i.a square wave with an amplitude of 1 V and fundamental frequency 2 kHz
Multiplying cosines
ii.a single rectangular pulse with height 2 V and width 50 ms
iii.a cosine wave with amplitude 1 V and frequency 3 kHz multiplied by another cosine wave with amplitude 1 V and frequency 20 kHz. There is no problem in evaluating out1. I got the answer. Again with out1, I want to multiply cos(pi*x) and cos(pi*y), because that is the definition of fourier sereis in two dimension.Iam getting an error message saying that Error using * Inner matrix dimensions must agree.
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Introduction: describe system & explain question and why it is interesting
Describe model: what is being included/excluded; how do different pieces fit together; derive model/equations
[somewhere in the Introduction or Description, explain previous relevant models & why yours is different]
Describe data: what are they? from where do they come? how reliable are they?
Analyze model: explain math/computations; give results
Conclusion: what is the answer to the question, from results? discuss answer; How might model be extended/improved?
References: standard bibliographical format; citations in text; not Wikipedia.
Mathematical models are an abstract model that uses mathematical language to describe the behaviour of a system.
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Geometry and The Pythagorean Theorem Geometry is a very broad field of mathematics composed of a wide range of tools that can be used for problem solving.
Geometry and The Pythagorean Theorem
In this module, you are going to research three examples of the implementation of geometry that would employ the use of the Pythagorean Theorem as a problem-solving tool.
The examples you find can come from several different fields of study and applications such as construction, city planning, highway maintenance, art, architecture, and communications, to name a few. The examples you find must clearly demonstrate the use of the Pythagorean Theorem as a tool.
Geometry and The Pythagorean Theorem Application Situations
Your textbook—Chapter 10, “Modeling with Geometry”—would be a good reference to consult for some examples illustrating the use of the Pythagorean Theorem in applied situations.
For each example you share in your post, address the following:
Demonstrate the use of the Pythagorean Theorem in the solution of this problem.
How is the Pythagorean Theorem applied to help solve this problem in this application?
Why would the Pythagorean Theorem be applied instead of employing some other mathematical tool?
What tools, unique to this application, would be necessary to get the measurements needed to apply the Pythagorean Theorem?
Are there other geometrical concepts that are necessary to know in order to solve this problem?
Are there any modern tools that help solve this kind of problem that either provides a work around, or that rely heavily upon, the Pythagorean Theorem?
When constructing your response, consider the theories, examples, and concepts discussed in your readings this module, and refer to them to support your conclusions.
Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.
PowerPoint on Scenarios and Solution for Calculus Create a 10- to 12-slide Microsoft® PowerPoint® presentation that describes the various scenarios and solutions to each of your team’s selected examples
generated in Weeks Two, Four, and Six.
PowerPoint on Scenarios and Solution for Calculus
Include at least one math problem from each of the scenarios you created.
Present your project to the class.
· For Online and Directed Study students, these are Microsoft® PowerPoint® presentations with notes.
Format any citations in your presentation consistent with APA guidelines.
Ok, so this is a group project so you would only be doing between 3-4 slides for me on week 6, and I will be attaching all the required documents and
discussions we did on week 6. The summary I will send you at the end is the summary we sent to the professor once the weekly discussion was over. No one has
added any references, but you can cite our class text book, Thomas’ Calculus 12th edition.
Low Attainers in both English and Mathematics critical analysis of teaching, learning and assessment for low attainers in English and mathematics to be split into two parts – English and maths approx. 1500 words each section
Low Attainers in both English and Mathematics
English- focus is on the specific nature of high-quality attainment in speaking and listening in the primary and early years curriculum? what are the
implications for teaching, learning, and assessment for lower attainers Maths -focus- critically discuss how mathematical models and images can support mathematical understanding of children who are attaining at a lower level.
Consider their effectiveness in the development of mathematical language and vocabulary.
Mathematics Teaching to Children I am from Australia and would like it to be in Australian spelling. write 3 SMART targets relating to how you will develop your numerate identity.
