# "Mathematics / Statistics" Essays

#### Math and Chosen Profession Essay …

Essay |
3 pages (936 words)

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3

SAMPLE TEXT:

Math and Chosen Profession

When most people think about the careers of firefighters and paramedics, they will often associate it with physically going into dangerous places to save lives. A good example of this can be seen with the heroic roles of many paramedics and firefighters after the 911 terrorist attacks. In these situations, they were demonstrating visceral force and determination during the course of doing their jobs. However, there is also a mental aspect of these career fields that must be taken into account. To fully understand what is happening requires looking at: how Algebra and the Metric system are utilized as part of their daily responsibilities. Together, these elements will provide the greatest insights as to the role of both areas for these career fields. ("911 Memorial for America's Heroes," 2007) (Monteclavo, 2011)

Describe how the Concept can apply to Firefighters and Paramedics

In both jobs there is a heavy reliance on using Algebra and the Metric system in conjunction with each other. For firefighters, this will occur through utilizing these areas when determining the right amounts of foam, water pressure and oxygen that is available. This will have a direct impact on their ability to quickly extinguish the blaze. (Monteclavo, 2011)

Paramedics must be able to use Algebra to make quick conversions when dealing with drugs and other medication. At the same time, they have to accurately work between the English and the Metric systems. These two factors can have an impact on the ability of paramedics to stabilize the patient (which increases their chances of survival). (Monteclavo, 2011)

Describe how to use Algebra / the Metric System and Provide Examples of Situations

Like what was stated previously, both career fields are dependent upon the use of Algebra and the Metric system in correlation with each other. In the case of firefighters, this is an everyday part of the job that requires them to make mathematical calculations instantaneously. This will determine how quickly they are able to fight the fire and save lives. (Monteclavo, 2011)

For example, during the course of a fire, the crews will use Algebra and the Metric system to decide how much water should be delivered to a particular area. As the flames are reacting to the water, is when these conversions will have to be adjusted higher and lower. In most cases this involves using Algebra to predict the right amount of pressure. At the same time, Algebra must be utilized to convert between the English and the Metric systems. This is illustrating how all firefighters will use both Algebra and the Metrics system to decide the best way to fight fires. (Monteclavo, 2011)

In the case of paramedics, the must use Algebra and the Metric system during the course of their daily activities. A good example of this can……
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#### Inductive Manner or a Deductive Research Paper …

Research Paper |
2 pages (728 words)

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2

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Within every quantitative study, it is always possible to conclude that the effect is not a result of the "cause" but this is not considered very likely when the relationship between the variables is very strong.

Types of quantitative research designs include experimental/quasi-experimental, case-study, longitudinal, cross-sectional.

Qualitative research methods. Qualitative research methods are conducted based on a topic idea rather than a firm research question, and the inquiry progresses by looking at the data for patterns that coalesce into themes. As the themes emerge from the data being collected, the researcher considers the relationship between the themes from the current study and what has been learned from previous research on the same topic. In this way, qualitative research explores a topic, beginning with the specific and moving toward the general. Data collection in a qualitative research design is collected from people, from the field (a group of people in a particular setting or situation), and it is iterative, or circular. The iterative nature of data collection in qualitative research means that the data builds upon itself to allow patterns to be seen, which in turn can trigger more -- and sometimes different -- types of data collection, picking up data in a manner akin to rolling a snowball. The thoughts and impressions that qualitative researchers have during the process of collecting data are recorded, and become part of the data collection and analysis process. As data is collected from different sources and in different ways over the course of a single qualitative inquiry, triangulation occurs, which aids in data verification. Once a data set is considered deep, or large enough, the data will be interpreted by the researcher.

Types of qualitative research approaches include ethnography, phenomenology, grounded theory, and field research (Trochum, 2006). Note, too, that qualitative research can utilize many of the same forms of research approaches as quantitative research, such as case-study, longitudinal, cross-sectional.

References

Shuttleworth, M. (2011). Quantitative research design. Experiment-Resources. Retrieved http://www.experiment-resources.com/quantitative-research-design.html

Trochum, W.M.K. (2006). Qualitative approaches. Research Methods Knowledge Base, Social Research Methods. Retrieved http://www.socialresearchmethods.net/kb/qualapp.php…
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#### Algebra -- Trig -- Writer Research Paper …

Research Paper |
2 pages (586 words)

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2

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6. Find the reference angle for the following angle: -386degrees

Converting the degrees to a positive, one gets the following calculations:

360 -- 386 = -26-360 -- 26 = 334 degrees. The angle is in Quadrant IV. The reference angle can then be calculated as the following:

360 -- A = 360 -- 334 = 26 degrees.

Answer: The reference angle of -386 degrees is 26 degrees.

7. Use reference angles to find the exact value of the expression: -7n

tan-

4

tan (-7?/4) -7?/4 = -2? + ?/4

From the unit circle, one can see that the reference angle is ?/4

cos (?/4) = sqrt (2)/2

sin (?/4) = sqrt (2)/2

tan (?/4) = [sqrt (2)/2] / [sqrt (2)/2)] = 1

Answer: tan (-7?/4) = 1.

8. Using the unit circle, find the value of the trigonometric function: n tan-

6

From the unit circle, for ?/6, x = sqrt (3)/2 and y = 1/2

tan (?/6) = sin (?/6)/cos (?/6) = [sqrt (3)/2] / (1/2) = sqrt (3)

Answer: tan (?/6) = sqrt (3).

9. Find the value of sin (-120degrees)

Using the unit circle, one can find that the angle -120 degrees is found in the following calculations:

360 -- 120 = 240 degrees.

Looking at the unit circle, x = sin (240) = -1/2

Answer: sin (-120) = -1/2.

10. Find the reference angle for the following angle: 69 degrees

The angle lies on Quadrant I, therefore the reference angle is the same.

Answer: The reference angle is 69 degrees.

11. Using the unit circle, find the value of the trigonometric function: 3n

sec-

2

Using the unit circle,……
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#### Algebra, Trig Find the Radian Research Paper …

Research Paper |
1 pages (342 words)

Bibliography Sources:
2

SAMPLE TEXT:

That said, s = unknown, r = 5, and ? = 70 degrees.

degrees converted to radians 1.22 radians s = (5)(1.22) = 6.1 yards.

Answer: The length of the arc is 6.1 yards.

5. Convert the following angle to degrees: n or pie radians converted to degrees ? * 180/? 180 degrees

Answer: radians is equal to 180 degrees.

6. Classify the angle 101 degrees as acute, right, obtuse, or straight.

Answer: The angle of 101 degrees is obtuse.

7. Draw the following angle in standard the position: 7n or 7 pie

Convert to degrees first, which can be gained by the following:

7? * 180/? = 1260 degrees 1260 -- 360 = 900-900 -- 360 = 540

540 -- 360 = 180.

Answer: The angle would be a straight angle with a measure of 180 degrees.

