100 moles of a mixture containing 45.9 wt% methane and remainder propane are burned with 40% excess oxygen. There is 80% conversion of both methane and propane. Given MWs: CH4= 16, C3H8= 44, O2= 32, H2O = 18, CO2= 44

a) Balance the following reactions:____ CH4 + ____ O2 -->____ CO2+ ____ H2O

____ C3H8 + ____ O2--->____ CO2 + ____ H2O (I understand this and have it correct)

b) How many moles of O2 must be supplied for 80% conversion of both methane and propane?

c) What is the exit composition of the combustion reactor in mole percents?

PLEASE SHOW ALL WORK LEADING TO ALL CALCULATED VALUES

Consider a Ricardian model. There are two countries called Australia and New Zealand and two goods called beer and cheese. In Australia the unit labour requirement for a beer is 10 hours and for a cheese is 10 hours. In New Zealand the unit labour requirement for a beer is 4 hour and for a cheese is 1 hour. Australia has an endowment of 2000 hours of labour. New Zealand has an endowment of 400 hours of labour.

1 Draw a production possibility frontier (PPF) diagram for Australia and a PPF diagram for New Zealand. Cheese must be on the vertical axis and beer must be on the horizontal axis.

2 For both countries state the opportunity cost of producing a beer.

3 Suppose now that we have trade between the countries and the world price is 2 cheeses for 1 beer. For each country draw in the budget constraint. For each country label the production point on the diagram.

4 Denote the world prices in dollars as PB and PC respectively. Denote the respective quantities of beer and cheese consumed in New Zealand (following trade, of course) as DB and DC . Using this notation, write out an expression for the value of consumption in New Zealand. [Just a one-line answer]

5 Write out the budget constraint for New Zealand. That is, set the value of consumption equal to the value of production. [Again just a one-line answer]

6 Rearrange the budget constraint, showing all the steps, so that DC is on the left-hand side and everything else is on the right-hand side so the vertical intercept and slope are apparent. [Please see the next page]

7 While the ratio of prices is apparent from Question 3, we will assume from here on that PC=$1 and PB=$2. If 100 beers are consumed in New Zealand, how many cheeses will be consumed in New Zealand? Now if only 50 beers are consumed, how many more cheeses will be consumed?

8 For both countries calculate the hourly wage rate once international trade is allowed to take place (obviously for each country there can only be one wage rate in this model).

The restaurant owner Lobster Jack wants to find out what the peak demand periods are, during the hours of operation, in order to be better prepared to serve his customers. He thinks that, on average, 60% of the daily customers come between 6:00pm and 8:59pm (equally distributed in that time) and the remaining 40% of customers come at other times during the operating hours (again equally distributed). He wants to verify if that is true or not, so he asked his staff to write down during one week the number of customers that come into the restaurant at a given hour each day. His staff gave him the following data:

Help the manager figure out if his instincts are correct or not. Use a Chi-Squared test to see if the observed distribution is similar to the expected. Use the average demand for a given time as your observed value.

A 25.0 mL sample of 0.125 molL−1 pyridine (Kb=1.7×10−9) is titrated with 0.100 molL−1HCl.

Calculate the pH at one-half equivalence point.

Calculate the pH at 40 mL of added acid.

Calculate the pH at 50 mL of added acid.

A statistical program is recommended.

A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow.

(a)

Develop an estimated regression equation showing how total points earned can be predicted from hours spent studying. (Round your numerical values to two decimal places.)

ŷ =

(b)

Test the significance of the model with α = 0.05. (Use the F test.)

State the null and alternative hypotheses.

H₀: β₀ = 0
H_a: β₀ ≠ 0

H₀: β₀ ≠ 0
H_a: β₀ = 0  

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₁ ≥ 0
H_a: β₁ < 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that the relationship between hours spent studying and total points earned is significant.

Reject H₀. We conclude that the relationship between hours spent studying and total points earned is significant.

Do not reject H₀. We conclude that the relationship between hours spent studying and total points earned is significant.

Reject H₀. We cannot conclude that the relationship between hours spent studying and total points earned is significant.

(c)

Predict the total points earned by Mark Sweeney. He spent 85 hours studying. (Round your answer to two decimal places.)

points

(d)

Develop a 95% prediction interval for the total points earned by Mark Sweeney. (Round your answers to two decimal places.)

points to  points

A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow.

(a)

Develop an estimated regression equation showing how total points earned can be predicted from hours spent studying. (Round your numerical values to two decimal places.)

ŷ =

(b)

Test the significance of the model with α = 0.05. (Use the F test.)

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₀ = 0
H_a: β₀ ≠ 0    

H₀: β₀ ≠ 0
H_a: β₀ = 0

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₁ ≥ 0
H_a: β₁ < 0

Find the value of the test statistic. (Round your answer to two decimal places.)

________

Find the p-value. (Round your answer to three decimal places.)

p-value = ______

State your conclusion.

Reject H₀. We cannot conclude that the relationship between hours spent studying and total points earned is significant.

Reject H₀. We conclude that the relationship between hours spent studying and total points earned is significant.     

Do not reject H₀. We conclude that the relationship between hours spent studying and total points earned is significant.

Do not reject H₀. We cannot conclude that the relationship between hours spent studying and total points earned is significant.

(c)

Predict the total points earned by Mark Sweeney. He spent 70 hours studying. (Round your answer to two decimal places.)

