# "Mathematics / Statistics" Essays

#### 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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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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#### Dominant Hemispheres Term Paper …

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2 pages (668 words)

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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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#### Physics Made Easy Term Paper …

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3 pages (814 words)

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¶ … 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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#### Cartesian Graph Is Approximately Essay …

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3 pages (846 words)

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If x is the number of plates of food eaten, and y is the price, the table of coordinates might be as follows:

Plates (x)

Price (y)

1

5

2

5

3

5

4

5

5

5

The equation for that would be represented by y=5 and the graph of the equation would be the same as in the sample graph for y=5 provided above.

Interestingly, in real life, what one would say about the line would probably only be true for a fixed set of x values. For example, it is impossible to eat a negative number of plates of food. Likewise, even all-you can eat buffets generally limit their diners to one meal-period, so that there is a finite number of plates the diner could consume. However, those conditions would actually change the form of the equation, transform it from a simple linear equation, and would not be represented by the conditions described.

What are the differences among expressions, equations, and functions? Provide examples of each.

An expression is "a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply and divide") (Highline Advanced Math Program, 2008, Algebraic expression).

Examples of expressions are:

y -- x

5y

An equation is "a math sentence that says that 2 things are equal. An equation always has an equal (=) sign. The thing or things that are on the left side of the equal sign are equal to the things on the right side of the equal sign" (Highline Advanced Math Program, 2008, Equation).

Examples of equations are:

x + 2 = y y -- x = 5

5y = 25

A function "relates each element of a set with exactly one element of another set (possibly the same set)" (Math is Fun, 2012). Functions are generally expressed as f (x).

Examples of functions are:

f (x) = x + 2

f (y)= 5y

References

Harmsworth, A.P. (2012). Plotting x-y graphs. Retrieved October 16, 2012 from GCSE.com website: http://www.gcse.com/maths/graphs3.htm

Highline Advanced Math Program. (2008). Algebraic expression. Retrieved October 16, 2012

from: http://home.avvanta.com/~math/def2.cgi?t=expression

Highline Advanced Math Program. (2008). Equation. Retrieved October 16, 2012

from: http://home.avvanta.com/~math/def2.cgi?t=equation

Math is Fun. (2012). What is a function? Retrieved October 16, 2012 from http://www.mathsisfun.com/sets/function.html

Rehill, G.S. (2012). Horizontal and vertical lines. Retrieved October 16, 2012……
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#### Long-Term Memory Demonstration Analysis Term Paper …

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2 pages (675 words)

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For me, I remembered the words relatively easily; yet, I began to have issues discerning whether or not the math problem was correct or not. My STM simply could not handle both stimuli, and so relied on the one I was more familiar with, which was the verbal visualization and practice.

The third demonstration tested the STM and our own ability to organize and categorize the stimuli we are being exposed to. The ability to rehearse categories can help take information out of the STM and into the long-term memory (LTM) because of shared common traits that help us compartmentalize and place information into various categories we are already familiar with in our LTM. Yet, our short-term store (STS) is often not capable enough of practicing the type of organization involved with LTM practices, and so when exposed to demonstrations such as Organization: Categories, it can be difficult to recall the information, even though we would have been able to conceive those categories from our LTM. Thus, it seems from this demonstration that organization tends to occur more in the LTM compared to the STM.

Finally, there was the Verbal Rehearsal demonstration. This was a test where the test taker had to say out loud a series of words. Some repeated several times, while other were seen only once. This tested the STS, but also what elements could possibly leak into the long-term store (LTS). It seemed that the words that were repeated the most were the easiest to recall. Thus, the more practice one have with these words, the more able they were to be recalled to the memory when-based to write the list. However, the words that were not repeated, or never repeated were almost lost in this exercise. This essentially does show that repetition and practice helps make the STM stronger for certain concepts.

References

MacKay, David J. (2011). The Cognitive Neuroscience of Memory. Inference Group. Web. Retrieved October 22, 2012 from http://www.inference.phy.cam.ac.uk/jmb86/memory.pdf…
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#### Design of an Automotive Control System to Follow a Drive Cycle A2 Coursework …

A2 Coursework |
14 pages (3,980 words)

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¶ … Automotive Control System to Follow a Drive Cycle.

