7) The population of the city varies indirectly with the water usage. City A has a population of 325,000 people and uses an average of 38,925,000 gallons of water per day. How many people are serviced within City B that produces 65,500,000 gallons of water per day?
8) Michael wins $500,000 (after taxes) in the lottery and decides to invest half of it in a 5-year CD that pays 6.95% interest compounded monthly. He invests the other half in a money market fund that retirement account that averages 3.5% interest compounded continuously over the 5-year period. How much money will he have altogether in the two accounts at the end of the 5-year period?
9) Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither. Show all work and explain your conclusion fully.
10) The average annual tuition and fees at all 4-year institutions in the US in 2002 was $17,800 and in 2011 was $ 24,600. Let y be the average tuition and fees in the year x, where x = 0 represents the year 2002.
a) Write a linear equation, in slope-intercept form, that models the growth in average tuition and fees at all 4-year institutions in the US in terms of the year x.
b) Use this equation to predict the average tuition and fees at 4-year institutions in the US in the year 2025.
c) Explain what the slope of this line means in the context of the problem.
11) Given the equation –x – 4y = 8:
a) Rewrite the equation in slope-intercept form.
b) Write an equation in point-slope form of the line through the point (-3, 1) perpendicular to the line with the equation given above.
c) Convert the equation found in part (c) to slope-intercept form.
d) Convert the equation found in part (c) to standard form, Ax + By = C, where A, B, and C are integers.
e) Graph both lines on one coordinate system. You may use the grid below or create your own.
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12) Show all work as you perform the indicated operations and simplify the result:
13) Show all work as you perform the indicated operations and simplify the result. Write the answer with positive exponents only.
14) Show all work as you perform the indicated operations and simplify the result:
15) Show all work as you multiply the polynomials and simplify the result:
End of exam: please do not forget to write and sign (or type) the required statement explained on Page 1 of the exam.
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Math012MidtermExam.docx
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