent the following information: A survey asked 100 people what kind of movies they like to watch. The results: 53 like comedies 50 like fantasy movies 60 like romantic movies 25 like comedy and fantasy 28 like romantic and fantasy 30 like comedy and romantic 5 like all three

    A Venn Diagram with three intersecting circles. The top circle is labeled Comedies. The bottom left is labeled Fantasy, and the bottom right is labeled Romantic. The intersection of the 3 circles in the middle has 5 in it. The intersection of only romantic and fantasy has 23, only fantasy and comedies has 20 and only comedies and romantic has 25. The parts of the diagram with no intersection have 7 for romantic, 2 for fantasy, and 3 for comedies. There are 15 outside the diagram.

    1. How many only like comedies?

      3

    2. How many like fantasy or comedy?

      78

    3. How many like comedy and romantic but not fantasy>

      25



  9. Test the validity of the following argument with a Venn diagram:

    10. Premise: If an employee is regularly late, then the employee will be fired.

    Premise: Sharon was fired.

    Conclusion: Sharon was regularly late.

    Is the argument valid or invalid?

    A Venn Diagram with one small circle completely inside a large circle. The large circle represents that the employee is fired. The small circle represents that the employee is regularly late. There is an X inside the regularly late circle. There is an X inside the fired circle that is not in the regularly late circle.

    The argument is invalid.

  10. Test the validity of the following argument with a Venn diagram.

    11. Premise: Some Pellissippi State students participate in the study abroad program.

    Premise: Angela participated in the study abroad program.

    Conclusion: Angela is a Pellissippi State student.

    Is the argument valid or invalid?

    A Venn Diagram with two intersecting circles. One circle represents PSCC students and the other circle represents participating in study abroad. There is an X in the intersection of the two circles. There is another X inside the study abroad circle only.

    The argument is invalid.

  11. Test the validity of the following argument with a Venn diagram.

    12. Premise: All red meat contains iron.

    Premise: Prime rib is red meat

    Conclusion: Prime rib contains iron.

    Is the argument valid or invalid?

    A Venn Diagram with a small circle completely inside a large circle. The large circle represents containing iron. The small circle represents red meat. There is an X inside the red meat circle.

    The argument is valid.

    For problems 12-15, identify if a logical fallacy was used in the argument; explain.

  12. The Wyoming toad has not been seen outside of captivity since 2002, so it must be extinct in the wild.

    13. Fallacy (Appeal to Ignorance); the toad may be good at hiding.

  13. After Will said that we should put more money into health and education, Warren responded by saying that he was surprised that Will hates our country so much that he wants to leave it defenseless by cutting military spending.

    14. Fallacy (Straw Man); Will did not say he wanted to decrease military funding.

  14. Every time I go to sleep, the sun goes down. My sleeping must cause the sun to set.

    15. Fallacy (Correlation Implies Causation); The sun would still set even if the person stayed awake all night.

  15. Jason told his friends that they should not swim in the river because there is a sign that says the river is contaminated by mercury.

    16. Reasonable argument

    Determine the truth value for the statements in problems 16-20.

  16. The sky is blue and grass is purple.

    17. False

  17. Pellissippi State Community College has a campus in Blount County or a campus in Anderson County.

    18. True

  18. Milk is a dairy product or yogurt is a dairy product.

    19. True

  19. Dogs are in the canine family and cats are in the feline family.

    20. True

  20. (Background information: Becky took out the kitchen trash and her mom gave her $1.00.) Statement by Becky’s mom: If you take out the trash, then I’ll give you a $5.00 allowance.

    21. False