Category: Algebra

Background
The rapid digitization of the business world has paved the way for a multitude of virtual startups. These companies, unhindered by physical infrastructure, leverage wireless internet services to run their operations. Your startup, Tech Solutions, consists of a diverse team scattered worldwide, collaborating on projects, and sharing large files. 
Objective
Your task is to identify the optimal wireless internet plan for the different profiles of users in your team, ensuring cost efficiency without compromising on the needed data. The team profiles are:  
Developers who regularly upload and download large files. 
Designers who utilize heavy graphics software and share high-resolution visuals.
Managers who mainly focus on communication (e.g., emails, video calls).
Sales and Marketing team that often requires a mix of communication tools, media sharing, and heavy browsing. 
Three service providers have put forth their packages: 
Mega Net: $20/month for up to 200 K-bytes. Additional data: $0.16/K-byte. 
Ultra Connect: $50/month for up to 1000 K-bytes. Additional data: $0.08/K-byte. 
Speed Wave: $100/month for up to 3000 K-bytes. Additional data: $0.04/K-byte. 
Tasks: 
(a) User Profiles: Estimate the monthly data usage for each team profile. Make an educated guess and tell which provider you think will eventually be chosen. Justify your assumptions. You will use these estimates to answer part (d). 
(b) Algebraic Models: Develop cost functions, C(x), for each plan based on data usage, x. Each function should be in the form of a piece-wise function. 
(c) Graphical Analysis: Plot the functions for each service provider. Analyze intersections to understand the best plan for different data usage levels. Graphing Utility InstructionsLinks to an external site.
Plotting the Functions:
Create a graph where the x-axis represents the amount of data usage, and the y-axis represents the cost.
For each service provider, there should be a distinct curve or line representing the cost as a function of data usage.
Each curve or line should be labeled or color-coded with a legend to distinguish between the service providers.
The graph should be appropriately scaled and labeled to ensure clarity and accuracy.
Identifying Intersections:
Accurately identify and mark the points where the curves or lines for the service providers intersect.
These intersections represent the data usage levels at which two service providers offer the same price.
Analysis of Intersections:
Analyze each intersection point to determine which service provider offers the best value before and after that data usage level.
For example, if Provider A and Provider B intersect at a certain point, students should be able to state which provider offers the best value for data usage levels below that point and which provider offers the best value for data usage levels above that point.
Implications for Best Plan Choices:
Based on the graph and the intersections, provide insights on which service provider offers the most cost-effective plan at different levels of data usage.
Highlight specific data usage thresholds where one plan becomes more cost-effective than another.
For example, “For data usage below X KB, Provider A is the most cost-effective, but for data usage above X KB, Provider B offers better value.” 
(d) Optimal Plans: Determine which plan is most cost-effective for each user profile based on the estimated data usages from part (a).  
(e) Company Savings: If Tech Solutions consists of 5 developers, 3 designers, 2 managers, and 4 sales/marketing members, calculate the potential savings of choosing the optimal plan for each profile versus the most expensive plan for all. 
(f) Feedback to Providers: Based on your findings, draft a proposal to one of the providers suggesting improvements to their packages to make them more competitive for your startup’s needs. 
Compose your project using MS Word and save as a .docx format. All information should be clear and legible, size 12 font. 
Project 1 Rubric
Project 1 Rubric
Criteria Ratings Pts
This criterion is linked to a Learning OutcomeUser Profiles: Estimate the monthly data usage for each team profile. Make an educated guess and tell which provider you think will eventually be chosen. Justify your assumptions.
15 to >13.0 pts
Meets Expectations
Provides clear and well-estimated monthly data usage figures for each team profile; Offers a robust justification for each assumption made, grounding them in logical or researched reasoning; Demonstrates a deep understanding of the user profiles and how their usage patterns might differ.
13 to >11.0 pts
Approaches Expectations
Provides estimated monthly data usage for each team profile, but some figures may lack precision; Justifies most assumptions, though some explanations might be brief or lack depth; Shows a general understanding of the user profiles but may not fully account for specific nuances in their usage patterns.
