Study the entries and answer the questions that follow. The prefixes ambi and amphi mean "both" or "around." The roots luc and lum mean "light." The prefix super means "above" or "over." The root magn means "great." List as many words as you can think of that contain the root magn or the prefix super.

The letters R, C and A can be combined in several different ways. a) Write the letters in as many different orders as possible. If a computer writes these three letters at random, calculate the probability that: b) the letters will be written in alphabetical order, c) the letter $R$ is written before both the letters A and C, d) the letter C is written after the letter A, e) the computer will spell the word CART if the letter T is added.

Sketch the region determined by the indicated constraints. Then find the minimum and maximum values of the objective function and where they occur, subject to the constraints. Objective function: z=6x+10y Constraints:

$$\begin{array}{r} {x \geq 0} \\ {y \geq 0} \\ {3 x+5 y \leq 15} \end{array}$$

A farmer takes 250 chickens to be sold at a market. In the first hour he sells 8% of his chickens. In the second hour he sells 10% of those that were left. a) How many chickens has he sold in total? b) What percentage of the original number did he manage to sell in the two hours?

Find the nth term of a sequence suggested by the pattern. $1, \frac{1}{2}, 3, \frac{1}{4}, 5, \frac{1}{6}, 7, \frac{1}{8}, \cdots$

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution.

$$\left\{\begin{aligned} 2 x+10 y+2 z &=6 \\ x+5 y+2 z &=6 \\ x+5 y+z &=3 \\ -3 x+15 y-3 z &=-9 \end{aligned}\right.$$

Factorise the following quadratic expressions: a) $x^{2}+6 x+5$ b) $x^{2}+6 x+8$ c) $x^{2}+6 x+9$ d) $x^{2}+10 x+25$ e) $x^{2}+22 x+121$ f) $x^{2}-13 x+42$

Choose the best answer. Which is NOT true of an El Nino-Southern Oscillation (ENSO) event? (a) It causes increased upwelling on the west coast of South America. (b) It causes wetter conditions in the southern United States. (c) It includes a reversal in tropical ocean currents. (d) It often begins near Christmas.

Choose the best answer for the following. The IPAT equation was developed to estimate (a) the affluence of a country's population. (b) the rate of demographic transition. (c) the impact of human lifestyles on Earth. (d) the gross domestic product of a country.

Barbara drew a rectangle with a width 5 inches shorter than its length. She measured the perimeter of the rectangle and found it to be 14 inches. Calculate the width of the rectangle.

Use a graphing utility to graph the function and determine whether the function is even, odd, or neither. $g(x)=2-x^{6}-x^{8}$

Data were collected from two rival airlines measuring the difference in the stated departure times, and the times the flights actually departed. The average departure time differences were recorded for each month for one year. The results are shown in the side-by-side stem-and-leaf plot given.

$$\begin{matrix} & \text{} & \text{} & \text{Difference in Departure Times (minutes)}\\ & \text{My Air Airlines} & \text{} & \text{} & \text{} & \text{Fly High Airlines}\\ & \text{5} & \text{0} & \text{0} & \text{7} & \text{8}\\ \text{9} & \text{5} & \text{1} & \text{1} & \text{4} & \text{5} & \text{6}\\ \text{6} & \text{0} & \text{0} & \text{2} & \text{4} & \text{7} & \text{9}\\ \text{4} & \text{3} & \text{3} & \text{3} & \text{0} & \text{2}\\ & \text{} & \text{0} & \text{4} & \text{5} & \text{9}\\ & \text{} & \text{} & \text{} & \text{} & \text{} & \text{2|4=24 minutes}\\ \end{matrix}$$

Describe the distribution of each data set.

The function $P(a)=0.014 a^{2}-5.073 a+327.287$ represents the population P (in millions) of Americans that were a years of age or older in 2012. (a) Identify the independent and dependent variables. (b) Evaluate P(20). Interpret P(20) in the context of this problem. (c) Evaluate P(0). Interpret P(0) in the context of this problem.

Rewrite the expression by rationalizing the denominator. Simplify your answer. $\frac{5 x}{\sqrt{14}-2}$