Hello Professors! I have attached the Project guidelines. Within the document you will find a list of potential topics to write on, I have chosen #1 Lotteries. Discuss how your state lottery works. For example: On average how many people play each week and how much do they spend? What are the theoretical chances of winning the grand prize and the smaller prizes? Do the theoretical chances agree closely with the observed number of winners? Do the theoretical chances agree closely with the advertised chances? Exactly how are lottery funds distributed? Is there? What are the advantages of an annuity vs. lump sum option for the grand prize winner?” Please make sure you open the PDF so you can read the full project guidlines in terms of detail and how to adress the work. I have also attached the grading rubric so you know what my instructor is looking for! thanks so much. JL

# Category: Mathematics

In your everyday life, you work with mathematical models. The following activity is an example of a scenario that you may encounter. Complete the calculations and submit them to your instructor. Provide reasoning and context to demonstrate how you solved the problem(s).

Scenario

Let’s pretend you have just received a check for $1,500 from a long-lost relative. With this money, you decide that you would like to remodel a room in your home. The room measures 16 feet 6 inches in width by 19 feet 3 inches in length. The height of the ceiling is 8 feet 9 inches. Your plan is to paint every wall and ceiling and buy new carpet for the floor. Assume that there are no doors or windows for ease of calculation.

Convert the length, width, and height measurements to fractional form. Be sure to reduce your fractions.

Convert the fractions you obtained in question 1 into decimals.

Calculate the square footage of your floor.

The carpet comes in rolls of 36 square feet. Calculate how many rolls of carpet will be needed.

Carpet costs $82 per roll. Calculate the cost of the new carpet.

Calculate the total surface area of each wall and ceiling.

Before you paint your walls and ceiling, you decide that you want to use a layer of primer. If a gallon of primer covers 100 square feet, calculate how many gallons of primer you will need to purchase.

A gallon of paint will cover 150 square feet. Calculate how many gallons of paint you will need to purchase to cover each wall and ceiling.

If the primer costs $49.95 per gallon, calculate the cost of the primer needed to cover the walls and ceiling.

If the paint costs $59.95 per gallon, calculate the cost of the paint needed to paint the walls and ceiling.

Calculate the total cost of materials for this project.

Apply a 6% sales tax on the total obtained in question 11.

Questions:

Were you able to come in under budget? If not, how would you be able to modify your plans?

What did you enjoy most about this activity?

How did this activity connect to the weekly material?

Are there any hints or reminders you would provide your fellow classmates if they were to attempt the same activity using an actual room in there home?

Make sure to provide an explanation for each of your responses. Be specific in your discussion.

Statistics can offer us an amazing way to understand our world. But they can also be misleading. It is important to understand how statistics are generated so that you can identify statistics that look reliable, and statistics that do not!

Look up an example of a time when statistics were used by an advertiser, news outlet, politician or other entity to mislead the reader and/or public.

Describe the scenario, the statistic involved, and the specific way the statistics are misleading.

What would be a more appropriate way to present the information, and what would the public likely conclude about the product or situation if the information had been presented appropriately? Must be in APA format and must cite sources.

Gerrymandering is the process of manipulating voting district boundaries in order to favor one particular party or class. Give an example of a case of gerrymandering in the United States.

Present an article, study, or other publication that discusses the use of mathematics to prevent gerrymandering.

In your own words, summarize the article/publication and describe the math (and use of math) involved.

must be in APA format and must cite sources.

You are the CEO of a medium-sized educational nonprofit organization. As is common with nonprofits, employee wages are not the most competitive, so other methods of employee motivation and morale must be fostered. For these reasons, you are interested in finding out if having more servantleadership-minded executives fosters greater workplace spirituality.

You have a hunch that an executive team that aspires towards servant leadership, fosters greater spirituality in the workplace. You also think this is something that is of greater importance for your female managers than for the male managers. You are thinking of sending your top executives through servant leadership training which is costly, and may be faced with resistance by some of them. Further, in the future, you plan to recruit individuals who have experience with and are dedicated to servant leadership. You may also want to make some policy changes to promote greater spirituality in the workplace.

You have identified a study which compared how important servant leadership was to male and female staff at a private non-denominational elementary school. The private school surveyed 40 employees (20 male and 20 female) using a Likert scale asking employees how important spirituality was in the workplace. The scale consisted of:

Not Very Important – Slightly Important – Important – Extremely Important

1 2 3 4

Since you believe in the importance of data-driven decision making, before you make any changes that may be disruptive to the organization’s culture, you conduct some secondary research via fee-based business databases to which you subscribe. You find a great study that helps to inform your problem.