Automotive control is a driving force within the automotive innovation. To lower fuel consumption, improved safety and lower exhaustive consumption as well as enhancing convenience and comfort function, there is a need to apply automotive control. Automotive control system is fundamental principles used for successful design of automobile automatic control…
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#### Simultaneously Term Paper …

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4 pages (1,229 words)

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This theory is committed to research and discovery through direct contact with the social world (Shah & Corley, 2006). It rejects priori theorizing. The fact that it rejects priori theorizing does not therefore mean that researches should enter the field lacking an understanding of the literature or the theoretical question to be addressed. Researchers have to generate theories out of their data collection experiences. Theory building involves identifying theoretical question of interest, choosing an appropriate research context, sampling within the context so that data collection facilitates the emerging theory (Shah & Corley, 2006). Choice of procedures for gathering and documenting data is the preserve of the researcher. Questions asked should explore new areas, uncover processes, lay bare poorly understood phenomena, understand ill structured linkages, and examine variables that cannot be studied by experimentation (Shah & Corley, 2006).

Theoretical sampling should endeavor to direct data gathering efforts towards collecting information that best supports the development of a theoretical framework. Samples chosen should support emergent theory or even refine and extend the emergent theory (Shah & Corley, 2006). Refining and extending emergent theory calls for settling on a data collection context that shows that the theory applies across a variety of contexts. For researchers to assign and create meaning from observations recorded in data constant comparison method has to be put in place. This helps in comparing incidents applicable to each category, integrating categories and their properties, focusing the theory, and writing the theory (Shah & Corley, 2006). These processes are integral in explaining patterns in the data. Constant comparisons made throughout the process of data collection influences data collection efforts and theory development.

Goel, Johnson, Junglas, & Ives (2011) propose and test a model to predict users' intention to return to virtual world to remedy organizations failure to lure customers and employees into their education, entertainment, and commerce initiatives. Goel et al. (2011) rely on the interactionist theory of place attachment to explain the links among the organizations construct model. Their hypothesis is grounded on the fact that the more meaningful the interactions that occur, the more meaningful a place will become. This is the basis of their focus on users' intention to return to the virtual world. Their method was tested through quasi-experiment conducted within Second Life. Experiments were done in the physical lab. Activities related to testing their research model were done in a simulated or virtual lab in Second Life. Social awareness was measured using instruments focused on perceived message understanding. Items were selected based on their definition of the social awareness concept. Measures of intention to return to Virtual World consisted of items that related to what users were able to do in the Virtual World and their intention to return to it for such purposes by choice. Evidence from the research shows that the data used in this research were drawn from experimental work that was conducted in the physical laboratory. It is worth noting that Goel et al. relied on the interactionist theory of place…
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#### Normal Distribution Term Paper …

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2 pages (804 words)

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We assume that Approach B (?1) will be more efficient than Approach A (?2). Thus, Ha: 1 - ?2 > 0. Approach B. is more efficient than Approach A. And Ho: 1 - ?2 < or = 0. There is no difference between Approach A and Approach B.

Research Question - t test for dependent samples

We use a matched sample design (dependent samples) for this question. We select a simple random sample of workers. Each worker first uses one Approach A and then the other Approach B. The order of the two approaches is randomly assigned to the workers, such that some workers perform Approach A first and some workers perform Approach B. first. In this manner, each worker provides a pair of data values, one for each approach. We will use a procedure based on the t distribution with n1 + n2 -- 3 degree of freedom. We assume that both populations have normal probability distribution and that the variances of the populations are equal. In the matched sample design, the variation between the workers is eliminated as a source of sampling error. Is there a mean difference between the work completion rates of the two approaches is the means of the difference between the values for the population of workers. Thus, the null hypothesis is that there is no difference between the means of the difference for the values of the two groups. However, we reject the null hypothesis since the completion times do differ between the two approaches.

Standard score -- "Also known as a z-score. A standard score gives us the position of a data value comparison to the mean. We also knew, by looking at the z score, whether this was a great score or not. Remember that a z score tells you, in standard deviation units, how far away the score is from the mean. Positive scores are above the mean while negative scores are below the mean. A z-score of 2.12 on a national exam is great. We have scored 2.12 standard deviations ABOVE the mean!! How rare is that? If we looked at our graph of a normal distribution below, we can see that going out just two standard deviations from the mean on each side covers at least 95% of the distribution. Our score puts us past that, into the less than 5% area in the tails of the distribution……
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#### Slow the Illusion of Validity Term Paper …

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2 pages (867 words)

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Nurses and firefighters are an example of experts whose intuition can be trustworthy -- political pundits and stockbrokers only display confidence, and thus the illusion of skill.

