keplers third law states that the square of the period of any planets orbit is proportional to the cube of the semimajor axis of the orbit. for the following, show all your work and dont skip steps

derive the exact expression relating the period (T) and the radius (r) for a planet in circular orbit by applying newtons second law for circular motion.

the orbital period of mars in its revolution around the sun is 1.88 years what average distance from the sun does the keplers thirdlaw predict for mars?

The law of mass conservation is another fundamental law in chemistry. this law states that matter can neither be created or destroyed, which means that in a chemical reactions where all the reactant is converted into product, the mass of reactant must be equaly equal to mass of product produced. A) consider 2 precipitation reactions B) experimental procedure that you can use in lab C) contemplate how you might visually represent this data (I) what variables might you need to plot (ii) how would your choice of graph illistrate the law of mass conservation

Contrast how the activity of the liver enzyme is altered in the following physiological states: (1) After a heavy meal. (2) After you have run half a mile. (3) After you have not eaten for 3 days. Does the activity of the muscle phosphorylase differ under these conditions?

1. NPV According to the text, the NPV rule states that "An investment should be accepted if the NPV is positive and rejected if it is negative." What does an NPV of zero mean? If you were a decision-maker faced with a project with a zero NPV (or very close to zero) what would you do? Why?

2. FORECASTING ERROR (RISK) What is a "forecasting error"? Why is it important to the analysis of capital expenditure projects?

A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $1,800 per month for the next three years and then $800 per month for two years after that. If the bank is charging customers 9.25 percent APR, how much would it be willing to lend the business owner? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

A company’s IT policy states that passwords should contain 14 characters with a mix of letters, numbers, and special characters. After reviewing the implemented policy within the IT system, it is noted that the current security settings stated that passwords only need to be 6 character long. Answer the following questions.

What are the threats?
What are the risks?
How would you mitigate the risks?

Stocks A and B have the following returns in each of the states given below.

The probability of the boom is 0.5, the probability of the normal economy is 0.3 and the probability of the recession is 0.2.
(a) Calculate the variance of the returns of A and the variance of the returns of B
(b) What is the covariance between the returns of A and B?

(c) What is the standard deviation of a portfolio of A and B with equal amounts invested in both?

CP Oil Inc. of the Unites States of America and AZ Oil of Australia are negotiating an international agreement to work together.

You work for CP Oil Inc. Your job is to ensure that the proper wording to allow for an international Arbitration is put into the contract in case there are any disputes.

1. What terms are you going to include in the contract?
2. Why?

1. Following are the returns on two assets and three states of the economy

1. What are the expected returns and standard deviations for these two stocks?
2. What do you interpret? Which stock is riskier?

The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives:

1. Use graphical sensitivity analysis to determine the range of probabilities of state of nature s ₁ for which each of the decision alternatives has the largest expected value. If required, round your answers to two decimal places.
   

   d1 is optimal for probability of s 1	≥ ??
   d2 is optimal for probability of s 1	≤ ??

2. Suppose P(s₁) = 0.85 and P(s₂) = 0.15. What is the best decision using the expected value approach?
   

   Best decision:

   ??

3. Perform sensitivity analysis on the payoffs for decision alternative d₁. Assume the probabilities are as given in part (b), and find the range of payoffs under states of nature s₁ and s₂ that will keep the solution found in part (b) optimal. Is the solution more sensitive to the payoff under state of nature s₁ or s₂?
   
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