What are the benefits of a free enterprise economy?

We often think of the American free enterprise economy as having several distinct "players" that ensure its success. These players include entrepreneurs, consumers, and the government. How do you fit in? How does the system benefit you? As a student, you may find that you need extra spending money to cover your school and your living expenses. You may begin thinking about becoming an entrepreneur by creating a small business that will earn you money. You may also decide to look into getting a job. Or you may visit your school's financial aid office to see if there is some form of government student aid, such as a loan, grant, or work-study program.

Answer the following questions:

3. What type of financial aid might be available to me through my school?

Natural gas provides 35.8% of U.S. energy. (Source: U.S. Energy Department.) The volume of a gas varies inversely as the pressure and directly as the temperature. (Temperature must be measured in degrees Kelvin (K), a unit of measurement used in physics.) If a certain gas occupies a volume of 1.3 liters at 300 K and a pressure of 18 newtons per square centimeter, find the volume at 340 K and a pressure of 24 newtons per square centimeter.

The manager of a small local airport must extend a runway if business jets are to be accommodated. However, the airport is practically surrounded by a suburban housing development, and residents are already complaining to the city council about the volume and noise of existing air traffic at the facility. Identify the decision alternatives and the possible states of nature that might occur after the decision is made.

In physics it is shown that the height s of a ball thrown straight up with an initial speed of 96 ft/sec from a rooftop 112 feet high is $s=s(t)=-16 t^{2}+96 t+112$ where t is the elapsed time that the ball is in the air. The ball misses the rooftop on its way down and eventually strikes the ground. At what time t will the ball pass the rooftop on its way down?

A small-business corporation is considering whether to replace some equipment in the plant. An analysis indicates there are five alternatives in addition to the do-nothing option, Alt. A. The alternatives have a 5-year useful life with no salvage value. Straight-line depreciation would be used.

$$\begin{matrix} \text{Alternatives} & \text{Cost (thousands)} & \text{Before-Tax Uniform Annual Benefits (thousands)}\\ \text{A} & \text{\$0} & \text{\$ 0}\\ \text{B} & \text{25} & \text{8}\\ \text{C} & \text{10} & \text{5}\\ \text{D} & \text{5} & \text{2}\\ \text{E} & \text{15} & \text{5}\\ \end{matrix}$$

The firm has a combined federal and state income tax rate of 38%. If the corporation expects a 8% after-tax rate of return for any new investments, which alternative should be selected?

In a physics lab, students measure the time it takes a small cart to slide a distance of $1.00 \mathrm{~m}$ on a smooth track inclined at an angle $\theta$ above the horizontal. Their results are given in the following table.

Find the magnitude of the cart's acceleration for each angle. Show that your results are in close agreement with the formula, $a=g \sin \theta$.

After completing his Certified Financial Planner designation (CFP), Andre was excited about the prospects of working with small business owners and their employees regarding retirement planning. Andre wanted to show the value of an annuity program as one of the viable investment options in a salary reduction retirement plan. In addition, he wanted to demonstrate the substantial tax benefits that annuities can provide. For instance, qualified annuities (by definition) not only reduce your current taxable salary, they also accumulate earnings on a tax-deferred basis-meaning you don't pay taxes on the earnings until they are withdrawn. Andre was developing a spreadsheet to show the way that annuities could grow using various rates of return.

If an individual put the equivalent of $\$ 50$ per month, or $\$ 600$ annually into an ordinary annuity, how much money would accumulate in $20$ years at $3 \%$ compounded annually? How much at $5 \%$ ?

A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high-pitched. very annoying whine. From a wave perspective, the standing wave is equivalent to a sound standing wave in an open-open tube. In particular, both ends of the rod are anti-nodes. What is the fundamental frequency of a $2.0-\mathrm{m}$-long aluminum rod?

A small juice company spends $1200 per day on business expenses plus$1.10 per bottle of juice they make. They charge $2.50 for each bottle of juice they produce. How many bottles of juice must the company sell in one day in order to equal its daily costs?

The simplest cost function is the linear cost function, $C(x) = mx + b$, where the y-intercept b represents the fixed costs of operating a business and the slope m represents the cost of each item produced. Suppose that a small bicycle manufacturer has daily fixed costs of $1800 and each bicycle costs$90 to manufacture. What is the cost of manufacturing 14 bicycles in a day?

In physics it is shown that the height s of a ball thrown straight up with an initial speed of 96 ft/sec from a rooftop 112 feet high is $s=s(t)=-16 t^{2}+96 t+112$ where t is the elapsed time that the ball is in the air. The ball misses the rooftop on its way down and eventually strikes the ground. What is the average speed of the ball from t = 0 to t = 2?

An economist wishes to predict the market value of owner-occupied homes in small midwestern cities. She has collected a set of data from 45 small cities for a 2-year period and wants you to use these as the data source for the analysis. The data are stored in the file Citydatr. She wants you to develop two prediction equations: one that uses the size of the house as a predictor and a second that uses the tax rate as a predictor.

a. Plot the market value of houses (hseval) versus the size of houses (sizense), and then versus the tax rates (taxrate). Note any unusual patterns in the data.

b. Prepare regression analyses for the two predictor variables. Which variable is the stronger predictor of the value of houses?

c. A business developer in a midwestern state has stated that local property tax rates in small towns need to be lowered because if they are not, no one will purchase a house in these towns. Based on your analysis in this problem, evaluate the business developer’s claim.

In the movie The Rocketeer, a teenager discovers a jet-powered backpack in an old barn. The backpack allows him to fly at incredible speeds. In one scene, however, he uses the backpack to rapidly accelerate an old pickup truck that is being chased by "bad guys." He does this by bracing his arms against the cab of the pickup and firing the backpack, giving the truck the acceleration of a drag racer. Is the physics of this scene "Good," "Bad," or "Ugly?" Explain.

A study reported in the Journal of Small Business Management concluded that self-employed individuals do not experience higher job satisfaction than individuals who are not self-employed. In this study, job satisfaction is measured using 18 items, each of which is rated using a Likert-type scale with 1-5 response options ranging from strong agreement to strong disagreement. A higher score on this scale indicates a higher degree of job satisfaction. The sum of the ratings for the 18 items, ranging from 18-90, is used as the measure of job satisfaction. Suppose that this approach was used to measure the job satisfaction of lawyers, physical therapists, cabinetmakers, and systems analysts. The results obtained for a sample of 10 individuals from each profession follow.