A real estate investor buys two properties. Monthly net income from the first property (an apartment building) is $1,000 times the number of apartments that are rented out, minus $1,800 in property taxes and maintenance expenses. The number of apartments that are rented out is a random variable, X, with mean 20 and standard deviation 3. Monthly net income from the second property (a parking lot) is ninety percent of revenue (the management company takes the other ten percent), minus $1,200 in property taxes and maintenance. Revenue is a random variable, Y, with mean $20,000 and standard deviation $200. The correlation between the number of apartments rented out (X) and revenue from the parking lot (Y) is 0.4.

a. Calculate the real estate investor’s expected monthly net income from these two properties:

b. Compute the covariance from the correlation:

c. Calculate the variance of monthly net income from these two properties

Percentage-of-Completion and Completed Contract Methods

Philbrick Company signed a three-year contract to provide sales training to the employees of Elliot Company. The contract price is $1,200 per employee and the estimated number of employees to be trained is 400. The expected number to be trained in each year and the expected training costs follow.

Required

For each year, compute the revenue, expense, and gross profit reported assuming revenue is recognized using the following method.
(Do not round until your final answers. Round your answers to two decimal places.)

1. Percentage-of-completion method, where percentage-of-completion is determined by the number of employees trained.

2. Percentage-of-completion method, where percentage-of-completion is determined by the costs incurred.

3. Completed contract method.

Percentage-of-Completion and Completed Contract Methods

Philbrick Company signed a three-year contract to provide sales training to the employees of Elliot Company. The contract price is $1,200 per employee and the estimated number of employees to be trained is 400. The expected number to be trained in each year and the expected training costs follow.

Required

For each year, compute the revenue, expense, and gross profit reported assuming revenue is recognized using the following method.
(Do not round until your final answers. Round your answers to two decimal places.)

1. Percentage-of-completion method, where percentage-of-completion is determined by the number of employees trained.

2. Percentage-of-completion method, where percentage-of-completion is determined by the costs incurred.

3. Completed contract method.

2. Balance sheet

The balance sheet provides a snapshot of the financial condition of a company. Investors and analysts use the information given on the balance sheet and other financial statements to make several interpretations regarding the company’s financial condition and performance.

Cute Camel Woodcraft Company is a hypothetical company. Suppose it has the following balance sheet items reported at the end of its first year of operation. For the second year, some parts are still incomplete. Use the information given to complete the balance sheet.

Given the information in the preceding balance sheet—and assuming that Cute Camel Woodcraft Company has 50 million shares of common stock outstanding—read each of the following statements, then identify the selection that best interprets the information conveyed by the balance sheet.

Statement #1: Cute Camel’s net collection of inventory items increased by more than the firm's sales between Years 1 and 2.

This statement is Incorrect or correct , because:

a) The accruals balance decreased by $176 million between Years 1 and 2

b) Total inventories of raw materials, work-in-process, and final goods increased from $2,970 million to $3,712 million between Year 1 and Year 2

c) Total inventories of raw materials, work-in-process, and final goods decreased by $742 million between Year 1 and Year 2

Statement #2: In Year 2, Cute Camel Woodcraft Company was profitable.

This statement is incorrect or correct , because:

a) Cute Camel’s retained earnings account increased between the end of Years 1 and 2

b) Cute Camel’s total assets increased between Years 1 and 2

c) The cash and equivalents account increased between Years 1 and 2

Statement #3: One way to interpret the change in Cute Camel’s accounts receivable balance from Year 1 to Year 2 is that more customers purchased new items on credit rather than paying off existing credit accounts.

This statement is incorrect or correct , because:

a) The decrease from $1,266 million to $1,013 million implies a net decrease in accounts receivable and that more customers are paying off their receivables balances than are buying on credit

b) The change from $2,970 million to $3,712 million reflects a net accumulation of new credit sales

c) The $253 increase in accounts receivable means either that Year 1’s existing credit customers are not paying off their owed balances and new or existing customers are making additional purchases on credit, or that Year 1’s credit customers have repaid their owed balances and Year 2 credit sales have exceeded Year 1’s credit sales

Based on your understanding of the different items reported on the balance sheet and the information they provide, which statement regarding Cute Camel Woodcraft Company’s balance sheet is consistent with U.S. Generally Accepted Accounting Principles (GAAP)?

a) The company’s debts should be listed from those carrying the largest balance to those with the smallest balance.

b) The company’s debts should be listed in order of their liquidity.

c) The company’s debts are listed in the order in which they are to be repaid.

