In 1998 Ben took both the SAT (Scholastic Aptitude Test) and the ACT (American College Test). On the mathematics section of the SAT, he earned a score of 624. On the mathematics section of the ACT, he earned a score of 31. For the SAT the mean was 512 and the standard deviation was 112. For the ACT the mean was 21 and the standard deviation was 5.

Explain how you could translate ACT scores such as 15, 20, 25, and 30 into equivalent SAT scores if you know the mean and standard deviation of each exam.

The following statements describe situations where functions relate two quantitative variables. For each situation: $\bullet$ if possible, give a rule for the function that is described. $\bullet$ determine whether the given function has an inverse. $\bullet$ if an inverse exists, give a rule for that inverse function (if possible) and explain what it tells about the variables of the situation. (a.) If regular gasoline is selling for $3.95 per gallon, the price of any particular purchase p is a function of the number of gallons of gasoline g in that purchase. (b.) If a school assigns 20 students to each mathematics class, the number of mathematics classes M is a function of the number of mathematics students s in that school. (c.) The area of a square A is a function of the length of each side s. (d.) The number of hours of daylight d at any spot on Earth is a function of the time of year t.

Does Molly Moore's situation in the Dhahran International Hotel more closely resemble the situation of Mary Chesnut or of Randolph McKim? Explain your answer.

It's common folk wisdom that drinking cranberry juice can help prevent urinary tract infections in women. In 2001 the British Medical Journal reported the results of a Finnish study in which three groups of 50 women were monitored for these infections over 6 months. One group drank cranberry juice daily, another group drank a lactobacillus drink, and the third drank neither of those beverages, serving as a control group. In the control group, 18 women developed at least one infection, compared to 20 of those who consumed the lactobacillus drink and only 8 of those who drank cranberry juice. Does this study provide supporting evidence for the value of cranberry juice in warding off urinary tract infections? a) Is this a survey, a retrospective study, a prospective study, or an experiment? Explain. b) State the hypotheses. c) Check the conditions. d) How many degrees of freedom are there? e) Find $\chi^{2}$ and the P-value. f) State your conclusion.

How can embryological evidence be used to show phylogenetic connections that are not evident from either the study of morphology or the study of the fossil record?

If people understood the mathematics involving probabilities and lotteries as you now do, do you think they would continue to spend hundreds of dollars per year on lottery tickets? Explain your answer.

Moving Ladder A ladder 25 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 2 feet per second.

Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

For more information on the mathematics of moving ladders see the article "The Falling Ladder Paradox" by Paul Scholten and Andrew Simoson in the January 1996 issue of The College Mathematics Journal.

Show that a triangle formed by two sides that lies on the coordinate axes and the third side is to pass through the point (2,5), it is impossible to assign a slope to the third side that maximizes the area of the triangle

A triangle is to be formed as follows: two sides are to lie on the coordinate axes and the third side is to pass through the point (2, 5). Assign a slope to the third side that minimizes the area of the triangle.

A ball slides off a shelf with a  $3 \mathrm{~m} / \mathrm{s}$  horizontal velocity. If it takes the ball  $0.45 \mathrm{~s}$  in mathematics to reach the floor, then where does it settle horizontally with relation to the shelf?

Determine whether the study is an observational study or an experiment. Explain. (a) Researchers conduct a study to determine whether body mass index (BMI) influences the frequency of migraines. To conduct the study, researchers asked 162,576 people for their BMIs and the numbers of migraines they have per month. (b) Researchers conduct a study to determine whether taking a multivitamin daily decreases the risk of major cardiovascular events among men. To perform the study, researchers studied 14,641 men and had one group take a multivitamin daily and had another group take a placebo daily.

State an example of a question that could be better answered by gathering data in an observational study than it could by gathering data in an experiment. Elaborate on why an observational study would be more appropriate. Then state an observational study that would answer the question.

Fill in the blank spot in the following sentence.

The science of $\underline{\phantom{\text{justekst}}}$ studies the relationship between living things and their environment.

Use your notes to compare and contrast the differences between a Federal Work-Study program and a non-Federal Work-Study program.