A sailboat runs before the wind with a constant speed of 3.5 m/s in a direction 28 ∘ north of west. You may want to review (Pages 89 - 92) .

How far west has the sailboat traveled in 22 min?

How far north has the sailboat traveled in 22 min?

The Nile River runs from east to west. Assume the water in the Nile is electrically neutral while still conducting, and that the ions (both positive and negative in equal concentration) are carried with the flow of the water. What would the electric potential of the north side of the river be in comparision to the southern side due to the lorentz force on the ions. Remember that the magnetic field of the earth has northern and southern components.

Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1 per poster. She has fixed costs of $250. Her variable costs are $2,000 for the first thousand posters, $1,600 for the second thousand, and then $1,000 for each additional thousand posters. Instructions: Round your answers to 3 decimal places.

a. What is her AFC per poster (not per thousand!) if she prints 1,000 posters?

2,000?

10,000?

b. What is her ATC per poster if she prints 1,000?

2,000?

10,000?

c. If the market price fell to 95 cents per poster, would there be any output level at which Karen would not shut down production immediately? (Yes/ No)

A subway has good service 70% of the time and runs less frequently 30% of the time because of signal problems. When there are signal problems, the amount of time in minutes that you have to wait at the platform is described by the pdf probability density function with signal problems = pT|SP(t) = .1e −.1t But when there is good service, the amount of time you have to wait at the platform is probability density function with good service = pT|Good(t) = .3e −.3t You arrive at the subway platform and you do not know if the train has signal problems or is running with good service, so there is a 30% chance the train is having signal problems. (a) What is the probability that you wait at least 1 minute if there is good service? (b) What is the probability that you wait at least 1 minute if there are signal problems? (c) After 1 minute of waiting on the platform, you decide to re-calculate the probability that there are signal problems conditioning on the fact that your wait will be at least 1 minute long (since you have already waited 1 minute). What is that new probability? (d) After 5 minutes of waiting, still no train. You re-calculate again. What is the new probability?

Carlos lives in Philadelphia and runs a business that sells pianos. In an average year, he receives $851,000 from selling pianos. Of this sales revenue, he must pay the manufacturer a wholesale cost of $476,000; he also pays wages and utility bills totaling $281,000. He owns his showroom; if he chooses to rent it out, he will receive $71,000 in rent per year. Assume that the value of this showroom does not depreciate over the year. Also, if Carlos does not operate this piano business, he can work as an accountant, receive an annual salary of $34,000 with no additional monetary costs, and rent out his showroom at the $71,000 per year rate. No other costs are incurred in running this piano business.

Complete the following table by determining Carlos’s accounting and economic profit of his piano business.

Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1 per poster. She has fixed costs of $250. Her variable costs are $1,800 for the first thousand posters, $1,500 for the second thousand, and then $900 for each additional thousand posters.

Instructions: Round your answers to 3 decimal places.

a. What is her AFC per poster (not per thousand!) if she prints 1,000 posters?

     What if she prints 2,000 posters?

     What if she prints 10,000 posters?

b. What is her ATC per poster if she prints 1,000?

     What if she prints 2,000?

     What if she prints 10,000?

  c. If the market price fell to 85 cents per poster, would there be any output level at which Karen would not shut down production immediately? Yes or No
  

The probability a cat runs into another room for no reason is 73%. When Miss Cat sees her toy there is an 83% chance she will run to it and a 17% she will run into another room.

Given that Miss Cat has run into the other room what is the probability she saw her toy?

Gayle runs at a speed of 3.30 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayle's mass is 47.0 kg, the sled has a mass of 5.25 kg and her brother has a mass of 30.0 kg.