P-value and statistical significance:

The two-tailed P value equals 0.0002

By conventional criteria, this difference is considered to be extremely statistically significant.

Confidence interval:

The mean of Group One minus Group Two equals -1.00

95% confidence interval of this difference: From -1.49 to -0.51

Intermediate values used in calculations:

t = 4.1560

df = 38

standard error of difference = 0.241

INSTRUCTIONS

Summarize the findings from the study:

What do the means between Male and Female suggest?

Is the standard deviation acceptable, or does it make you question the validity of the data?

What does the t-test measure? What do the t-test results suggest?

What are the benefits of conducting research prior to making a leadership decision? Are there times or circumstances under which it would be best to make a decision that is contrary to the research?

Provide an example of a situation in which – as a leader – you might choose to go against the research data.

REQUIREMENTS

APA formatting is required, including title page and reference page.

Minimum citations: 2 citations per part, textbook source = 1 out of total.

Word count: 500-750

According to the 1980 Census, the United States population was approximately 226,540,000 in 1980. It grew to approximately 323,120,000 at the beginning of 2016. Using Census data for 1980 and estimates derived from mortality data for 2016, we arrive at the population estimates given in the table below:

The table below provides the year, total population, and population estimates for three age categories.

Year Total Population Ages 15 – 24 Ages 25 – 44 Ages 45-64

1980 226,540,000 42,475,000 62,707,000 44,497,000

2016 323,120,000 43,500,000 85,150,000 84,300,000

The National Center for Health Statistics published a document entitled “Health, United States, 2015: With Special Feature on Racial and Ethnic Health Disparities” that includes a table listing the leading causes of death in 1980 by age bracket. The CDC further produced a National Vital Statistics Reports that provided similar information for the year 2016.

Using the Causes of Death in 1980 and 2016 spreadsheet located under the Discussion: Causes of Death in 1980 and 2016 Resources, you will find the leading causes of death in both 1980 and 2016 for the three age categories. Each of the first 3 questions has both a computational part and a discussion part. To get full credit for each of the discussion parts, please cite a reference to support your claims. This should not be an excessively difficult task: you can easily find information online for most of the illnesses or other causes listed in the report. All you need to do is provide the website you used (though other resources are also permitted if you prefer to use one of those).

Assuming that the population numbers in the above table are relatively accurate, use the Causes of Death in 1980 and 2016 spreadsheet to compute the deaths per 1000 people for each age group in both 1980 and 2016.

Deaths per 1000 people is computed using the formula

Deaths per 1000 = (# of deaths) / (total population of age category)

Do not round your answer to the nearest whole number, provide at least 3 decimal places (but no more than 5).

Give these 6 values (e.g. deaths per 1000 people for ages 15–24 in 1980) and then cite a reference to discuss what might account for the changes between the deaths per 1000 in 1 of these 3 age categories between 1980 and 2016.

Besides the changes in the overall death rate in the past 3 decades, the leading causes of death vary somewhat between 1980 and 2016. Choose 1 of the 3 age ranges and select 1 cause of death from the Discussion Data spreadsheet that strikes you as noteworthy and that appears in both the 1980 and 2016 lists. For the cause of death that you selected, compute the number of deaths per 1000 in both 1980 and 2016 for your chosen age group. Do not round your answer to the nearest whole number, provide at least 3 decimal places. Cite a reference to discuss the possible reasons for any changes in the rates over this period.

Not only do the leading causes of death vary across time, but they also vary significantly for different age ranges. Looking only at the 2016 data, choose a cause of death that appears in both the 25–44 and 45–64 age categories and compute the number of deaths per 1000 people for both age categories. Do not round your answer to the nearest whole number, provide at least 2 decimal places. Cite a reference to discuss a possible reason for any differences in these values as people advance in age.

Contemplating causes of death might strike some people as unpleasant or even morbid. However, the Bible encourages us to give some thought to the fact of our own mortality. Ecclesiastes 7:2–4 says: “It is better to go to the house of mourning than to go to the house of feasting, for this is the end of all mankind, and the living will lay it to heart. Sorrow is better than laughter, for by sadness of face the heart is made glad. The heart of the wise is in the house of mourning, but the heart of fools is in the house of mirth.” It is interesting to consider why the author of Ecclesiastes encourages the wise to go to the house of mourning and the living to lay the end of all mankind to heart. What value might there be in thinking about the, admittedly uncomfortable, subject of the end of all mankind? What comes to your mind when you consider this topic?

