Need assistance in completed this week 2 of assignments. Week 2 Algebra Talk Variation is a great example of how mathematics is used to model and solve real-world problems. Many fields of study contain examples of the three different kinds of variation:Direct variation (for example, y = kx)Inverse variation (for example, y = k/x)Joint variation (for example, z = kxy)Definition of Joint VariationJoint variation is the same as direct variation with two or more quantities.That is:Joint variation is a variation where a quantity varies directly as the product of two or more other quantities.Let's first understand direct variation.Direct variation occurs when two quantities change in the same manner.That is:Increase in one quantity causes an increase in the other quantity.Decrease in one quantity causes a decrease in the other quantity.For example:The cost of a pencil and the number of pencils you buy.Buy more pay more….Buy less pay less.Direct variation between variables x and y can be expressed as:y = kx, where ' k' is the constant of variation and k ≠ 0.y = kxz represents joint variation. Here, y varies jointly as x and z. More Examples on Joint Variationy = 7xz, here y varies jointly as x and z.y = 7x2z3, here y varies jointly as x2 and z3."Math DictionaryThe variable is in the bottom of a fraction or in the denominator. (The Opposite of Direct Variation) In an inverse variation, the values of the two variables change in an opposite manner - as one value increases, the other decreases. For example, a biker traveling at 8 mph can cover 8 miles in 1 hour. If the biker's speed decreases to 4 mph, it will take the biker 2 hours (an increase of one hour), to cover the same distance. Please start by addressing one or more of the following topics to get the discussion going:How would you describe the difference between direct variation and joint variation in words? Use examples to help illustrate.Pick a field of study of interest to you and give an example of variation in that field. Some possible areas to consider are: Economics, Finance, Geometry and Physics. Example: If your hourly pay rate is $15/hour, then your weekly pay p is given by the formula p=15h where h is the number of hours worked in a week. So, your weekly pay varies directly as the number of hours worked in a week with the constant of variation = 15.Most formulas are actually examples of variation. Pick a well-known formula and describe the type of variation as well as the constant of variation, k. Example: The area A of a triangle with base b and height h is given by the formula A=½bh. So, the area of a triangle varies jointly as the base and height (both direct) with the constant of variation = ½.Give an example from real life where composite functions are utilized. For ideas, you may look it up on the internet or find examples in the book. Week 2 Weekly Summary When posting here in the Weekly Summary section please do not post "answers only" but rather show how you obtained your answers in a step by step manner. If your solution is correct, it is in your best interest for us to see how you obtained the answer. If your solution is incorrect, showing your steps will help us to follow your process and we can then work together to find your mistake. No bonus points will be awarded for answers without explanations.A maximum of 5 or .25% bonus points will be awarded for 5 correct answers with step by step explanations.The weekly summary answers and explanations will be posted in the Announcement section by Friday of each week. Please try to work each problem without pasting and copying or you will defeat your purpose of learning. Credit will only be given for "original" work. Please feel free to study the explanations, learn the problem, and create your own step-by-step explanation for bonus points . You may post your explanations throughout the term (please remind your instructor in the General Questions thread to grade your problems if you have posted after Sunday).NOTE: You may submit a photo of your neat, hand-written work rather than a Word Document. Find the vertex of the parabola f(x) = x2 - 16x + 63.Find the x- and y-intercepts of the cubic function f(x) = (x+4)(2x-1)(x-1).If f(x) = x2-2x-24 and g(x) = x2-x-30, find (f-g)(x).If f(x) = x+4 and g(x) = 2x2-x-1, evaluate the composition (g o f)(2).If f(x) = x+4 and g(x) = 2x2-x-1, find the composition (f o g)(x).Write the following sentence as an equation: y varies directly as x.Write the following sentence as an equation: x is directly proportional to y and is inversely proportional to the cube of z.What are the zeros of the parabola: f(x) = x2 - 7x + 10 (that is, what are the x-intercepts or the points where the graph crosses the x-axis)?What is the vertical asymptote of the rational function f(x) = 3x / (2x - 1)?What is the horizontal asymptote of the rational function f(x) = 3x / (2x - 1)?

Based on the class sample, you will create a 95% confidence interval for the mean age and the proportion of males in the population of all online college students.Note: The goal of the project is to practice making a confidence interval for a mean and proportion with real data. Do not worry about failed assumptions tests and do not make corrections for small sample size. Use primary methods described in text and used on homework.Using the same excel sheet as last week, answer the following in the “week 5” tab:For the average age, form a 95% confidence interval:What distribution should be used?What is the critical value?What is the error bound?What is the lower bound?What is the upper bound?How do we interpret the results, in context of our study?For the proportion of males, form a 95% confidence interval:What distribution should be used?What is the critical value?What is the error bound?What is the lower bound?What is the upper bound?How do we interpret the results, in context of our study?

