Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:

*Contains direct materials, direct labor, and variable manufacturing overhead.

Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to “get things under control.” Upon reviewing the plant’s income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:

*Based on machine-hours.

During June, the plant produced 5,000 pools and incurred the following costs:

1. Purchased 24,500 pounds of materials at a cost of $2.95 per pound.

2. Used 19,300 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)

3. Worked 4,600 direct labor-hours at a cost of $7.70 per hour.

4. Incurred variable manufacturing overhead cost totaling $5,070 for the month. A total of 1,300 machine-hours was recorded.

It is the company’s policy to close all variances to cost of goods sold on a monthly basis.

Required:

1. Compute the following variances for June:

a. Materials price and quantity variances.

b. Labor rate and efficiency variances.

c. Variable overhead rate and efficiency variances.

2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month.

Deakin Ltd has just recently published following financial information:

Expected earnings per share $20

Deakin’s market beta 0.8

Earnings per share to be retained by the firm 30%

Growth rate in earnings per share 7% p.a.

Required:

1. Calculate Deakin's P/E ratio if the expected return on the ASX300 is 12% p.a. and the return on 10 year Commonwealth Government Bonds is 4% p.a. What does this ratio tell you?

2. Calculate Deakin's share price using P/E ratio calculated in Part 1.

The COVID-19 crisis has led to unprecedented fiscal measures. Use the IS-LM curves as well as the AD-AS curves to show the impacts of Congress and President Trump’s stimulus relief actions. Be sure to label all axes and curves. In one or more paragraphs explain what should happen when we assume the MPC is 0.8 and both spending and tax measures are taken to heal the economy. What part does a democrat majority congress and a republican president play in these decisions. Also, discuss the impact on all variables and economic agents. Be sure to indicate the direction of movement for all variables.

The grade point averages​ (GPA) for 12 randomly selected college students are shown on the right. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed.

2.2 3.4 2.9 1.8 0.8 4.0 2.4 1.3 3.9 0.5 2.4 3.3 ​

(a) Find the sample mean.

x = _____ ​(Round to two decimal places as​ needed.) ​

(b) Find the sample standard deviation.

s= ______ (Round to two decimal places as​ needed.)

​(c) Construct a 95​% confidence interval for the population mean mu.

A 95​% confidence interval for the population mean is( ____, ____ ) . ​(Round to two decimal places as​ needed.)

A thin circular sheet of glass with a diameter 5 meters is rubbed with a cloth on one surface and becomes charged uniformly. A chloride ion (a chlorine atom which has gained one extra electron) passes near the glass sheet. When the chloride ion is near the center of the sheet, at a location 0.8 mm from the sheet, it experiences an electric force of 8e-15 N, toward the glass sheet. In this problem, use the value ε₀ = 8.85e-12 C²/(N·m²)

How much charge is on the surface of the glass disk? (give amount, including sign, and correct units)

Coal is carried from a mine in West Virginia to a power plant in New York in hopper
cars on a long train. The automatic hopper car loader is set to put 75 tons of coal into
each car. The actual weights of coal loaded into each car are normally distributed, with
mean μ = 75 tons and standard deviation σ = 0.8 ton.

(a) What is the probability that one car chosen at random will have less than 74.5 tons
of coal?

(b) What is the probability that 20 cars chosen at random will have a mean load weight
of less than 74.5 tons of coal?

The daily rainfall in Japan (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.4.

Consider the overall rainfall in 365 days, and use mgfs and their properties to prove that this is Ga (292, 0.4).

1. Use the central limit theorem to approximate the probability that the annual rainfall exceeds 800mm (write down the analytical formula and the code used to calculate the cdf value).

2. Compare the approximate value obtained with the exact counterpart (include the R code used to calculate the cdf value).

3. Use R to produce a graphical representation that compares the true and approximate densities (include both the code and plot).

Sickle cell anemia is a recessive disorder caused by a mutation in the hemoglobin A gene. Persons with the disease have a variety of serious health issues related to fragile and sickling red blood cells including premature death, and infants sometimes die from complications. In regions of central Africa where malaria is endemic, the relative fitnesses for individuals that are homozygous for the wild type hemoglobin allele (Hb^A), heterozygous (Hb^AHb^S), and homozygous for the sickle cell allele (Hb^S) are 0.8, 1.0 and 0.1 respectively. The selection coefficient for someone of Central African ancestry who is an Hb^A/Hb^A homozygote born and raised in Chicago would be ____

This question relates to standing waves.

A) Does a closed pipe have a higher or lower fundamental frequency than an open pipe of the same length?

B) If the length of an open tube is 0.8 m, experimentally find the: fundamental frequency and the frequencies of the third and fifth harmonic.

C) We have only addressed the variables of length, wave speed, harmonic number and frequency. These seem to be adequate to fully describe the frequency of a standing wave. But we know that when a musician tightens a guitar string, the frequency of the sound changes. Which of these independent variables changes value when a string is tightened?