The business manager of a 90 unit apartment building is trying to determine the rent to be charged. From past experience with similar buildings, when rent is set at $400, all the units are full. For every $20 increase in rent, one additional unit remains vacant. What rent should be charged for maximum total revenue? What is that maximum total revenue? To help solve the above scenario, perform an internet search for Profit Parabola or Applications of Quadratic Functions. List the URL of one of the applications that you find. URL ___________________________________________________________________

Go to http://www.purplemath.com/modules/quadprob3.htm to see the process used for determining the quadratic function for revenues R(x) as a function of price hikes x on page 3 with the canoe-rental business problem. Use this process to determine the quadratic function that models the revenues R(x) as a function of price hikes x in the apartment building scenario above. 

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = 2 + 2 sqrt(x) , y = (6 + x) / 3

Suppose that the batting averages in baseball are normally distributed so that the mean is .258 and the standard deviation is 0.04. What is the probability that a player has a batting average of

(A) More than .258?

(B) More than .298?

(C) More than .318?

Determine if ∑(-1)^n/(4n-7), n=0 to infinity, absolutely or conditionally converges or diverges?

Find value of a6 of the Tayler series found by a0, a1x, a2x^2+...

A computer store compiled data about the accessories that 500 purchasers of new tablets bought at the same time they bought the tablet. Here are the results: 411 bought cases 82 bought an extended warranty 100 bought a dock 57 bought both a dock and a warranty 65 both a case and a warranty 77 bought a case and a dock 48 bought all three accessories 58 bought none of the accessories Find the probability that a randomly selected customer bought:  

E. At most one of the accessories.

F. At most two of the accessories

..........................................................

9.The choices for problem number 30 part e from the book are given below. a. 0.116 b. 0.380 c. 0.794 d. 0.861 e. 0.567

10. The choices for problem number 30 part f from the book are given below. a. 0.096 b. 0.380 c. 0.120 d. 0.904 e. 0.851

Find f(t) if L(f)=s/(s^2+16)^2.

Solve the differential equation: y' + 2y = cos 5x

2. The Cost, $C, of hiring a repairman for H hours is given by C = 50 + 25h.

A. What does the repairman charge to walk in the door? B. What is his hourly rate?

3. The population a town, t years after it is founded, is given by P(t) = 5000 + 350t.

A. What is the population when it is founded? B. What is the population of the town two years after it is founded?

4. Find the slope and Y-intercept for each of the following:

a. -2y= -5x+9

b. Y = -16 - 4(-5 -3x)

c. 4x + 3y =-12

d. 5y - 3x - 10 = 0 5.

Find the equation of a line that passes through (6,7) and (6,1)

6.Find an equation of a line that is parallel to 3x + 5y = 6 and passes through (0, 5)

7. The total cost C of a yellow cab call lasting N minutes is $4.75 plus an additional charge of $2.50/mile.

A. Use a linear equation to describe the scenario B. How long was the cab ride if the total cost of the fare was $38.50?

Solve the following system of equations algebraically and check

a. 7x + 5y = -1

11x + 8y = -1

b. 5x + 2y = 1

2x - 3y = 27

8. Solve the following system of equationss graphically.

Y = -2X + 7

Y = 4X + 11

For the function f(x)=x^5-5x^3 determine:

a. Intervals where f is increasing or decreasing

b. Local minima and maxima of f,

c. Intervals where f is concave up and concave down, and,

d. The inflection points of f

e. Sketch the curve and label any points you use in your sketch.

For Calculus Volume One GIlbert Strange

Find the maximum and minimum values of f subject to the given constraints. Use a computer algebra system to solve the system of equations that arises in using Lagrange multipliers. (If your CAS finds only one solution, you may need to use additional commands. Round your answer to four decimal places.)

f(x, y, z) = ye^{x − z};    9x² + 4y² + 36z² = 36,  xy + yz = 1

Integrate products and powers of tangent and secant where secant has an odd exponent and tangent has an even exponent

Evaluate ∫tan^2 xsec^5 xdx using reduction formulas. Include +c in your answer and put parentheses around the argument of trigonometric functions.