Heat treating is often used to carburize metal parts, such as gears. The thickness of the carburized layer is considered a crucial feature of the gear and contributes to the overall reliability of the part. Because of the critical nature of this feature, two different lab tests are performed on each furnace load. One test is run on a sample pin that accompanies each load. The other test is a destructive test, where an actual part is cross-sectioned. This test involves running a carbon analysis on the surface of both the gear pitch (top of the gear tooth) and the gear root (between the gear teeth). Table 12-6 shows the results of the pitch carbon analysis test for 32 parts.

1. Fit a regression model using all five regressors. Write out the equation. Summarize this analysis by providing the equation, ?², and list the standard errors.    What does the analysis of variance indicate?
2. Check for multicollinearity. Explain your findings.
3. Describe what you notice about the p values for the regressors. Construct a t-test on each regression coefficient. What can you conclude about the variables in this model? Use an alpha = 0.05.
4. Prepare a normal probability plot of the residuals and check the adequacy of the model.

On a beautiful day you decide to go for a bicycle ride. First you ride for 10 miles at 30 degrees south of east and then for 8.0 miles at 60 degrees north of west. What is the magnitude of your displacement?  

options:

One gallon of gasoline in an automobile's engine produces on the average 9.5 kg of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States and each car covers a distance of 5300 miles at a consumption rate of 21 miles per gallon.

In a random sample of eleven ​people, the mean driving distance to work was 23.3 miles and the standard deviation was 5.4 miles. Assume the population is normally distributed and use the​ t-distribution to find the margin of error and construct a 95​% confidence interval for the population mean μ. Interpret the results. Identify the margin of error.

(round to one decimal place)

. In a random sample of five people, the mean driving distance to work was 25.4 miles and the standard deviation was 5.2 miles. Assume the random variable is normally distributed and use a tdistribution to find the margin of error and construct confidence intervals for the population mean at the following confidence levels: (4 points each) a. 85% b. 90% c. 99%

Suppose one gallon of gasoline produces 1.19×10⁸ J of energy, and this energy is sufficient to operate a car for 21.1 miles. An aspirin tablet has a mass of 324 mg. If the aspirin could be converted completely into thermal energy, how many miles could the car go on a single tablet? Please explain units needed in each equation!

A car rental agency is considering a modification in its oil change procedure. currently, it uses a type X filter, which cost $4.25 and must be changed every 9,000 miles along with oil (4 quarts.) Between each oil change , one quart of oil must be added after each 500 miles. The proposed filter (typeY) has to be replaced every 4,000 miles (along with 4 quarts of oil) but does not require any additional oil between filter changes. If the oil costs $1.14 per quart, what is the maximum acceptable price for the Type Y filter?

A. $7.97

B. $15.94

C. $17.93

D. 58.87

A Toyota Prius is a full hybrid electric automobile that costs $30,000 with 55 mpg. A Toyota Yaris is a normal car that runs on gasoline, and costs $15,000 with 35 mpg. After 100,000 miles, the Prius requires a battery replacement that costs $3,000. Suppose you drive 10 miles per day and 1 gallon of gas costs $4. How much would you have to spend on gas for each car after 10 years? Which car would cost you more money after 10 years? How much different are the gas prices between the Prius and the Yaris (10 miles per day x 10 years)?

You operate an auto store that sells tires. You are concerned about warranty returns on the tires. Company records show that the probability warranty repair for a tire in the first 90 day is .05. You are tracking the sales of three tires. What is the mean for this binomial distribution?

a. .15

b. .19

c .25

d. .35

ABC Trucking Company realized that on an annual basis the distance traveled is normally distributed with a mean of 50,000 miles and a standard deviation of 12,000 miles. How many miles will be traveled by at least 80% of the trucks? (Hint: Think about the left side of the normal curve!)

a. 39,920

b. 43,500

c. 41,000

d. 38,670

Complete the following conversions using dimensional analysis

1. 320 pennies to number of nickels

2. 320 nickels to number of American dollars

3. 750cm to feet

4. 750cm to miles

5. 316nm to yards

6. 12 meters/seconds to miles/hour

7. $9.50/hour to pennies/day

8. 3.5 millimeters/min to liters/hour

9. 35 centimeters/day to meters/second

10. 35 meters/seconds to miles/year

Please explain every step to help me better understand. Also, please, type out your responses so I can legibly read. Thank you so much.