8. Convert -60 degrees to radians. Express the answer as a multiple of pie.

-60 = 300 degrees

Conversion from degrees to ? is the following:

300 * ?/180 = 150?/90……
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#### Algebra -- Trig Evaluate Research Paper …

Research Paper |
2 pages (668 words)

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2

SAMPLE TEXT:

Use Cramer's rule to solve the given system: 2x + 4y =14, 4x + 3y =18

In matrix format, one gets:

[ 2-4 ] [ x ] = [ 14 ]

[ 4-3 ] [ y ] = [ 18 ]

Using Cramer's rule, one gets:

x = [(14)(3) -- (4)(18)] / [(2)(3) -- (4)(4)] = (42 -- 72) / (6 -- 16) = -30 / -10 = 3

y = [(2)(18) -- (14)(4)] / [(2)(3) -- (4)(4)] = (36 -- 56) / (6 -- 16) = -20 / -10 = 2

Answer: x = 3, y = 2.

6. Write the augmented matrix for the following system of equations:

2x + 7z = 64, 8y + 6z = 40, 3x -- 2y + 4z = 46

Answer:

[ 2-0-7 | 64 ]

[ 0-8-6 | 40 ]

[ 3 -2-4 | 46 ]

7. Write the augmented matrix for the following system of equations:

7x + 4y + 5z = 62, 5x + 3y + 2z = 47, 3x + 7y + 8z = 63

Answer:

[ 7-4-5 | 62 ]

[ 5-3-2 | 47 ]

[ 3-7-8 | 63 ]

8. Use Cramer's rule to solve the given system: 4x + 5y =12, 3x + y = -2

In matrix format, one gets:

[ 4-5 ] [ x ] = [ 12 ]

[ 3-1 ] [ y ] = [ -2 ]

Using Cramer's rule, one gets:

x = [(12)(1) -- (5)(-2)] / [(4)(1) -- (5)(3)] = (12 -- (-10)) / (4 -- 15) = 22 / -11 = -2

y = [(4)(-2) -- (12)(3)] / [(4)(1) -- (5)(3)] = (-8 -- 36) / (4 -- 15) = -44 / -11 = 4

Answer: x = -2, y = 4.

9. Evaluate the determinant: | -9, -7|

| 4, 5|

Determinant of a square matrix can be solved by the following equation: A =……
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#### Algebra, Trig Solve the System Research Paper …

Research Paper |
2 pages (859 words)

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2

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7. Solve the system: 3x + 4y = 40, x -- 2y = 0

2(x -- 2y) = 0 2x -- 4y = 0

(3x + 4y) + (2x -- 4y) = 40 + 0 5x = 40 x = 8

Substituting x for the first equation: 3(8) + 4y = 40-24 + 4y = 40 4y = 16 y = 4

Answer: x = 8, y = 4.

8. Solve the system: x + 6y = 24, -6x + 5y = -21

6(x + 6y = 24) 6x + 36y = 144

(6x + 36y) + (-6x + 5y) = 144 + (-21) 6x + 36y -- 6x + 5y = 123 41y = 123 y = 3

Substituting y for the first equation: x + 6(3) = 24 x + 18 = 24 x = 6

Answer: x = 6, y = 3.

9. Solve the system: x + y + z= -1, x -- y + 3z = -17, 2x + y + z = -2

Equation 1: (x + y + z) + (x -- y + 3z) = -1 + (-17) 2x + 4z = -18

Equation 2: (x -- y + 3z) + (2x + y + z) = -17 + (-2) 3x + 4z = -19

Equation 2 -- Equation 1: (3x + 4z) -- (2x + 4z) = -19 -- (-18) x = -1

Substituting x into Equation 1: 2(-1) + 4z = -18 -2 + 4z = -18 4z = -16 z = -4

Substituting x and z into first equation: -1 + y + (-4) = -1 -5 + y = -1 y = 4

Answer: x = -1, y = 4, z = -4.

10. Solve the system: 3x + 4y = -2, x = -2y

Substitute x for the first equation: 3(-2y) + 4y = -2 -6y + 4y = -2 -2y = -2 y = 1

Substitute y for the second equation: x……
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#### Algebra, Trig Given F (X) Research Paper …

Research Paper |
2 pages (446 words)

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2

SAMPLE TEXT:

The above equation can be re-written as follows:

(x -- 0)^2 + (y -- 0)^2 = 100, where (h, k) is (0, 0), and r^2 = 100 = 10^2, r = 10.

Answer: For x^2 + y^2 + 100, the center (h, k) = (0, 0), and the radius r = 10.

6. Find the midpoint of the line segment with the given end points: (2,1) and (6,8)

The midpoint formula is the following: midpoint = ([(x1 + x2) / 2], [(y1 + y2) / 2])

(x1, y1) = (2, 1) and (x2, y2) = (6, 8)

Therefore ([(2 + 6) / 2], [(1 + 8) / 2]) = (8/2, 9/2) = (4, 9/2) or (4, 4.5)

Answer: The midpoint of the line segment is at (4, 9/2) or (4, 4.5).

7. Given f (x) = 8x -- 2 and g (x) = 2x -- 3, find f -- g f -- g = f (x) -- g (x) = (8x -- 2) -- (2x -- 3) = 8x -- 2 -- 2x + 3 = 6x + 1

Answer: f -- g = 6x + 1.

8. Write the standard form of the equation of the circle with the given center (-2, -4) and radius 6

The standard form of a circle……
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#### Algebra, Trig Algebra-Trig Find Research Paper …

Research Paper |
1 pages (361 words)

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2

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Evaluate: f (x) = 3x^2 -- 4x -- 3 at f (x -- 1)

f (x -- 1) = 3(x -- 1)^2 -- 4(x -- 1) -- 3 = 3(x^2 -- 2x + 1) -- 4x -- 4 -- 3

= 3x^2 -- 6x + 3 -- 4x -- 7 = 3x^2 -- 10x -- 4

Answer: f (x -- 1) = 3x^2 -- 10x -- 4.

6. Determine whether the given function is even, odd, or neither: f (x) = x^3 -- 5x

To test a function for even, odd, or neither property, plug in -- x for x, and simplify.

f (-x) = (-x)^3 -- 5(-x) = -x^3 + 5x

Because the final expression is the exact opposite of f (x), it stands that the function is odd

Answer: f (x) is odd.

7. Find the domain and range of: {(7, -2), (-6,-4), (-9,-9),(-5,-5),(6,6)}

Domain is all values of x: 7, -6, -9, -5, 6

Range is all values of y: -2, -4, -9, -5, 6

Answer: Domain = {-9, -6, -5, 6, 7}, Range = {-9, -5, -4,……
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#### New Knowledge on Which Decisions and Actions Essay …

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3 pages (944 words)

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3

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¶ … new knowledge on which decisions and actions can be founded (Hughes & Hayhoe 2007). Here, new knowledge is created through the collection and analysis of observations in a systematic way. Further, research concerns itself with the articulation of truths (generalized) from given instances. For instance, research on reader behavior looks at the behavior of readers in general and not a particular reader's behavior in isolation.

Basically, qualitative research concerns itself with clarifying human experience. Below are examples in which case qualitative research comes in handy as far as human experience is concerned.