Mathematics Teaching to Children
prepares a brief action plan for the smart target using templates with a table and clear subheadings for each section. write a 250 word to reflect upon your maths
competency in relation to teaching maths to children. make specific links to early years learning framework and Australian curriculum. Find and share 10
different examples of numeracy related learning outcomes from the EYLF and Australian curriculum for a foundation to year 2 ( five from each). include an 800-word discussion detailing what opportunities you could provide to address 8 of the 10 learning outcomes in early childhood or early primary learning environment. for the remaining 2 learning outcomes write a 200-word explanation of how you would use ICT to develop children’s engagement with numeracy and maths. honestly whatever you can do for me would be great as it is due ASAP.
Experiments on Dependent and Independent Variables Order Instructions:
Experiments on Dependent and Independent Variables
Redo the experiments section (Section 8, Section 9, and Section 10). The following four points are guidelines/requirements.
1)The experiments must be critical experiments. (Refer to Lave and March section 3.2.2.)
2)You must have enough critical experiments to distinguish all of your models from each other. Remember, if an experiment predicts the same result for each model, then it is not a good experiment.
3)All of the experiments must be natural experiments (as defined by Lave and March – and in class).
4)Make sure that you specify which model is supported by a particular experimental outcome. And make sure that for each experiment you discuss more than one outcome.
3. You will have to operationalize all of the variables used in the experiments, and you will have to indicate which variables are dependent variables and which variables are independent variables. (This is the only completely new thing you have to be doing for this assignment.)
4. Realize that we are expecting more at this point. Just because you received nine or ten points on your previous assignment does not mean that you will earn as many points for the same work here.
The form of this exercise should look like this:
1)Everything from Exercise Two, not including the section on natural experiments. (This consists of the first seven parts of Assignment Two.)
2)Description of the first critical experiment
a)Describe the experiment.
b)State which is the independent and dependent variables.
c)State how you are going to operationalize the variables.
d)Describe the outcomes and state which model each outcome supports
3)Description of the second critical experiment.
a)Describe the experiment.
b)State which are the independent and dependent variables.
c)State how you are going to operationalize the variables.
d)Describe the outcomes and state which model each outcome supports
Experiments on Dependent and Independent Variables Sample Answer
Critical experiments
Model one: Women are more eager for love. Generally speaking, women appear to be more eager for love in many films, novels and stories. They suddenly fall in love with someone after the first meet.
Model two: Men are the support of the families, so they spend more time on studying and working than searching for love. Men regard to career or job as the most crucial thing after graduation. They need to make money and support their family, so they have to work hard before getting married.
Model three: Women like children, so they want to have their children after marriage. (They want to become a mother.) Usually, women are playing the role of taking care of children in most families since they are merciful.
Experiment 1: After graduation, women prefer to get married to men who are older.
Dependent variable: Older men. For a marriage to take place, the man must be older than the woman.
Independent variable: Marriage. Marriage has to take place after graduation.
Outcome: 1. Women are sensitive to the age of since they are considered to age more than men. A woman wants to look younger than the man hence will look for a man that is older to get married to.
Since women want to get married after graduation more than their male counterparts, they have to seek older men, or they will wait for long before getting married.
Implications: 3. Men have less to worry about in the sense of marriage like giving birth and taking care of children is mostly left to women. Men are just supposed to provide financially and are therefore not eager to get married before they get stable income.
Men have more responsibility to take care for and mostly prefer younger women. Since they have to marry women that have already graduated, they have first to concentrate on their job as they wait for the younger women to graduate.
The experiment supports model two.
Experiment 2: Marriage does not require a person to be financially stable.
Dependent variable: Marriage
Independent variable: Financial stability
To make the variables work, men and women must be eager for marriage after graduation.
Implications: 1. Women will fall in love with a man even if he doesn’t have money since they just want to be loved hence they can get married without being financially stable.
