1. You are given Pr(A) = 0.3, Pr(B) = 0.5 and Pr(A ∪ B) = 0.6. (a) WhatisPr(A∩B)?

(b) What is Pr(notA)?

2. A bag contains 30 balls of the same size. Each ball is either red or green.

The probability of choosing a green ball is 0.7. How many of the balls are red?

3. Given nPr =42 and nCr =7 find the value of r?

4. We have Pr(A|B) = 0.3 and Pr(B) = 0.45. What is Pr(A ∩ B)?

5. How many 3 digit numbers can be created from the set {1, 2, 3, 4, 5, 6} if the digits cannot be repeated?

6. What is the probability of choosing 10 cards at random from a standard deck of 52 cards and getting exactly 2 queens?

7. What is the variance of the numbers 3, 7, and 8?

8. We have a discrete probability distribution where P r(X = 1) = 0.2,

Pr(X = 2) = 0.3 and Pr(X = 3) = 0.5. Determine μ.

9. We have a discrete probability distribution where P r(X = 1) = 0.6,

Pr(X=3)=0.1,Pr(X=5)=0.3andμ=2.4. Determineσ2.

10. We have a binomial distribution where the probability of success is 0.4 and the number of trials is 3,000. What is the variance of the distribution?

HELP 1-10!!!!!!!!

8. This question has to do with calculating the multiplier. Please answer questions 8a through 8c below.

  8a. Define and write the formula for the multiplier.

8b. Compute the multiplier if the MPC=0.3. Interpret the multiplier you just calculated.

8c. An Economist estimates that the MPC is now 0.7 because he received information that a company like GM are very optimistic about the future sales of their cars and trucks, so an economic expansion is inevitable. Calculate the new multiplier. Interpret the new multiplier you just calculated. Did the multiplier get smaller or bigger when the MPC rises to 0.60? Why? What does this do to consumption and investment for cars and trucks and other goods produced and bought in the U.S. economy? Is an economic expansion possible if the MPC had risen from 0.3 to 0.7? Does disposable income fall or rise when MPC rises from 0.3 to 0.7? Explain. Calculate the new multiplier and compare it with the multiplier you just calculated in 9b and then explain your results.

Note: Please label your graphs and axes on graph problems and please show your work and calculations and your steps on the math problems.

Carbon fossil fuels are utilized to power our vehicles, make oil, and even t-shirts. The EPA has determined that a car transforms a gallon of octane (C8H18) to 33.7 kWh (kilowatt*hours, an expression of energy) in order to power a vehicle.

1. Provide the balanced equation for the complete combustion of octane.

2. If a truck is able to drive 360 miles on a tank of octane (22 gallons) how much energy is needed to move the vehicle one mile? What mass of CO2 is produced per gallon of octane? (the density of octane is 0.703 g/mL)

3. According to the L.A times there are 253 million cars on American roads. Assuming that each car is driven 50 miles each day, five days a week determine the mass and volume of the CO2 produced and mass of octane needed to power them for a year (assuming 20 miles per gallon)?

On January 1, 2021, the Excel Delivery Company purchased a delivery van for $46,000. At the end of its five-year service life, it is estimated that the van will be worth $4,000. During the five-year period, the company expects to drive the van 165,000 miles.

Required:
Calculate annual depreciation for the five-year life of the van using each of the following methods.

rev: 05_15_2019_QC_CS-168776, 11_22_2019_QC_CS-191707

Exercise 11-1 (Algo) Part 1

1. Straight line.

2. Double-declining balance. (Round your answers to the nearest whole dollar amount.)

Years Depreciatiation

2021

2022

2023

2024

2025

3. Units of production using miles driven as a measure of output, and the following actual mileage: (Do not round intermediate calculations.)
miles Depreciation

2021 35,000

2022 37,000

2023 28,000

2024 33,000

2025 34,000

Tunnel Problem

You are going to build a tunnel 10 miles long with a shaft at one end and a portal at the other. It is part of the first phase of the gateway tunnel to New York.

* The shaft is 185 ft. deep to the invert of the tunnel and 22 ft. excavated diameter.

* The tunnel is 26 ft. excavated diameter in competent sandstone and limestone.

* The profile of the shaft is as follows: From the surface down- 15 feet of fill; 30 feet of sand and clay; 20 feet of silty gravel; 40 feet of limestone and 80 feet of sandstone.

* Groundwater is 35 feet down.

* The tunnel runs for 5 miles in sandstone and 5 miles in limestone.

Determine the following:

1. Using a TBM, how long will it take to excavate the tunnel?

2. Will blasting need to be done anywhere? If so, where?

The average dog can run 0.4 miles before having to stop, with a standard deviation of 0.09 miles, and the distribution of these distances is roughly normal. We take a sample of 16 dogs and prescribe a daily training routine. After completing training, the dogs had a mean run distance of 0.45 miles. We will use a 0.10 significance level to see whether the training can increase mean run distance for all dogs.

a. What is the population?

b. What is the sample?

c. What is an individual?

d. What is the variable?

e. Is the variable quantitative or qualitative?

f. State the null hypothesis.

g. State the alternate hypothesis

. h. Give the tail type.

i. Compute the test statistic.

j. Compute the observed significance level (?-value).

k. Make a statistical conclusion

. l. State your conclusion in plain English.

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.

Using Excel Data Analysis, find the value of the test statistic. (Round your answer to two decimal places.)

Use the estimated regression equation (Y-hat = 8.098 + -0.344X) to develop a 95% confidence interval for the expected number of days absent for employees living 7 miles from the company. (Round your answers to one decimal place.)

_______Days to _______ Days

You wish to take an Excel course. You may enroll at one within your school or you may take a community class at the local library. You've gathered the following information to aid in your decision-making process.

Required:

a. Indicate in the table above which costs are relevant and which are not relevant in the choice between these two alternatives.

b. What is the differential cost between the two alternatives?

SHOW ALL WORK AND CALCULATIONS!

Match each scenario below with the most appropriate inferential technique. Group of answer choices

We want to test if at least half of students at a university feel as if the dorms need to be renovated.

We want to estimate the average number of calories in a combo meal at fast food restaurants.

The population standard deviation is unknown.

We want to test if the average number of miles that motorists drive between oil changes is greater than the recommended 3000 miles while assuming a population standard deviation of 1000 miles.

We want to test if high school marching bands are equally made up of freshmen, sophomores, juniors, and seniors.

We want to test if the average starting salary of software engineers out of college is greater than \$70,000. The population standard deviation is unknown. We want to estimate the proportion of people who speak more than one language fluently.