We all know the Earth exerts gravity on us, but other objects in the solar system also pull on us. In the following series of problems we will investigate how strong gravity is for a person standing on the surface of the Earth from various objects in the solar system. You can answer the following series of questions using Newton's Law of Gravity; use the units given and the Gravitational Constant, G = 6.67 ×10-11 m3/kg/s2.

1. What is the force of gravity due to the Earth on a 46.0 kg ASTR 110 student standing on the equator during Spring Break. DATA: Equatorial radius of the Earth 6.378×10⁶ meters; mass of the Earth 5.98×10²⁴ kg.
2. What is the force of gravity due to the Moon on a 46.0 kg ASTR 110 student standing on the equator during Spring Break. DATA: mean distance to the Moon 3.84×10⁸ meters; mass of the Moon 7.36×10²² kg.
3. When Jupiter is on the same side of the Sun as the Earth the distance between the Earth and Jupiter can be as small as 6.30×10¹¹ m. Knowing this, what is the maximum force of gravity due to Jupiter on a 46.0 kg ASTR 110 student standing on the equator during Spring Break. DATA: Mass of Jupiter = 1.90×10²⁷ kg.
4. Some people claim that the location of Jupiter can have dramatic consequences on human events on Earth. For comparison to the last problem, what is the force of gravity due to a 100 kg person hugging a 46.0 kg ASTR 110 student. Assume the distance between the students is 0.3 meters.

Problem 6 (Inference via Bayes’ Rule)
Suppose we are given a coin with an unknown head probability θ ∈ {0.3,0.5,0.7}. In order to infer the value θ, we experiment with the coin and consider Bayesian inference as follows: Define events A1 = {θ = 0.3}, A2 = {θ = 0.5}, A3 = {θ = 0.7}. Since initially we have no further information about θ, we simply consider the prior probability assignment to be P(A1) = P(A2) = P(A3) = 1/3.
(a) Suppose we toss the coin once and observe a head (for ease of notation, we define the event B = {the first toss is a head}). What is the posterior probability P(A1|B)? How about P(A2|B) and P(A3|B)? (Hint: use the Bayes’ rule)
(b) Suppose we toss the coin for 10 times and observe HHTHHHTHHH (for ease of notation, we define the event C = {HHTHHHTHHH}). Moreover, all the tosses are known to be independent. What is the posterior probability P(A1|C), P(A2|C), and P(A3|C)? Given the experimental results, what is the most probable value for θ?
(c) Given the same setting as (b), suppose we instead choose to use a different prior probability assignment P(A1) = 2/5,P(A2) = 2/5,P(A3) = 1/5. What is the posterior probabilities P(A1|C), P(A2|C), and P(A3|C)? Given the experimental results, what is the most probable value for θ?

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

Using Excel's Data Analysis Exponential Smoothing tool, forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3.

For example, help me to understand how to complete the exponential smoothing forecast model for Stock A.

Date Forecast A

9/3/2010 ____

9/7/2010 ____

9/8/2010 ____

9/9/2010 ____

9/10/2010 ____

9/13/2010 ____

9/14/2010 ____

9/15/2010 ____

9/16/2010 ____

9/17/2010 ____

9/20/2010 ____

9/21/2010 ____

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

With the help of the Excel Exponential Smoothing tool, I was able to forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3 (ie, damping factor of 0.7). I was also able to calculate the MAD of each of the stocks:

MAD of Stock A = 1.32

MAD of Stock B = 0.37

MAD of Stock C = 0.41

MAD of Stock D = 0.26

MAD of Stock Exchange = 83.85

Help me to calculate the Mean Square Error (MSE) of the stocks.

I need Urgent on the correct way to solve this, step by step process. The answers are 7.62, 7.62,6.92,20% and 7.41. Please HELP!!!

Hula Enterprises is considering a new project to produce solar water heaters. The finance manager wishes to find an appropriate risk adjusted discount rate for the project. The (equity) beta of Hot Water, a firm currently producing solar water heaters, is 1.1. Hot Water has a debt to total value ratio of 0.3. The expected return on the market is 0.09, and the riskfree rate is 0.03. Suppose the corporate tax rate is 35 percent. Assume that debt is riskless throughout this problem. (Round your answers to 2 decimal places. (e.g., 0.16)) a. The expected return on the unlevered equity (return on asset, R0) for the solar water heater project is__ %. b. If Hula is an equity financed firm, the weighted average cost of capital for the project is ___%. c. If Hula has a debt to equity ratio of 2, the weighted average cost of capital for the project is ___%. d. The finance manager believes that the solar water heater project can support 20 cents of debt for every dollar of asset value, i.e., the debt capacity is 20 cents for every dollar of asset value. Hence she is not sure that the debt to equity ratio of 2 used in the weighted average cost of capital calculation is valid. Based on her belief, the appropriate debt ratio to use is ___%. The weighted average cost of capital that you will arrive at with this capital structure is___ %.