There are a lot of responsibilities that arise after marriage and men are the ones looked upon. Though there is love, a man has to consider having finances before marriage.
Children are part of the family and to bring out children requires finances. It is, therefore, impeccable that financial stability is established before getting married.
The experiment supports model one.
Experiment 3: Men and Women get married to get children
Dependent variable: Children
Independent variable: Marriage
Outcomes: 1. Love and financial stability do not have to exist for children to be born. A man and a woman can just get married and have children.
There are expenses that must be incurred for the pregnancy and the whole process of giving birth.
The experiment supports model three.
Experiments on Dependent and Independent Variables Work Cited
March and Lave, 1993. An introduction to models in the social sciences.
Odds Ratio OR and Relative Risk RR Order Instructions: MHS506 Biostatistics
Module 4 – SLP
ODDS RATIO, RELATIVE RISK, AND ANOVA
Calculate the OR and the RR from the data provided. Calculate the OR for diabetes (outcome) with a family history of diabetes (exposure).
Odds Ratio OR and Relative Risk RR
Calculate the RR for allergies (outcome) with a family history of allergies (exposure). Write up the sentences to interpret the OR and RR that is calculated. Show your calculations and discuss the significance of each, OR and RR. Make sure to include Hill’s Criteria in discussions of potential causality. Given the 95% Confidence Interval, can you determine if the result is statistically significant?
Odds Ratio and 95% CI Calculator
http://easycalculation.com/statistics/odds-ratio.php
Relative Risk Calculator
http://easycalculation.com/statistics/relative-risk.php
SLP Assignment Expectations
Length: SLP assignments should be at least 2 pages (500 words) in length.
References: At least two references must be included from academic sources (e.g. peer-reviewed journal articles). Required readings are included. Quoted material should not exceed 10% of the total paper (since the focus of these assignments is critical thinking). Use your own words and build on the ideas of others. When the material is copied verbatim from external sources, it MUST be enclosed in quotes. The references should be cited within the text and also listed at the end of the assignment in the References section (APA format recommended).
Organization: Subheadings should be used to organize your paper according to question
Format: APA format is recommended for this assignment. See Syllabus page for more information on APA format.
Grammar and Spelling: While no points are deducted for minor errors, assignments are expected to adhere to standards guidelines of grammar, spelling, punctuation, and sentence syntax. Points may be deducted if grammar and spelling impact clarity.
The following items will be assessed in particular:
• Achievement of learning outcomes for SLP assignment.
• Relevance—all content is connected to the question.
• Precision—specific question is addressed; statements, facts, and statistics are specific and accurate.
• The depth of discussion—points that lead to deeper issues is presented and integrated.
• Breadth—multiple perspectives and references, multiple issues/factors considered/
• Evidence—points are well-supported with facts, statistics, and references.
• Logic—presented discussion makes sense; conclusions are logically supported by premises, statements, or factual information.
• Clarity—writing is concise, understandable, and contains sufficient detail or examples.
• Objectivity—use of the first person and subjective bias are avoided.
Odds Ratio OR and Relative Risk RR Sample Answer
Introduction
Odds Ratio (OR) and Relative Risk (RR) are widely used in medical sciences to determine whether A’s presence or absence (exposure) has an association with presence or absence of B, and subsequently help quantify the association in terms of causality or causal effect (Viera, 2008).
Calculation Results
Odds Ratio
Table 1: Odds Ratio for Diabetes Data Summary
Risk
Disease Status
Present
Absent
Total
Family history of diabetes present (exposure)
89 (a)
23 (b)
112
Family history of diabetes absent
20 (c)
168 (d)
188
Total
109
191
300
Where, a&b = Positive Test Values c&d = Negative Test Values
Calculated Odds Ratio (OR) using the easy calculation Odds Ratio Calculator = 32.5043; and 95% Confidence Interval = from 16.9344 to 62.3896
The calculated OR result of 32.5043 (OR>1) shows that exposure is associated with higher odds of the outcome, which in this case indicates that there is an association between a person who has been exposed (i.e. presence of family history of diabetes) and diabetes (outcome).