__________ points

(d)

Develop a 95% prediction interval for the total points earned by Mark Sweeney. (Round your answers to two decimal places.)

______points to _____points

Statistical Process Control

T. Crews, Inc. has been contracted to make Foolio. The recipe calls for 100 milligrams of taurine in each 16-ounce bottle. To make sure that they are in compliance, T. Crews has pulled eight bottles of Foolio from its last eleven batches and tested them for taurine content. The data from these tests is below.

Use this data for questions 8 – 14.

1. What is UCL_X-bar?

a. Less than 100.00

b. Between 100.00 and 102.00

c. Between 102.01 and 104.00

d. Between 104.01 and 106.00

e. Greater than 106.00

2. What is LCL_X-bar?

  a. Less than 96.00

b. Between 96.00 and 97.00

c. Between 97.01 and 98.00

d. Between 98.01 and 99.00

e. Greater than 99.00

3. All points on the X-bar chart are within the control limits.

4. Is this process considered in control?

a. Yes, because all points on the r-chart are within the control limits

b. Yes, because all points on the r-chart and x-bar chart are within the control limits

c. No, because points on the r-chart or x-bar chart are not within the control limits

d. No, because points on R chart are too close to average

5. When an activity has two precedent activities, its early start time is equal to:

a) The later of the two precedent activities’ “Early Start” times

b) The activity’s start time minus its duration

c) The earlier of the two precedent activities’ “Early Finish” times

d) The later of the two precedent activities’ “Early Finish” times

6. An obstacle to supply chain integration is

a) information sharing between partners

b) limited supply chain visibility

c) considering the capabilities of partners when creating new processes

d) joint investment between firms in a supply chain

5.6.2.  Programming Challenge : Song with Parameters

Here’s another song, The Ants Go Marching, that is very similar to the This Old Man song in its repetitive structure.

 The ants go marching one by one, hurrah, hurrah
 The ants go marching one by one, hurrah, hurrah
 The ants go marching one by one
 The little one stops to suck his thumb
 And they all go marching down to the ground

 The ants go marching two by two, hurrah, hurrah
 The ants go marching two by two, hurrah, hurrah
 The ants go marching two by two
 The little one stops to tie his shoe
 And they all go marching down to the ground

 The ants go marching three by three, hurrah, hurrah
 The ants go marching three by three, hurrah, hurrah
 The ants go marching three by three
 The little one stops to climb a tree
 And they all go marching down to the ground
 

1. Print out the The Ants Go Marching song and circle the repeated parts of the song.

2. In the active code window below, create a method or methods that takes parameters to print out a verse. The method(s) should be abstract enough to work for all 3 verses. Use good commenting for your methods that describe the @param. For the autograder, make sure you create a method called verse that takes 2 parameters.

3. In the main method, create an object of the class and call the method(s) you created in the last step to print out 3 verses of the song. Can you add more verses?

Create method(s) with parameters to print out verses of the song The Ants Go Marching. https://www.lyrics.com/lyric/5526512/The+Ants+Go+Marching

public class Song
{
// Create at least 1 method called verse that takes 2 parameters
// that can be used to print out the verses of the song The Ants Go Marching

public static void main(String args[])
{
// Create a Song object and call its method(s) to print out
// the verses of The Ants Go Marching
// There should be atleast 1 method called verse that takes 2 arguments.

}
}

championship swimmers take about 22 seconds and about 30 arm strokes to move through the water in a 50 meter freestyle race.

A) A swimmers metabolic power is 800 W. if the efficiency for swimming is 25%, how much energy is expended moving through the water in a 50 m race?

B) if half the energy is used in arm motion and half in leg motion, what is the energy expenditure per arm stroke?

C) Model the swimmers hand as a paddle. During one arm stroke, the paddle moves halfway around a 90 cm radius circle. If all the swimmers forward propulsion during an arm stroke comes from the hand pushing on the water and none from the arm, what is the average force of the hand on the water?

D) How much cal should the swimmer consume from food for such a race?

E) How much energy would be lost in form of thermal energy?

ou have learned that earnings functions are one of the most investigated relationships in economics. These typically relate the logarithm of earnings to a series of explanatory variables such as education, work experience, gender, race, etc. (a) Why do you think that researchers have preferred a log-linear specification over a linear specification? (b) To establish age-earnings profiles, you regress ln(Earn) on Age, where Earn is weekly earnings in dollars, and Age is in years. Plotting the residuals of the regression against age for 1,744 individuals looks as shown in the figure: Do you sense a problem? (c) You decide, given your knowledge of age-earning profiles, to allow the regression line to differ for the below and above 40 years age category. Accordingly you create a binary variable, Dage, that takes the value one for age 39 and below, and is zero otherwise. Estimating the earnings equation results in the following output (using heteroskedasticity-robust standard errors): = 6.92 – 3.13 × Dage – 0.019 × Age + 0.085 × (Dage × Age), R2 = 0.20, SER = 0.721. (38.33) (0.22) (0.004) (0.005) Sketch both regression lines: one for the age category 39 years and under, and one for 40 and above. Does it make sense to have a negative sign on the Age coefficient? Predict the ln(earnings) for a 30 year old and a 50 year old. What is the percentage difference between these two? (d) The F-statistic for the hypothesis that both slopes and intercepts are the same is 124.43. Can you reject the null hypothesis? (e) What other functional forms should you consider?