How far away is a star that has a parallax of 0.03 seconds of arc? 0.3 parsecs/333.3 parsecs/33.3 parsecs/3.3 parsecs

If you took a measuremnt for a stars position in March, using parallex when is the optimum month for the next measurement? Sept /Oct/ April/ any month

The nearest stars have been catalogued using parallax what is the range of the stars found in this catalogue? 4 to 100 parsecs/ 2 to 1000 parsecs/ 10 to 50 parsecs/ all stars out to 500 parsecs

Compared to close stars, the parallax angle is ________________ for more distant stars. Smaller/ larger/ the same as/ unrelated to distance of stars

Why are astronomers much more interested in the luminosity of a star than its apparent brightness? because the luminosity tells us how bright a star really is, while apparent brightness only tells us how bright it happens to look from Earth/because luminosity can be measured exactly, but apparent brightness can only be roughly estimated/because the luminosity also tells us what elements the star is made of, while apparent brightness cannot tell us a star's chemical make

Using the results from question 2, answer the following questions:

1. Suppose p_x =5, p_z =2 and Y =50. What is the optimal bundle consumed? (Label this as the initial bundle)
2. Now suppose that the price of good x decreases to p_x = 2.5. Now what is the optimal bundle consumed? (Label this as the final bundle)
3. Calculate the decomposition bundle associated with this price change. (The answers won’t be integers)
4. Calculate the Income Effect, Substitution Effect, and Total Effect for good x.

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Results from question 2:
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Consider a market with two goods, x and z that has the following utility function U = x^0.2z^0.8

a) What is the marginal rate of substitution?

b) As a function of the price of good x (px), the price of good z (pz) and the income level (Y ), derive the demand functions for goods x and z.

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a) Marginal rate of substitution is the rate at which the consumer is willing to give up one good in order to obtain one more unit of the other good.

In this case, marginal rate of substitution = marginal utility of good x / marginal utility of good z

Marginal utility of the two goods can be calculated by differentiating the utility function with respect to that good keeping the other good constant.

Marginal utility of good x = 0.2x^-0.8z^0.8

Marginal utility of good z = 0.8x^0.2z^-0.2

So, marginal rate of substitution = 0.2x^-0.8z^0.8 / 0.8x^0.2z^-0.2

= 0.2x^-1/0.8z^-1 = 2z/8x = z/4x is the answer.

b) The budget line equation of the above question can be written as:

p_xx + p_zz = Y

The demand functions of the two goods can be calculated by using the optimal condition that is,

Marginal rate of substitution = p_x / p_z

So, z/4x = p_x / p_z

z = 4x ( p_x / p_z)

Putting the value of z in the budget line equation above,

p_xx + p_z [4x ( p_x / p_z)] = Y

p_xx + 4p_xx = Y

5p_xx = Y

x = Y / 5p_x is the answer.

Now, putting the value of x in the equation of z derived above,

z = 4x ( p_x / p_z)

z =  4 X (Y / 5p_x) X ( p_x / p_z)

z = 4Y / 5p_z is the answer.

7. The evaporation of water cools the surroundings, and the condensation of this vapor
   1. Does nothing
   2. Warms the surroundings
   3. Increases the value of the latent heat of vaporization
   4. Decreases the value of the latent heat of vaporization

8. The heat involved in the change of phase form solid ice to liquid water is
   1. Latent heat of vaporization
   2. Latent heat of fusion
   3. Latent heat of condensation
   4. None of the above
9. More molecules are returning to the liquid state than are leaving the liquid state. This process is called
   1. Boiling
   2. Freezing
   3. Condensation
   4. Melting
10. The temperature of a gas is proportional to the
    1. Average velocity of the gas molecules
    2. Internal potential energy of the gas
    3. Number of gas molecules in a sample
    4. Average kinetic energy of the gas molecules
11. The specific heat of soil is 0.2 cal/g⁰C, and the specific heat of water is 1 cal/g⁰C. This means that if 1 kg of soil and 1 kg of water each receives 1 kcal of energy, ideally,
    1. The water will be warmer than the soil by 0.8 ⁰C
    2. The soil will be 4 ⁰C warmer than the water
    3. The soil will be 5 ⁰C warmer than the water
    4. The water will warm by 1 ⁰C, and the soil will warm by 0.2 ⁰C
12. Styrofoam is a good insulating material because
    1. It is a plastic material that conducts heat poorly
    2. It contains many tiny pockets of air
    3. Of the structure of the molecules that make it up
    4. It is not very dense
13. As a solid undergoes a phase change to a liquid, it
    1. Releases heat while remaining at a constant temperature
    2. Absorbs heat while remaining at a constant temperature
    3. Releases heat as the temperature decreases
    4. Absorbs heat as the temperature increases
14. Which of the following contains the most heat
    1. A bucket of water at 0⁰C
    2. A barrel of water at 0⁰C
    3. Neither contains ay heat since the temperature is zero
    4. Both have the same amount of heat
15. Conduction best takes place in a
    1. Solid
    2. Fluid
    3. Gas
    4. Vacuum
16. Convection best takes place in a(an)
    1. Solid
    2. Fluid
    3. alloy
    4. Vacuum
17. The phase change from ice to liquid water takes place at
    1. Constant pressure
    2. Constant temperature
    3. Constant volume
    4. All of the above
18. Which of the following has the greatest value for liquid water?
    1. Latent heat of vaporization
    2. Latent heat of fusion
    3. Both are equivalent
    4. None of the above is correct