Example 1: A study of how human beings relate with each other from the ages of 18 to 30.

Example 2: A study of how culture impacts on the performance of school going children.

Example 3: A study of the relationship between monetary compensation and employee motivation

Example 4: A study of the relationship between upbringing and child delinquency

Example 5: A study of how gay tendencies impact on an individual's interaction with members of the opposite sex.

Question 3

The process in this case (in relation to question 2) would be conduction of interviews which are categorized as a type of non-numerical data on which qualitative methods rely on. Therefore, interviews can be used as the source data while seeking to identify the meaning of experiences humans undergo.

Question 4

While inductive reasoning is mainly used in qualitative research, quantitative research makes use of deductive reasoning (Kumar 2011). That is, in quantitative research, the focus generally zeroes in on the specific rather than the general. However, in qualitative research, larger theories are inferred to by the use of small observations.

Question 5

By undertaking hypothesis testing of the research question given, I will be seeking to either prove or disprove the same. The checklist I would rely on in this case is outlined by Hughes & Hayhoe (2007).

I will first come up with the test hypothesis whilst ensuring that I single out both the dependent and the independent variable.

Secondly, to ensure that I remain focused on the test's primary concern, I will develop the null hypothesis from the test hypothesis.

Next, I will engage in data collection after which I will feed the data collected into separate columns of a spreadsheet.

I will then engage in sample size tallying (for each group) using the COUNT function and then compute each group's mean using the AVERAGE function. Next I will, compute each group's standard deviation using the function STDEV.

On computing the standard deviation, I will seek to find out the p value using the TTEST function.

The next step in this case will be to use the p value I computed in the previous step as the basis for null hypothesis acceptance or rejection. According to Hughes & Hayhoe (2007), the null hypothesis can typically……
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#### Algebra, Trig Perform the Indicated Research Paper …

Research Paper |
1 pages (322 words)

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2

SAMPLE TEXT:

Perform the indicated operation and simplify completely:

(x^3 + 3xy - 8y^2) - (6x^3 + 8xy + y^2)

(x^3 + 3xy - 8y^2) - (6x^3 + 8xy + y^2) = x^3 + 3xy -- 8y^2 -- 6x^3 -- 8xy -- y^2

= -5x^3 -- 5xy -- 9y^2

9. Perform the indicated operation and simplify completely:

[2x / (4x + 2)] * [(6x + 3) / 5)]

[2x / (4x + 2)] * [(6x + 3) / 5)] = (12x^2 + 6x) / (20x + 10) = [6x (2x + 1)] / [10(2x +……
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#### Scientific Notation, Its Uses Research Paper …

Research Paper |
2 pages (499 words)

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2

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(All nonzero digits are considered to be significant digits, also any digits that express the precision of a measurement instead of its magnitude.) This is the coefficient.

2. Find the exponent by counting the number of places from the decimal to the end of the number. Numbers smaller than 1 will have a negative exponent.

Using scientific notation not only gives a way of writing very large and very small numbers, it also makes it easier to do calculations as well. The rule for multiplication is: To multiply numbers with scientific notation, multiply the coefficients together and add the exponents. The base remains 10.

The rule for division is: To divide numbers with scientific notation, divide the coefficients and subtract the exponents. The base remains 10.

The rule for addition and subtraction: When adding or subtracting in scientific notation, the numbers must be expressed as the same power of ten. This rule will often involve changing the decimal place of the coefficient.

Note that the rules of exponents apply to the process of calculating scientific notation:

Any number raised to the power of zero equals one.

Any number raised to the power of one is equal to itself.

Any number raised to the nth power is equal to the product of the number used as a factor n times.

Works Consulted

BookRags. (2011). Scientific notation. Retrieved September 18, 2011 from: http://www.bookrags.com/research/scientific-notation-mmat-04/

Curran, G. (2008). Science help……
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#### Observation of Phenomenon Aurora Borealis and Mammatus Clouds Essay …

Essay |
2 pages (534 words)

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0

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¶ … Natural Phenomena

Observing the Aurora Borealis

The Aurora Borealis phenomenon is breathtaking to watch, both aesthetically as well as conceptually and philosophically. At the simplest level, it emits color schemes that are not typically seen in the atmosphere. Second, it produces types of apparent motion that are sometimes seen in a fluid medium on earth, but rarely elsewhere, especially in the sky overhead.

My initial thoughts while watching the Aurora Borealis had to do with the monumental significance such phenomena would naturally have represented to ancient people. There is lifelikeness to the horizontal movement of the phenomenon that would suggest a consciousness to ancient observers with the capacity of human intellectual curiosity. It is almost inconceivable that ancient observers would have attributed the lightshow to anything other than some sort of Divine demonstration of power. The phenomenon also makes me more aware of the sheer range of atmospheric manifestations that are possible. In that respect, it serves as a reminder that the phenomena we see on a regular basis are only a small portion of the range of possibilities. My observation also reminded me that it is probably the case that the atmospheric phenomena of every planet large enough to have an atmosphere are unique to that planet.

However, my most overwhelming reaction to the Aurora Borealis is appreciation and awe at the human intellect for having the capacity to quantify such incredible natural phenomena in mathematical terms. It was while imagining how complex the formulas of Lorentz, Maxwell, Faraday, and other mathematicians and theoretical physicists who provided technical descriptions of the unimaginable. It was……
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#### Python Programming Tkinter Essay …

Essay |
2 pages (449 words)

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0

SAMPLE TEXT:

The result of function will be displayed in the label. Value of label is displayed as "0" by default, after each function control will automatically go to first text box to rewrite the text values.

HOW INTERFACE WILL BE DISPLAYED:

This process involves following steps:

Import GUI class named as tkinter

A class named as "simpleapp" is being inherited from tkinter.

Call constructor of inherited class

Save reference of inherited class to parents widget

Create a grid

Initially a value of "0" will be assigned to "FirstNumberVar" and "SecondNumberVar."

Displaying string values in first two rows of first column.

Add four buttons to grid labeled with their functionality used to be perform.

Add a label to grid displaying initial value of "0."

FUNCTIONS USED:

This program has following main functions:

OnAdd:

Perform addition on input values and display result in label

OnSubtract:

Perform subtraction on input values and display result in label

OnMultiply:

Perform multiplication on input values and display result in label

OnDivide:

Perform division on input values and display result in label

OnPressEnter:

It will display the first string value and a text of "you pressed enter" in label

CONCLUSION:

Main goal of this assignment was to develop an understanding of how to develop a static interface application using TK GUI toolkit which belongs to Tkinter module……
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#### Nonlinear Aerostatics Stability Analysis of Suspension Bridges Literature Review Chapter …

Literature Review Chapter |
10 pages (3,491 words)

Style: Harvard | Bibliography Sources:
5

SAMPLE TEXT:

Su, Luo & Yun (2010) performed an aerostatic reliability of bridges with long spans. According to their study, the response surface Monte Carlo method (RSMCM) is suggested to be suitable for the analysis of the reliability of both the aerostatic stability and the aerostatic response for various types of long-span bridge structures. In these bridges, the nonlinear effects that come… [read more]

#### Social Research There Are Several Explanations Essay …

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3 pages (956 words)

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Social Research

There are several explanations for an observed relationship that need to be examined and dismissed before a true relationship can be established. First, it is possible that an observed relationship is merely coincidental; using large sample sizes that seem to show the same relationship can diminish this risk. Also, an external cause influencing both of the observed factors could exist, which is why testing or controlling all other variables is necessary to show the validity of a relationship. Finally, it is possible that a researcher bias exists, and again controlling the research methods and variables can help to limit exposure in this area.