Chapter 23: The Outside View

There are two different approaches to forecasting, the "inside view" and the "outside view." Individual members of a committee may think the committee's task can be accomplished in 1 or 2 years, but an external study of such committees can note that it usually takes 8 to 10 years, even though the individual members are still predicting 1 or 2 years. In many cases, we can have an accurate view of "baseline" predictions for something (i.e., the most likely result statistically), but fail to apply that information to making our own prediction because we are "inside" the situation. The "planning fallacy" describes when someone making plans estimates or predicts too optimistically. This can be avoided with "reference class forecasting" where the prediction is measured in advance against a comparable baseline. This optimism bias of the "inside view" explains why people do things when the odds are against them -- ranging from starting wars, to filing a lawsuit, to starting a small business. But taking the outside view goes against our instincts.

Chapter 24: The Engine of Capitalism

This chapter continues the examination of the "optimism bias" discussed in the previous chapter. Optimism is frequently the reason why people or institutions take on significant risks. A small business in the U.S.A. has a 35% chance of lasting 5 years, yet entrepreneurs will repeatedly attempt to start small businesses because of the optimism bias. So in some sense optimism is the engine of capitalism, since it permits entrepreneurs to start businesses despite the fact that 2 out of 3 businesses will fail within 5 years. The optimism bias gives people the illusion of control -- especially regarding outside factors (such as competition or general economic conditions). Competitor neglect is the bias where people making decisions do not evaluate the possible actions of the competition, because they are focused on their own action and their own coherent narrative. The WYSIATI principle discussed earlier causes people to be overconfident: they do not have an accurate measure of uncertainty. As a way of overcoming the optimism bias, Kahneman suggests a policy called the "premortem" -- before an organization takes a major decision, ask all individuals to imagine that, 1 year from now, the decision was taken and was a horrible failure. Then ask them to imagine the reasons they'd give for explaining the failure in 1 year. This allows individuals to use……
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#### Inductive Manner or a Deductive Research Paper …

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2 pages (728 words)

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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 …

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2 pages (586 words)

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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 Evaluate Research Paper …

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2 pages (668 words)

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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 Find the Radian Research Paper …

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1 pages (342 words)

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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 Solve the System Research Paper …

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2 pages (859 words)

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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 …

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2 pages (446 words)

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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 …

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1 pages (361 words)

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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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#### Algebra, Trig Perform the Indicated Research Paper …

Research Paper |
1 pages (322 words)

Bibliography Sources:
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)

Bibliography Sources:
2

SAMPLE TEXT:

(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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#### 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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#### Evaluator, Researcher or Observer Watches Essay …

Essay |
8 pages (2,052 words)

Bibliography Sources:
1

SAMPLE TEXT:

-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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#### National and State Subject Matter Essay …

Essay |
2 pages (720 words)

Style: MLA | Bibliography Sources:
2

SAMPLE TEXT:

One such California-specific standard is: "verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems" (Common Core Standards, California Department of Education: 74).

Regarding Algebra I, the standards for the subject in California are defined as pertaining to three critical areas: "deepen and extend understanding of linear and exponential relationships; contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; extend the laws of exponents to square and cube roots; and apply linear models to data that exhibit a linear trend" (Common Core Standards, California Department of Education:60). In contrast, the federal Common Core standards begin with a more theoretical discussion of algebraic equations, what they contain, and algebraic distinction between equations and inequalities.

The standards of both California and the federal Common Core contain a great deal of overlap, similar to their congruence with geometry standards. For example, both require that students: "explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method" (Common Core Standards, Official Website CCSS.Math.Content.HSA-REI.A.1; California Department of Education 65). As with the geometry section, California includes several state-specific guidelines regarding the capabilities of students such as the ability to "solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context," which more specifically guides the type of approaches teachers must present in the classroom, usually with a greater emphasis on contextual applications of abstract theories (Common Core Standards, California Department of Education 65).

