Curly Hair is a Brazilian start-up that offers a wide portfolio of hair products (shampoo, conditioner, foam, serum…) specifically designed to take care of curly hair.

Curly Hair manufactures its products in three different plants and sells them in five markets around the country. The plants have a certain manufacturing capacity. In the tables below, you can find the demand for each market, the capacity of each plant, and the distances (in miles) between plants and markets.

The operations manager of the company proposes to redesign the transportation network and start using some distribution centers (DCs) as an intermediary step between plants and final markets. There are four DCs that could be used. These DCs have a certain capacity and they cannot be used as warehouses (they do not keep stock), products must just flow through them.

In the tables below you will find the maximum capacity of each DCs, the distances between plants and DCs, and the distances between DC and markets.

The inbound transportation cost (from plants to DCs) is 2.61 Brazilian reals per liter per mile, and the outbound transportation cost (from DCs to markets) is 3.02 Brazilian reals per liter per mile. There is also a fixed cost of 5,000 Brazilian reals for each DC that the company decides to use.

Design a distribution network that can use these DCs. What is the optimal cost (transportation + fixed cost) under this new situation?

An oil tanker has hit a sand bar and ripped a hole in the hull of the ship. Oil has begun leaking from the tanker. The oil is leaking from the ship forming a circle around it. The radius of the circle is increasing at a rate of 2.3 feet per hour. Please assist the Wild Life Federation with the following calculations. Thank you in advance for your assistance. (Round all answers to the nearest tenths place unless otherwise specified, use the π button on your calculator for calculations.) 1) A) Write the radius of the circle as a function of time. Use t as the symbol to represent time (you will need to use the information found in the news clip above.) B) What is the radius of the circle after 2 hours? C) What is the radius of the circle after 2.5 hours? D) If the oil tanker is 250 yards from shore, when will the oil first reach the shoreline? (Remember to convert to feet) 2) Write the area of the circle as a function of the radius. Use the symbol r to represent the radius. 3) A) Using the functions found in questions 1 and 2, write a function that represents area as a function of time. B) What is the area of the circle after 2 hours? C) What is the area of the circle after 2.5 hours? D) What is the area of the circle after 3 hours? E) What is the area of the circle after 3.5 hours? Math 171 Unit 1 Lab 4) Compute the average rate of change per hour for the area from 2 to 2.5 hours. 5) Compute the average rate of change per hour for the area from 3 to 3.5 hours. 6) Based upon the results found in questions 4 and 5 what is happening to the average rate of change of the area of the circle as time passes? (Increasing, Decreasing, Constant?) 7) If the tanker is 250 yards from the shore, how long will it be until 8 miles of shoreline is contaminated with oil? Round to the nearest number of days. (For the benefit of this problem, the shore is straight and if you were to draw a line perpendicular to the shore 250 yards you would find the boat, the spread will be 4 miles to either side of the ship, refer to the diagram below. Hint 1mi=5280 ft.) A) Use the figure below and find the length of the radius in feet. B) Using your formula from problem 1A, find the time in hours. C) The original question asks for the time measured in days. Convert your answer from 7B to days, rounding to the nearest number of days. Radius Radius 250 yds 4 miles 4 miles

An energy company wants to choose between two regions in a state to install​ energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the​ regions, the average wind speed is calculated for

60

days in each region. The mean wind speed in Region A is

13.7

miles per hour. Assume the population standard deviation is

2.7

miles per hour. The mean wind speed in Region B is

15.3

miles per hour. Assume the population standard deviation is

3.1

miles per hour. At

alphaαequals=0.05,

can the company support the​ researcher's claim? Complete parts​ (a) through​ (d) below.​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

What is the​ claim?

A.

The wind speed in Region A is not greater than the wind speed in Region B.

B.

The wind speed in Region A is the same as the wind speed in Region B.

C.

The wind speed in Region A is less than the wind speed in Region B.

D.

The wind speed in Region A is not less than the wind speed in Region B.