A Type I error occurs when the null hypothesis is falsely rejected. In this type of error, the correlation, relationship, or explanation advanced by the alternative hypothesis is accepted -- meaning the null hypothesis is rejected -- due to false observations and/or analyses. A Type II error occurs when the null hypothesis is not rejected even though evidence that it should be rejected actually exists. For instance, the correlation proposed by an alternative hypothesis might actually exist, but due to an error this correlation is not observed or is not seen as significant by the researcher, resulting in continued acceptance of the null hypothesis.

3)

A null hypothesis would be that there is no correlation between caseload size and child welfare worker stress. A one-directional research hypothesis would be that as the size of a caseload increases, the amount of stress experienced by the child welfare worker with this case load also increases. In the research that would investigate this hypothesis, caseload size would be the independent variable or the cause in the causal relationship hypothesized, while child welfare worker stress would be the dependent variable, or the effect.

4)

Probability sampling is also known as random sampling, and can be used to infer information and observations about the general population from which the sample is drawn. In other words, a large enough random sample population drawn from a general population pool would be expected to match that general population in demographics and proportion, and thus the probability of a specific outcome in the population would be the same or similar to observations in the general population. Nonprobability sampling can be useful, but is not entirely random and so cannot be used to make assumptions about a general population.

5)

Some advantages of questionnaires are the ability they provide for respondents to give detailed answers, and the removal of the researcher from the direct data gathering process (i.e. respondents can fill out questionnaires in their own time) reducing research bias or influence on the results. Disadvantages, however, include the potential for misinterpretation or differing interpretations among respondents, reducing the validity of the questionnaire's measures and conclusions. Reduced control generally can be a problem.

6)

Interviews have a strong advantage in the ability of……
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#### Alcohol Abuse Among the Elderly Essay …

Essay |
2 pages (533 words)

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0

SAMPLE TEXT:

¶ … Sampling error" is the term applied to the discrepancy and possibility of being misled by observing only a sample of a total population instead of the whole population itself. Generally speaking, the larger and more diverse the sample population is, the lower the risk of sampling error, because the sample will be more representative

A sampling distribution of means is a distribution of means collected from different sample populations. That is, it is a distribution created by calculating the mean of specific responses given by subjects within several distinct sample populations. For instance, if the mean from sample a is two, from sample B. is three, from sample C. is two and so on, the sample distribution of means would show the data spread of these means (around two or three, in this example).

3)

The central limit theorem basically states that no matter what the distribution of original data is, the sampling distribution of the mean will approach a normal distribution, and the larger the sample is (for many distributions and for the sampling distribution of the mean) the closer it will approximate a normal distribution.

4)

The confidence level of a data set or figure is the degree of certainty that one can have in that figure or data set, whereas the confidence interval is the actual range of data that is contained in the confidence level percentage of the data set.

5)

Statistical significance refers to whether or not an observed trend, correlation, or other relationship actually appears to exist after rigorous examination of the numbers, and not merely due to……
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#### Search for Knowledge or Data Essay …

Essay |
3 pages (1,154 words)

Bibliography Sources:
3

SAMPLE TEXT:

¶ … search for knowledge or data about a matter, investigating the subject via scientific methodology. The primary process of research is to discover, interpret, and (in the case of applied research) use certain methods that will lead to more reliable, evidence-based knowledge about our world.

The research process is based on the following steps: 1. Articulation of the topic and literature review or observations; 2. Researcher's hypothesis; 3. Conceptual definitions and operational definitions of investigated concept; 4. The scientific gathering of data; 5. The scientific analysis of data; 6. Modifying or support of hypothesis, and 7. Conclusion (Trochim, 2006).

Qualitative research is often best used when the sample under study cannot be analyzed in the laboratory and one wants richer information on that population sample. It is usually applied to people. Five examples are: (i) Margaret Mead's case study and observations of Samoa; (ii) the in-depth analysis and observations of a program in order to assess its operational success (e.g.. Of UNICEF); (iii) assessing individual people (e.g. children (as was done with Piaget's clinical method) to assess the way they work; (iv) naturalistic observation- studying a culture in an unobserved natural manner; or (v) investigating biographical details of an individual's life.

3. On one level, this may be called 'interviewing' either individually or through focus groups where the researcher (using open-ended or closed-ended questions or a mixture of both) elicits the opinions and particular perspective / experience, and so forth, from an individual on a certain matter.

On a deeper level, this may be described as phenomenological research (conducted through protocol methodology) where the participant is asked to record naive descriptions of his experience and the researcher closely assesses these (Breakwell, Hammond, & Fife-Schaw, 2000).

4. The arguments for quantitative research revolve around the fact that bias is more closely screened out when the study is conducted in a rigid laboratory-type methodology with statistical data and measurements used to quantify their significance.

The qualitative approach, however, maintains that many cases, especially those involving humans, cannot always be assessed in such a manner. Certain data (such as emotions of hostility, love etc.) are too abstract to be measured, and humans and events involving humans are too chaotic to be 'pinned down' and quantified in a laboratory environment.

6. The checklist here would involve operational definitions of the following variables: Concepts involved in 'caring': the range of activities that involve looking after the cat and the intensity to which individual does so. Life expansion would be defined -- i.e., the exact amount of years that would be used as measurement to indicate that caring for cat does prolong life; hypothesis would also consider the phraseology 'living alone' -- does he/she have close friends / immediate / extended family who care for individual; is he/she involved in community events and, if so, to which extent; does he/she receive social support in any particular manner and the extent of this social / family support would be considered. Furthermore, 'Northwestern region' would be defined.…
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#### Chi-Square With Base Hypothesis That All Political A-Level Coursework …

A-Level Coursework |
3 pages (731 words)

Bibliography Sources:
6

SAMPLE TEXT:

¶ … Chi-Square with base hypothesis that all political groups contribute equal amounts.

b) Chi-square with base hypothesis appropriate to the attitude question asked.

c) T-test.

d) Chi-square with base hypothesis of equal average salaries between regions.

Perform a chi-square test of the following data:

a) Regulation is the best way to ensure a safe workplace

Managers

Blue-collar workers

Agree

Disagree

Totals

One potential hypothesis for this data is that managers and blue-collar workers do not have very different opinions about regulation. Some regulations may make the workplace safer for managers as well as blue-collar workers. Many blue-collar workers are politically conservative, which would influence them against over-regulation of the workplace. So, the expectations for my chi-square test will be:

Managers

Blue-collar Workers

Agree

Disagree

No Opinion

Total

Expected

Obtained

(Obs-Exp)^2/Exp

Man-agree

62

58

0.258064516

Man-disag

29

34

0.862068966

Man-NA

9

8

0.

