1. Find the sum of the first 5 terms of the geometric series.
2. Find the product, if possible.
3. A contractor has 150 feet of fencing with which to fence a rectangular parking lot. If the lot is feet long, express the area of the parking lot as a function of the length.
4. Solve the equation:
5. Find the zeros of the polynomial function and state the multiplicity of each.
6. In 1998, a DVD player sold for about $450.00. In 2005, the average price was $50.00. What is the average rate of change in price per year?
7. An astronaut on the moon throws a baseball upward. The astronaut is 6 feet, 6 inches, tall and the velocity of the ball is 30 feet per second. The height of the ball is approximated by the function defined by where is the number of seconds after the ball was thrown. How many seconds will it take for the ball to return to the surface?
8. Graph Make sure you label the
9. Find the domain of the function.
10. Solve the equation. If necessary, round to the nearest thousandths.
11. Find the future value of at 5% compounded semiannually for 9 years.
12. How long will it take for $5000 to grow to $8400 at an interest rate of 6% if interest is compounded continuously? Round to the nearest tenth.
13. Solve for the indicated variable.
14. Use the graphing calculator to graph the piecewise defined function.
16. Find the vertex of the parabola given
17. Factor into linear factors given that is a zero of
18. Find the logarithm using the common logarithms and the change-of-base formula. Round to the nearest thousandths.
19. Evaluate the determinant:
20. Graph the solution set of the given system of inequalities.
21. Find the first six terms of the sequence.
22. Evaluate the series:
23. Find the equation of the inverse of if it is a one-to-one function.
24. Solve the equation:
25. Write the expressions as a sum, difference, or product of logarithms. Assume that all variables represent positive real numbers.
26. Write the system of equations that corresponds to the augmented matrix.
27. For the following arithmetic sequence, find
28. Find the sum of the first terms of the given arithmetic series.
29. Evaluate the series:
30. Write the binomial expansion of the expression:
31. In a typical diabetic, the level of insulin might be given by the following, where is the blood sugar level, in appropriate units, at time measured in hours from the time of injection.
Suppose a patient takes insulin at 6 AM. The blood sugar at 10AM is what?
32. The world population reached 6 billion people in 1999. The exponential function
approximately projects the world population (in billions of people) years after 1999. According to this function in how many years will the world population reach 8 billion?
33. Graph the equation:
34. Determine visually whether the function is even, odd, or neither.
35. Find the vertical and horizontal asymptote(s) for the following function:
36. Simplify. Write answers in the form where and are real numbers.
37. Find when
38. Write the equation of a line. Give answers in standard from. Hint: Use point-slope formula. Given: x-intercept (3, 0) and y-intercept (0,-2)
39. Write the equation of the line thru the given point and perpendicular to the vertical line.
thru (-5,6), perpendicular to
40. A 3-oz serving of roasted, skinless chicken breast contains 140 Cal, 27 g of protein, 3 g of fat, 13 mg of calcium, and 64 mg of sodium. One-half cup of potato salad contains 180 Cal, 4 g of protein, 11 g of fat, 24 mg of calcium, and 662 mg of sodium. One broccoli spear contains 50 Cal, 5 g of protein, 1 g of fat, 82 mg of calcium, and 20 mg of sodium. (Source: Home and Garden Bulletin No.72, U.S. Government Printing Office, Washington, D.C. 20402)
a) Write matrices C, P, and B that represent the nutritional values of each food.
b) Find and tell what the entries represent.
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