Let Region A be sample 1 and let Region B be sample 2. Identify

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0H0​:

mu 1μ1

▼

less than<

not equals≠

greater than>

greater than or equals≥

less than or equals≤

mu 2μ2

Upper H Subscript aHa​:

mu 1μ1

▼

less than or equals≤

less than<

greater than or equals≥

greater than>

not equals≠

mu 2μ2

​(b) Find the critical​ value(s) and identify the rejection region.

The critical​ value(s) is/are

z 0z0equals=nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What is the rejection​ region? Select the correct choice below and fill in the answer​ box(es) within your choice.

​(Round to three decimal places as​ needed.)

A.

zless than<nothing

B.

zless than<nothing

or

zgreater than>nothing

C.

zgreater than>nothing

​(c) Find the standardized test statistic z.

zequals=nothing

​(Round to two decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

▼

Reject

Fail to reject

Upper H 0H0.

There

▼

is not

is

enough evidence at the

55​%

level of significance to

▼

support

reject

the​ researcher's claim that the wind speed in Region A is

▼

not greater than

less than

the same as

not less than

the wind speed in Region B.

Click to select your answer(s).

QUESTION 1

1. Computers in some vehicles calculate various quantities related to car performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer-calculated mpg, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up.

   The data for a random sample of 20 of these the mpg values given in the csv file under variables Computer, Driver and Difference = (Computer – Driver).

   (Q1-9)Question: You suspect that that the car on-board-computer has been over-estimating the 41-mpg stated at the car-manufacturing website.

   Download the data file, Ch5_FuelEfficiency.csv, from Blackboard, and get the basic descriptive statistics for all three variables: Computer, Driver and Difference, using the following R codes:

   mydata <- read.csv("Ch5_FuelEfficiency.csv")

   #install.packages("pastecs")

   library(pastecs)

   stat.desc(mydata)

   The mean values for variables Computer, Driver and Differrence are 43.17, 40.44 and 2.73, respectively.

   Part I: Statistical inference for variable “Computer”

   1. Implement the hypothesis testing.

   a. State the hypotheses.

   Question 1: choose the right hypotheses for this problem.

   		H0: = =41   vs.    Ha: > 41
   		H0: = =41   vs.    Ha: ><41
   		H0: = =41   vs.    Ha:   ≠ 41
   		H0: = =43.17   vs.    Ha:   >43.17

2. QUESTION 2

3. b. Perform the test of significance using α = 5% and state/interpret your conclusion.

   Known:  n = 20, = 43.17 (Statistic), s = 4.41 (we use this as an estimate for σ)

   Question 2: What is the standard error?_________

   		4.41
   		3.5
   		3
   		0.9861

Given the monthly returns that follow:

Calculate R²:   

Alpha:   %

Beta:   

Average return difference (with signs):   %

Average return difference (without signs)   %

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $584,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.30 per trap and believes that the traps can be sold for $5 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 10%. Use the MACRS depreciation schedule.

a. What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

b. By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $584,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.30 per trap and believes that the traps can be sold for $5 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 10%. Use the MACRS depreciation schedule.

a. What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

b. By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)

I need an to check my answer with 4 decimal places:

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.4 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $682,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.30 per trap and believes that the traps can be sold for $5 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 8%.

a. What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

b. By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)

Use the MACRS depreciation schedule.

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $6.3 million. The equipment will be depreciated straight line over 6 years to a value of zero, but in fact it can be sold after 6 years for $672,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.70 per trap and believes that the traps can be sold for $7 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 35%, and the required rate of return on the project is 9%. Use the MACRS depreciation schedule. Year: 0 1 2 3 4 5 6 Thereafter Sales (millions of traps) 0 0.5 0.7 0.8 0.8 0.7 0.5 0

a. What is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

b. By how much would NPV increase if the firm depreciated its investment using the 5-year MACRS schedule? (Do not round intermediate calculations. Enter your answer in whole dollars not in millions.)

Sally measures the amount of CO₂ in a pint soda bottle by weight loss; she shakes the bottle vigorously and then slowly opens the cap, letting the gas escape. Three measurements on Brand X indicate a loss of 2.2 ± 0.2 g of gas, while three measurements on Brand Y shows a loss 2.4 ± 0.3 g. (The ± indicates standard error.) Do Brands X and Y have different amount of CO₂?