Read the following post.  Substantively comment on the entry comments of no less than 200 words.

I feel a bit blind-sided as to how much slavery still existed today, 27 million souls. I can only assume that many people were not aware of the mass murders of Jews during World War II. One of my favorite spiritual guys speaks of morality saying “Really accepting ‘what is’ depends on self-awareness, knowing your true existence – Being what is. When we know our essential nature as absolute bliss consciousness, we transcend the man-made notions of right and wrong borne of dualistic awareness, yet we imbibe the inherent virtues of being such as love, compassion, truth, joy, and wisdom. These qualities are not cultural or social values of morality, but inherent expressions of existence itself.” Deepak Chopra. I feel that Slavery today and WWII both have something to do with the morality of a few men that make the decisions to carry out ill intent. The majority of mankind is good at the core and of sound morality.

In life you can look at two sides of a coin. You can choose to focus on the people that bring you down, say that you can’t succeed in life that people are just faking it or going through the motions. You can also choose to see the good in people, to assume the best case scenario, to believe that they are being genuine (unless proved otherwise). The dangers of customary behavior is believing that everyone out there is just being nice to you or smiling at you because it is a custom and not because they really mean it. Truth be told, there are likely people out there that are not 100 percent genuine, but let me ask you this, is it better to assume that everyone is genuine and be a happy fulfilled person, open to new friendships or connections or assume that everyone is just going through the motions?  The later options seem pretty empty.

Customary behavior could be defined as behavior that is accepted by the general standards or behaviors of society. Bohme states that customary behavior and morality cannot comingle, “Morality only arises, only when for good reasons, one deviates from customary behavior…” I do not feel that this is necessarily true. I feel that a huge part of my day and my co-workers days are filled with compassionate care. I feel that one can be moral and continue on with customary behavior. Politeness is customary behavior yet I also feel the same behavior could be heart-felt emotion. I respect you and think highly of you therefore I want to be polite to show you I care about you. Another example that Bohme uses is commitment is deemed to be a customary behavior at a work place for example. Bohme indicates that this is faked because everyone is expected to be committed. This view point is focused on the negative, yes there are likely a few employees that ‘fake’ their commitment to their team, jobs, career; although I think there are many more people in the job force that work where they work because they are vested in what they are doing and because they care. I work for a non-profit agency and the nurses do not work there because they are paid more, they work there because of the mission, because of the team work, and because of what we stand for.

There is a very unsettling feeling to know that the everyday items that my family and I support the slave trade business. I think that most people agree that Slavery should be abolished. The challenge is how do we do anything to affect change? Kevin Bales speech was very informative and made me want to take action, but he didn’t really offer us solutions on how to take on the slave trade owners. I assume that one would start by not purchasing any of the materials on the survey’s website. After the survey I was shocked to learn the survey telling me that I was supporting the enslavement of 77 souls. The Conditions that make it possible for all people to be a part of the social ‘customary practices that sustain the structures of slavery is ignorance of slavery and when and where it happens.  I am not totally aware of what products are made by slaves or products that have materials forged by slaves. This video clip has driven me to dig deeper and conduct my own research to learn more about slavery. I am a mother of three beautiful children, and to see the mothers being reunited with their children who had been released from slavery was so emotional. I cannot imagine the heart wrenching feelings those mothers went through when their children, or any family member for that matter was taken from them; what a helpless situation. I still believe that most people are good and have a high moral fiber. Some situations like this one seem to be in the hands of people with powerful positions and not of the unknowing consumer. The United States government should have some responsibility of knowing where or how our products are coming into our country. If the US citizens are aware of Slavery you can be sure our government is aware, why is our government not doing something about this?

Class Section

Homework Assignment 7.3
18 points
Print out this assignment and write your name on it and turn it in instead of answering the
questions on notebook paper. You may print front and back if you wish. Be sure to include your
first name and last name. Put your class section number on the area of the line above “Class
Section”.
Problems 1 – 6: Find the function f (x) that will make the given equation an identity. The
function f (x) may be a trig function, algebraic function, or constant function.
Each problem has a solution. Simplify all answers.
1.

cos(2x)
= f 2(x)
1 – tan2(x)

2.

f (x) = _______________________

3.

cos2(x)
1 – 1 + sin(x) = f (x)

1 + cos(2x)
= f (x)
sin(2x)

f (x) = _______________________

cos(x)
= f (x)
1 + sin(x)

f (x) = __________________________

4.

f (x) = _______________________

5.

tan(x) +

 x
 x
tan   + cot   = 2 f ( x)
2
2

f (x) = ___________________________

6.

cos(x)
1 + sin(x)
+
= 2f (x)
1 + sin(x)
cos(x)

f (x) = ___________________________

Problems 7 – 11: Verify each identity. Provide all necessary details.
7.

sec2(θ) csc2(θ) = sec2(θ) + csc2(θ)

8.

cos(2θ)
= cos(θ) – sin(θ)
cos(θ) + sin(θ)

9.

tan(θ )
θ 
tan   =
 2  sec(θ ) + 1

10. sin(2θ) =

2 tan(θ)
1 + tan2(θ)

11. sin(2x) – tan(x) = tan(x) cos(2x)

Problems 12 – 14:

Show that each of the following is not an identity.

