In a survey of 2000 adults 50 years and older of whom 60% were retired and 40% were pre-retired, the following question was asked: Do you expect your income needs to vary from year to year in retirement? Of those who were retired, 45% answered no, and 55% answered yes. Of those who were pre-retired, 38% answered no, and 62% answered yes. If a respondent in the survey was selected at random and had answered yes to the question, what is the probability that he or she was retired? (Round your answer to three decimal places).

A scuba tank has a volume of 2000 cm3 . For very deep dives, the tank is filled with 50% (by volume) pure oxygen and 50% pure helium.

a.) How many molecules are there of each type in the tank if it is filled at 25 ∘C to a gauge pressure of 19 atm ?

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

b.) What is the ratio of the average kinetic energies of the two types of molecule?

c.) What is the ratio of the rms speeds of the two types of molecule?

Assume that the market demand function is: Q(D) = 2000 - 5P And the market supply function is: Q(S) = 100 + 5P Assume that the government passes legislation that sets the maximum price to $100 a unit. Which of the following statements are correct (multiple statements may be correct)?

1.) At a legally mandated price of $100 a unit, quantity demanded is equal to 1050 and quantity supplied is equal to 1050, therefore the legally mandated price has no impact on the market.

2.) At a legally mandated price of $100 a unit, quantity demanded is equal to 1500 and the quantity supplied is equal to 600, therefore the shortage is equal to 900 units.

3.) At a legally mandated price of $100 a unit, quantity demanded is equal to 600 while quantity supplied is equal to 1500, therefore there is a surplus in the market of 900 units, not a shortage.

4.) At a legally mandated price of $100 a unit, quantity demanded rises from 1050 units to 1500 units and quantity supplied falls from 1050 units to 600 units, resulting in a shortage of 900 units.

In reference to the year 2000 national census, the distribution of United States households according to type of living arrangement is given in the table below. An SRS of 500 households gives the observed frequencies, by household type, for the city of Aurora, Illinois.

Ethnic Origin    Census Percent    Observed frequency from sample

Married, with children                        25%                                                  95

Married, with no children                    20%                                                110

Single parent                                    5%                                                    35

Single individual                               15%                                                 65

One person                                      20%                                                 120

Other (roommate, etc.)                      15%                                                   75

Using a significance level of 0.05, test the claim that the Aurora distribution fits the distribution obtained by the census personnel.

In a dual-combustion cycle, the maximum temperature is 2000 ?C and the maximum pressure is 70 bar. Calculate the cycle efficiency and the mean effective pressure when the pressure and temperature at the start of compression are 1 bar and 17 ?C, respectively. The compression ratio is 18/1.

ANSWERS(63.7%; 10.54 bar)

The demand function for buying some plants is p(q) = 2 − q 2000 . The cost function for producing q plants is C(q) = 1000 + 0.2q.

(a) Find the marginal profit function.

(b) Find where the marginal profit function is equal to 0.

(c) Show that we get a local maximum at the value found in part (b).

A 2 by 4 wood beam (E = 2000 ksi) with an allowable flexural stress of 1200 psi is subjected to bending around it's strong axis. Determine the % increase in flexural moment capacity if the beam is reinforced by 2 0.25" steel (E = 30000 ksi) plates with an allowable flexural stress of 24000 psi at the top and the bottom of the beam respectively.

Suppose that in a community of 2000 people 10 people hear a rumor initially and 100 have heard it 1 day later. a)find a formula for the number of people who have heard the rumor t days after it began b) find the number of people who have heard the rumor 10 days after it began c) determine how long it will take for 500 people to hear the rumor (exponential growth)

10. Labor endowment in country A and B are 1000 and 2000 respectively. The labor productivity for good x in country A is 5 units of labor per unit output and for good Y in country A is 10 units of labor per unit output. The labor productivity for good x in country B is 10 units of labor per unit output and for good Y in country B is 4 units of labor per unit output.

Draw and answer the following:

Price Ratios before trade

Pattern of trade

World Pre trade production

World Post trade production

Gains from trade and trade triangle

If international price ratio were closer to country A’s pre trade price ratio which country benefits the most from trade and why?

Does it matter where the consumer is consuming pre trade in this model? In other words, does it impact pre trade prices?