11 to >9.0 pts
Below Expectations
Provides estimates for monthly data usage, but several figures are questionable or lack clarity; Offers limited justifications for assumptions, and some may be based on unclear or flawed reasoning; Demonstrates a surface-level understanding of the user profiles with significant oversights in estimating their usage.
9 to >0 pts
Limited Evidence
Fails to provide coherent estimates for monthly data usage or omits several team profiles; Provides minimal to no justification for assumptions or bases them on entirely flawed reasoning; Lacks a clear understanding of the user profiles, leading to largely incorrect or misguided estimates.
15 pts
This criterion is linked to a Learning OutcomeAlgebraic Models: Develop cost functions, C(x), for each plan based on data usage, x. Each function should be in the form of a piece-wise function
15 to >13.0 pts
Meets Expectations
Accurately develops cost functions C(x) for each plan. Each function is correctly structured as a piece-wise function, capturing all pricing tiers and overage costs. Demonstrates a comprehensive understanding of the plan structures and represents them correctly in algebraic form.
13 to >11.0 pts
Approaches Expectations
Develops cost functions C(x) for each plan but may have minor inaccuracies or omissions. Most functions are in the form of a piece-wise function, but there might be slight formatting or structural errors. Generally, understands the plan structures but may miss some subtleties in their algebraic representation.
11 to >9.0 pts
Below Expectations
Attempts to develop cost functions C(x), but there are notable errors or missing elements. Some functions are not in the correct piece-wise structure or contain significant misrepresentations of the plan costs. Demonstrates a limited understanding of the plan structures, leading to flawed algebraic models.
9 to >0 pts
Limited Evidence
Fails to provide coherent cost functions C(x) for the plans or omits significant portions. Does not correctly use the piece-wise structure or misapplies it entirely. Lacks a clear understanding of the plans, leading to largely incorrect or incomplete algebraic models.
15 pts
This criterion is linked to a Learning OutcomeGraphical Analysis: plot the functions for each service provider. Analyze intersections to understand the best plan for different data usage levels.
15 to >13.0 pts
Meets Expectations
Accurately plots the functions for each service provider on a suitable and well-labeled scale. Clearly identifies and marks intersections. Provides a comprehensive analysis of the intersections, correctly interpreting the implications for the best plan choice at different data usage levels.
13 to >11.0 pts
Approaches Expectations
Plots the functions for each service provider but may have minor inaccuracies or scale issues. Identifies intersections, but annotations may lack clarity. Provides an analysis of the intersections but may miss some subtleties in interpreting the best plan choice at specific data usage levels.
11 to >9.0 pts
Below Expectations
Attempts to plot the functions, but there are notable inaccuracies, or the scale is inappropriate. Struggles to correctly identify and mark intersections. Provides a partial or flawed analysis of the intersections and struggles to relate them to the best plan choices.
9 to >0 pts
Limited Evidence
Does not correctly plot the functions for the service providers or omits them entirely. Fails to identify intersections or misidentifies them. Offers little to no analysis of the intersections, and any provided interpretation is largely incorrect or unrelated to the task.
15 pts
This criterion is linked to a Learning OutcomeOptimal Plans: Determine which plan is most cost-effective for each user profile based on the estimated data usages from part (a).
15 to >13.0 pts
Meets Expectations
Accurately determines the most cost-effective plan for each user profile, making full use of the estimated data usages provided in part (a). Provides clear justification for each plan selection, grounding choices in the developed algebraic models. Demonstrates a comprehensive understanding of how data usage impacts plan cost and correctly applies this knowledge to the user profiles.
13 to >11.0 pts
Approaches Expectations
Determines the cost-effective plan for most user profiles, but there might be minor oversights or inaccuracies. Provides justifications for most plan selections, though some might be brief or lack depth. Shows a general understanding of the relationship between data usage and plan cost but may miss specific nuances in cost-effectiveness for some user profiles.
11 to >9.0 pts
Below Expectations
Attempts to determine the most cost-effective plan for user profiles, but several choices are questionable. Offers limited justifications for selected plans, with some explanations based on unclear or flawed reasoning. Demonstrates a limited understanding of how data usage impacts plan cost, leading to significant errors in plan selection for some user profiles.
