A pizzeria charges $11 for a large cheese pizza. The pizzeria is offering a special deal. If you buy 3 large cheese pizzas, you can choose to get a fourth cheese pizza free. Is the cost of the pizzas a function of the number of pizzas purchased? Explain.

Graph the exponential function. Find the y-intercept and the asymptote. Describe how the graph is transformed from the graph of its parent function.

$$j ( x ) = - \frac { 1 } { 3 } \left( 4 ^ { x } \right)$$

At Figaro's Pizzeria, large pizzas usually sell for $\$ 12.50$ and at this price an average of 320 large pizzas are sold each weekend. Using a survey and years of experience, the manager of Figaro's believes that for each $\$ 0.25$ decrease in price, 16 additional pizzas will be sold. (a) What price should be charged to maximize revenue? What is the maximum revenue? (b) What selling price(s) will generate exactly $\$ 4800$ in revenue?

Determine the sum of the first 100 even natural numbers.

The members of the PTA are ordering pizza for a meeting. They plan to order 2 cheese pizzas for every 3 pepperoni pizzas they order. How many cheese pizzas will they order if they order 15 pepperoni pizzas?

Determine whether the set

$$\mathcal { B }$$

is a basis for the vector space V.

$$V = \mathscr { P } _ { 2 } , \mathcal { B } = \left\{ 1,2 - x , 3 - x ^ { 2 } , x + 2 x ^ { 2 } \right\}$$

Give examples of two sets that meet the given conditions. If the conditions are impossible to satisfy, explain why. The two sets are equal but not equivalent.

What are the speaker's religious beliefs in "The First Snowfall", and in what way are they helpful for him to cope with his pain?

Use the Law of Sines or the Law of Cosines to solve the triangle. $A=24^{\circ}, a=10, b=6$

For an arithmetic sequence, the first term is A(1) = 3. Each successive term adds 2 to the previous term. Another arithmetic sequence has the rule B(n) = 5 + (n-1)d, where n is the term number and d is the common difference. If the graphs of the two sequences are parallel, what is the value of d? Explain.

Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.

$$\int _ { 2 } ^ { \infty } \frac { d v } { \sqrt { v - 1 } }$$

Evaluate the expression. Write your answer in scientific notation and standard form.

$$\left( 6.1 \times 10 ^ { - 3 } \right) \left( 8 \times 10 ^ { 9 } \right)$$

A jet engine at 7000-m altitude takes in 45 kg/s of air and adds 550 kJ/kg in the combustion chamber. The chamber cross section is 0.5 m², and the air enters the chamber at 80 kPa and 5°C. After combustion the air expands through an isentropic converging nozzle to exit at atmospheric pressure. Estimate (a) the nozzle throat diameter, (b) the nozzle exit velocity, and (c) the thrust produced by the engine.

Find the exact value of each expression. Write the answer as a single fraction. Do not use a calculator.

$$\sin \frac { 11 \pi } { 4 } \cos \frac { 5 \pi } { 6 } + \cos \frac { 11 \pi } { 4 } \sin \frac { 5 \pi } { 6 }$$