Relative Risk
Table 2: Relative Risk for Allergies Data Summary
Risk
Disease Status
Present
Absent
Total
Family history of allergies present (exposure)
89 (a)
59 (b)
148
Family history of allergies absent
91 (c)
61 (d)
152
Total
180
120
300
Where; a = Exposed Group Positive Outcome, b = Exposed Group Negative Outcome, c = Control Group Positive Outcome, d = Control Group Negative Outcome
Calculated Relative Risk (RR) using the EasyCaculation Relative Risk Calculator = 1.0045
The calculated RR of 1.0045 shows that, a person with family history of allergies (exposure) would be 1.0045 times as likely to have allergies (outcome) as persons without family history of allergies presence. This means the relative risk of person has been exposed (i.e. presence of family history of allergies) to develop allergies is comparable to that of a person who has not been exposed.
Odds Ratio OR and Relative Risk RR Discussion
Given the 95% Confidence Interval, it is possible to determine whether the result is statistically significant. This is because, when OR<1, it means that exposure is associated with lower odds of outcome; whereas when OR>1, it means that exposure is associated with higher odds of outcome (Bailey, 2008). However, when R=1 it means that exposure does not affect odds of outcome; hence, the null hypothesis for OR is that, when OR is greater that 1, then presence of condition A is regarded to have causal effect on condition B in a manner that having condition B raises (relatively to not having B) the odds of having condition A (Viera, 2008). Using this information, the calculated OR (32.5043) and 95% Confidence Interval (16.9344 to 62.3896), the result can be stated to be statistically significant. This means that, the causal effect between a people who have been exposed (i.e. presence of family history of diabetes) and diabetes (outcome) is statistically significant. As a result, based on Hill’s criteria of causality (plausibility) the association is aligned with currently accepted pathological process understanding because diabetes may be hereditary meaning genetic predisposition (exposure due to family diabetes history) is likely to cause diabetes (Höfler, 2005).
The RR calculation result of 1.0045 times, this means the relative risk of person has who has been exposed (i.e. presence of family history of allergies) to develop allergies is comparable to that of a person who has not been exposed. As a result, based on Hill’s criteria of causality (strength or effect size) presence of a small association does not rule out a causal effect, even though when the association is larger it means that there is more likely that it is causal and vice versa (Robbins, Chao & Fonseca, 2002). Thus, due to the weak association for allergies (outcome) with a family history of allergies (exposure), the causal effect cannot be confirmed to be statistically significant (Glass et al., 2013)
Odds Ratio OR and Relative Risk RR Conclusion
In conclusion, it is clear that OR and RR can be used to determine the causal effect or causality of an exposure to a particular medical or epidemiological characteristic (i.e. diabetes and allergies). OR is used to determine not only the presence of the association, but also whether it is statistically significant, whereas RR determines how strong the association is. Using OR, association with higher odds outcome between exposure (i.e. family history of diabetes) and diabetes (outcome) has been determined to be statistically significant; while RR shows weak association between allergies (outcome) with a family history of allergies (exposure).
Project management; problems,formulas and calculations
Project management; problems,formulas and calculations
Order Instructions:
All formulas and calculations must be shown
Problem 1.
Arsenal Electronics is going to construct a new $1.2 billion semiconductor plant and has selected four towns in the Midwest as potential sites. The important location factors and ratings for each town are as follows:
Scores (0 to 100)
Location Factor Weight Abbeton Bayside Cane Creek Dunnville
Work ethics 0.18 80 90 70 75
Quality of life 0.16 75 85 95 90
Labor laws/unionization 0.12 90 60 60 70
Infrastructure 0.10 60 50 60 70
Education 0.08 80 90 85 95
Labor skill and education 0.07 75 65 70 80
Cost of living 0.06 70 80 85 75
Taxes 0.05 65 70 55 60
Incentive package 0.05 90 95 70 80
Government regulations 0.03 40 50 65 55
Environmental regulations 0.03 65 60 70 80
Transportation 0.03 90 80 95 80
Space for expansion 0.02 90 95 90 90
Urban proximity 0.02 60 90 70 80
Recommend a site based on these location factors and ratings.
