# Mathematics

## Political Analysis

Make sure you look and see if you are able to do it! Adjust accordingly if needed. IBM SPSS STATISTICS REQUIRED. Chapters 7 and 8

## Probability Cost

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?

## Kelson Sporting Equipment

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catchers model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:((For full details open Lab 2 question file and check the ETECH 899 Sample Report document for the expected answer file format))The company is interested in maximizing the total profit contribution. List of tasks (use this list for writing your report) to be completed for this problem:1. Define the linear programming problem to be solved in your own words.2. Develop a mathematical model to represent the problem.3. Find the optimal solution using the graphical solution procedure using the Desmos graphing calculator at www.desmos.com (Links to an external site.) by providing a screen capture of the graph. (a tutorial for Desmos graphing calculator is given at Provide the link of the graph giving the optimal solution. Develop a Microsoft Excel spreadsheet to solve the problem. Include the normal view and the formula view of the Excel spreadsheet in your report by capturing the screen. Run the Excels Solver tool to determine the optimum solution while capturing parts of the screen to explain your entire process and the results. How many hours of production time will be scheduled in each department? What is the slack time in each department? Are any of the constraints redundant? If so, which ones? Upload an Excel spreadsheet file.

## Quality Progress

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

## Skills to Calculate Probability

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?

## Continuity and Discontinuity of a Function

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

## Hyperbolic Plane

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

## Type II Error

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%?

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