Company X and Company Y have been offered the following rates per annum on a 10 million 5-year loan: Fixed Rate Floating Rate Company X 6.2% LIBOR + 0.3% Company Y 7.8% LIBOR + 1% Company X requires a floating rate loan; company Y requires a fixed rate loan. Design a swap that will net a bank acting as intermediary 0.3 percent per annum and which will be equally attractive to X and Y. You need to draw a diagram to indicate the interest rate flows.

The distribution of the number of siblings for students at a large high school is skewed to the right with mean 1.8 siblings and standard deviation 0.7 sibling. A random sample of 100 students from the high school will be selected, and the mean number of siblings in the sample will be calculated. Which of the following describes the sampling distribution of the sample mean for samples of size 100 ?

A

Skewed to the right with standard deviation 0.7 sibling

B

Skewed to the right with standard deviation less than 0.7 sibling

C

Skewed to the right with standard deviation greater than 0.7 sibling

D

Approximately normal with standard deviation 0.7 sibling

E

Approximately normal with standard deviation less than 0.7 sibling

The distribution of height for a certain population of women is approximately normal with mean 65 inches and standard deviation 3.5 inches. Consider two different random samples taken from the population, one of size 5 and one of size 85.

Which of the following is true about the sampling distributions of the sample mean for the two sample sizes?

• Both distributions are approximately normal with mean 65 and standard deviation 3.5.

  A

• Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

  B

• Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.

  C

• Only the distribution for size 85 is approximately normal. Both distributions have mean 65 and standard deviation 3.5.

  D

• Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

E

The distribution of wait times for customers at a certain department of motor vehicles in a large city is skewed to the right with mean 23 minutes and standard deviation 11 minutes. A random sample of 50 customer wait times will be selected. Let x¯W represent the sample mean wait time, in minutes. Which of the following is the best interpretation of P(x¯W>25)≈0.10 ?

• For a random sample of 50 customer wait times, the probability that the total wait time will be greater than 25 minutes is approximately 0.10.

  A

• For a randomly selected customer from the population, the probability that the total customer wait time will be greater than 25 minutes is approximately 0.10.

  B

• For a randomly selected customer from the population, the probability that the sample mean customer wait time will be greater than 25 minutes is approximately 0.10.

  C

• For a random sample of 50 customer wait times, the probability that the sample mean customer wait time will be greater than 23 minutes is approximately 0.10.

  D

• For a random sample of 50 customer wait times, the probability that the sample mean customer wait time will be greater than 25 minutes is approximately 0.10.

E

The currency drain ratio is 0.2 and the desired reserve ratio is 0.5.

What is the money multiplier?

The money multiplier is __.

The Long Run Economy

a)   An economy has a savings rate of s = 0.2 and capital depreciates at a rate of δ=0.1. Output is produced using the production function:

?(?) = ?√(?)(?),

Where Y(t) is GDP, K(t) is the capital stock, L(t) is the number of workers. TFP A has the value of A=2. Assume that the working population is constant in size.

a) What will GDP per capita in the economy be in the long run (steady state)?

b)   In this same economy where s=0.2, what is the consumption function in this economy (i.e., what is consumption as a function of income)?

c)   If there is no government spending or taxation in this economy what is the real interest rate r in the long run (steady state) if the investment function is

? = 3.6 − 8?.

d)   What is inflation π in the long run (steady state) if the supply of money grows at 5% a year?

e)   What is the nominal interest rate i in this economy in the long run?

f) What is the long run (steady state) frictional unemployment rate in this economy if unemployed workers have a 97% chance of finding a job each month and 3% of workers separate from their jobs each month?

Consider the following time series data.

a) Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7? (Round your answer to two decimal places.)

Forecast=?

(e)Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.

Consider the following time series data.

a) Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7? (Round your answer to two decimal places.)

Forecast=?

(e)Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.