Works Cited

Common Core Standards. California Department of Education. ca.gov. [21 Oct 2013] http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf

Common Core Standards. Official Website. [21 Oct 2013]

http://www.corestandards.org/Math/Content/HSG/introduction…
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#### Frequency Distribution of Rejected Circuit Term Paper …

Term Paper |
1 pages (346 words)

Bibliography Sources:
0

SAMPLE TEXT:

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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#### Predictors of the Transition Data Analysis Chapter …

Data Analysis Chapter |
3 pages (971 words)

Bibliography Sources:
3

SAMPLE TEXT:

That allowed three categories to be analyzed, but I determined that there were also three other reasons why multinomial logistic regression was used. These other reasons were incorporating such a complex sampling design, examining multicollinearity between all the covariates, and managing any missing data with multiple imputation. By taking all those steps, better conclusions could be drawn by the authors.

Level of Significance

The concept of "level of significance" is important because it provides a likelihood that the sample chosen for the study will not be an accurate representation of the current population (Denzin & Lincoln, 2011). If a level of significance is very low for a study, that would indicate that the authors are highly confident that the results can be replicated (Gorard, 2013). For example, if the level of significance is 0.05, there is a 95% chance that the study can be replicated, and if the level of significance is 0.01, there is a 99% chance that the study can be replicated (Franklin, 2012). Testing this level begins with the null hypothesis, as that is where many quantitative studies begin (Franklin, 2012). The 0.01 and 0.05 significance levels are the two most commonly seen levels in the majority of educational research (Denzin & Lincoln, 2011).

Significance Level for the Current Study

I believe the level of significance reported in this study falls within the 0.01 range. I think that because it provides a large sample of people and a clear, direct way to conduct the study, which allows the study to be easily replicated by others. The authors of the study indicated that another group of data from the same age group would produce essentially the same results, because of the way the study was conducted and the analysis of the information itself (Park, Weaver, & Romer, 2009). Because the study is clear and follows quantitative methods, and because it creates a strong null hypothesis to test, I believe it is easily able to be replicated by many other researchers in the future.

I feel that the examination of longitudinal data is an important strength of the study, as are the maximization of the information available and how easy it is to generalize the results to adolescents throughout the United States. However, I also think that other factors that were not included in the model could affect smoking behavior. With that in mind, it is important to remember that the significance level for the study is a measure of what the authors of that study believe to be accurate, and that it can vary.

References

Denzin, N.K., & Lincoln, Y.S. (2011). The SAGE Handbook of qualitative research ( 4th ed.). CA: Sage Publications.

Franklin, M.I. (2012). Understanding research: Coping with the quantitative-qualitative divide. London/New York: Routledge

Gorard, S. (2013)……
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#### Hypnosis in Investigation Essay …

Essay |
2 pages (859 words)

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2

SAMPLE TEXT:

The hypnotist should present situations as true as possible and maintain the accuracy of information derived from the subject.

The other problem with hypnosis is that the subject often tend to exhibit increases in suggestibility to leading questions and misleading post-event information. For instance, there is likelihood of the subject incorporating into their accounts details suggested to them by the hypnotist. Unfortunately, even with much skill and attention, the hypnotist cannot avoid making suggestions to the subject. Such suggestions are not necessary verbal, but can be communicated through attitude, character, and expectations of the hypnotist. Other forms of communication may include tonal variation in voice, and body language (Lynn and Sherman, 2000). However, the hypnotists should try as much as possible to avoid giving deliberate suggestions to subject, this way the subject will give independent account of events thereby improving the accuracy of information. This is very important because the hypnotist has power over the hypnotized individual and can easily manipulate the subject, the intentions must always be right.

One other problem associated with hypnosis is that the confidence of the subject usually increases regardless of accuracy (Anderton, 1986). For instance, the subject could be very confident that the information he/she is giving is accurate even when it is incorrect. This confidence will lead to continuous giving of false information without realization. This confidence if usually created by the fact that the subject is controlled by the hypnotist and whenever the hypnotist agrees with the information given then the subject will feel the information is correct even when it is not. This confidence can however be used positively by ensuring that the subject is led into giving correct information.

Taking into consideration the problems associated with hypnosis, it should not be used at all since such information cannot be reliable. The law should therefore require the exclusion of testimony obtained from previously hypnotized witnesses, this is because the witness, as a matter of fact, has been rendered incompetent to testify. Hypnosis should be restricted to clinical use where there is a desired change in a patient which is more positive.

REFERENCES

American Psychological Association, Division of Psychological Hypnosis. (1994). Definition and description of hypnosis. Contemporary Hypnosis, 11, 143.

Anderton, C.H. (1986). The forensic use of hypnosis. In F.A. De Piano & H.C. Salzberg (Eds.),

Clinical applications of hypnosis (pp. 197-223). Norwood, NJ: Ablex.

Lynn, S.J. & Sherman, S.J. (2000). The clinical importance of sociocognitive models of hypnosis: Response set theory and Milton Erickson's strategic interventions. American Journal of……
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#### Exercise Choosing the Selection Method Essay …

Essay |
2 pages (561 words)

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0

SAMPLE TEXT:

Application of assessment

Maria

Lori

Steve

Jenna

Education

6

3

3

10

Work Experience

10

3

10

Reject

Math skills

10

Reject

3

6

Verification knowledge

Reject

10

3

6

Interpersonal skills

10

6

6

6

Work motivation

6

6

3

10

a. The applicant who scored the best are Maria and Jenna

b. The fact that one candidate would score poorly in one area, indeed at times a reject and score very well in another area presented a challenge of whether to discard or still consider for next level of interview.

c. Yes, I would change the threshold used in assessing the areas, especially work experience, maths and verification knowledge.

Maria

Lori

Steve

Jenna

Education

60

30

30

Work Experience

30

Reject

Math skills

Reject

30

60

Verification knowledge

Reject

30

60

Interpersonal skills

60

60

60

Work motivation

60

60

30

Total

a. Maria scored the highest

b. Yes she is the best since she scores well in the very important fields like work experience and interpersonal skills which are important for a bank teller.

c. Lori and Steve scored the lowest.

Analysis of the answers

1. The most important here is the work experience since as a teller, the turnover of clients and accuracy is of essence and an experienced person here can do better than a new person.

2. Recorded

3. The least important a scores in Math and work motivation

4. Done

Maria

Lori

Steve

Jenna

Education

60

30

30

Work Experience

60

Reject

Math skills

50

Reject

15

30

Verification knowledge

Reject

30

60

Interpersonal skills

60

60

60

Work motivation

30

30

15……
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#### Math Inequalities Ozark Furniture Essay …

Essay |
2 pages (628 words)

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0

SAMPLE TEXT:

However, the company does not have to produce to its maximum. If the company received an order for 125 modern rockers and 50 classic rockers, the point (125,30) would lie inside of the shaded area. The resulting equation would be 15(30) + 12(125) = 1950, which is less than or equal to the 3,000 board feet. However, it is critical to realize that the line serves to maximize the number of rockers that can be created in conjunction with another type of rocker. The point (125,200) falls outside of the shaded area created by the inequality. 15(200) + 12(125) = 4500. As 4,500 is not less than or equal to 3,000, it is clear that Ozark cannot manufacture this particular combination of rockers with its existing lumber supply.

When the chain furniture store faxes an order for 175 modern rocking chairs and 125 classic rocking chairs to Ozark, a quick glance at the graph demonstrates that Ozark cannot fulfill the order. The point (175,125) does not fall on the line or inside the shaded area created by the equation, but, instead, falls to the right of the line, indicating that the limits set by the amount of available board would be exceeded by the order. To verify this, one can test the equation for the total number of board feet used and see if the total number of board feet used would exceed the 3,000 board feet limit. Taking away the limitation, that equation becomes: 15C + 12M= total number of board feet. Substituting in numbers yields the equation: 15(125) + 12(175) = 3,975 board feet. Obviously, 3,975 board feet is not less than or equal to 3,000 board feet. The company would need 3,975 feet to fulfill that order. They presently have 3,000 feet. To find out how many additional……
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#### Pythagorean Theorem Ahmed Has Half Research Paper …

Research Paper |
1 pages (379 words)

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0

SAMPLE TEXT:

The coefficient is negative, there will be positive and negative factors. Two factors of -20 should add up to -8. 10 and 2 are factors of 20 that would also add up to 8 if the greater factor is negative and lower factor, positive. The result are two binomials to be solved using zero factor.

(x -- 10) (x + 2) = 0

After solving the binomials, the result is a compound equation expressed as follows (also the possible solutions for the problem):

x = 10 or x = -2

Considering the values of x solved through Pythagoras theorem, x=10 is more plausible given the buried treasure problem (negative distance is not applicable in the problem presented).