Answer 1:
Problem 2.
Sawyer Furniture is one of the few remaining domestic manufacturers of wood furniture. In the current competitive environment, cost containment is the key to its continued survival. Demand for furniture follows a seasonal demand pattern with increased sales in the summer and fall months, culminating with peak demand in November.
The cost of production is $16 per unit for regular production, $24 for overtime, and $33 for subcontracting. Hiring and firing costs are $500 per worker. Inventory holding costs are $20 per unit per month. There is no beginning inventory. Ten workers are currently employed. Each worker can produce 50 pieces of furniture per month. Overtime cannot exceed regular production. Given the following demand data, use Excel Solver to design an aggregate production plan for Sawyer Furniture that will meet demand at the lowest possible cost.
Input: Beg. Wkrs 10 Regular $16 Hiring $500
Units/wkr 50 Overtime $24 Firing $500
Beg. Inv. 0 Subk $33 Inventory $20
Month Demand Reg OT Subk Inv #Wkrs #Hired #Fired
Jan 500 500 0 0 0 10 0 0
Feb 500 500 0 0 0 10 0 0
Mar 1000 1,000 0 0 0 20 10 0
Apr 1200 1,000 200 0 0 20 0 0
May 2000 1,000 1,000 0 0 20 0 0
Jun 400 400 0 0 0 8 0 12
Jul 400 400 0 0 0 8 0 0
Aug 1000 1,000 0 0 0 20 12 0
Sep 1000 1,000 0 0 0 20 0 0
Oct 1500 1,500 0 0 0 30 10 0
Nov 7000 3,500 3,500 0 0 70 40 0
Dec 500 500 0 0 0 10 0 60
Total 17,000 12,300 4,700 0 0 246 72 72
Answer 2:
Problem 3.
Complete the following MRP matrix for Item X. Determine when orders should be released and the size of those orders.
Item: X LLC: 0 Period
Lot Size: Min 50 LT: 2 1 2 3 4 5 6 7 8
Gross Requirements 25 30 56 25 100 40 30 20
Scheduled Receipts 50
Projected on Hand 30
Net Requirements
Planned Order Receipts
Planned Order Releases
Release orders in periods 1 through 5 for quantities of 50, 50, 56, 50, and 50 respectively.
Answer 3:
Problem 4.
Fibrous Incorporated makes products from rough tree fibers. Its product line consists of five items processed through one of five machines. The machines are not identical, and some products are better suited to some machines. Given the following production time in minutes per unit, determine an optimal assignment of product to machine:
Machine
Product A B C D E
1 17 10 15 16 20
2 12 ?9 16 ?9 14
3 11 16 14 15 12
4 14 10 10 18 17
5 13 12 ?9 15 11
Answer 4:
Problem 5.
The following probabilistic activity time estimates are for a CPM/PERT network.
Time Estimates (days) Time Estimates (days)
Activity a m b Activity a m b
1 1 2 ?6 ?7 1 1.5 2
2 1 3 ?5 ?8 1 3 5
3 3 5 10 ?9 1 1 5
4 3 6 14 10 2 4 9
5 2 4 ?9 11 1 2 3
6 2 3 ?7 12 1 1 1
Determine the following:
a. Expected activity times
b. Earliest start and finish times
c. Latest start and finish times
d. Activity Slack
e. Critical Path
Expected Project duration and standard deviation.
Answer 5:
SAMPLE ANSWER
Problem 1 Answer
To determine appropriate location
Based of the above calculations the appropriate site location is Bayside
Problem 2 Answer
Problem 3 Answer
Release orders in periods 1 through 5 for quantities of 50, 50, 56, 50, and 50 respectively.
