A fire chief wants to relate the amount of fire damage in major residential fires to the distance between the residence and the nearest fire station in order to get approval to add a fire station. The chief performs a study using a sample of fifteen recent fires in the town. The following table shows the result of the study.

a. Is there a strong or weak correlation between distance and dollar loss? What is the correlation between the two?
b. What is the estimated dollar loss if the distance of the fire station was 10 miles, 5 miles, and 2.5 miles.

Andrea would like to organize SHO as either an LLC (taxed as a sole proprietorship) or a C corporation. In either form, the entity is expected to generate an 10 percent annual before-tax return on a $860,000 investment. Andrea’s marginal income tax rate is 35 percent and her tax rate on dividends and capital gains is 15 percent. Andrea will also pay a 3.8 percent net investment income tax on dividends and capital gains she recognizes. If Andrea organizes SHO as an LLC, Andrea will be required to pay an additional 2.9 percent for self-employment tax and an additional 0.9 percent for the additional Medicare tax. Further, she is eligible to claim the full deduction for qualified business income. Assume that SHO will pay out all of its after-tax earnings every year as a dividend if it is formed as a C corporation.

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.7 m/s2 for 3.8 seconds. It then continues at a constant speed for 8.5 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 206.78 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop. 1) How fast is the blue car going 2.7 seconds after it starts? 3) How far does the blue car travel before its brakes are applied to slow down? What is the acceleration of the blue car once the brakes are applied? 5) What is the total time the blue car is moving? What is the acceleration of the yellow car?

Fasting concentrations (mmol/L) of glucose in blood were measured in a sample of diabetic patients implanted with a new insulin delivery platform.

Computer simulations of the platform predicted a fasting glucose level of 4.5 mmol/L.

Use a statistical test to fundament your opinion on whether the data is consistent with the model prediction.

1. Identify suitable null and alternative hypotheses.
2. Is a t-test is suitable for this problem. Why?
3. Calculate critical values for a significance level of 0.01. Is the data is consistent with the computer model? Justify
4. Calculate p-value. Is the data is consistent with the computer model? Justify.

Typhoon Corp. has estimated the following activity rates, activity consumption, and direct costs for their Whirlpool Surfboard product line. Assume that Typhoon plans to manufacture and sell 100,000 units of the Whirlpool Surfboard product, generating $15,000,000 in sales revenue. What is the Whirlpool Surfboard product line profit using activity-based costing? Activity Activity Rate Customer relations $2,000 per customer Product design $10,000 per design Manufacturing $50 per machine hour Organization-sustaining N/A Traceable Direct Costs Cost per unit Direct Material $40.00 Direct Labor $27.00 Shipping $4.00 Whirlpool Surfboard Activity Consumption 400 customers 80 designs 50,000 machine hours A. $10.9 million B. $3.8 million C. $7.9 million D. $8.3 million

1. A search using the Web search engine Bing^TM for "asteroid" yielded 24.8 million Web sites containing that word. A search for "comet" yielded 95.0 million sites. A search for sites containing both words yielded 3.8 million sites. How many Web sites contained either "asteroid" or "comet" or both? HINT [See Example 1.]
million sites

2. On a particularly boring transatlantic flight, one of the authors amused himself by counting the heads of the people in the seats in front of him. He noticed that all 26 of them either had black hair or had a whole row to themselves (or both). Of this total, 23 had black hair and 8 were fortunate enough to have a whole row of seats to themselves. How many of the black-haired people had whole rows to themselves?
people

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. Assume the population standard deviations are not the same. The following is the amount ($000) earned per month by a sample of 15 Claiborne models:

A.) Find the degrees of freedom for unequal variance test. (round down to nearest whole #)

B.) State the decision rule for 0.10 significance level. (round to 3 decimal places)

C.) Compute the value of the test statistic. (round to 3 decimal places)

4. Calculate the equilibrium concentration of Ag⁺ (aq) in a solution that is initially 0.150 M AgNO₃ and 0.500 M KCN. The formation constant for [Ag(CN)₂]^- (aq) is K_f= 1.0 x 10²¹

a. 8.9 x 10^-21 M

b. 2.3 x 10 ^-21 M

c. 4.3 x 10 ^-22 M

d. 7.5 x 10 ^-22 M

e. 3.8 x 10 ^-21 M

5. If a solution of Pb(NO₃)₂ (aq) is mixed with a solution of NaBr(aq), what condition would cause precipitation of PbBr₂ (s) to occur?

a. When [Na⁺][NO₃^-] < K_sp for PbBr₂

b. When [Pb²⁺][Br ^-]² < K_sp for PbBr₂

c. When [Pb²⁺][Br ^-] < K_sp for PbBr₂

d. When [Pb²⁺][Br ^-]² > K_sp for PbBr₂

e. When [Pb²⁺][Br ^- ] > K_sp for PbBr₂

Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data168.dat. Find the correlation between the two variables. Use these five numbers to find the equation of the regression line for predicting length from time. Use the same five numbers to find the equation of the regression line for predicting the time an icicle has been growing from its length. (Round your answers to three decimal places.)

time    length
10      3.3
20      .6
30      3.8
40      6.7
50      8.7
60      10.6
70      10.1
80      12.4
90      15.3
100     14.1
110     17.4
120     18.2
130     19.7
140     23.1
150     23.7
160     27.9
170     27.9
180     29.4