Mathematics

During the recent election season, you saw many instances where polls were taken and reported, along with the confidence level of the estimate. For example, a poll showed that one candidate had a “”voting for” level of 37%+/-4. The opposing candidate had a score of 39%+/-4 at a 95% confidence level. Because the poll is not a census sample, a sample may be “good” but will have variation around the TRUE population proportion or mean. Thus, the poll is an estimate. The +/- value establishes a range within which the true population proportion is said to be, give a certain level of confidence. However, the reporter said that the second candidate had “a slight lead”. Is this a true statement? Why could it be argued that the scores are “statistically the same”? For more information on Population Proportion read this: https://en.wikipedia.org/wiki/Population_proportion

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

 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

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

Remember to show all work and use correct notation to earn full credit.1.Solve the following quadratic equation for x: 2x 2 ? 5x + 7 = 02. Among all pairs of numbers whose difference is 28, find the pair whose product is minimum. What is the minimum product?3. (a) Solve the following quadratic equation for x: x 2 ? 7x + 10 = 0 (b) (4 points) Use your answer from part (a) to help solve the following quadratic inequality: x 2 ? 7x + 10 ? 0 • Sketch a graph of your solution on a horizontal number line. • Express your solution using interval notation.4. Solve the following radical equation for x: ? 17 ? x ? 3 = x Remember to check your solutions! If there are no solutions, state NO SOLUTIONS.5. Solve the following rational equation for x: 1 x ? 6 + x x ? 2 = 4 x 2 ? 8x + 12 Hint: Factor the quadratic denominator. Remember to check your solutions! If there are no solutions, state NO SOLUTIONS.

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

Problem 5.1 What Is Straight in a Hyperbolic Plane?a. On a hyperbolic plane, consider the curves that run radially across each annular strip. Argue that these curves are intrinsically straight. Also, show that any two of them are asymptotic, in the sense that they converge toward each other but do not intersect.b. Find other geodesics on your physical hyperbolic surface. Use the properties of straightness (such as symmetries) you talked about in Problems 1.1, 2.1, and 4.1.c. What properties do you notice for geodesics on a hyperbolic plane? How are they the same as geodesics on the plane or spheres, and how are they different from geodesics on the plane and spheres?Hint for 5.1 a)Some of you seem to be having trouble visualizing 5.1a. This is because on the hyperbolic soccer ball model that most of you made, you can’t see the annuli. You can see the annuli on a crocheted hyperbolic plane, but so far only one person has turned in a crocheted plane. This YouTube video records the construction of an annular hyperbolic plane, which should help you visualize the asymptotic lines on the hyperbolic plane.Problem 7.1 and Problem 8.2 Due date: Feb 28th7.1The Area of a Triangle on a Spherea. The two sides of each interior angle of a triangle A on a sphere determine two congruent lunes with lune angle the same as the interior angle. ‘Show how the three pairs of lunes determined by the three interior angles, a, f, y, cover the sphere with some overlap. (What is the overlap?)Draw this on a physical sphere, as in Figure 7.2b. Find a formula for the area of a lune with lune angle 6 in terms of 6 and the (surface) area of the sphere (of radius p), which you can call Sp. Use radian measure for angles.Hint: What if <9is n? ji/2?c. Find a formula for the area of a triangle on a sphere of radius p.8.2

Scaffolding of concepts in math instruction is imperative for students to master concepts and develop strong mathematical literacy. Math is a subject that naturally continues to deepen students’ comprehension of concepts as they progress through the grade levels. For example, during primary grade instruction, students learn basic addition concepts. In later grades, addition comprehension develops into repeated addition that in turn leads into an understanding of multiplication and so on. Building a strong mathematical foundation in early education using various learning strategies in units of study ensures that the teacher is meeting the needs of all learners. For this assignment, select a grade level K-3 and at least one state standards related to mathematical operations. Using the “COE Lesson Plan Template,” develop a lesson based on your selected standards. As you are developing your lesson, consider how to create objectives that measure students’ actions and incorporate differentiated learning to meet the needs of students at, above, and below grade level. For this assignment, you do not need to complete the “Multiple Means of Expression” section in the “COE Lesson Plan Template.” As you develop your lesson, consider how this lesson would scaffold with other lessons. Below your lesson plan, write a 150-250 word reflection describing the following: What knowledge and skills would need to be taught before this lesson to make sure students are able to retain the content? What lessons would logically be taught after this lesson to take students to the next level of understanding? How would you differentiate to meet the needs of students above and below grade level? APA format is not required, but solid academic writing is expected. readings- https://lopes.idm.oclc.org/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=116991181&site=ehost-live&scope=site https://lopes.idm.oclc.org/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=123323488&site=ehost-live&scope=site https://lopes.idm.oclc.org/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=123903475&site=ehost-live&scope=site https://www.verywellfamily.com/universal-design-learning-4141046 https://dreme.stanford.edu/news/math-games-excite-young-minds  http://thinkmath.edc.org/resource/kindergarten  For more information on Mathematical Foundation read this: https://en.wikipedia.org/wiki/Mathematics?wprov=srpw1_0

A company makes and sells charm bracelets. The cost of producing x bracelets is represented by the functionC(x) = 180 + 8x. The revenue earned from selling x bracelets is represented by the function R(x) = 20x.Write and simplify a function P that represents the profit made from selling x bracelets.How many bracelets must the company sell to break even?