Work-agree

62

66

0.258064516

Work-disag

29

24

0.862068966

Work-NA

9

10

0.

2 = 2.46

This does not exceed the critical value of 3.84 for a chi square test with ? = 0.05 and df = 1. Therefore, we can assume that these data are not significantly different from the expected values, and do not violate the null hypothesis.

b) Ownership of residence

Male

Female

Yes

25

16

No

7

8

Totals

32

24

In this case, we are testing current numbers against the null hypothesis that home ownership has equalized across genders. The expected value table is:

Male

Female

Yes

23.4

17.6

No

8.6

6.4

Totals

32

24

Expected

Obtained

(Obs-Exp)^2/Exp

M-Yes

23.4

25

0.105400697

M-No

8.6

7

0.288095238

F-Yes

17.6

16

0.140534262

F-No

6.4

8

0.384126984

In this case as well, we fail to violate the null hypothesis, ?2 = 0.92.

c) Age of shopper

Store a

Store B

20-34

27

73

35-54

31

82

55+

11

93

Totals

69

The null hypothesis in this case is that both stores draw equally from the same age groups, although Store B. draws more customers overall. The expected value table is:

Store a

Store B

20-34

21.8

78.2

35-54

24.6

88.4

55+

22.6

81.4

Totals

69

Expected

Obtained

(Obs-Exp)^2/Exp

20-34

21.8

27

1.25830064

35-54

24.6

31

1.66726748

55+

22.6

11

5.98240235

20-34……
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#### Journal of Physics and Medicine in Biology Book Review …

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¶ … Journal of Physics and Medicine in Biology: Manuscript 653

"A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density" by Webb and Nahum (1993)

The following paper critically evaluates the basis of the article entitled Re: "A model for calculating tumour control probability in radiotherapy including the…
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#### Evaluator, Researcher or Observer Watches Essay …

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8 pages (2,052 words)

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-1, 0, +1, +2). In the first example the lower the total for each question the lower the respondent's opinion of the subject of that question, the negative value would be 1 rising through 5. In the second example, the negative value would start at -2, 0 would be neutral, and +2 would be the positive value.

Indexing on the other hand is placing responses in certain categories. An example of indexing would be when an evaluation seeks to determine the impact and the productivity of a school or program. Indexing could take place by numbering how many participants attempted a certain action and at the same time attempting to number how much of an impact those participants were having on the action.

#4 A null hypothesis generally offers the researcher a method for proving or disproving a hypothesis. For example a researcher may come up with a hypothesis and wishes to prove that the hypothesis is true. The researcher could therefore come up with a null hypothesis that helps to do so. An example might be if someone bought and sold stocks and bonds every single day that showed a certain return and that return was higher than another method such as buying and holding a stock. The null hypothesis would state that there is no difference between the two methods. If the person were to conduct tests and prove that there was a significant difference, then the null hypothesis is false (Investopedia, 2010).

The alternative hypothesis is usually contradictory to the null hypothesis. The researcher is normally attempting to prove a certain hypothesis, if the null hypothesis is disproven, then the alternative hypothesis is proven. Both the null and the alternative hypothesis (together) should cover the entire gamut of the study. An example of a null hypothesis might be that a new drug has no significant advantages to the patient. In this case the alternative hypothesis would be that the new drug does have a significant advantage to the other treatment. A two sided alternative hypothesis might be that the new drug has either significant advantages or disadvantages to the current treatment.

Methods of determining whether the null hypothesis have any significant differences than the alternative hypothesis is done through the use of tests of significance. A test of significance does not say whether the null hypothesis is true or the alternative hypothesis is true, instead what the test of significance does is that it determines if there is any significance between the null and alternative hypothesis. Two tests of significance include the Chi Square test and the Survey System.

Finally, there are two types of errors that can occur in testing statistical hypothesis. Each of the errors concerns the incorrect conclusions that can take place after the testing. When a null hypothesis is incorrectly rejected despite the fact that the null hypothesis is true, that is called a Type 1 error. The Type 1 error differs from the Type 11 error in that the null hypothesis is…
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#### Function Establishes the Relationship That Exists Case Study …

Case Study |
2 pages (434 words)

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Function establishes the relationship that exists between different variables, more precisely, between the input and output variables. The input variables will be linked to the output result through a general formula or function: through the input of the variables into the formula, the final output will result. One important condition for a relation to be considered a function is for each x value to result one and solely one f (x) value.

A linear function is a function which has only one variable and it is, at the same time, a first degree function. The general formula of a linear function is f (x) = ax + b, where a and b are real constants and x is the input variable.

As previously mentioned, the standard form of a linear function is f (x) = ax + b.

The slope of a line is a in the function f (x) = ax + b. As such, the formula to calculate a is a = (f (x) -- b)/a

Let C. be the number of cups that are sold and P. The price for which the cups are sold. The total money that can be raised through the lemonade stand is given by the function f (P) = C * P, following the notation previously mentioned. In that……
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#### Spiritual Principle: For Unto Term Paper …

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2 pages (446 words)

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Spiritual Principle:

For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath. (KJV Matthew 25:29)

Students will learn to investigate and solve piecewise functions; they will learn to explore exponential functions by extending properties of exponents to include all integers; they will learn to solve quadratic equations in one variable by using factoring, square roots, and the application of the quadratic formula; and, they will be able to discuss functions and their inverses by using concepts such as one to oneness, domains and range.

Suggested Activities and Experiences:

Divide students into groups of approximately six each. Students will make a table and graph in pencil. Three students in the group will graph the linear function and three will graph the quadratic equation. The group of six will come together and put their graphs together and describe and evaluate the piecewise functions.

2. Students will memorize exponent integers and be able to explain their characteristics. Once these concepts are understood, students will move on to solving simple exponential equations and inequalities as well as graphing functions. To assist the students, games such as MathDork (http://www.mathdork.com/games/asteroidsexp3/asteroidsexp3.html) can be played at home or during computer lab time at the school.

3. To solve quadratic equations, students will……
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#### Qualitative vs. Quantitative Research Essay …

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2 pages (622 words)

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Qualitative vs. Quantitative Research

This article analyzes the distinctions between Qualitative and Quantitative Research Methodologies and discusses seven distinct research criteria and how each method differs regarding them. This first Criterion, Epistemological Assumptions, also generally describes the features of both methods. Quantitative research seeks to discover and objective and quantifiable reality independent of feelings or thoughts about it. While qualitative research ascribes beliefs, feeling and thoughts regarding reality and describes it in a varying non-absolute scale. Often the researchers own beliefs about what they are trying to accomplish can influence their selection of research methods. But the parameter for choosing one or the other generally guided by criterion two, Purpose. If the purpose of the study is to garner information about a predictive future state, than quantitative research is generally chosen. More aligned with number theory, quantitative analysis can yield more predictable and graphic results for decision making based on current states. In other words, "generalizability" is the key. Whereas, if a study's purpose is to understand and interpret research that requires a more in-depth methodology that will dig deeper into motivations and beliefs, qualitative methods are usually employed. Here also sample size has less relevance that in quantitative research.

