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Math 181: Final Test

This test may be taken with a calculator and any number of hand-written notes. Computers or books and other printed material, be they copies, printouts, or typed, are not allowed.
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Solve each of the following systems of linear equations.

____________________ 1.
____________________ 2.
Roger has recorded the time he spent on an exercise bike and the the number of watts he generated while on the bike for each of 7 days. He believes that there is a linear relationship between time and watts such that he could express the number of watts generated as a linear function of the time he spent on the bike. Use the data given below to produce the regression equation expressing watts as a linear function of time. Express your answers to 4 decimal places.
____________________ 3.
____________________ 4. For the data given in problem 3, give the correlation coefficient of the regression equation that you produced as the answer to problem 3. (Give your answer rounded to 4 decimal places.)
____________________ 5. For the data and your answer for problem 3, use the regression equation to produce the expected value of watts at time

Use the following matrices to do the following problems:

____________________ 6.
____________________ 7.
____________________ 8.
____________________ 9.

____________________ 10.-13.
____________________ 14.
____________________ 15.
____________________ 16.
____________________ 17.
____________________ 18.
____________________ 19.
____________________ 20.
____________________ 21.
____________________ 22.
____________________ 23.
____________________ 24.
____________________ 25.
____________________ 26.
____________________ 27. For the following two sets

choose the strongest correct statement from the selections below:
  1. A B
  2. A B
  3. B A
  4. B A
  5. B and A are disjoint

____________________ 28. The statement "" is correctly symbolized by which statement below:
  1. D E
  2. D E
  3. D E
  4. E D
  5. E D
____________________ 29. For the sets which of the following is true?
  1. 4 F and 4 G
  2. 4 F and 4 G
  3. 4 F and 4 G
  4. 4 F and 4 G
  5. none of the above
____________________ 30. For the sets which of the following is true?
  1. 36 F and 36 G
  2. 36 F and 36 G
  3. 36 F and 36 G
  4. 36 F and 36 G
  5. none of the above
____________________ 31. For the sets which of the following is true?
  1. 27 F and 27 G
  2. 27 F and 27 G
  3. 27 F and 27 G
  4. 27 F and 27 G
  5. none of the above

____________________ 32. Which of the choices given below make both of the statements
correct?
  1. A={2,6,9}   B={2,4,6,8}   C={3,6,9}
  2. A={2,3,6,9}   B={2,6,8}   C={3,4,6,8}
  3. A={2,6,8}   B={2,4,6,8}   C={2,3,6,9}
  4. A={2,4,8,9}   B={2,3,6,8}   C={2,4,6,9}
  5. A={4,8,9}   B={2,4,6,9}   C={2,3,6,8}
____________________ 33. Given the following sets:
Which of the following is true?
  1. AB     CD     AC
  2. AB     BC     CD
  3. AB     BC     CD
  4. AB     BC     CD
  5. AB     BC     CD
The following table shows the sales of products A, B, C, D, and E over the years 2005 through 2009. Questions 34 and 35 make reference to this chart.
2005 2006 2007 2008 2009 Total
One of these products is being sent back to us for inspection.
____________________ 34.
____________________ 35.
____________________ 36.

The following table gives the probabilities of four events A, B, C, and D along with the probabilites of the various intersections. Questions 37 through 42 make reference to this chart.

____________________ 37.
____________________ 38.
____________________ 39.
____________________ 40.
____________________ 41.
____________________ 42.
Use the following TABLE 1 for the next 3 problems:
____________________ 43. Find the mean of the values in Table 1 above:
____________________ 44. Find the median of the values in Table 1 above:
____________________ 45. Find the population standard deviation of the values in Table 1 above:

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©Roger M. Palay     Saline, MI 48176     December, 2011