Required ResourcesRead/review the following resources for this activity:OpenStax Textbook: Chapter 2, 6, and 7LessonWeeks 3 and 5 Excel SpreadsheetsScenario/SummaryThis week's lab highlights the use of probability and normal distribution.Follow the directions below to gather data, calculate using Excel spreadsheets, and interpret the results.DeliverablesThe deliverable is a Word document with your answers to the questions posed below based on the data you find.Required SoftwareMicrosoft WordMicrosoft ExcelSteps to Complete Week 5 LabUse the Weeks 3 and 5 spreadsheets to help you answer the questions below.Step 1: Survey or measure 10 people to find their heights. Determine the mean and standard deviation for this group by using the Week 3 Excel spreadsheet. Post a screen shot of the portion of the spreadsheet that helped you determine these values. How does your height compare to the mean (average) height of the group that you surveyed? Is your height taller, shorter, or the same as the mean of your group?Data Example of 10 people with different heightsStep 2: Give some background information on the group of people you used in your study. You might consider using the following questions to guide your answer.How did you choose the participants for your study (sampling method)?What part of the country did your study take place in?What are the age ranges of your participants?How many of each gender did you have in your study?What are other interesting factors about your group?Step 3: Use the Week 5 Excel spreadsheet for the following.(Use the Empirical Rule tab from the spreadsheet). Determine the 68%, 95%, and 99.7% values of the Empirical Rule in terms of the ten heights in your height study.What do these values tell you?Post a screen shot of your work from the Week 5 Excel spreadsheet. Week 5 Spreadsheet Example(Use the normal probability tab from the spreadsheet). Based on your study results, what percent of the study participants are shorter than you? What percent are taller than you?Post a screen shot of your work from the Week 5 Excel spreadsheet.Example: If my height is 73 inches, then 20.86% of the relevant population is shorter. The other 79.14%, of course, is taller.Week 5 Spreadsheet ExampleStep 4: Be sure your name is on the Word document, save it, and then submit it under "Assignments" and "Week 5: Lab".GradingThis activity will be graded based on the Week 5 Lab Rubric.Course Outcomes (CO): 3, 4, 5CriteriaRatingsPtsThis criterion is linked to a Learning OutcomeMeasures of Central Tendency and Variation12.0 ptsAddresses all elements of the following: *10 height values *mean of data *standard deviation of data *screenshot of values calculated on spreadsheet *comparison of heights10.2 ptsAddresses 4 out of 5 of the following: *10 height values *mean of data *standard deviation of data *screenshot of values calculated on spreadsheet *comparison of heights8.4 ptsAddresses 3 out of 5 of the following: *10 height values *mean of data *standard deviation of data *screenshot of values calculated on spreadsheet *comparison of heights6.6 ptsAddresses 1 or 2 out of 5 of the following: *10 height values *mean of data *standard deviation of data *screenshot of values calculated on spreadsheet *comparison of heights0.0 ptsNo Effort12.0 ptsThis criterion is linked to a Learning OutcomePopulation Data and Sampling Techniques15.0 ptsAddresses all elements of the following: *Sampling method *Location *Age group of participants *Gender of participants *Other factors about participants12.75 ptsAddresses 4 out of 5 of the following: *Sampling method *Location *Age group of participants *Gender of participants *Other factors about participants10.5 ptsAddresses 3 out of 5 of the following: *Sampling method *Location *Age group of participants *Gender of participants *Other factors about participants8.25 ptsAddresses 1 or 2 out of 5 of the following: *Sampling method *Location *Age group of participants *Gender of participants *Other factors about participants0.0 ptsNo Effort15.0 ptsThis criterion is linked to a Learning OutcomeProbability, and Measures that would follow a normal distribution in life sciences15.0 ptsAddresses all elements of the following: *Empirical Rule values *Interpretation of Empirical Rule values *Screenshot of Empirical spreadsheet *Interpretation of Normal Distribution spreadsheet values *Screenshot of probabilities/ percentiles12.75 ptsAddresses 4 out of 5 of the following: *Empirical Rule values *Interpretation of Empirical Rule values *Screenshot of Empirical spreadsheet *Interpretation of Normal Distribution spreadsheet values *Screenshot of probabilities/ percentiles10.5 ptsAddresses 3 out of 5 of the following: *Empirical Rule values *Interpretation of Empirical Rule values *Screenshot of Empirical spreadsheet *Interpretation of Normal Distribution spreadsheet values *Screenshot of probabilities/ percentiles8.25 ptsAddresses 1 or 2 out of 5 of the following: *Empirical Rule values *Interpretation of Empirical Rule values *Screenshot of Empirical spreadsheet *Interpretation of Normal Distribution spreadsheet values *Screenshot of probabilities/ percentiles0.0 ptsNo Effort15.0 ptsThis criterion is linked to a Learning OutcomeGrammar and Formatting8.0 ptsLab is easy to read and presents material in a logical order with no grammatical errors.6.8 ptsLab is easy to read and presents material in a logical order. There are a few grammatical errors but they do not distract from readability.5.6 ptsLab is easy to read and has few grammatical errors, but it is not logically organized.4.4 ptsThere are significant grammatical errors and organizational issues that distract from readability.0.0 ptsNo Effort8.0 ptsTotal Points: 50.0