Raw Data, criterion three, is presented quite differently in these methods. Quantitative data, as the word implies, regards quantity or numerical differentiation as key. It is not so much what is said, but how many times an instance occurs or what value can be placed upon it. Whereas qualitative data is usually composed of words whose meanings regarding information can include various media and formats as well.

The next criterion, emphasis, is similar to purpose, as it is the overall intention of the study and the researcher point-of-view. In quantitative research the emphasis is on repeatability and predictability. The results show that there is a trend or tendency and that they……
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#### Regression Analysis Is the Technique Term Paper …

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2 pages (567 words)

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Regression analysis is the technique used to express the linear relationship between two variables. With this technique we can estimate the value of the dependent variable (Y) based on a selected value of the independent variable (X). This kind of analysis is mostly used to determine if sales numbers of a product a are related to the number of TV advertisements for that particular product during a specific timeframe. The mathematical equation for the line used to estimate the value of variable Y on the basis of variable X is also known as the regression equation (general form of linear regression equation: Y1 = a + bX) (Lind, Marchal, & Wathen, 2005).

Y1

= read Y prime, is the predicted value of Y for a selected X value a = is the Y-intercept, or the estimated value of Y when X = 0

b

= is the slope of the line, or the average change in Y1

X

= any value of the independent variable that is selected

Linear regression is used to make predictions about a single variables value. In other words, it is used for discovering the equation for a line that most closely fits the given data (Lind, Marchal, & Wathen, 2005). That linear equation is then used to predict values for the data. For example: A sales manager wants to know if more sales calls will sell more copy machines, and by how much the number of calls have to increase to reach a certain number of sales for those machines. The main components are the slope and the intercept, also the standard errors and confidence intervals. Furthermore the correlation coefficient, and standard deviation are components of the linear regression analysis.

Simple regression - the simple……
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#### Dislocation Dynamics in an Anisotropic Stripe Pattern Research Paper …

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3 pages (769 words)

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Crystal Review

A review of "Dislocation Dynamics in an Anisotropic Stripe Pattern"

This paper reviews the findings of a specific published study regarding the patterns that emerge form dislocation occurring across domain walls in physical systems, and specifically anisotropic stripe patterns. Different electromagnetic and conductive patterns emerge due to the striped patterns that are created by distortion movement occurring parallel to domain walls, and the study reviewed examines the nature of these variances and the degrees of distortion and pace of change that occur. Analysis of the article published as a result of the study is also conducted form a quantitative and qualitative/critical perspective, for which other related studies and information are utilized.

Topological defects occur in almost all crystals, though they vary in their mathematical complexity and the solutions/theories that have been used to examine and explain the various defects. Boundary conditions, which in crystals take the form of domain walls, cause these topological defects, defined as the dislocation of the crystal. These distortions their causes and their effects have all become major areas of study; the study of topological defects has increased as it becomes clear that they are the dominant pattern in many kinds of physical systems, including in crystals. Uniform systems have yielded simpler understandings in regards to their topological defects than non-uniform systems, providing the impetus for the study reviewed and for this critical analysis of this study.

The article does an admirable job of providing an overview of the research regarding domain growth and topological defects generally, though the language is highly technical -- unnecessarily so, at points. The temporal evolution of these patterns and domain shifts in uniform and homogenous systems of several different types, including fluid systems and magnetic systems, are provided in the introductory material to provide an avenue for comparison and analysis in the striped systems analyzed by the researchers. Electroconvection is identified as an anisotropic system, with its own specific patterns of development: normal and oblique rolls. Specification and understanding of the impact of non-isotropism in systems on the electroconvection, however, remains largely underdeveloped, and the authors make a good case for the necessity of their study and both the understanding and the attention it provides to this unique yet fairly common occurrence.

The anisotropy of domain wall growth is identified as the……
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#### Scaling Application of Measurement Term Paper …

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2 pages (710 words)

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Scaling can be considered to be a major aspect of exploratory type research and can answer questions like what dimensions are the basis for a set of ratings for example. However, the best use for scaling is for scoring purposes. In other words, scaling is an excellent medium for collecting responses to a given set of items that it is easy to assign a single number with that number indicating an overall attitude or belief.

Scaling then can be said to be a branch of measurement involving the inherent construction of an item that equates 'qualitative constructs with quantitative metric units.' This tool descended from psychology and education because these areas each needed a means for measuring things prior to scaling that were technically no measurable. So it is therefore not difficult to understand why so many individuals simply do not understand scaling. The basic idea of scaling comes from two time periods, unidimensional for instance comes methods developed throughout the first half of the twentieth century and are now usually named after their inventors while later in the 1950s and 1960s, theorists got more involved and created the more difficult concepts of multidimensional scaling.

So in conclusion, "it is important to realize that although a scale is an instrument that can be used alone, it is often integrated into a larger and more complex instrument, such as a survey. (Trochim 2008, p 131) Scaling is a tool that helps clear abstract ideas into measurable context. This work then aimed to discuss the role of scales in research and research design and to point out that measurements that incorporate scale data are often incorporated into learners' quantitative research projects and dissertations. For that reason, it is critical to clearly identify the purpose of scaling and how it can best be utilized in these types of projects. Scaling as a science of measurement is based on specific rules and often assigns objects with numbers so they can measure abstract objects to one another.

References

Trochim……
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#### Hypothesis and Stats Thesis …

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John and Sons Company: Null Hypothesis and Test of Statistical Significance

The null hypothesis often states the opposite of what an experimenter is attempting to prove (Lane 2009). The experimenter wants or expects to disprove the null, which is expressed as H0. For example, presume that the John and Sons Company wants to open a new factory overseas and take advantage of lower wages abroad, but is concerned about the potential quality implications of this move upon the product, as John and Sons have had quality-control problems in the past with their overseas operations. The H0 would be: 'there is no statistically difference in the number of defects in a batch of the product manufactured in country X versus a batch manufactured in the United States.' (Hence the term null hypothesis -- that there is no difference). The alternative hypothesis, expressed as H1, would be that there was a statistically significant difference in the number of defects found in the batches made in country X versus the United States. "This alternative hypothesis states that the relationship observed between the variables cannot be explained by chance……
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#### Vectors and Force Thesis …

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Algebraic Vectors

a) an (x, y) coordinate system would be appropriate; movement will occur both along the sidewalk (i.e. down the street) and across the sidewalk (between the buildings/yards and the curb), requiring a two-dimensional coordinate system

b) a simple x coordinate system or number line is sufficient; the tightrope walker will only be moving in a single direction (albeit wit positive and negative relative magnitude)

c) as stated, only an (x, y) coordinate system would be needed, but in reality a three-dimensional (x, y, z) coordinate system is required to plot submarine and aircraft movements, as travel can occur along the two dimensions of the cardinal directions (i.e. forward-back or North-South and right-left or East-West), as well as vertically (up and down).

b.

3.

a.

b.

