Mathematics

1. In the article “The tools of Quality Part IV: Histograms” (Quality Progress, September 1990, Vol. XXIII, No.9, pp.75-78) data are presented on the gain of 120 amplifiers. These data are reproduced below. a) Construct a stem-and-leaf display step by step. Category Interval=1 (7,8,9,10,11 as stems, and decimal number as leaf) (3pts). b) Comment on the shape of the display in a. Can you make an assumption that the data follows a normal distribution? Why? (2pt)c) Construct a stem-and-leaf display step by step. Category Interval=0.5 (7.0?X<7.5, 7.5?X<8, 8.0?X<8.5, ….(1pts) 8.110.48.89.77.89.911.78.09.39.08.28.910.19.49.27.99.510.97.88.39.18.49.611.17.98.58.77.810.58.511.58.07.98.38.710.09.49.09.210.79.9.78.78.28.98.69.59.48.88.38.49.110.17.88.18.88.09.28.47.87.98.59.28.710.27.99.88.39.09.69.910.68.69.48.88.210.59.79.18.08.79.88.58.99.18.48.19.58.79.38.110.19.68.38.09.89.08.98.19.78.58.29.010.29.58.38.99.110.38.48.69.28.59.69.010.78.610.08.88.6 Please be noted: you are not expected to use Excel Histogram function in this problem. In the next assignment, this function must be used. 2. An experiment in chemistry looked at the effect of temperature on the solubility of salt in water. Below are data on the solubility of Potassium Chloride (KCL). Construct a scatter plot of the data and comment on the relationship between temperature and solubility using Microsoft Excel. (3pts)Temp. °C 0 10 20 30 40 50 60 70 80 90 100 Solubility 29.6 28.0 33.6 38.1 34.2 42.6 44.8 48.1 56.5 55.46 2.9

Demonstrate skills to calculate probability. Construct basic graphsCalculate and compute descriptive statistics. Calculate probabilities for a normal distribution. Demonstrate skills using the Central Limit Theorem. Construct confidence intervals. Calculate Student’s t-Distribution. Estimate population means. Estimate population proportions. Compare population means. Conduct hypothesis testing. Perform a chi-square test. Calculate and interpret the correlation between two variables due after 3 hours anyone can help?

How does math statistics work?

Define the continuity and discontinuity of a function and explain it with examples to make a presentation on PowerPoint.

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

A manufacturer claims that a motor will not draw more than 1.5 amperes under normal conditions.  A factory engineer suspects the claim is low and plans a test on 36 such motors.  Suppose the standard deviation among motors is 0.9 amperes.  If the “true” mean is 1.8 amperes, what is the probability of a Type II error ( beta risk ) and the power of the test associated with each of the following levels of significance:  10%,  5%, and 1%?

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

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

using prior and posterior distribution method what is the resulting distribution given you have a Poisson distribution as prior

Write a program for the second order Runge-Kutta Method with automatic step control to solve ordinary differential equation systems.  Store the results so that they can be used later to construct a table and to draw the curve as y(t) versus t or in systems y_1 versus y_2. Test the program with the problem y_1^’=-y_(2,) ? y?_2^’=y_1 with initial conditions ? y?_1 (0)=1,? y?_2 (0)=0. Verify that the exact solution represents uniform motion along the unit circle in the plane ?(y?_1,y_2). Stop the calculations after 10 revolutions (t=20?). Perform experiments with different tolerances and determine how small the tolerance should be so that the circle on the screen does not become thick. When applying the program to solve a second order equation, in the resulting system the unknowns represent the solution and of the original equation and its derivative y^’. Consider 6 values of the solution and construct an interpolation polynomial and show that the roots of y^’ are points of possible y-end.  TP:  Implement all the root search algorithms studied in classes.