Define the term “standard deviation”. Why is it important to know the standard deviation of a data set and understand how to use it as a tool to compare two different sets of data?

Research and identify an article related to your research topic of interest that discusses standard deviation.

Share a summary of the standard deviation results.

Is the standard deviation acceptable such that the findings are deemed reliable? Why or why not?

Curve-fitting Project – Linear Model

Instructions

For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r2 (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below.

A Linear Model Example and Technology Tips are provided in separate documents.

Tasks for Linear Regression Model (LR)

(LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label appropriately. (Highly recommended: Post this information in the Linear Model Project discussion as well as in your completed project. Include a brief informative descriiption in the title of your posting. Each student must use different data.)

The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the project, and your posting provides an opportunity for some feedback. Remark: Students may choose similar topics, but must have different data sets. For example, several students may be interested in a particular Olympic sport, and that is fine, but they must collect different data, perhaps from different events or different gender.

(LR-2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.)

(LR-3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line.

(LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two.

(LR-5) Find and state the value of r2, the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?

(LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.

(LR-7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting.

You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.

Here are some possible topics:

Choose an Olympic sport — an event that interests you. Go to https://www.olympic.org/olympic-results and collect data for winners in the event for at least 8 Olympic games (dating back to at least 1980). (Example: Winning times in Men’s 400 m dash). Make a quick plot for yourself to “eyeball” whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different event.) After you find the line of best fit, use your line to make a prediction for the next Olympics (2014 for a winter event, 2016 for a summer event ).

Choose a particular type of food. (Examples: Fish sandwich at fast-food chains, cheese pizza, breakfast cereal) For at least 8 brands, look up the fat content and the associated calorie total per serving. Make a quick plot for yourself to “eyeball” whether the data exhibit a relatively linear trend. (If so, proceed. If not, try a different type of food.) After you find the line of best fit, use your line to make a prediction corresponding to a fat amount not occurring in your data set.) Alternative: Look up carbohydrate content and associated calorie total per serving.

Choose a sport that particularly interests you and find two variables that may exhibit a linear relationship. For instance, for each team for a particular season in baseball, find the total runs scored and the number of wins. Excellent websites: http://www.databasesports.com/ and http://www.baseball-reference.com/

Part 1 – Artwork (14 marks) Your artwork must adhere to the following guidelines: 1. You are required to use Desmos (https://www.desmos.com/calculator) to create a piece of artwork. 2. The artwork must be present in all four quadrants. 3. You must use at least one of each of the following graphs (parabolas, hyperbolas, circles, cubics and exponentials). 4. A variety of colours may be used. 5. All lines and curves must be created using Desmos and mathematical equations. Do not include pictures or words. 6. While there is no limit to the number of graphs that can be used to create the artwork, a sensible number should be employed to make creating and assessing manageable 7. Ensure the x and y axes are shown with a scale on each axis and the gridlines are visible. Below is a template that should be filled in regarding the graphs being used. You must choose at least 10 different types of graphs and describe the parent function, the translations, reflections and dilations that have been made to create your graph, and then a brief summary of why you made the changes and how it affects your artwork. b) Find two of your graphs that intersect. Use simultaneous equations to solve for the point of intersection. (It is advised that these graphs are parabolas or straight lines.) c) Look at your parabola. Verify using algebra (using either factorisation / quadratic formula /completing the square) that the x-intercepts (or potential x-intercepts) match the x-intercepts in your artwork. If your parabola does not cross the x-axis, your working out should verify this. d) Choose one graph. Verify using algebra that the y-intercept matches the y-intercept in your artwork.

You will be representing a map by a graph and finding the coloring of the graph that uses the fewest number of colors. Complete the following tasks: Part 1: Find the county map of New Hampshire and create a graph that represents it. Counties should be represented as the vertices and the edges should be drawn between them when two counties share a border. Determine if your graph is 2-colorable, 3-colorable, or 4-colorable. Discuss how you found your answer to part (b) and what real-world applications there might be for your findings. Part 2: Draw a map of a fictional state consisting of four counties that is 3-colorable. Discuss your method for creating the map in part (a). Be sure to explain how you verified that your map is indeed 3-colorable. Additional Requirements: The paper must be written in 3rd person. Cite and integrate at least one credible outside source. Your textbook is a credible resource. Include a title page, introduction, body, conclusion, and a reference page. Be sure this is in paragraph format, not numbered answers like a homework assignment.