You are thinking of making your home more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. Each compact fluorescent light bulb costs $4 and saves you an average of$2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of$0.20 per year in energy costs. Your home has 60 light fittings and 1,100 sq. ft. of uninsulated exterior wall. You can spend no more than $1,200 and would like to save as much per year in energy costs as possible. How many compact fluorescent light bulbs and how many square feet of insulation should you purchase? How much will you save in energy costs per year?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. My work with complex numbers verified that the only possible cube root of 8 is 2.

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 500 eggs and 900 cups of cream. How many quarts of each flavor should you make in order to use up all the eggs and cream?

State if each number is rational, irrational, or not a real number. Justify your answer. √-1/4

What is overregularization?

Enormous State University’s Business School is buying computers. The school has two models to choose from: the Pomegranate and the iZac. Each Pomegranate comes with 400 MB of memory and 80 GB of disk space, and each iZac has 300 MB of memory and 100 GB of disk space. For reasons related to its accreditation, the school would like to be able to say that it has a total of at least 48,000 MB of memory and at least 12,800 GB of disk space. Draw the feasible region that shows the number of each kind of computer it can buy. Find the corner points of the region.

A neutron consists of one “up” quark of charge +2e/3 and two “down” quarks each having charge -e/3. If we assume that the down quarks are

$$2.6 × 10^-15$$

m apart inside the neutron, what is the magnitude of the electrostatic force between them?

Solve each equation. Check for extraneous solutions. |x - 4| + 3 = 1

The position of the particle is given by $s = (2t^2 - 8t + 6) ~\text{m}$, where $t$ is in seconds. Determine the time when the velocity of the particle is zero, and the total distance traveled by the particle when $t = 3 ~\text{s}$.

Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college$60,000, while each section of Computer Methods has 10 students and earns the college $20,000. Assuming the college wishes to offer a total of six sections, to accommodate 210 students, and to bring in$260,000 in revenues, how many sections of each course should it offer?

A rugby player runs with the ball directly toward his opponent's goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball's velocity relative to the field does not have a positive x component. Suppose the player runs at speed 3.5 m/s relative to the field while he passes the ball with velocity

$$\vec { v } _ { B P }$$

relative to himself. If

$$\vec { v } _ { B P }$$

has magnitude 6.0 m/s, what is the smallest angle it can have for the pass to be legal?

In the context of nuclear fission reactors, state what is meant by: a. uranium enrichment b. moderator c. critical mass.

Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. This exercise is based on the following table, which shows the closing prices on January 9, 2009, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day.

$$\begin{matrix} \text{Tech Stocks} & \text{Close} & \text{Change}\\ \text{AAPL (Apple)} & \text{\$90.58} & \text{-2.12}\\ \text{MSFT (Microsoft)} & \text{\$19.52} & \text{-0.60}\\ \text{NOK (Nokia)} & \text{\$15.21} & \text{-0.16}\\ \text{NT (Nortel)} & \text{\$0.39} & \text{0.10}\\ \text{RIMM (Research in Motion)} & \text{\$47.99} & \text{1.49}\\ \text{S (Sprint Nextel)} & \text{\$2.59} & \text{0.01}\\ \text{Non-Tech Stocks}\\ \text{DIS (Walt Disney)} & \text{\$22.31} & \text{-0.59}\\ \text{DUK (Duke)} & \text{\$15.27} & \text{-0.14}\\ \text{ED (Con Ed)} & \text{\$39.66} & \text{0.20}\\ \text{FE (First Energy)} & \text{\$48.90} & \text{1.14}\\ \text{MO (Altria Group)} & \text{\$15.48} & \text{0.38}\\ \text{NVS (Novarnis)} & \text{\$48.16} & \text{-1.46}\\ \end{matrix}$$

On the morning of January 9, 2009, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. a. How many possible collections are possible? b. You tend to have bad luck with stocks-they usually start going down the moment you buy them. How many of the collections in part (a) consist entirely of stocks that declined in value by the end of the day? c. Using the answers to parts (a) and (b), what would you say your chances were of choosing a collection consisting entirely of stocks that declined in value by the end of the day?

Suppose you were conducting a survey to try to determine what portion of voters in your small town support a particular candidate for mayor. Consider each of the following methods for sampling the voting population of your town. State whether each is likely to produce a representative sample and explain your reasoning. a. Ask every voter on your block. b. Randomly pick one house from each block in the neighborhood and survey the homeowner. c. Survey each person at the I-Jump Pancake Restaurant after church on Sunday morning. d. Ask people who are leaving the twice-yearly town hall meeting. e. Visit every tenth person on the county's voter registration list.