A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 19% were under 20 years old, 13% were in the 20- to 35-year-old bracket, 29% were between 36 and 50, 24% were between 51 and 65, and 15% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: Time ten years ago and today are independent.
H₁: Time ten years ago and today are not independent.

H₀: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are independent.
H₁: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are not independent.    

H₀: The distributions for the population 10 years ago and the population today are the same.
H₁: The distributions for the population 10 years ago and the population today are different.

H₀: The population 10 years ago and the population today are independent.
H₁: The population 10 years ago and the population today are not independent.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100   

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(iv) Conclude the test.

Since the P-value < α, we reject the null hypothesis.

Since the P-value ≥ α, we reject the null hypothesis.    

Since the P-value ≥ α, we do not reject the null hypothesis.

Since the P-value < α, we do not reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that the age distribution of the population of Blue Valley has changed.

At the 1% level of significance, there is sufficient evidence to claim that the age distribution of the population of Blue Valley has changed.

Dealing Cards

Write a program that deals a deck of card into 4 hands – Each hand having 13 cards.

• Your program should do the followings
  • use an array to randomly select 52 cards and deal it into 4 hands.
  • Print each hand unsorted
  • Identify the face value of each hand and display it.
  • You should create a class called Card, and all the methods should be defined within the card class.

Hints – Import below java utility to use the random function.

import java.util.*;

Random rand = new Random();

int r = rand.nextInt(52); // this will generate random numbers between 0-52

to get a value between 1-13, use the mod function and get the remainder

if your number is 15, 15%13 has a remainder of 2. 2 is your face card.

---------------------------------------------------------------------------

11 = jack

12= Queen

13= King

Card is a CLUB - If your generated number is between (1-13)

Card is a Diamond - If your generated number is between (14-26)

Card is a Spade - If your generated number is between (27-39)

Card is a Heart - If your generated number is between (40-52)

Your program output should look like this below

----------------------------------------------------------------------------------------------------------------------------------

Deck of cards shuffled into 4 hands

8 1 7 18 43 26 31 2 12 3 40 22 4

29 9 10 11 5 35 47 36 25 14 17 39 23

21 52 6 46 38 48 24 16 27 32 13 45 42

49 44 50 20 37 34 51 15 28 30 19 33 41

Face of cards in each Hand

Hand 1:

       Clubs: 8 1 7 2 Q 3 4

       Diamonds: 5 K 9

       Spades: 5

       Heart: 4 1

Hand 2:

       Clubs: 4 9 10 J 5

       Diamonds: Q 1 4

       Spades: 3 9 10 K

       Heart: 8

Hand 3:

       Clubs: 6 K

       Diamonds: 10 8 J 3

       Spades: K Q 1 6

       Heart: K 7 9

Hand 4:

       Clubs: K

       Diamonds: 7 2

       Spades: J 8 2 4

Heart: 6 3 10 5 J Q

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 2x³ + xy² + 5x² + y²

Local Maximum Value(s) = 125/27

Local Minimum Value(s) = ?

Saddle Point(s) (x,y,f) = ?

.

2. Find the indicated partial derivative.

f(x, y) = sqrt 2x + 5y ; f_y(5, 3)

f_y(5, 3) =

An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce portions of the antibiotic were stored for equal lengths of time at each of the following Fahrenheit temperatures: 40, 55, 70, and 90. The potency readings observed at the end of the experimental period were

Potency reading, y: 49 38 27 24 38 33 19 28 16 18 23

Temperature, x: 40 40 40 55 55 55 70 70 70 90 90

a) Find the least-squares line appropriate for these data.

b) Calculate the 95% confidence intervals for B₀ and B₁

An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce portions of the antibiotic were stored for equal lengths of time at each of the following Fahrenheit temperatures: 40, 55, 70, and 90. The potency readings observed at the end of the experimental period were

Potency reading, y: 49 38 27 24 38 33 19 28 16 18 23

Temperature, x: 40 40 40 55 55 55 70 70 70 90 90

a) Find the least-squares line appropriate for these data.

b) Calculate the 95% confidence intervals for B₀ and B₁

Problem 5-49 Amortization Schedule (LG9)