Computing for the binomials at x=10:

The treasure lies 10 paces……
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#### Tag Members of a Population Term Paper …

Term Paper |
2 pages (733 words)

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SAMPLE TEXT:

The assignment is to solve for y and identity the type of equation that results when solving for y. The number sentence given is: y-1/x+3 = -3/4. Using cross multiplication gets rid of the denominators and yields the following equation: 4(y-1) = -3(x+3). The goal is then to isolate y on the left side of the equation, which gives one an equation solving for y. Without additional information, the equation cannot be solved for either the numerical value of x or y because doing so requires multiple equations or providing what x or y is. This information suggests immediately that the equation represents not a single set of coordinates, but a line. As a result, one is already thinking that the end-result of the process will be an equation for a line. The slope, intercept form of an equation for a line is popularly represented as y=mx + b where m represents the slope of the line and b represents the y intercept of the line. (The y intercept is the point on the line where it intercepts the y axis; in other words, the y intercept is the point on the line where x=0). Knowing this basic form of an equation helps guide the shaping of the equation as one solves for y.

The first step is to multiply each side of the equation. 4(y-1) becomes 4y-4. -3(x+3) becomes -3x -9. The equation them comes 4y-4 = -3x -9. The next thing to do is to add 4 to both sides as the next step in isolating y. The resulting equation is 4y= -3x -9 + 4 or 4y=-3x-5. One then divides both sides by 4 to continue isolating y. The resulting equation is y=(-3x-5)/4. The four is distributed throughout the equation, yielding the following equation y=-3/4x -5/4. That equation is an equation for a line with the slope -3/4 and a y intercept of -5/4. The y intercept provides the solver with a set of numbers that can be applied to the equation (0,-5/4). Plugging these numbers back into the equation allows one to eliminate the possibility of an extraneous response. y-1/x+3 = -3/4. Does (-5/4- 1) / 3 = -3/4? -5/4-4/4=……
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#### Bottling Company the Mean Case Study …

Case Study |
2 pages (541 words)

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I'm not entirely sure what the third possibility would be. Either the measurement is off or the amount of liquid is off -- I'm curious what the third option might be here. It seems that there could not be too many other options available.

To avoid the problem in the future requires dealing with whichever is the major problem here. It is reasonable to assume that with two possible problems, the solution lies with identifying which of the possible problems is the issue and just dealing with that. So the problem can be addressed as follows. If the issue is that the measures are off, then the measuring devices need to be recalibrated. If the issue is that the filling device is off, then the filling device needs to be recalibrated. Clearly, some third party equipment that has been independently calibrated will be needed, in order to define the parameters by which we are measuring. But at the end of the day, the critical factor is that once all of the devices have been recalibrated, the problem should be solved and no more will there be issues with underfilling of bottles.

The important thing here is that we are quite confident that the bottles are not filling as much as they need to be. To get onside with the government, we need to work with a 95% confidence interval and the results on these bottle fills are nowhere near that. It is evident that the bottle fills are well below expectations. As a……
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#### Dispel Article Review …

Article Review |
2 pages (919 words)

Bibliography Sources:
1

SAMPLE TEXT:

1045). If these considerations are not met then the proposed question may not be appropriate for research study.

Other considerations include statistical consideration such as the statistical power needed to find a significant result, the costs associated with the proposed project, and alternative ways to answer the question. Research questions are often quantitative in nature and many questions did not lend themselves to quantitative measurements (Beya & Nicoll, 1998, p. 1045-1046).

Discussion/Conclusions

There is no formal discussion section, but affect the entire paper is a discussion of the practicality of research in specific instances and when students should consider using research and type of questions/qualifications the need to be met in order to use research to answer particular questions. Beya and Nicoll (1998) state that for some issues, such as the notion that hospital -- laundered surgical attire is the most appropriate higher for reducing infection in the hospital, are not answer my research but instead by sound scientific principles. There are no research studies that the authors know of to support this notion; however, it is a universal practice in hospitals. There are many important questions that can be answered by research and many that cannot.

Personal Reaction

I found the paper interesting and generally agree with the assumptions and conclusions of the authors. However, the authors lose a lot of credibility in the very beginning of the paper when they discuss the notion of proof. There correct in assuming that a single research study really proves anything; however, there notion that research studies seek to "disprove" the null hypothesis is blatantly wrong (Beya & Nicoll, 1998, p 1044). In fact, formal statistical reasoning attempts to reject the null hypothesis in favor of the alternative hypothesis. Neither can be proven or disproven and in quantitative research studies the null hypothesis, which states that the measurement of two or more variables is equal (no difference), is rarely true to begin with if the variables are measured on a continuous interval or ratio level scale. It is the degree to which the difference is significant that the researcher attempts to ascertain.

