In a hypothetical experiment, electrical current of 15 AMPs driven by an applied potential of 100 volts passes through a cylindrical rod (3 mm in diameter and 7 cm long). Recall, the power is calculated by power(Watts) = potential(VOLTS) x current(AMPS). The electrical power heats the cylindrical rod to a high temperature. The rod is inside of a ceramic tube (ID = 12 mm). The wall temperature of the ceramic tube is 600 C (maintained at this stead temperature by air cooling on the outside). Assuming that convection and conduction between the resistor and the ceramic tube are negligible compared to thermal radiation, estimate the surface temperature of the rod. The emissivity of the ceramic tube is 0.9 and the emissivity of the resistor is 0.8.

1. Write the chemical equation for the reaction of an antacid containing magnesium hydroxide, Mg(OH)₂, with stomach acid (hydrochloric acid, HCl) and then balance the equation.

2. If a tablet of the antacid neutralized 41.4 mL of 0.150 M hydrochloric acid then how many grams of magnesium hydroxide was in the tablet?

(Show calculation)

3.Concentrated gastric acid is about 0.16 molar in concentration (0.16 M HCl), corresponding to a pH of 0.8. In the stomach, however, the solution becomes diluted to a pH between 1 and 2. Using the information from Q.5 calculate how many milliliters of gastric acid can be neutralized by 1 tablet of antacid?

(Show calculation)

A state policymaker is thinking about reducing taxes to boost the local GDP. However, she is concerned about negative effects on the budget and orders a survey to gauge her voter’s consumption behaviour. The relevant information is summarized below.  

C = 600 + 0.8(DI)

Multiplier:

1 / 1−mpc

14. What is the size of the multiplier?

15. Assume she goes through with her plan and reduces taxes. As a consequence, she generates a tax revenue of T=100. By how much will consumption increase? By how much Savings?

16. Use your results from Q14 and Q15 to calculate the eventual increase in GDP resulting from the tax policy.

Answer two (2) of the following essay questions.

1) How do automatic stabilizers, on both the expenditure and revenue sides of the budget, respond when the economy is in 1) a contractionary 2) an expansionary gap?

2) How much should the government 1) increase spending or 2) cut taxes when the economy is in a contractionary gap equal to 500 billion and the MPC equals 0.8.

3) According to the classical school of economists, the economy is self-correcting. Explain why the economy will automatically move to long run equilibrium (potential output) when it is in an expansionary and in a contractionary gap.

4) Give an account of how an increase in government spending can lead to an increase in the trade deficit.

The price of natural gas varies from country to country. Suppose the country price is normally distributed with a mean of $5 per thousand cubic feet and standard deviation of $0.8.

(a) What is the first quartile of the price of natural gas? What is the 95th percentile of the price of natural gas? Show your work.

(b) We are analyzing a group of seven countries. What is the probability that the price of natural gas would exceed $5 in more than five of those countries? Show your work.

(c) Take two countries and assume that their prices of natural gas are independent. What is the probability that the price of gas is lower than $4 in at least one of them?

You and a team of scientists are interested in understanding whether your weight gain drug was useful to help underweight population to gain weight. For your sample of 25 people, their weight was measured before, and then post the drug administration. The difference in their weight, was measured and calculated by POST – PRE. The sample had an average difference of + 0.8 lbs, with a standard deviation of 1.5 lbs. Does your sample suggest that your weight gain drug was useful in helping underweight population gain weight? Test your hypothesis at 5% significance. a. Hypothesis and identify/calculate the critical value. (5pts) Ho: Ha: Critical Value: b. Calculate the statistics (10 pts) c. Conclusion (5pts)

In the two-period model of consumption, suppose that the first period income is $5,000 and the second period income is $5,500 for both Jill and Jack. The interest rate is 10 percent. Jack’s lifetime utility function is ?1 + ?2 while Jill’s lifetime utility function is ?1 + 0.8?2.

1)Draw a graph that represents the common budget constraint that Jill and Jack face.

2)Draw indifference curves of Jill and Jack in separate graphs and compare the slopes of the indifference curves with the slope of the budget constraint curve.

3)Determine the optimal consumption in period 1 and 2, for both Jill and Jack.

4)If there is a borrowing constraint, whose consumption is affected by that?

A project under consideration has an internal rate of return of 13% and a beta of 0.8. The risk-free rate is 3%, and the expected rate of return on the market portfolio is 13%.

a. What is the required rate of return on the project? (Do not round intermediate calculations. Enter your answer as a whole percent.)

b. Should the project be accepted?

c. What is the required rate of return on the project if its beta is 1.80? (Do not round intermediate calculations. Enter your answer as a whole percent.)

d. If project's beta is 1.80, should the project be accepted?

A ) Required rate of return__________%

B) Accept the Project = Yes or No

C) Required rate of return __________%

D) Accept the project = Yes or No

Real GDP, consumption, and the marginal propensity to consume (MPC) for five hypothetical countries are shown in the table below.

a. Enter the current level of saving in the appropriate column in the table.

b. Now suppose that GDP increases by $20 billion in each of the five countries. What would be the new level level of saving in each country? Show your answers in the table below.

Payroll Entries Widmer Company had gross wages of $314,000 during the week ended June 17. The amount of wages subject to social security tax was $282,600, while the amount of wages subject to federal and state unemployment taxes was $39,000. Tax rates are as follows: Social security 6.0% Medicare 1.5% State unemployment 5.3% Federal unemployment 0.8% The total amount withheld from employee wages for federal taxes was $62,800. If an amount box does not require an entry, leave it blank. a. Journalize the entry to record the payroll for the week of June 17. b. Journalize the entry to record the payroll tax expense incurred for the week of June 17.