A man is hiking at a park. At the beginning, he followed a straight trail. From the starting point, he traveled two miles down the first trail. Then he turned to his left by 30 degree angle to follow a second trail for one point five miles. Next, he turned to his right by 160 degree angle and follow a third trail for one point seven miles. At this point he was getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead him deeper into the woods. He would like to take a shortcut directly through the woods. How far to his right should you suggest him to turn, and how far do he have to walk, to go directly back to his starting point?

Q1: The man has to turn ____ degree to the right and walk ___ miles to the starting point.

A meteorologist who sampled 35 randomly selected thunderstorms found that they had a mean speed of travel across a state of 16 miles per hour and a standard deviation of 1.5 miles per hour

find a 98% confidence interval for the population mean travel speed for the thunderstorms across a state ( round to 1 decimal place)

Find the margin of error ( round to 1 decimal place)

if the meteorologist wants her estimate to be within 0.3 with 98% confidence, what is the sample size required ? the answer has to be a whole number

Amy Lloyd is interested in leasing a new Honda and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow:

Amy decided to choose the lease option that will minimize her total 36-month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision, she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her $10,764 if she drives 12,000 miles per year, $12,114 if she drives 15,000 miles per year, or $13,464 if she drives 18,000 miles per year.

a. What is the decision, and what is the chance event?

b. Construct a payoff table for Amy’s problem.

c. If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches?

d. Suppose that the probabilities that Amy drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What option should Amy choose using the expected value approach?

e. Develop a risk profile for the decision selected in part (d). What is the most likely cost, and what is its probability?

f. Suppose that after further consideration Amy concludes that the probabilities that she will drive 12,000, 15,000, and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. What decision should Amy make using the expected value approach?

How have sports changed since the 1940s? Are some of the issues raised in the film still present?

Adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ that is greater than 115.

The random variable X has the following probability distribution.

The variance of this distribution is

Background
Hotel One is one of the two hotels serving Dayville, a small town in the US Midwest. Fifty percent of its customers are out-of-town visitors to the local college, 30 percent are visiting Dayville for business purposes, and the remaining 20 percent of Hotel One’s customers are leisure travelers. The hotel is within one mile from campus, approximately four miles from the city center, and eight miles from the airport. It is easy to reach by car, taxi, or city bus. You are a manager of Hotel One. Your facility consists of 150 rooms, all of which are standard rooms with two double beds. Your only competitor in Dayville, The Other Hotel, has fewer rooms (100), but 20 of their rooms are luxury suites with king beds and a sofa couch (the other 80 are standard rooms with two double beds). This is the extent of the information provided to you at this point.

Assignment
In order to better understand your unit’s operating environment, you are asked to provide your estimate of the demand equation that would account for various factors that affect your customer traffic. This will be done by using regression techniques. The first step in estimating a demand equation is to determine what variables will be used in the regression. Please provide detailed answers to the following questions:
1. What do you think should be the dependent variable in your demand equation? What units of measurement for that variable are you going to adopt? Please provide a detailed explanation for these choices.
2. Please request information about up to five independent (explanatory) variables for your demand equation. For each variable you request, (i) provide reasons why you expect it to be
important for your analysis and (ii) explain the expected sign of the relationship between the proposed independent variable and your proposed dependent variable.
3. Show the exact demand equation you are proposing to estimate.

leadership: the "great man" traits that make an effective leader, this period range from Circa 450BC to the 1940s.

Under normal driving conditions, car tires can generate a fiction coefficient of approximately 0.7. Antilock braking systems can increase the effective coefficient of friction to as high as 1.0. For car traveling 65 miles an hour, determine the stopping distance for coefficients of friction of 0.7 and 1.0. How much more time do antilock brakes give the driver to respond. Also, why have antilock brakes not produced reductions in crash rates that were anticipated from this calculation?