Mathematics

Calculus, originally called infinitesimal calculus or “the calculus of infinitesimals”, is the mathematical study of continuous change. When they were introduced who objected to them.

Note: For all the questions, provide detailed solution steps. Question 1: (80 points, 20 each) a. Find the equation of the line that passes through the point (-6, 3) and has the slope 7.  b. Find the equation of the line that passes through the points (4, -3) and (12, 1).  c. Find the equation of the line with an x-intercept of 3 and a y-intercept of -4. d. Find the equation of the line if y-intercept is 4, and the line is parallel with the x-axis.  Question 2:   (10 points, 5 each) Graph the function: a) 2x -3y = -4. b) 4 + 2y = 3x. Question 3: (Bonus).  (10 points/5 each) The budget of a company per month is given by the equation F(x) = 4x-2, find the budget: a. After 5 years. b. After 7.5 years.

Chapter 6: More Practice With Normal Distributions. As a part of preparation for this week’s test, let’s practice with another case related to the Normal distribution. Assign your numbers for mean ? and standard deviation ?. Then select a number “A” below mean ?, and a number “B” above mean ?. Use Appendix Table for the Normal Distribution to find the probability that x is between A and B: P (A < x < B). Here are steps to follow: convert A to z score (let's call it za), convert B to z score (let's call it zb).; From Appendix table find area under curve to the left of za and to the left of zb. That will give you P (z < za) and P (z < zb). If za or zb are not in the table, change your A or B. Use formula: P (A < x < B) = P (za < z < zb) = P (z < zb) - P (z < za) Don't just assign numbers, make an example from a real situation where this technique can be applied. For instance, see Chapter 6 section 6.3 example 6.11 on page 281 of eText: Intelligence Quotients example. Create your own scenario and values.

Using the Internet, the text, or another reliable source such as a newspaper or periodical site, (not a scholastic or school site like Khan Academy and not Wikipedia), research some important data that has been presented in graph or table format. Make sure to cut and paste the chart or table; if that is not possible, paste a link to the webpage. (Check it to be sure it links correctly.) Present your graph and fully explain the information it is representing. Pose two questions regarding the data and graph or chart for your fellow students to consider and respond to in your post.

Looking for someone to answer my questions and pretty much be at my side for the exam. If I do not know an answer I will send you the problem and you must give step- by – step instructions to answer the question. 4 minutes per question are given. Total of 2 hour exam. Needs to be started by 10pm.

Given the following polynomial function:

Suppose a chair manufacturer is producing in the short run (with existing plant andequipment). The manufacturer has observed the following levels of production correspondingto different numbers of workers:a. Calculate the marginal and average product of labor for this production function.b. Does this production function exhibit diminishing returns to labor? Explain.c. Explain intuitively what might cause the marginal product of labor to become negative.2. The marginal product of labor in the production of computer chips is 50 chips per hour. Themarginal rate of technical substitution of hours of labor forhours of machine capital is !”What is the marginal product of capital?

Combination of research question 1 and 2 into one comprehensive research questionDo the level of education for married women, the household size by race (Black and White American race), and the level of married men’s self-esteem significantly affect the level of intimate partner violence against married women (IPV) in the United States of America while keeping their per capita income controlled• Independent Variables: the level of education for married women, the household size by race (Black and White American race), and the level of married men’s self-esteem.• Dependent Variable: the level of intimate partner violence against married women (IPV).• Control variable: the level of per capital personal income.

Prepare a 2-3 page (hypothetical) model-based recommendation to the next MSU president on how to increase the happiness of the Montclair State University undergraduate student body.1. Describe your model. What 5-6 factors (independent variables) would you consider to include in a model of the overall level of happiness of a college’s student body? (e.g. class size, overall enrollment, location, recreation, grade policy, etc.) Which factors would be positive and which negative? Is this data available? If not, where would you find it?2. Where would Montclair State rank (decile) among all colleges in the U.S., in your opinion? Why?a) Name a school that would be higher-ranked. Why do you think it would be ranked higher?b) Name one lower-ranked. Why?3. Over which factors in your hypothetical model do the Montclair State Unversity administration have the most control over? What would recommend as the TOP 3 metrics for the new President of MSU to focus on with the goal of increase the happiness of MSU students?**Use the link below and google for data andmore information**https://ourworldindata.org/happiness-and-life-satisfaction

Write an essay about Fermat’s Last Theorem – The Theorem and Its Proof: An Exploration of Issues and Ideas [1993] and your reaction to itWho is its main character? You may feel that the man is the main character, or you may feelthe equation is its main character. Be sure to mention both.Why have I shown this to you now? What does the content have to do with logic?Comment on what was interesting, surprising, or in general what you learned aboutmathematicians or the culture of mathematicsNote a few of the mathematicians, aside from Wiles:Note any of comments or stories that caught your attention:What is Fermat’s Last Theorem, and why is it, and the proof, interesting?What does Fermat’s Last Theorem, or its proof, contribute to the practical world?What did you observe about problem solving techniques?