Without resolving vectors into components, no understanding of relative motion can actually be established. Vectors are inconsequential if not stated and understood in relation to a fixed point (usually the starting point of the vector).

35m

15m

=25(

=65(

a b

15/sin90 = a/sin25 15/sin90 = b/sin65

15 x sin25 = a 15 x sin65 = b

6.34=a 13.59 = b d+b = 48.59 a = 6.34

48.592+6.342 = 2401.18

( 2401.18 = 49

c = 49 = magnitude

49/sin90 = 6.34/sinA

49 x sinA = 6.34

sinA = 6.34/49

sinA = .129

A ( 7.43( = direction d

c

A

2.5km

5.2km

A

B

B = 180 -- (35-22)

B = 173(

sinB = .122

b2……
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#### Experimental Research Design the Research Process Research Proposal …

Research Proposal |
8 pages (2,184 words)

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25

SAMPLE TEXT:

Experimental Research Design

The research process is stated to be of the nature that utilizes scientific techniques in the investigation of phenomenon and a research process that is focused on acquisition of new knowledge about the phenomenon. (Experiment Resources, 2009) the Experimental method is stated to require the basis of "observable, empirical and measurable evidence, to be termed scientific" and…
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#### Algebra Suppose You Have a Lemonade Stand Research Proposal …

Research Proposal |
1 pages (355 words)

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Algebra

Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.

C = -60P + 240

Take a look at the table below and write out an equation for f (x).

f (x) -2-2-6-10

f (x) = 4x +

Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f (x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi-part relations so consider all parts when deteriming if they are funcitons.

a. f (x)……
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#### Precalculus II Leaning Tower of Pisa Term Paper …

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2 pages (496 words)

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Precalculus II

Leaning Tower of Pisa

The Leaning Tower of Pisa was originally 184.5 ft high. but, currently, the tower is leaning slightly from its original perpendicular state. At a distance of 123 feet from the base of the tower, the angle of elevation to the top of the tower is found to be 60°. Find the approximate angle that the tower is leaning from its original perpendicular state. Then, find the towers current height.

The current height of the tower is BD in the scratch. We can find BD from triangle ABD:

BD=AB*sin

We can find AB using cosine theorem:

BC^2= AC^2+AB^2- 2*AB*AC*cos

BC=184.5

AC=123 cos

25=15129+ AB^2 -2*AB*123*0.5

AB^2-123*AB-18911.25=0 solving this equation we should find only positive root:

D=123^2+4*18911.25

D=90774

D=301.287

AB=(123+301.287)/2

AB=212 sin

A=0.866

BD= 212*0.866

BD=183.59

Answer: tower's height is 183.59 ft.

Part II: Lost Treasure

While scuba diving in Bermuda, you discover a treasure map in a pirate schooner. The map directed them to an area that was no longer there. So, they had to re-create the map by treasure map experts.

The directions on the map read as follows:

From the tallest palm tree, sight the highest hill. Drop your eyes vertically until you sight the base of the hill.

Turn 40° clockwise from that line and walk 70 paces to the big red rock.

From the red rock, walk 50 paces back to the sight line between the palm tree and the hill. Dig there for the treasure.

Mission: Draw the……
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#### Pre Calculus II Project Setup: The X-Axis Term Paper …

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2 pages (452 words)

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Pre Calculus II Project

Setup: the x-axis as the water level. The origin is the midpoint between the two x-intercepts/support bases. The clearance level is a horizontal line at QUOTE. Three points are given that are the same for both parabola and semiellipse: the first is the y-intercept, which occurs at 350' above the water, or QUOTE; the two other points are the x-intercepts. The distance between the two supports is 1050', and since the y-intercept bisects both shapes, the x-intercepts are at QUOTE and QUOTE. Therefore, the three points are: QUOTE, QUOTE, and QUOTE.

The equation for the parabola can be obtained using those three points. The parabola is centered, so the x-term is not added to or subtracted from before being multiplied by its coefficient. The parabola must also be negative to create the necessary shape. Using the y-intercept, we can create the preliminary equation QUOTE, where a is a coefficient that must be solved for. To do this, we use an x-intercept. Thus:

To find the width of the channel through which the tanker can pass, one must find the length of the value of x when the parabola is intersected by the horizontal line QUOTE. Hence:

Hence, the parabolic bridge allows 234.287 ft of clearance from the centerline, or about 470 ft in all.

The equation for the ellipse is found in……
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#### Physics Made Easy Term Paper …

Term Paper |
3 pages (814 words)

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1+

SAMPLE TEXT:

¶ … velocity is velocity averaged over a given period of time, represented as change in distance divided by time. Instantaneous velocity is the limit of the average velocity as time tends to zero, or more simply put, the average velocity over an infinitesimally small period of time. Acceleration is the rate of change of velocity. (Winnipeg)

Scalar values represent magnitude only, and can be used across different coordinate systems. Mass is a scalar quantity - for example, 1kg. Vectors include both magnitude and direction. Force is a vector quantity - for example, a 1kg rock on Earth is being pulled by gravity with a force of about 10N toward the center of the Earth.

Position is the product of velocity and time. Velocity is the product of acceleration and time.

A vt at The magnitude of frictional force is the product of the force pushing two objects together and the coefficient of friction between the two objects. The coefficient of friction cannot be calculated without the aid of a complex computer simulation. It is normally determined experimentally. The coefficient of sliding friction between two objects is determined by measuring the acceleration experienced one of the objects while sliding across the other with all other forces acting on it in a state of equilibrium The coefficient of static friction between two objects is determined by applying force to one of the objects while it is stationary, and measuring the force required before the object begins sliding. The magnitude of the gravitational force between two objects is the product of the masses of each object divided by the square of the distance between them.

In order to perform calculations on a projectile, orbiting body or other object that is not moving linearally, it is convenient to split up its motion and/or forces in to component vectors. Component vectors are the portions of the vectors that line up with the coordinate system. For example, an arrow fired upward and north at a velocity of 4m/s has a velocity of 2m/s up and 2m/s north according to the Pythagorean theorem. The theorem can again be used to re-integrate the component vectors in to the actual vector after performing calculations. (Koehler)

Centripetal force is the force required to maintain its speed while moving in a circle. An object moving in a straight line will continue to do so unless acted upon by an outside force. The centripetal force can be supplied……
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#### Dominant Hemispheres Term Paper …

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2 pages (668 words)

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1+

SAMPLE TEXT:

Since I am very organized, detail-oriented and an extreme perfectionist, I believe that I am left sided dominant. The left side processes information in a linear manner, from part to whole, by taking pieces, lining them up and arranging them in a logical order, then drawing a conclusion (Left pp). Moreover, the left brain processes in sequence, thus these individuals are list makers, and enjoy making master schedules and daily planning (Left pp). As left sided dominant individuals complete a task, they take great pleasure in checking them off the list when the tasks have been accomplished (Left pp). And because these individuals learn in sequence, most of them are good spellers, and are good at math (Left pp). The left brain processes symbols easily, and since many academic pursuits deal with symbols, such as letter, words, and mathematical notations, left brained people tend to be comfortable with linguistic and mathematical endeavors, and have no trouble memorizing vocabulary words or math formulas (Left pp).

