Brady is a figure skater. He finds a few of the jumps he does to be difficult, but the rest are easy for him. He must include four jumps in his routine. He always makes the first jump a difficult one. After a difficult jump, there is a 0.4 probability that he'll do another difficult jump, and otherwise he'll do an easy one. After an easy jump, there is a 0.2 probability that he'll do another easy one, and otherwise he'll do a hard one.  

What is the probability that the final (fourth) jump of his routine will be an easy one?    

What is the probability that all four jumps of his routine will be difficult ones?    
Enter your answers as whole numbers or decimals.

Mulitple Choice please answer all 3 no need to go in Depth

One mole (mol) of glucose (molecular mass = 180 daltons) is.

If the pH of a certain soda drink is 2, what is the hydrogen ion concentration in that drink?

Which chemical group is most likely responsible for an organic molecule behaving as a base?

Principles of Macroeconomics

Consider two economies (US and CAN) that begin in steady state. The two countries are identical. The production function is:

? = ?? + ?

Suppose the following parameter values:

? = 1, ? = 0.1, ? = 0.2, ? = 1000

Then, a strong earthquake destroys 90% the steady state physical capital in CAN and 10% the steady state physical capital in US.

Assume these new levels of steady state physical capital become the starting levels of capital for each economy at period 0: ?₀.

Find the growth rate of output for each economy between the periods 0 and 1. Do you observe the catch-up effect (Mankiw, Chapter 12) in this case? Explain in terms of the level of output and its corresponding growth rate.

Consider the following daily time series representing the number of clients visiting the Small Business Development Center over the previous 10 days.

Step 1 of 2: What is the Simple Exponential Smoothing Forecast for day 11 (t = 11) assuming that the smoothing constant, alpha = 0.2?
Round to 2 decimal places.

Step 2 of 2: What is the Simple Exponential Smoothing Forecast for day 11 (t = 11) assuming that the smoothing constant, alpha = 0.75?
Round to 2 decimal places.

1.) How many milligrams of sodium chloride should be used in compounding the prescription?

*Type in your answer to 2 decimal places. Do not forget the unit

2.)

How many milliliters of a 0.9% solution of NaCl should be used to prepare the prescription?

*Type in your answer to 2 decimal places. Do not forget the unit

Discrete random variables X and Y have joint probability mass function defined by the table below.

X= { 0 , 1 , 2 } , Y= { − 2 , 0 , 2 }   

A.) Evaluate the expected value of X (round to 2 decimal digits)

B.) Evaluate the variance of X (round to 2 decimal digits)

C.) Evaluate the covariance of X and Y. (round to 2 decimal digits) Are X and Y independent?

D.) Let W=3X-2Y+4. What is the mean of W? What is the standard deviation of W? (round to 2 decimal digits)

Based on the balance sheet below, answer the following questions.

a) Based on the balance statement above, calculate the level of capital that Melvin's must hold to satisfy the minimum equity ratio (5%)

b) Based on the balance statement above, calculate the level of capital that Melvin's must hold to satisfy the risk based Basel requirement (8%)

c) which of the two requirement is more stringent in this case? If so, why?  

(3) The US produces about 12 million barrels of oil per day and consumes about 22 million barrels per day (mbpd). Global production and consumption are about 100 mbpd. About 0.75 mpbd come from federal land, and about 1.75 mbpd come from federal waters (primarily the Gulf of Mexico). The current oil price is about $50, the elasticity of oil supply is 0.1 and the elasticity of oil demand is -0.2.

a. Using these numbers, calculate the long-term effect on prices and quantities of banning drilling on federal land.

b. Using these numbers, calculate the long-term effect on prices and quantities of banning drilling on federal land and federal waters.

Suppose the economy is experiencing a recessionary gap of $0.5 trillion. The marginal propensity to consumer is MPC = 0.2. To mitigate or close the gap, the fiscal government need to choose between two options: increase government spending G or decrease taxes. Fill in the gaps with numerical answers unless otherwise instructed. Round your answers to one decimal place (for example, 1.25 ~ 1.3).

1. The value of the spending multiplier is at most equal to .
2. The value of the tax multiplier is at most equal to .
3. Suppose the government chooses to not change the taxes. Then, it should increase spending by at least $ trillion in order to close the gap.
4. Suppose the government chooses to not change government spending. Then, it should decrease taxes by at least $ trillion in order to close the gap.

1. For what kinetic energy is the de Broglie wavelength of an electron equal to its Compton wavelength? Express your answer in units of mc2 in doing the calculation, and then use mc2 = 0.5 MeV.(Answer: 0.2 MeV)

2. A beam of electrons with energy 1.0 eV approaches a potential barrier with U = 2.0 eV, whose width is 0.10 nm (see a figure below). Estimate the fraction of electrons that tunnel through the barrier. (Hint: use the relation of probability and the wave function, and the expression for wave function for barrier penetration)

3. Calculate the Fermi energy of sodium (n= 2.65·10^28 m^-3). This metal has a single valence electron per atom.(Answer: 3.25 eV.)