Use the following information of a hypothetical economy to answer this question: National Income (Y) = 5,200; Government Budget Deficit = 150; Disposable Income (Yd) = 4,400; and Consumption (C) = 4,100. The value of Investment (I) is

Group of answer choices

A150

B260

C270

D280

Enone of the above

Suppose that the economy is characterized by the money demand function with nominal income $Y = 4000 and money supply . Which of the following is false?

Group of answer choices

A equilibrium money demand is 200

B the equilibrium interest rate is i = 0.025

C an increase in nominal income will increase the equilibrium interest rate

D an increase in the money supply will decrease the equilibrium interest rate

E the equilibrium interest rate i = 0 if central bank increases money supply to

Suppose the population of a country is 100 million people, of whom 50 million are working age. Of these 50 million, 20 million have jobs. Of the remainder: 10 million are actively searching for jobs; 10 million would like jobs but are not searching; and 10 million are discouraged workers. The labour force participation rate is

Group of answer choices

A 0.6

B 0.3

C 0.8

D 0.4

Assume the economy is initially operating at the natural level of output. Suppose that individuals decide to increase their saving. Which of the following must increase in both the short run and median run equilibria?

Group of answer choices

A output

B interest rate

C price level

D investment

E consumption

Due to tides mean sea level off of Newport Beach reaches a height of 1.3 meters during high

tide and 0.3 meters during low tide. Successive high tides occur every 12 hours (43,200

seconds). A buoy with mass m = 40 kg is floating in the ocean off of Newport Beach.

1) Relevant concepts/equations. (5 points.)

2) Assume we begin to measure the buoy’s displacement at High tide which occurs exactly

at 12:00 am (0 seconds). Also assume we can model the buoy’s displacement as a simple

undamped oscillation. What is the Amplitude and phase angle for the buoy’s

displacement? (10 points)

3) During one half cycle of six hours (21600 seconds), the buoy’s displacement passes

through an angle of 180 degrees. From this information, what is the angular frequency

ω of the buoy? (5 points)

4) Using your previous answer, what is the force constant ‘k’ acting on the buoy? (5 points)

5) What is the maximum velocity of the buoy? What is the maximum acceleration of the

buoy? (10 points)

6) What is the energy of the buoy due to tidal displacement? (5 points)

7) How much work is done during one low tide to high tide cycle? How much Power per

hour is required to accomplish this? (Assume g = 9.81 m/s^2 compare your answer to a

65W light bulb which uses 65 watts per hour). (10 points)

Exercise 1. Firm Supply in the Short Run

Consider a firm with the following production function: y=L^½K^½. The cost function is C=w∙L+r∙K.

1. In the short-run the input K is given at K=100. What is the short-run production function y(L)?

2. Let w=0.1 and r=1. What is the cost function C(y)? Using the expression y(L) you found in part a, transform it into L(y) and plug it into the cost function C(L) to get C(y). Was a minimization necessary? Why or why not?

3. Given C(y) you find in part b, find AC(y) and MC(y). What is the firm’s short-run supply function S(p)?

4. At what level of y is the average cost minimized?

5. When the market price is p=0.2, how much does the firm supply? Find S(0.2). What is the firm’s profit? What is the firm’s producer surplus? How many workers does the firm employ? Find L.

6. When the market price is p=0.1, how much does the firm supply? Find S(0.1). What is the firm’s profit? What is the firm’s producer surplus? How many workers does the firm emply? Find L.

7. When the market price is p=0.3, how much does the firm supply? Find S(0.1). What is the firm’s profit? What is the firm’s producer surplus? How many workers does the firm emply? Find L.

Due to tides mean sea level off of Newport Beach reaches a height of 1.3 meters during high

tide and 0.3 meters during low tide. Successive high tides occur every 12 hours (43,200

seconds). A buoy with mass m = 40 kg is floating in the ocean off of Newport Beach.

1) Relevant concepts/equations. (5 points.)

2) Assume we begin to measure the buoy’s displacement at High tide which occurs exactly

at 12:00 am (0 seconds). Also assume we can model the buoy’s displacement as a simple

undamped oscillation. What is the amplitude and phase angle for the buoy’s

displacement? (10 points)

3) During one half cycle of six hours (21600 seconds), the buoy’s displacement passes

through an angle of 180 degrees. From this information, what is the angular frequency ω of the buoy? (5 points)

4) Using your previous answer, what is the force constant ‘k’ acting on the buoy? (5 points)

5) What is the maximum velocity of the buoy? What is the maximum acceleration of the

buoy? (10 points)

6) What is the energy of the buoy due to tidal displacement? (5 points)

7) How much work is done during one low tide to high tide cycle? How much Power per

hour is required to accomplish this? (Assume g= 9.81m/s^2 , compare your answer to a 65W light bulb which uses 65 watts per hour.)