Problem 4 Answer
A table showing time taken to produce the products by each machine
Product
Machine
Totals
A
B
C
D
E
1
17
10
15
16
20
78
2
12
9
16
9
14
60
3
11
16
14
15
12
68
4
14
10
10
18
17
69
5
13
12
9
15
11
60
Totals
67
57
64
70
74
335
To get the optimal assignment of product for machine the percentage of total time taken by each machine to produce the five products with regards to the total time to produce all products by all machines is calculated as follows:
Machine B is the most optimal since it utilizes the least percentage of time (i.e. 17%) to produce all the products.
Problem 5 Answer
The formulas:
Where;
Activity
t
ES
EF
LS
LF
S
1
8
0.44
0
8
1
9
1
2
6
1.00
0
6
0
6
0
3
3
0.44
0
3
2
5
2
4
5
2.78
8
13
16
21
8
5
3
0.11
6
9
6
9
0
6
4
0.11
3
7
5
9
2
7
2
0.00
3
5
14
16
11
8
7
1.78
9
16
9
16
0
9
4
0.44
9
13
12
16
3
10
4
0.44
13
17
21
16
8
11
9
1.00
16
25
16
25
0
12
4
4.00
15
27
15
25
2
Where;
Expected activity times (ES); Earliest start and finish times (EF); Latest start and finish times (LS); Activity Slack (LF); and Critical Path (S)
However, the expected project duration and standard deviation are:
Project duration = sum of each activity time (durations) = 59 days
Standard Deviation = sum of all standard deviations = 12.54 days
The matrix has eigenvalues1=3 and 2=−2. Let’s find the eigenvectors corresponding to 1=3. Let v=v2v1. Then(A−3I)v=0 gives us
2−3−1−4−1−3v1v2=00 from which we obtain the duplicate equations
−v1−4v2−v1−4v2=0
If we let v2=t, thenv1=−4t. All eigenvectors corresponding to1=3are multiples of1−4 and thus the eigenspace corresponding to1=3is given by the span of1−4. That is,1−4is a basis of the eigenspace corresponding to 1=3.
Repeating this process with 2=−2, we find that
4v1−4V2−v1+v2=0
If we let v2=t then v1=t as well. Thus, an eigenvector corresponding to2=−2 is 11 and the eigenspace corresponding to 2=−2 is given by the span of11. 11is a basis for the eigenspace corresponding to 2=−2.
Problem 3
Problem 5
Problem 14
Problem 22
Problem 25
Matrices A2 and A3 cannot be diagonized because for a square matrix A, wherever A is similar to diagonal matrix then the matrix is diagonizable.
Problem 15-24: Eigenvalues & Eigenvectors Matrices
Problem 15
Since all entries are ≥ 0 and each column sums to 1, this A is a Markov matrix. Thus we know that λ1 = 1 is an eigenvalue. Since tr(A) = λ1 + λ2 = 3/2, we conclude λ2 = 1/2 is another eigenvalue. We diagonalize it using the matrix S of eigenvectors:
= → =
This last matrix product equals
Problem 19
False
True
True
False
References
Bhatti, M. A. (2012). Practical Optimization Methods with Mathematica Applications. New York, NY: Springer.
Edwards, C. H., & David E. Penney, D. E. (2009). Differential Equations: Computing and Modeling. Upper Saddle River, CA: Pearson Education, Inc.
Shores, T. S. (2007). Applied linear algebra and matrix analysis. New York, NY: Springer Science+Business Media, LLC.
Strang, G. (2003). Introduction to linear algebra. Wellesley, MA: Wellesley-Cambridge Press
Strang, G. (2006). Linear algebra and its applications. Belmont, CA: Thomson, Brooks/Cole Publishers.
Strang, G. (2009). Eigenvalues and Eigenvectors. Boston, MA: Lord Foundation of Massachusetts.
