The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assign ing line positions on voting ballots. Among 4 l different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line. Find the probability of 40 or more top lines for Democrats.

A pizzeria charges $11 for a large cheese pizza. The pizzeria is offering a special deal. If you buy 3 large cheese pizzas, you can choose to get a fourth cheese pizza free. Is the cost of the pizzas a function of the number of pizzas purchased? Explain.

The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.

Which probability is relevant for determining whether 40 first lines for Democrats is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 40 first lines for Democrats significantly high?

Simplify.

$$7d^5 • d^2$$

For the given functions f and g, find: $f \circ f$, $f(x)=x^{2}+1 ; \quad g(x)=\sqrt{x-1}$

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the rose r=4 sin 2

$$\theta$$

and inside the circle r=2

A study was conducted to compare automobile gasoline mileage for three formulations of gasoline. Four automobiles, all of the same make and model, were used in the experiment, and each formulation was tested in each automobile. Using each formulation in the same automobile has the effect of eliminating (blocking out) automobile-to-automobile variability. The data (in miles per gallon) follow.

Formulation, Automobile 1, Automobile 2, Automobile 3, Automobile 4 A, 25.7, 27.0, 27.3, 26.1 B, 27.2, 28.1, 27.9, 27.7 C, 26.1, 27.5, 26.8, 27.8

a. Do the data provide sufficient evidence to indicate a difference in mean mileage per gallon for the three gasoline formulations? b. Is there evidence of a difference in mean mileage for the four automobiles? c. Suppose that prior to looking at the data, you had decided to compare the mean mileage per gallon for formulations A and B. Find a 90% confidence interval for this difference. d. Use an appropriate method to identify the pairwise differences, if any, in the average mileages for the three formulations.

Determine whether the set

$$\mathcal { B }$$

is a basis for the vector space V.

$$V = \mathscr { P } _ { 2 } , \mathcal { B } = \left\{ 1,2 - x , 3 - x ^ { 2 } , x + 2 x ^ { 2 } \right\}$$

Give examples of two sets that meet the given conditions. If the conditions are impossible to satisfy, explain why. The two sets are equal but not equivalent.

Write an equation of each line. slope = (5/9); (10, 4)

Matt invested $2000 in stocks and bonds. This year the bonds paid 8% interest, and the stocks paid 6% in dividends. Matt received a total of$144 in interest and dividends. How much money did he invest in stocks? in bonds?

Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.

In a study of the Ornish weight loss program, 40 subjects lost a mean of 3.3 lb after 12 months (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction,” by Dansinger et al., Journal of the American Medical Association, Vol. 293, No. 1). Methods of statistics can be used to show that if this diet had no effect, the likelihood of getting these results is roughly 3 chances in 1000.

Two lenses, separated by a distance of 21.0 cm, are used in combination. The first lens has a focal length of +30.0 cm; the second has a focal length of -15.0 cm. An object, 2.0 mm long, is placed 1.8 cm before the first lens. (a) What are the intermediate and final image distances relative to the corresponding lenses? (b) What is the total magnification? (c) What is the height of the final image?