Furthermore, the left side of the brain deals with reality, with the way things really are, thus when left brain students are affected by the environment, they simply adjust to it (Left pp). These individuals want to know the rules so that they can follow them (Left pp). In fact, if there are no rules for a given situation, they will most likely make up some rules in order to follow them (Left pp). Because they insist on rules, then they are aware of the consequences for not following them, such as not turning in a paper on time or failing a test, therefore left brained students are seldom late with papers or fail tests (Left pp).

Work Cited

Left Vs. Right. Retrieved October 04, 2005 from:

http://brain.web-us.com/brain/LRBrain.html

Right Brain vs. Left Brain. Encyclopedia of Educational Technology. Retrieved October 04, 2005 from:

http://coe.sdsu.edu/eet/articles/dominance/index.htm…
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#### Algebra Like Many Other Languages Term Paper …

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1 pages (305 words)

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Keplar's laws relate to the orbit of an object moving around another in space as elliptical, with the stationary object located at one of the focal points of the ellipse. Simply put, the Earth travels around the sun in an ellipse, and the sun is a focal point in that ellipse; likewise for a satellite traveling around the earth.

Using Algebra, Keplar understood:

Ra=a (1+e) and Rp=a (1-e)

Where a = semi-major axis of the ellipse e= eccentricity of the ellipse

So that the elliptical shape of the orbit is the result of the inverse square force of gravity.

For instance, the eccentricity for a circle is zero. Earth's eccentricity is only 0.0167, while Pluto, the planet with the largest eccentricity, is .25.

Visually, this is what Keplar sought to explain:

Mathematically, however, linear algebra makes the picture an easily understood, computable……
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#### Stochastic Modeling Is a Mathematical Term Paper …

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2 pages (665 words)

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1+

SAMPLE TEXT:

The optimal policy from such a model is a single first-stage policy and a collection of recourse decisions (a decision rule) defining which second-stage action should be taken in response to each random outcome [5].

Solution approaches to stochastic programming models are driven by the type of probability distributions governing the random parameters. A common approach to handling uncertainty is to define a small number of scenarios to represent the future. In such cases, it is possible to compute a solution to the stochastic programming problem by solving a deterministic equivalent linear program. These problems are typically very large-scale problems, and so, much research effort in the stochastic programming community has been devoted to developing algorithms that exploit the problem structure, in particular in the hope of decomposing large problems into smaller more tractable components. When the probability distributions of random parameters are continuous, or there are many random parameters, one is faced with the problem of constructing appropriate scenarios to approximate the uncertainty. One approach to this problem constructs two different deterministic equivalent problems, the optimal solutions of which provide upper and lower bounds on the optimal value z* of the original problem.

Stochastic programming has been applied to a wide variety of areas in engineering. Some of the engineering problems such as electrical generation capacity planning, machine Scheduling, timber management, traffic management, automobile inventory management, and lake level management are complex indeterminate problems that require stochastic solutions.

References

[1] A. Prekopa. Stochastic Programming. Kluwer Academic Publishers, Netherlands, 1995.

[2] S.R. Tayur, R.R. Thomas, and N.R. Natraj. An algebraic geometry algorithm for scheduling in the presence of setups and correlated demands. Mathematical Programming, 69(3):369-401, 1995.

[3] C.C. Caroe and R.Schultz. Dual decomposition in stochastic integer programming. Operations Research Letters, 24:37-45, 1999.

[4] R. Hemmecke and R. Schultz. Decomposition of test sets in stochastic integer programming. Mathematical Programming, 94:323-341, 2003.

[5] H.D. Sherali and B.M.P. Fraticelli. A modification of Benders' decomposition algorithm for discrete subproblems: An approach for stochastic programs with integer……
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#### Personality Impressions Term Paper …

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4 pages (1,195 words)

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0

SAMPLE TEXT:

Burkard, Alan W. And Knox, Sarah (2004). Effect of therapist color blindness on empathy and attributions in cross-cultural counseling. Journal of Counseling Psychology, 51:4, 387-397.

Whether research investigations are designed on the basis of an experimental, descriptive, historical, or case study format there must exist a clearly defined research question which informs the reader as to the specific intent of the research undertaken. When the research design is experimental or descriptive there must follow a well-formulated testable null hypothesis. Should these two research tenets not be in place then the research is said to be ad hoc and of little useful propose with respect to the validity and reliability of content knowledge. The present article reviewed and authored by Burkard and Knox (2004) can be best described as ad hoc research and did not follow the best-fit practice for effective research. The reasons for this summary statement is based upon the following reasons:

research question is to be presented at the beginning of a research investigation and if designed as an experimental of descriptive study a testable null hypothesis (es) follows. Buckard and Knox did not formally present a research question and the hypotheses presented were not only directional and non-testable (i.e., null form) but also highly biased as well: "...we hypothesized that those therapists were higher in color blindness racial attitudes..." "...we predicted that therapists' color blindness would be related to...." "..we predicted therapists' color blind racial attitudes would..." (p. 389). Continuing one step further, the research investigators failed to even alert the reader as to the research problem even though they presented a great deal of information pertaining to the overall area of study. At no time is a research investigator permitted to pre-formulate a direction that a sequence of events might take. All that a research is permitted to do is hypothesize that no differences, effects, or relationships will be uncovered as a result of the investigation. The reason being is that without a testable null hypothesis a research investigator cannot explain why something some thing did happen, and not why something did not happen. Therefore a research investigator must always begin with a statement (null hypothesis) that something will not happen.

With respect to the sample used in the study the authors failed to alert the reader as to the randomness of selection. When samples are chosen on the basis of non-randomization, the statistical tool chosen to analyze the day must be "re-fitted" to accommodate for non-randomization of selection.

The data analysis discussed in the report (p. 391-393) makes reference to an ANOVA and Pearson "r" coefficient analysis. These two particular statistical tools are employed to determine effects/differences and relationships between and amongst the variables under investigation. As there exists no rationale for seeking differences or effects the use of the ANOVA technique is circumspect. For there to exist legitimacy for the use of the ANOVA technique the reader should have been presented a testable null hypothesis stating effects and/or differences between and amongst the variables…
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#### Frequency Distribution of Rejected Circuit Term Paper …

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In any statistical analysis the standard deviation mathematical quotient is representative of the degree to which a difference exists between a score distance and the mathematical mean of the group. As the Excel Program only permits cells up to a 30 count the more conventional hand calculation method was used. For the current set of data the calculated standard deviation is expressed by the following formula:

((((2-((()2

N = 38

(X = 684

((X)2 = 467,856

((2 = 12,528

Standard Deviation = ±2.416

A standard deviation of ±2.416 for the ungrouped date suggests that the rejection of the circuit boards within each week fluctuates above and below its mean of rejection by approximately ±2.416 points.

With a mean rejection rate of 18 pieces per week rejection the probability of a 15 piece rejection rate is highly probable with a standard deviation of ±2.416 (15 + 2.415 = 17.415). Caution must be exercised at this point, as "predictive" statistical measures must……
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