9 to >0 pts
Limited Evidence
Fails to coherently determine the most cost-effective plans for the user profiles or omits significant portions. Provides minimal to no justification for selected plans or bases them on entirely flawed reasoning. Lacks a clear understanding of data usage implications on plan cost, resulting in largely incorrect or misguided plan recommendations.
15 pts
This criterion is linked to a Learning OutcomeCompany Savings: If Tech Solutions consists of 5 developers, 3 designers, 2 managers, and 4 sales/marketing members, calculate the potential savings of choosing the optimal plan for each profile versus the most expensive plan for all.
15 to >13.0 pts
Meets Expectations
Accurately calculates the total cost of the optimal plan for each profile, considering the number of team members in each category. Correctly calculates the total cost of the most expensive plan for all members. Precisely determines the potential savings between the two scenarios and presents the result clearly.
13 to >11.0 pts
Approaches Expectations
Calculates the total cost for most profiles accurately but might have minor inaccuracies or omissions. Mostly accurate in calculating the total cost of the most expensive plan, with slight discrepancies. Determines the potential savings, but the calculation might have minor errors or lack clarity in presentation.
11 to >9.0 pts
Below Expectations
Attempts to calculate the total cost for each profile, but there are notable errors or missing elements. Significant discrepancies in calculating the total cost of the most expensive plan. Struggles to correctly determine the potential savings, with multiple errors present.
9 to >0 pts
Limited Evidence
Fails to provide coherent calculations for the total costs or omits significant portions. Cannot correctly calculate the total cost of the most expensive plan. Provides minimal to no determination of the potential savings or gets it entirely incorrect.
15 pts
This criterion is linked to a Learning OutcomeFeedback to Providers: Based on your findings, draft a proposal to one of the providers suggesting improvements to their packages to make them more competitive for your startup’s needs.
15 to >13.0 pts
Meets Expectations
Presents a well-structured proposal that clearly addresses specific shortcomings of the chosen provider’s package based on the findings. Provides concrete suggestions for improvements that are aligned with the startup’s needs. Incorporates relevant data and analysis from previous parts to support the recommendations.
13 to >11.0 pts
Approaches Expectations
Presents a proposal that addresses some of the shortcomings of the provider’s package but might lack depth or detail in some areas. Offers suggestions for improvements, though some might be general or not entirely aligned with the startup’s needs. Uses some data and analysis from previous parts but might not fully integrate them into the recommendations.
11 to >9.0 pts
Below Expectations
Attempts to draft a proposal, but it lacks coherence or misses significant elements. The suggestions for improvements are either too vague, not particularly relevant, or lack justification. Limited use of data and previous findings, leading to weakly supported recommendations.
9 to >0 pts
Limited Evidence
The proposal is either extremely brief, largely off-target, or missing entirely. Provides minimal to no meaningful suggestions for improvements. Fails to incorporate any relevant data or findings from previous parts.
15 pts
This criterion is linked to a Learning OutcomeOrganization and Flow
5 to >4.0 pts
Meets Expectations
Cohesive/ Effective organization and flow
4 to >2.0 pts
Approaches Expectations
Adequate organization and flow
2 to >1.0 pts
Below Expectations
There are issues with the organization and flow
1 to >0 pts
Limited Evidence
The organization and flow are unclear
5 pts
This criterion is linked to a Learning OutcomeSpelling and Grammar
5 to >4.0 pts
Meets Expectations
No spelling or grammar errors
4 to >2.0 pts
Approaches Expectations
Spelling and grammar are mostly error-free
2 to >1.0 pts
Below Expectations
There are a few spelling and grammar errors
1 to >0 pts
Limited Evidence
There are many spelling and grammar errors
5 pts
Total Points: 100

To solve the equation 3?3−2?2+7?−5=03×3−2×2+7x−5=0, you can try factoring, but in this case, it doesn’t seem to factor easily. So, you can use numerical methods like the Newton-Raphson method or the bisection method to approximate the roots.

You are a financial advisor helping a client plan for retirement. Your client has a certain amount of money to invest in two different types of investment products: bonds and stocks. The bonds yield a fixed annual return of 4% interest, while the stocks yield a variable annual return of 8% interest. Your client wants to invest a total of $50,000.
