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ou’ll be using the same 4 numbers written in the same order. The only thing that will change in each expression will be the tools you’ll use from your toolbox. The tools that you’ve learned so far for order of operations are parentheses, exponents, multiplying, dividing, adding, and subtracting.
Here are the four numbers. Keep them in this order:
18 2 4 3
Here are the tools in your toolbox:
The 2 and 3 represent exponents, so you are allowed to square or cube a number.
Listed below are the values you need to create.
21 =
67 =
-6 =
103 =

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ies examined in class. This paper is not a literature review, though a literature review is part of your work. As this course takes place in a compressed timeline, I provided some suggestions for research topics. Feel free to use one of these as a springboard or propose your own.
At the end of the second week of class, students submit a three-page research paper prospectus. A research prospectus is a preliminary plan for conducting a study. This is not a detailed and technical research proposal, but rather, an analysis of the issues likely confronted in such a study. In essence, it is a preliminary proposal of work.
Research Paper Prospectus Elements
To complete the Research Paper Prospectus, consider the following elements. While the prospectus is limited to three pages of body content, remember, students must cover each of these areas as relevant to the plan for research:
Research Problem. What is the research problem? A problem is a situation when left untreated, produces a negative consequence for a group, an institution, or a(n) individual(s). What makes it a problem? For whom? Who says so?
Assumptions. On what assumptions is the work based? Which assumptions are verifiable in literature? Which assumptions are speculative?
Theoretical Issues. What theoretical issues arise from the study? For example, "theoretically," how is the problem and suspected results explained to other scholars? Is there a behavior view? A social systems view? Are there other theoretical orientations to consider in the study's design?
Literature Review. What, in general, does the literature say about the topic? While more development is expected for the final paper, a review of major theories, research, and writers in the field is needed.
Research Questions. Based on the problem, what are the research questions to be answered? How and why will answering the questions contribute to solving the research problem? Remember....a research question can only be answered with empirical data or information.
General Research Plan. In general, what research is necessary to answer the research question. What kind of data is needed? Specify the type, such as surveys, observations, or interviews. Who is to be studied and why? How is the data reduced and made sense of? How is the quality of the data assured?
Anticipated Difficulties and Pitfalls. What kind of difficulties and pitfalls are expected in a study of this nature? What can be done to prevent them or minimize their effects?
Anticipated Benefits. Who will benefit from the fact this research is undertaken? How? Why? Who might be disturbed by this proposed study? How? Why?
Paper Format Requirements
The Research Paper Prospectus is presented in standard APA 7 format, with a cover page, running head, body, and references list. The cover page and references do not count toward the three-page requirement. The body uses headers and in-text citations in the manner prescribed by APA. Students should include any references they know at the time they submit the prospectus, though it is expected the references may change or increase in number. Full and complete adherence to APA is required.
APA Basics
As APA format is the rule, remember the formatting rules shown on the Sample Paper (Links to an external site.):
Times New Roman, 12pt
1" margins on all sides
Double spaced, with extra line spaces removed (see below)
Page numbers in the upper right
Two spaces after concluding punctuation
150-250 word abstract with keywords
APA-style in-text citations and quote format. Use the Purdue OWL in-text citation information (Links to an external site.)to help you.
Alphabetical (by author) reference page with correct reference format. DO NOT trust the reference generator in your word processing program. It is WRONG! Use the Purdue OWL references information (Links to an external site.)to correctly structure references and do so manually.

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eople experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 14 people, based on means and standard deviations given in the article. Assume the population is approximately normal. Perform a hypothesis test to determine whether the mean weight loss is greater than 20 pounds. Use the =α0.10 level of significance and the critical value method.
22.5 28.5 7.6 24.1 21.5 12.9 17.3
21.2 37.6 33.8 12.1 36.3 24.1 19.4

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de by credit card; you think this is true at your store as well. On a typical day you make 20 sales.
Show that this situation can be modeled by a binomial distribution. For credit, you must discuss each of the criteria required for a binomial experiment.
Define the random variable x in this scenario, using the context of the problem.
List all possible values of x for this situation.
On one trial for this scenario, what does “success” mean? Explain using the words of the problem.
What is the probability of success in this scenario?
What is the probability of failure in this scenario?
Probability Distribution Instructions¬¬¬¬
In Excel, create a probability distribution for this scenario.
Label Column A as “x” and Column B as “P(x).”
In Column A, list the numbers 0 to 15.
In Column B, use BINOM.DIST.RANGE to calculate the probability for each x value.
Highlight the probability cells, then right click and select Format Cells. Format the probability cells as “Number” and have Excel show 4 decimal places.
Create a probability histogram using the probabilities you calculated. Format and label it properly. Be sure to use the “Select Data” button to change the x-axis so it correctly lists the x-values.

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uminum and steel. The company has available 38 comma 160 units of steel and 48 comma 380 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 8, 12 and 16 units of steel and 15, 10, and 20 units of aluminum. The company makes $4 per 1-speed bike, $6 per 3-speed, and $16 per 10-speed. Use the simplex method to complete parts (a) and (b).
(a) How many of each type of bicycle should be made in order to maximize profit? What is the maximum profit?
Set up the linear programming problem. Let x 1, x 2, and x 3 represent the numbers of 1-, 3-, and 10-speed bicycles, respectively, and let z be the total profit.
▼
Minimize
Maximize
zequals
nothing
subject to
8 x 1 plus 12 x 2 plus 16 x 3
▼
greater than
less than or equals
greater than or equals
less than
nothing
15 x 1 plus 10 x 2 plus 20 x 3
▼
greater than
less than or equals
less than
greater than or equals
nothing
x 1greater than or equals0, x 2greater than or equals0, x 3greater than or equals0.
(Do not factor. Do not include the $ symbol in your answers.)
Set up the initial simplex tableau and use the Simplex Method to solve.
The maximum profit is $
nothing. To get that profit, the company should make
nothing 1-speed bicycle(s),
nothing 3-speed bicycle(s), and
nothing 10-speed bicycle(s).
(Type whole numbers.)
(b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A.
When the profit is maximized, all of the steel is used but
nothing units of aluminum remain unused.
(Type a whole number.)
B.
When the profit is maximized, some of each material remains unused. Specifically,
nothing units of aluminum and
nothing units of steel remain unused.
(Type whole numbers.)
C.
When the profit is maximized, all of the available aluminum and steel is used.
D.
When the profit is maximized, all of the aluminum is used but
nothing units of steel remain unused.
(Type a whole number.)

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lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 .
(a) On what open intervals contained in 0
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ng systems of linear equations.
The assigned question is,
The number of wet days in a year for one town is 47 days greater than the number for a second town. The sum of the numbers of wet days for one year in these two cities is 285. How many wet days occur in each town?

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900
2. 4,180
3. 32,879
4.78,600
5.251,031
6. 699,900

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics