Mathematics

 Debate the following statement: “Correlation means Causation.” Determine whether this statement is true or false, and provide reasoning for your determination, using the Possible Relationships Between Variables table from your textbook. For more information on Correlation read this: https://en.wikipedia.org/wiki/Correlation_and_dependence

Completing Gauss -Jordan Elimination With A 3×3 Matrix solve the system For more information on Gauss -Jordan Elimination read this: https://en.wikipedia.org/wiki/Frobenius_matrix

Discussion Forum 2Previous  Next Prompt Design an experiment to determine the empirical probability that a person will randomly select a can of Coke when given a cooler with equal numbers of cans of both Coke and Pepsi. (NOTE: each person considerately replaces the can after they have selected it, so the total number of cans will stay the same throughout the experiment.)Calculate the empirical probability after five persons. Calculate the empirical probability after ten persons. What is the theoretical probability that a person selected at random would select the Coke? Analyze: How does the empirical probability in your experiment compare to the theoretical probability of selecting the Coke? Why are the probabilities not the same? Post your calculations and respond with your analysis. Read two other posts and comment. For more information on Empirical Probability read this: https://en.wikipedia.org/wiki/Empirical_probability

All of us are used to multiple-choice tests. If all the exam questions have a choice of 4 different responses (a,b,c,d) what is the probability of randomly guessing the right answer? See! You are all naturally mathematicians! How does this relate to the formulas regarding probability? For example, if the probability of a correct answer was .25, what would the mean (aka expected value) of the distribution be if the sample size was 100? Hint: mean=np For more information on Dexter Masters read this: https://en.wikipedia.org/wiki/Dexter_Masters

Please read the “Final_Project-Diet and Cholesterol_AS2.dox” file ID #:2083927The description states that your report may “be no longer than four pages in total…”. For simplicity (and legibility), please use either Times New Roman, Calibri, or Arial font with a  minimum font size of 11 and have a minimum 1.5 spacing. You will submit either a .doc or .pdf file. In addition to the written report file, we are also requiring a separate “.do” file outlining all statistical procedures you may have used with appropriate comments. Please do not copy and paste your code into your word file. For more information on Biostatistics read this: https://en.wikipedia.org/wiki/Biostatistics

When students are learning mathematical operations and skills, the concepts and skills will build upon each other. It is important for teachers to plan meaningful learning progressions in their lessons to help with this learning process. Higher-order questioning within a lesson plan can help ensure skill mastery before the next learning concept is introduced. Part 1: Partial Lesson Plan Select a 1-5 grade level and a corresponding Arizona College and Career Ready Standard or other state standard based on the Number and Operations in Base Ten domain. Using the “COE Lesson Plan Template,” complete the lesson plan through the Multiple Means of Engagement section, making sure the activities are supported by the recommendations found in the topic materials. Include appropriate support and guidance to help students learn related academic language. Part 2: DOK Essential Questions Upon completion of the partial lesson plan, draft 20 essential questions to guide meaningful learning progressions and foster problem-solving for students with disabilities, using the “DOK Questions Template.” Five of the questions should activate prior knowledge and the remaining 15 questions should be based on the progression of the lesson activity, probing the four Depth of Knowledge (DOK) levels. Using four of the questions you drafted, one from each DOK level, identify the following using the DOK Questions Table within the “DOK Questions Template”: Examples of student responses Rationale of why chosen question meets DOK level APA format is not required, but solid academic writing is expected. This assignment uses a rubric. Review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion. You are required to submit this assignment to LopesWrite. Refer to the LopesWrite Technical Support articles for assistance. For more information on Mathematical Operations and Skills read this: https://en.wikipedia.org/wiki/Mathematics_education

Symmetries of Parallel Transported LinesConsider two lines, r and r’, that are parallel transports of each other along a third line, l. Consider now the geometric figure that is formed by the three lines and look for the symmetries of that geometric figure.What can you say about the lines r and rl Do they intersect? If so, where? Look at the plane, spheres, and hyperbolic planes.If a transversal cuts two lines at congruent angles, are the lines, in fact parallel in the sense of not intersecting?Suggestions can be found on the book.Problem 9.1, 9.2 and 10.1 Due date is March 6thProblem 9.1 Side-Side-Side (SSS)Are two triangles congruent if the two triangles have congruent corresponding sides?SuggestionsStart investigating SSS by making two triangles coincide as much as possible, and see what happens. For example, in Figure 9.2, if we line up one pair of corresponding sides of the triangles, we have two different orientations for the other pairs of sides as depicted in Figure 9.2. Of course, it is up to you to determine if each of these orientations is actually possible, and to prove or disprove SSS. Again, symmetry can be very useful here. 6n a sphere, SSS doesn’t work for all triangles. The counterexample in Figure 9.3 shows that no matter how small the sides of the triangle are, SSS does not hold because the three sides always determine two different triangles on a sphere. Thus, it is necessary to restrict the size of more than just the sides in order for SSS to hold on a sphere. Whatever argument you used for the plane should work for suitably defined small triangles on the sphere and all triangles on a hyperbolic plane. Make sure you see what it is in your argument that doesn’t work for large triangles on a sphere.

CompetencyIn this project, you will demonstrate your mastery of the following competency:Apply statistical techniques to address research problemsPerform hypothesis testing to address an authentic problemOverviewIn this project, you will apply inference methods for means to test your hypotheses about the housing sales market for a region of the United States. You will use appropriate sampling and statistical methods.ScenarioYou have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report:Are housing prices in your regional market higher than the national market average?Is the square footage for homes in your region different than the average square footage for homes in the national market?For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?You are given a real estate data set that has houses listed for every county in the United States. In addition, you have been given national statistics andgraphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and providea reportto the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below.DirectionsIntroductionPurpose: What was the purpose of your analysis, and what is your approach?Define a random sample and two hypotheses (means) to analyze.Sample: Define your sample. Take a random sample of 100 observations for your region.Describe what is included in your sample (i.e., states, region, years or months).Questions and type of test: For your selected sample, define two hypothesis questions and the appropriate type of test hypothesis for each. Address the following for each hypothesis:Describe the population parameter for the variable you are analyzing.Describe your hypothesis in your own words.Describe the inference test you will use.Identify the test statistic.Level of confidence: Discuss how you will use estimation and conference intervals to help you solve the problem.1-Tailed TestHypothesis: Define your hypothesis.Define the population parameter.Write null (Ho) and alternative (Ha) hypotheses.Specify your significance level.Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.Summarize your sample data using appropriate graphical displays and summary statistics.Provide at least one histogram of your sample data.In a table, provide summary statistics including sample size, mean, median, and standard deviation.Summarize your sample data, describing the center, spread, and shape in comparison to the national information.Check the conditions.Determine if the normal condition has been met.Determine if there are any other conditions that you should check and whether they have been met.Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.Calculate the hypothesis statistics.Determine the appropriate test statistic (t).Calculate the probability (p value).Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.Relate the p value and significance level.Make the correct decision (reject or fail to reject).Provide a conclusion in the context of your hypothesis.2-Tailed TestHypotheses: Define your hypothesis.Define the population parameter.Write null and alternative hypotheses.State your significance level.Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.Summarize your sample data using appropriate graphical displays and summary statistics.Provide at least one histogram of your sample data.In a table, provide summary statistics including sample size, mean, median, and standard deviation.Summarize your sample data, describing the center, spread, and shape in comparison to the national information.Check the assumptions.Determine if the normal condition has been met.Determine if there are any other conditions that should be checked on and whether they have been met.Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.Calculate the hypothesis statistics.Determine the appropriate test statistic (t).Determine the probability (p value).Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.Relate the p value and significance level.Make the correct decision (reject or fail to reject).Provide a conclusion in the context of your hypothesis.Comparison of the test results: See Question 3 from the Scenario section.Calculate a 95% confidence interval. Show or describe your method of calculation.Interpret a 95% confidence interval.Final ConclusionsSummarize your findings: Refer back to the Introduction section above and summarize your findings of the sample you selected.Discuss: Discuss whether you were surprised by the findings. Why or why not?What to SubmitTo complete this project, you must submit the following:Project Two Template: Use this template to structure your report, and submit the finished version as a Word document.

Respond to one or more of the following in a minimum of 175 words:This week we learn about the foundations of geometry. Geometry uses various modes of thinking. Describe inductive and deductive reasoning. Provide some examples from everyday life that compare and contrast these two ways of thinking?Where in your world do you see segments, rays, and angles? If you were going to explain these geometric figures to someone how would you describe them?Discuss the different types of angles we will be learning this week and also discuss some special angle pairs.

Topic: Categories of continuity: uniform continuity, absolute continuity, Lipschitz continuityThe written portion of this project should be around 5-7 pages (before references). Each write-up should include the following three components:1- Historical context/motivation.2- Detailed mathematical explanation.3- Discussion of how the results/ideas/concepts are used more broadly.In terms of writing style, write as though you were writing part of a textbook (directed to college students who are taking upper classes). In the “detailed mathematical explanation” make sure to explain any new notation, provide plenty of justification for the steps in the proof, and explain as best as you can the overall strategy of the proof.Please include a references section at the end.you can use the book I uploaded.please do not Plagiarism