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When an object moves

under the influence of constant force (without air resistance),

its path is parabolic. This is the path of a ball

thrown near the surface of a planet or other celestial

object. Suppose two balls are simultaneously thrown

upward at a 45_ angle on two different planets. If their

initial velocities are both 30 mph, then their rectangular

coordinates (in feet) can be determined by the function

Æ’1×2 = x –

g

1922

x2 ,

where g is the acceleration due to gravity. The value

of g will vary with the mass and size of the planet.

(Source: Zeilik, M., S. Gregory, and E. Smith, Introductory

Astronomy and Astrophysics, Saunders College

Publishers.)

On Earth, g = 32.2, and on Mars, g = 12.6. Find

the two equations, and determine the difference in the

horizontal distances traveled by the two balls.

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Hospital Readmission As of October 1, 2012, hospitals in the United States with excessive numbers of readmissions based on the Centers for Medicare and Medicaid Services (CMS) data were penalized. Therefore, it is important for hospitals to identify the risk factors associated with readmission. The following data represent statistics on patients readmitted within 30 days and those not readmitted within 30 days of being discharged at a community hospital. Conduct the appropriate test for each variable that might be associated with readmission (age, length of stay, and so on). Researchers wonder if:

• the readmits tend to be older

• is length of stay longer for readmits

• were a higher proportion of readmits admitted the previous calendar year

• were a higher proportion of readmits discharged in winter

• were a higher proportion of readmits on the cardiac floor

Write a short report detailing your findings.

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Visual versus Textual Learners Researchers wanted to know whether there was a difference in comprehension among students learning a computer program based on the style of the text. They randomly divided 36 students of similar educational level, age, and so on, into two groups of 18 each. Group 1 individuals learned the software using a visual manual (multimodal instruction), while group 2 individuals learned the software using a textual manual (unimodal instruction). The following data represent scores that the students received on an exam given to them after they studied from the manuals.

(a) What type of experimental design is this?

(b) What are the treatments?

(c) A normal probability plot and boxplot indicate it is reasonable to use Welch’s -test. Is there a difference in test scores at the  level of significance?

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You have graduated with a business degree, and you have worked for three years for a small management consulting firm. Ivan Steeger (1352 Bull Run Road, Milltown, OR 97111) is a client who has been involved with several businesses in the past. He expects to be the major provider of equity capital for a new mail-order low-fat cookie business. His co-owners, who have baking expertise and a talent for developing recipes, will run the business. The owners are about to meet to determine what equipment they will purchase for the business. Ivan gives you the following information about the business and their plans:

• Ivan will be providing about 25% of the financing; the remainder will be debt. Ivan will probably have to give his personal guarantee for much of the debt. The exact amount of debt will depend on the price of the equipment they decide to purchase.

• They expect business growth of about 20% for each of the first five years.

• All of the equipment has an expected life of at least five years. They will definitely purchase mixing and baking equipment. They must decide whether to add equipment that will shape cookies automatically, or hire employees to do the shaping.

• They also must decide what capacity they prefer in their initial equipment purchase. Smaller-capacity equipment would handle their expected demand for the first two years, operating eight hours a day. Equipment with twice the capacity would cost approximately 50% more.

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