Nonetheless, the authors provide a sufficient checklist of questions/qualifications that novice researchers can use to decide whether a particular question of interest or idea is one that is amenable to a formal empirical research study. Moreover, the authors' discussion of how to ascertain practicality and feasibility for particular research study is particularly important to enthusiastic, novice, researchers who think that any question should be empirically validated.

References

Beyea, S.C., & Nicoll, L.H. (1998). Dispelling the myth that……
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#### Theory-Building, Applied Research Journal …

Journal |
2 pages (577 words)

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1

SAMPLE TEXT:

The researcher assumes the alternative hypothesis is true. Rejecting the null hypothesis suggests that the alternative hypothesis may be true.

Qualitative research begins with the specific and moves toward the general. The data collecting process in qualitative research is field-based and personal. Patterns emerge from the data during the process of analysis. Throughout the data collecting process, researchers typically record their thoughts and impressions about the emerging data patterns. Qualitative researchers gather data about their research from many different sources, using a process called triangulation to ensure that data can be verified. When enough data has been collected, the researcher will interpret the data.

A research study includes an abstract, a very brief introduction, and a literature research of relevant theoretical articles that serves as the larger introduction to the research. The methodology section includes the statement of purpose, researchable questions, the research design, the instrumentation, the participants, the data collection methods and the procedures for analysis. The discussion section includes the results of the data collection and the discussion. This section also usually includes the benefits and limitations of the study, as well as recommendations for future study.

The research study reports or summaries are written as how-to reports, experimental reports, or empirical research or experimental replication. The philosophical grounding of the research includes scientific realism, social constructivism, advocacy-liberatory, and pragmatism. Research procedures require and institutional review board, and article summary sheets, usually produced in pdf format. The summary reports of the research may be emailed to and from a lit of subscribers via listserv.

References

Lodico, M., Spaulding, D., & Voegtle, K. (2010). Methods in educational research: From theory to practice (2nd ed.) San Francisco, CA: John Wiley &……
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#### Theory of Numbers and Operations A2 Outline Answer …

A2 Outline Answer |
3 pages (1,036 words)

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Theory/Knowledge of Numbers/Operations

The student in Question A1 will earn an A if the teacher rounds the student's percentage to a whole number. 299 divided by 334 equals .89520958, which would come to 89.5%. Rounding up 89.5 to a whole number makes this 90%, which is the requirement for an A grade.

The student in Question A2 will presumably not receive an A if 89.5 is truncated down to 89%.

Truncating an income tax rate of 27.8% would mean disregarding what follows the decimal point. A taxpayer would prefer a rate of 27% to a rate of 27.8% because this means the taxpayer gets to retain almost 1% (in reality 4/5 of a percentage point) of income that would otherwise be paid to the government in taxes.

The government requires the taxpayer to round up a 27.8% tax rate rather than truncate it for precisely this reason. This would be rounded up to 28% and would also save trouble if, for example, the taxpayer's income already was reckoned down to the last cent -- this could leave a tax bill that is reckoned in tenths or hundredths of a single cent, which is an amount that cannot be paid in real currency. A hypothetical taxpayer with a 27.8% tax rate who earned one dollar last year could not be expected to pay the government .278 cents, because there is no coinage to designate four-fifths of one penny.

C1. Let us suppose we are calculating a 27.8% income tax for a hypothetical income of 50,000 dollars. This is simple for mental math. The 27.8% tax for 100,000 can be calculated mentally -- it is 27,800 dollars, a little more than a quarter. Now we only need to divide this number mentally by 2, in order to get the calculation for 50,000 (which is one-half of 100,000), and it comes out to $13,900 as the 27.8% tax on a $50,000 income.