Setting up Equations for Investments (15 points):
Define two variables to represent the amount invested in bonds and stocks, respectively.
Write a system of linear equations to represent the total amount invested and the total annual interest earned from both types of investments.
Use the given information to set up the equations.
Solving the System of Equations (20 points):
Solve the system of linear equations using an appropriate method (substitution, elimination, or matrices).
Determine the amount invested in bonds and stocks to maximize the total annual interest earned.
Optimizing the Investment (15 points):
Calculate the total annual interest earned when the investment is optimized.
Discuss the significance of optimizing the investment in terms of maximizing returns for retirement planning.
Linear Programming (25 points):
Formulate a linear programming problem to maximize the total annual interest earned subject to the constraint that the total investment does not exceed $50,000.
Use graphical or algebraic methods to find the optimal solution.
Interpret the solution in the context of the problem.
Reflection (10 points):
Write a reflection on the process of solving the financial planning problem.
Discuss the relevance of systems of linear equations and linear programming in financial decision-making.
Reflect on how this assignment has enhanced your understanding of mathematics in finance.
Submission Guidelines:
Present your solutions in a well-organized format.
Clearly label each step of your calculations.
Submit your assignment as a PDF document, including any necessary graphs or diagrams.

Hello! Please let me know if you have any questions. Attached are the questions on the first page. There is no other necessary materials before starting. Please make sure to have clear handwriting. Make sure the number nine does not look like the letter g. Make sure the variable x looks like an x and not some other type of symbol. Overall, please have neat and legible handwriting. Please only use the indicated methods asked for in the directions. If you have any questions please message me. I will be happy to clear anything up. Their are example problems in the PDF as well, the pages attached have titles at the top to what question they refer to. Again, please feel free to contact me with any questions. MUST complete the problems using the specific method asked. Please refer to other example questions for more guidance, and please solve them the exact way mentioned and showed in the examples.

apply relevant economic principles and formulas to arrive at the solutions. 
algebraic manipulations and understand Keynesian macroeconomic theory required to complete it.
There is no formal word limit.  As is usual for an exam, for this assessment you are not expected to include full referencing, but are
encouraged to cite the sources of key theories, models, case studies, statutes etc . 
This is an individual assessment: do not copy and paste work from any other source or work with any
other person during this exam. Text-matching software will be used on all submissions.
I will include another quesstion that we are required to pick one from. So pick whichever you find you could go more in detail and are able to make it human-like with the solving as well

In a deck of cards, what are the probability of drawing a red card? P(a)= 13/52 -13/13 = 1/4
P(a)=1/4

the material will be in conducting calculations to find the range and standard deviation of several sets of numbers. Additionally, levels of measurements will be revisited in light of applying them to data analysis.

Purpose
The purpose of this project is to assess your ability to:
Collect and display data.
Use Excel.
Calculate and interpret expected value.
Calculate the mean, media, and mode of data sets.
Determine whether data sets are normally distributed.
Apply the Central Limit Theorem.
Summarize and report findings.
OVERVIEW
This module you will turn in the third part of Project 2. This project consists of three parts.
Project 2-1: Identify the Distribution of a Sample – due in Module 9
Project 2-2: Find A Sampling Distribution of Sample Means – due in Module 10
Project 2-3: Final Submission – due in Module 11
Data that follows a normal distribution pattern is predictable and can be used to draw conclusions. However, many data sets do not follow a normal distribution pattern, and a small sample may not follow the normal distribution even if it comes from a normally distributed population. The Central Limit Theorem tells us that the distribution of sample means will not only be normally distributed, but also, if we have enough samples, the sampling distribution will have a mean that is approximately the same as 𝜇, and a standard deviation that is close to 𝜎𝑛.
To see this, let’s continue the experiment using sets of randomly generated integers.
ACTION ITEMS
Open your saved Excel file as submitted for Part 2.
Review your gradebook feedback and make any required corrections to Parts 1 or 2.
Complete the tab labeled “Part 3 – Calculate” by using Excel formulas to do the following:Calculate the mean and standard deviation for each of the 4 data sets from Parts 1 and 2.
