A skater is doing skating with his arms stretched out, as soon he brings his arm closed to his body, his rotation speed increases significantly. Explain this phenomenon in the light of law of conservation of angular momentum.

IV. Continuity

The mass flow rate and the volume flow rate are always the same in a closed pipe. Why do you think that has to be the case? (Try and think about what might happen if the rates were not the same).

The Cares act provided cash payments to the majority of households in the U.S. Using AD-AS model, explain how it would affect the U.S. economy. What would determine the effectiveness of this policy. Does it matter if the economy is closed or open?

Prove the following Theorems:

1. A finite union of compact sets is compact.

2. Any intersection of compact set is compact.

3. A closed subset of a compact set is compact.

4. Every finite set in IRⁿ is compact.

Under the physician’s cooperative model, if the supply price of physicians were to rise, how would this affect the equilibrium staff size in the open-staff case? How would it affect the optimal staff size in the closed-staffed case?

Describe the operation of an OPAMP-based oscillator using the concept of a basic oscillator feedback circuit. Your description must include all pertinent equations relating the overall closed loop gain and the open-loop and feedback gain

1.Currently, individuals can work up to 80 hours each week at a pre-tax wage of $20 per hour, but they face a constant 20% payroll tax, which reduces their after tax wage to $16 per hour. The government is considering imposing a negative income tax. Under this tax policy, everyone is given $300 each week, and everyone and anyone can supplement her income further by working. To pay for the negative income tax, the payroll tax rate will be increased to 50%.

a. Using the leisure-consumption model, draw the budget constraints faced by workers before and after the proposed negative income tax. Label the original constraint BL0and the post-policy constraint BL1. Make sure to label axes, intercepts, and intersection points.

b.True/False/Uncertain: A worker who maximizes utility by working 40 hours before the negative income tax is implemented will reduce her number of hours worked after the negative income tax is implemented. Support your response using both graphical and theoretical analysis. You may show your graphical analysis in your diagram in part A. You may assume the worker’s indifference curves have the typical shape.

# R Hypothesis Tests

install.packages("dplyr")

tScore_before <- c(40, 62, 74, 22, 64, 65, 49, 49, 49)

tScore_after <- c(68, 61, 64, 76, 90, 75, 66, 60, 63)

# Create a data frame

my_data <- data.frame(

                group = rep(c("Score Before", "Score After"), each = 9),

                scores = c(tScore_before, tScore_after)

                )

# Print all data

print(my_data)

#Compute summary statistics by groups

library(dplyr)

group_by(my_data, group) %>%

summarise(

    count = n(),

    mean = mean(scores, na.rm = TRUE),

    sd = sd(scores, na.rm = TRUE)

)

# Compute Unpaired Two Sample t-test

res <- t.test(tScore_before, tScore_after, var.equal = TRUE)

res

# Compute independent t-test

res <- t.test(scores ~ group, data = my_data, var.equal = TRUE)

res

#test whether the average score before score is less than the average after score, type this:

t.test(scores ~ group, data = my_data,

        var.equal = TRUE, alternative = "less")

The instructions say to include a snippet of the graph created but I do not get a graph after running this code. Just wanted to make sure there is not one.

N0PV Corporation is considering buying a cost saving machine. The new machine costs $1 million and will last for 10 years. The new machine will be linearly depreciated over 10 years. Assume that they expect the machine to be worthless after 10 years. If they decide to buy the new machine, they will sell the old machine for $200,000. The current book value of the old machine is $250,000. The old machine has a remaining life of 2 years in which the remaining book value is linearly depreciated. The new machine will result in a cost saving of $130,000 every year before tax. Assume a tax rate of 30%. N0PV uses the company WACC to evaluate the project as it has the same risk as N0PV in general and will be financed with the same mix of equity and debt. The equity beta of N0PV is 1.5. The risk-free rate is 2% and the expected return on the market is 7%. The cost of debt before tax is 4%. The market value of debt to equity is 1. If they decide not to do the project they can use the old machine for another 10 years. If they decide to keep the old machine (and not buy the new one) the old machine will be worthless after 10 years.

Question: What is the present value (after tax) of the annual cost savings?

Predict the number of people arrested for drug possession in 2016 and 2017 from the data Year # of People Arrested 2006 1,519,760 2007 1,361,658 2008 1,321,824 2009 1,387,915 2010 1,179,728 2011 1,143,931 2012 1,237,708 2013 1,203,323 2014 982,169 2015 801,560 2016 2017 2018