Find the general antiderivative of f and check your answer by differentiating.

$$f ( x ) = 12 e ^ { x } - 5 x ^ { - 2 }$$

During your first week of training for a marathon, you run a total of 10 miles. You increase the distance you run each week by twenty percent. How many miles do you run during your twelfth week of training?

Multiply. Express each result in scientific notation.

$$\left( 9 \times 10 ^ { - 3 } \right) \left( 7 \times 10 ^ { 8 } \right)$$

Solve each inequality and graph the solutions.

$$- 3 > \frac { 1 } { 3 } r$$

On a summer day in New Orleans, Louisiana, the pressure is 1 atm: the temperature is $32^{\circ} \mathrm{C}$; and the relative humidity is 95 percent. This air is to be conditioned to $24^{\circ} \mathrm{C}$ and 60 percent relative humidity. Determine the amount of cooling, in kJ, required and water removed, in kg, per $1000\ \mathrm{m}^{3}$ of dry air processed at the entrance to the system.

Consider a six-sided die that has 1 dot on one side, 2 dots on two sides, and 3 dots on three sides. IF the die is rolled twice, determine the probability of rolling two 2's.

A 150 g copper bowl contains 220 g of water, both at 20.0$^\circ$C. A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100$^\circ$C. Neglect energy transfers with the environment. How much energy (in calories) is transferred to the water as heat?

Find the start, elapsed, or end time. Start time: 11:00 A.M. Elapsed time: 4 hours 5 minutes. End time: ________

In an industrial process, products of combustion at a temperature and pressure of 2000 K and 1 atm, respectively, flow through a long, 0.25-m-diameter pipe whose inner surface is black. The combustion gas contains $\mathrm{CO}_{2}$ and water vapor, each at a partial pressure of 0.10 atm. The gas may be assumed to have the thermophysical properties of atmospheric air and to be in fully developed flow with $\dot{m}=0.25 \mathrm{kg} / \mathrm{s}$. The pipe is cooled by passing water in cross flow over its outer surface. The upstream velocity and temperature of the water are 0.30 m/s and 300 K, respectively. Determine the pipe wall temperature and heat flux. Hint: Emission from the pipe wall may be neglected.

Solve each equation with rational exponents. Check all proposed solutions.

$$( x - 4 ) ^ { \frac { 2 } { 3 } } = 16$$

Solve the equation. 4x + 11 = 4x - 24

Simplify the expression. Write your answer using only positive exponents.

$$\frac { b ^ { - 5 } } { a ^ { 0 } b ^ { - 8 } }$$

The table shows the population of bacteria in a petri dish at various times. If the pattern continues, what will the bacteria population be at 6:00 P.M.?

$$\text{Bacteria Population}\\ \begin{array}{|l|c|c|c|c|} \hline \text{Time} & \text{8.00 A.M.} & \text{10: 00 A.M.} & \text{12.00 P.M.} & \text{2.00 P.M.}\\ \hline \text{Population} & \text{100} & \text{200} & \text{400} & \text{800}\\ \hline \end{array}$$

Which of the following statements is true concerning the equation x + 3 = 7? (a) To find the value of x, add 3 to each side. (b) To find the value of x, add 7 to each side. (c) To find the value of x, find the sum of 3 and 7. (d) To find the value of x, subtract 3 from each side.