Calculate the expected standard deviation of the sampling distribution of the sample means.Note, you may either calculate these directly on this tab using cell references, or calculate these using formulas on your original sheets and copy/paste the values into the designated area of the calculation sheet.
Explain how your graphs tables and calculations of the mean and standard deviations relate to the Central Limit Theorem.
View the Project 2 Final Report Example.Download Project 2 Final Report Example.
Download and complete the Probability Project 2-3 – Final Report.Download Probability Project 2-3 – Final Report.
Submit the completed first draft of your assignment. Your work will automatically be checked by Turnitin.
Access your Turnitin report by reviewing your Submission Details for this assignment. Revise your work as needed based on the feedback.
By the due date indicated, re-submit the final version of your work containing your Final Report and the completed Excel file containing your data and graphs. Note: These items should be submitted at the same time. (If they are submitted separately, any subsequent uploads may override the first submission.)
Rubric
Project 2
Project 2
CriteriaRatingsPts
This criterion is linked to a Learning OutcomePart 1: Random generation of 100 integersGenerate 100 integers randomly using =INT(RAND()*(10)).
Count the frequencies using =countif( and verify the frequency table.
Create a table consisting of expected frequencies and sample(actual) frequencies.
Create a bar chart of the actual frequencies.
Create the expected frequencies (uniform) graph.
5 to >4.0 ptsOne hundred integers were randomly generated correctly using formulas in Excel. The frequencies of each integer (both expected and actual (sample)) are correctly represented in the frequency table. The bar charts of frequencies (both expected and actual (sample)) are accurate. The bar charts have an appropriate title and the axis labels and the x-axis are correct. Improvements were made based on feedback, if applicable.
4 to >2.0 ptsOne hundred (or fewer) integers were randomly generated using formulas in Excel. The frequencies of each integer may not be correctly represented in the frequency table. The bar chart of frequencies may not be accurate. The bar chart may contain errors within the title, axis labels and/or the x-axis. The expected (uniform) bar chart may contain errors. Some improvements may have been made based on feedback.
2 to >0 ptsNo integers were randomly generated or there are major errors in the generation affecting the bar chart and frequency tables. The bar chart, the expected (uniform) graph or frequency table may be missing. Little to no improvements were made based on feedback.
5 pts
This criterion is linked to a Learning OutcomePart 1: Random generation of 1000 integersGenerate 100 integers randomly using =INT(RAND()*(10)).
Count the frequencies using =countif( and verify the frequency table.
Create a bar chart of the actual frequencies.
Create the expected uniform graph.
4 to >3.0 ptsOne thousand integers were randomly generated correctly using formulas in Excel. The frequencies of each integer (both expected and actual (sample)) are correctly represented in the frequency table. The bar charts of frequencies (both expected and actual (sample)) are accurate. The bar charts have an appropriate title and the axis labels and the x-axis are correct. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsOne thousand (or fewer) integers were randomly generated using formulas in Excel. The frequencies of each integer may not be correctly represented in the frequency table. The bar chart of frequencies may not be accurate. The bar chart may contain errors within the title, axis labels and/or the x-axis. Some improvements may have been made based on feedback.
1 to >0 ptsNo integers were randomly generated or there are major errors in the generation affecting the bar chart and frequency tables. The bar chart or frequency table may be missing. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 1: AnalysesWrite two paragraphs comparing
the expected uniform graph to the bar chart of frequencies (n=100) and comparing the graphs of n=1000 to the graphs of n=100.
5 to >4.0 ptsThe analysis for the n=100 case is thorough and accurate. It compares and contrasts the expected uniform graph with the bar chart of actual frequencies. The analysis addresses if the same indicates a uniform distribution. The analysis for n=1000 compares and contrasts the graphs of both cases (n=100 & n=1000). Two additional observations are made. Improvements were made based on feedback, if applicable.
4 to >2.0 ptsThe analysis for both cases is present. There are some errors in the comparisons. Some improvements may have been made based on feedback.
2 to >0 ptsThere are no analysis paragraphs, or one of them is missing. If both are present, there are major errors in both of them. Little to no improvements were made based on feedback.
5 pts
This criterion is linked to a Learning OutcomePart 2: Distribution of Sample Mean n=4Create a data set consisting of 250 samples of size n=4.