12. cos(2θ) = 2cos(θ) sin(θ)

 t  sin(t )
13. sin   =
2
2

14. cos(2t) = 2cos(t)

Problems 15 and 16: Write each of the following as a product of trig functions. Simplify your
answers.
15. sin(6θ) + sin(3θ)

Answer: _________________________________________________________________

16. cos(5θ) – cos(θ)

Answer: __________________________________________________________________

Problems 17 and 18: Write each of the following as a sum or difference of trig functions.
Simplify your answers.

17. sin(6θ) sin(3θ)

Answer: _________________________________________________________________

18. cos(5θ) cos(θ)

Answer: _________________________________________________________________

This is for a disscussion board. 

Share with your peers the null and alternative hypotheses for a decision that is relevant to your life. This can be a personal item or something at work. Be sure that it is mathematical in nature.  Additionally, identify the Type I and Type II Errors that could occur with your decision‐making process. Be sure to quantify your hypotheses as much as possible and identify your variables.

For example, suppose a newspaper article stated that the average weight of cats is 5 lbs. Suppose you think that the average weight of cats is more than 5 lbs. Then the hypotheses are:

H0: μ < 5
Ha:  μ >5
Here  μ is the population average weight of cats. This would be an example of an Upper Tail test.

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A way of understanding hypothesis testing is to think of a court case:
Suppose Joe is accused of stealing an expensive diamond. Then there are 2 hypotheses:

H0: Joe is innocent (H0 is the assumption, the status quo, innocent until proven guilty)
H1: Joe is guilty (the alternative hypothesis)

The goal of the prosecutor is to collect evidence so that the judge switches over from H0 to H1.

You are assuming H0 is true. Thus, the goal of the prosecutor is to collect convicting evidence so compelling that it is very unlikely for an innocent person to have.

For example, it is very unlikely that an innocent person is found with the stolen diamond in hand, a video camera showing Joe near the scene, a map in Joe’s home of the Jewelry store,…,etc.

Since this is very unlikely to happen to an innocent person, the judge switches over by rejecting H0, innocent.

You want to the probability of convicting an innocent person to be small.
i.e. you want to minimize the probability of rejecting H0 given that H0 is true (Minimize the probability of a Type I error).

This can be written as the following conditional probability:
small= P( rejecting H0 | H0 is true) = the probability of convicting an innocent person

The probability above is called the probability of a Type I error. It is denoted with the Greek letter alpha.

P(Type I error) = P( rejecting H0 | H0 is true) = alpha
The statistician decides what alpha will be.

For example, the judge might draw the line at alpha=.001.

i.e.
.001= P( rejecting H0 | H0 is true) = the probability of convicting an innocent person.

Alpha is the borderline probability between innocent and guilty.

i.e. If Joe is assumed to be innocent and the evidence collected against him has a probability of less than .001 occurring, then the judge will reject H0 and accept Ha (guilty).

Business Math, Ch. 7

Why is the standard deviation big?

As you probably already know from your reading, standard deviation indicates the spread of the data. There can be many reasons that data has a big spread. Some common reasons are:

1.  That’s just the way the data happens.  An example of this would be if we were randomly choosing men anywhere in the world and measuring their height.  The possibility exists that we would choose the world’s tallest man and/or the world’s shortest man to include in our data. These heights would make our numbers look weird, but in fact, they are correct.

2.  There is a problem with the data.  This can happen for many reasons:

• The measurement was not done properly
• miscalibrated machinery
• The wrong units were used (years rather than days, net income versus gross income, etc.)
• The respondents in our sample misunderstood the question.  One example of this from my business would be when we asked a question about “talk shows” we did not anticipate that a large part of our sample would consider morning shows on music stations as “talk shows.”
• The procedure for measurement has changed over a period of time (for example, the way Autism is diagnosed has changed over the year, so including data from years past may not be accurate).
• Machinery is more sensitive and/or sophisticated and can now measure more and better than before.  For instance, now we are able to detect earthquakes and measure different attributes of hurricanes than we were in the 1800s.
• There is a typo in our data.
• The interviewer (in the case of an in-person interview) misunderstood the respondent’s answer, or recorded it incorrectly.

3.  There is an underlying variable that is causing variation in our data.  An example of this would be with our DJ example above. Most likely, the DJ with the higher standard deviation has a polarizing personality that causes one gender to like the DJ while the other does not, or the DJ appeals to a younger audience rather than an older audience, etc.   Another common example here would be if we were in retail looking at the number of transactions for a store, an underlying variable that we would need to account for before beginning the analysis would be that there are different sizes of stores.

Of course the lists above are not exhaustive, so there are more reasons, but these are some main points.  Have you encountered any of these scenarios in your job? If so, please share your experience with the class.

The experiment data in below table was to evaluate the effects of three variables on invoice errors for a company. Invoice errors had been a major contributor to lengthening the time that customers took to pay their invoices and increasing the accounts receivables for a major chemical company. It was conjectured that the errors might be due to the size of the customer (larger customers have more complex orders), the customer location (foreign orders are more complicated), and the type of product. A subset of the data is summarized in the following Table.

Table: Invoice Experiment Error

Customer Size: Small (-), Large (+)

Customer Location: Foreign (-), Domestic (+)

Product Type: Commodity (-), Specialty (=)

Reference: Moen, Nolan, and Provost (R. D. Moen, T. W. Nolan and L. P. Provost. Improving Quality through Planned Experimentation. New York: McGraw-Hill, 1991)

Use the date in table above and answer the following questions in the space provided below:

1.     Identify the effects of the factors studied in this experiment? Which are most important? Why?

2.     What strategy would you use to reduce invoice errors, given the results of this experiment?