A 11.0−m by 8.0−m by 4.0−m basement had a high radon content. On the day the basement was sealed off from its surroundings so that no exchange of air could take place, the partial pressure of 222Rn was 1.9 × 10−6 mmHg. Calculate the number of 222Rn isotopes (t1/2 = 3.8 days) at the beginning and end of 29 days. Assume STP conditions.

(Enter your answers in scientific notation.)

A ring of charge with radius R = 2.5 m is centered on the origin in the x-y plane. A positive point charge is located at the following coordinates: x = 17.1 m y = 3.8 m z = -16.3 m The point charge and the total charge on the ring are the same, Q = +81 C. Find the net electric field along the z-axis at z = 4.5 m.

E_{net,x =}

E_{net,y =}

E_{net,z =}

Generate the Simple linear regression results and Parameter estimates table in StatCrunch for the least-squares regression equation and include them with your submission.

Stock in Country Road Industries has a beta of 1.62. The market risk premium is 8.2 percent while T-bills are currently yielding 2.9 percent. Country Road's last paid annual dividend was $1.87 per share and dividends are expected to grow at an annual rate of 3.8 percent indefinitely. The stock sells for $25 a share. What is the estimated cost of equity using the average return of the CAPM and the dividend discount model?

At the center of a 50-mm-diameter circular ice rink, a 76 kg skater traveling north at 2.7 m/s collides with and holds onto a 61 kg skater who had been heading west at 3.8 m/s .

How long will it take them to glide to the edge of the rink?

Express your answer using two significant figures.

Where will they reach it? Give your answer as an angle north of west.

A 0.49 kg mass at the end of a spring vibrates 8.0 times per second with an amplitude of 0.10 m.

(a) Determine the velocity when it passes the equilibrium point.

m/s

(b) Determine the velocity when it is 0.10 m from equilibrium.

m/s

(c) Determine the total energy of the system.

J

(d) If the amplitude of oscillation were increased by a factor of 3.8, by what factor does the total energy change?

You decide to invest in a portfolio consisting of 40 percent Stock A, 40 percent Stock B, and the remainder in Stock C. Based on the following information, what is the expected return of your portfolio? State of Economy Probability of State Return if State Occurs of Economy Stock A Stock B Stock C Recession .18 - 18.6 % - 3.8 % - 22.7 % Normal .55 10.4 % 8.4 % 17.0 % Boom .27 28.4 % 15.7 % 31.6 .

We are going to derive the average number of moves for quicksort using a somewhatunusual partitioning algorithm. We partition on the first element. Take it out. Look for theright most element that is smaller and place it in the first position (which is the newly openedposition on the left side). Look for the left most element that is larger and place it in the newlyopened position on the right side. Starting from there look for the right most element that issmaller and place it in the the newly opened position on the left side. Starting from there lookfor the left most element that is larger and place it in the newly opened position on the rightside. Continue in this fashion until the pointers cross. Finally, put the partition element intothe hole, which is its final position in the sorted array.(a) Assume that the partition element ends up in positionq.i. What is the probability that an element originally to the left (of positionq) went tothe right (of positionq)?ii. What is the expected number of elements originally to the left that go to the right?iii. What is the probability that an element originally to the right went to the left?iv. What is the expected number of elements originally to the right that go to the left?v. What is the total expected number of moves (for partition)?(b) Write a recurrence for the expected number of moves (for quicksort).(c) Simplify the recurrence, but do not solve it.

1a. Derive government spending and tax multiplier in the Keynesian-cross model using calculus

1b. Consider the model of Keynesian cross with fixed planned investment expenditure, government spending and taxes. Assume that consumption function is given by C=a+mpc*(Y-T), where the parameter a >0 is called autonomous consumption, and the marginal propensity to consume satisfies 0< mpc <1. Compute equilibrium output (income) as a function of parameters (a and mpc) and exogenous variables. How does equilibrium output depend on a? mpc? Government spending? Taxes?

1c. Suppose that the real interest rate is 2% and expected inflation rate is 4%. What does Fisher equation predict nominal interest rate t

4. If a drop in government spending of $ 2 billion produces a drop in the economy's real GDP of $ 10 billion, what is the value of that country's PMC?

5. When the price level is fixed and the investment increases by $ 100, the equilibrium expense increases by $ 500.

a. Both the marginal propensity to consume and the multiplier is 0.2
b. The multiplier is 0.2.
c. The multiplier is 5.0.
d. The slope of the GA curve is 0.2.

6. All of the following statements about equilibrium spending are true except:
a. The unplanned investment in inventories is zero.
b. The planned aggregate expense equals the actual expense.
c. Planned aggregate spending equals real GDP.
d. The effective investment is less than the planned investment.