Calculate the mean of each sample set of 4 values by using =average(.
Verify the counts in the frequency table by using =countif.
4 to >3.0 ptsThe data set is correct. The mean is correct for each sample set. The frequency table was verified. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsThe data set and means are present, but there are errors with some of them. The frequency table may not have been verified. Some improvements may have been made based on feedback.
1 to >0 ptsThe data set was not created, the means were not calculated, nor was the frequency table verified. If the required parts are present, they contain major errors. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 2: Distribution of Sample Mean n=16Create a data set consisting of 1000 samples of size n=16.
Calculate the mean of each sample set of 16 values by using =average(.
Verify the counts in the frequency table by using =countif.
4 to >3.0 ptsThe data set is correct. The mean is correct for each sample set. The frequency table was verified. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsThe data set and means are present, but there are errors with some of them. The frequency table may not have been verified. Some improvements may have been made based on feedback.
1 to >0 ptsThe data set was not created, the means were not calculated, nor was the frequency table verified. If the required parts are present, they contain major errors. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 2: Analyses of the DistributionsWrite two paragraphs.
For n=4: compare the graph to previous distributions using at least two observations.
For n= 16: compare the graph to previous distributions using at least two additional observations.
4 to >3.0 ptsMeets Expectations
The analyses for both distributions contain the appropriate comparisons including observations. The information is correct and concise. Improvements were made based on feedback, if applicable.
3 to >1.0 ptsThe analysis for both cases is present. There are some errors in the comparisons. Some improvements may have been made based on feedback.
1 to >0 ptsThere are no analysis paragraphs, or one of them is missing. If both are present, there are major errors in both of them. Little to no improvements were made based on feedback.
4 pts
This criterion is linked to a Learning OutcomePart 3: Mean and Standard DeviationCalculate the mean and standard deviation for of the four data sets in Parts 1 and 2.
6 to >5.0 ptsThe means and standard deviations are all calculated and are correct.
5 to >1.0 ptsThe means and standard deviations are all calculated, but contain some errors.
1 to >0 ptsThe means and standard deviations are not calculated, or if they are there are major errors.
6 pts
This criterion is linked to a Learning OutcomePart 3: Expected Standard DeviationCalculate the expected standard deviation of the sampling distribution of the sample means.
3 to >2.0 ptsThe expected standard deviation of the sampling distribution of the sample means is calculated and is correct.
2 to >1.0 ptsThe expected standard deviation of the sampling distribution of the sample means is calculated but is incorrect.
1 to >0 ptsThe expected standard deviation of the sampling distribution of the sample means is not calculated.
3 pts
This criterion is linked to a Learning OutcomePart 3: AnalysisExplain how the graphs, tables and calculations of the mean and standard deviations relate to the Central Limit Theorem.
5 to >4.0 ptsThe analysis includes an in-depth explanation of how the findings related to the Central Limit Theorem. The analysis is thorough and succinct.
4 to >2.0 ptsThe analysis is included, but does not clearly relate the findings to the Central Limit Theorem. The analysis is not thorough and succinct.
2 to >0 ptsThe analysis is not included or if it is, it contains major gaps.
5 pts
This criterion is linked to a Learning OutcomePart 4: IntroductionWrite a brief overview of the purpose of this experiment and what the reader should expect to learn from this report.
3 to >2.0 ptsAn introduction is included. It describes the project and what a reader can expect to learn.
2 to >1.0 ptsAn introduction is included but it does not describe the project or does not describe what a reader can expect to learn.
1 to >0 ptsAn introduction is not included or if included, it contains major gaps.
3 pts
This criterion is linked to a Learning OutcomePart 4: Excel WorkbookFile is complete and submitted.
2 ptsThe Excel file is complete and contains all of the correct information.
1 ptsThe Excel file may not may not be complete or may be complete but has inaccuracies.
0 ptsThe Excel file was not submitted.
2 pts
This criterion is linked to a Learning OutcomePart 4: Graphs and TablesInclude copies of all tables and charts in the report. See the sample report for reference.
2 ptsAll tables and charts are included in the report.
1 ptsSome tables and charts are missing.