C2. Imagine that we had to divide 102.5 apple pies among four people. The easiest way to do this is by truncating: we truncate the number to 100 apples, and calculate that each of four people would take 25, then we concentrate actual division on the remaining 2.5 apples. Truncating could also be used to calculate a 15% tip for a bad waitress -- if the bill comes out to 102.5 dollars, we can truncate this to 100 and leave slightly less than 15% in recognition of lousy service. Rounding up can be convenient in estimating sales tax: if we know that a new laptop costs 899 dollars, and that Pennsylvania has a 6% sales tax, then we know to bring around 910 dollars to the computer store to cover the sales tax of the purchase. Rounding up can also be useful in making sure you have enough food for guests. If we are planning to have 17 persons at the Superbowl party and we estimate that each person can probably eat about 5.5 buffalo wings, then it makes sense to…
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#### Solutions to a Math Problem Reaction Paper …

Reaction Paper |
4 pages (1,249 words)

Bibliography Sources:
1

SAMPLE TEXT:

Problem Solving Report

The task that was proposed to the students was as follows: Conrad's Taxi Service charges $1.50 for the first mile and $.90 for each additional mile. How far could Mr. Kulp go for $20 if he gives the driver a $2 tip? (taken from Holtz and Malen). The students were 7th grade students, and a group of 5 students was formed. According to the instructions, the students worked separately to solve the problem, then jointly. It is interesting to note (and this will be further expanded when describing the choice and interaction between the students) that some of the students were able to solve the problem individually on their own and that, for them, the interaction phase implied convincing the other students of the viability of their solutions.

The standard used here was CCSS.MATH.CONTENT.7.EE.B.4, which states the "use of variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities" (Common Core). Particularly CCSS.MATH.CONTENT.7.EE.B.4.A was useful in this case, namely the solving word problems by conceiving equations of the form px + q = r and p (x + q) = r, where p, q, and r are specific rational numbers.

The group was formed relying on the principle of differentiation. To the degree to which this was possible, the aim was for a mixed group boys/girls. At the same time, there was a preference for an uniform representation knowledge-wise: the student were selected to have average math scores and no obvious aptitude or extraordinary performance in this field. In order to further study the interaction of particular individuals with the rest of the group, an ESL student was included in the group.

In terms of the learning trait, two of the students included in the group were known for their extracurricular activities in art-related areas, including drama, art and music. The reason they were selected was so as to compare their solution to the problem to the others'. One would want to understand whether particular hobbies or higher creativity provide different approaches and solutions to a math problem.

There were five students, three boys and two girls. They were also taking the same math class and this is how they were selected for the test. They were also among the best math students, so their proficiency was an additional argument in their selection. There was a meeting with their math teacher (and without the students) so as to understand more of their individual characteristics and personalities. With that in mind, this is how I have come to know so much about them.

This was important to understand whether someone who worked out the problem on his own would also be willing to share it with the others in the group or whether he preferred to wait for a group solution to be successfully worked out. It would also be interesting to understand whether some of the group participants would try to impose their…
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#### Gay and Lesbian Themes in Film A2 Coursework …

A2 Coursework |
2 pages (424 words)

Bibliography Sources:
0

SAMPLE TEXT:

Gopinath, Gayatri. "Queering Bollywood."

What does Gopinath mean by "queer diasporic viewing practices?"

What types of problems does a queer diasporic viewing practice present, in terms of biased readings into Indian-produced cinema? In other words, is Gopinath superimposing Western values onto Indian normative sexuality?

What evidence does Gopinath present of gender bending in Indian cinema?

How are gender bending, gender performativity, and homoeroticism portrayed in Indian cinema in general?

What evidence is there that Indian cinema contains deliberately subversive messages about sexuality?

Warner, Michael. "Normal and Normaller."

Does the institution of marriage contradict queer identity as being inherently oppositional to the dominant heteronormative culture?

Warner notes that gay marriage has until recently been less important than issues such as AIDS prevention, anti-gay violence, and "the saturation of everyday life with heterosexual privilege." Do you believe that the fight for marriage equality detracts from these causes?

3. How does marriage equality reconstruct marriage as a social institution, removing its patriarchal associations?

4. Do you agree with Warner that "as long as people marry, the state will regulate the sexual lives of those who do not," such as by de-legimizing consensual sex that does not fall within the established normative framework of marriage?

5. Marriage equality confers status as well as a veneer of……
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#### Stigmatization and Therapy Counseling of Gay Men Research Paper …

Research Paper |
11 pages (4,032 words)

Bibliography Sources:
1+

SAMPLE TEXT:

Unnatural sexual orientation is not an independent, standalone issue for those professing inclination towards same sex individuals for their sexual needs. Such individuals invariably face difficulties, humiliation, and consternation in many other areas of their lives, thereby being isolated, stigmatized, and finding it difficult to lead normative, meaningful life. In recent times, there are concerted efforts to address their concerns… [read more]