0 ptsThe tables and charts were not included in the report.
2 pts
This criterion is linked to a Learning OutcomePart 4: Mechanics
3 to >2.0 ptsBoth report and Excel workbook submitted. Report contains no grammatical or formatting errors.
2 to >1.0 ptsEither report or Excel workbook not submitted. Report contains some grammatical or formatting errors.
1 to >0 ptsReport and/or Excel workbook not submitted. Report contains major grammatical or formatting errors.
3 pts
Total Points: 50
attatched is a sample of what it should look like and also a outline to add answers. thanks so much in advance

Hello! Please let me know if you have any questions. Attached are the questions on the first page. There is no other necessary materials before starting. Please make sure to have clear handwriting. Make sure the number nine does not look like the letter g. Make sure the variable x looks like an x and not some other type of symbol. Overall, please have neat and legible handwriting. Please only use the indicated methods asked for in the directions. If you have any questions please message me. I will be happy to clear anything up. Their are example problems in the PDF as well, the pages attached have titles at the top to what question they refer to. Again, please feel free to contact me with any questions. MUST complete the problems using the specific method asked. Please refer to other example questions for more guidance, and please solve them the exact way mentioned and showed in the examples.

This assignment assesses your skills/knowledge on identifying polynomial and rational functions, the domain, using the graphical representation of these functions, and hence you will study the behavior- discontinuities, increasing, decreasing and extrema.
In real life situations the growth need not be smooth and always increasing or decreasing. The functional values may be having different turnings and may be disappearing at some points. These kinds of situations are represented by polynomial and rational functions. This assignment will enable you to identify such functions and interpret them mathematically and graphically.
You are required to complete all the 5 tasks in this assignment, answer the following questions, and show stepwise calculations. When you are instructed to make a graph in this assignment, please use GeoGebra graphing tool.
Task 1. Interpret the following graph in detail:(I) Identify the turning points, zeros, and x-intercepts.
(ii) Do you find any point or zero which has a multiplicity in the graph? If so, specify them with multiplicity and explain the reason.
(iii) Identify the degree and the polynomial as well as identify the domain in which the polynomial is increasing and decreasing.
(iv) Do we have local maximum/minimum here? If yes, find them.
(v) Find the remainder when the polynomial is divided by x-4.
Task 2. Given a polynomial: f(x) = x4 – 8×3 -8×2 +8x +7
(i)Use rational theorem and synthetic division to find the zeros of the polynomial
(ii) Draw the graph using GeoGebra graphing tool.
(iii) Identify its end behavior
Task 3. Given a function ” src=”https://my.uopeople.edu/filter/tex/pix.php/6a632a9cf828e20f00570b5551673896.png”>
(i) Find the horizontal and vertical asymptotes.
(ii) Find the domain of rational function. Show all steps.
(i) Identify the horizontal and vertical asymptotes (if any). Explain how you would find horizontal and vertical asymptotes of any rational function mathematically.
(ii) Identify the zeros of the rational function.
(iii) Identify the rational function.
Task 5. Before working on this task 5, please read the following reading:
Read page 238 of the following textbook will help you in understanding the concepts better.
Stitz, C., & Zeager, J. (2013). College algebra. Stitz Zeager Open Source Mathematics. https://stitz-zeager.com/szca07042013.pdf
An online courier service is ready to transport a diverse range of items to ensure efficient delivery. The agency requires boxes of various dimensions. Let’s now focus on creating open boxes that have fixed height for storing these items. Take a cardboard of length thrice of the width and cut the edge of all 4 corners with 15cms, then fold the cardboard to get an open box. Based on that information, answer the following questions:
(i) Find the volume of the open box, explain whether the resultant function is a polynomial or any other.
(ii) Find the possible domain for the volume function
(iii) If we wish to put a flexible item that has a volume of 12500 cubic cm, what dimensions of the box would be appropriate?
Submission Settings: Please complete all the 5 tasks in this assignment.
You may use a word document that addresses the questions mentioned above. The word document should be double-spaced in Times New Roman font, which is no greater than 12 points in size.      
Use APA citations and references if you use ideas from the readings or other sources. For assistance with APA formatting, view the Learning Resource Center: Academic Writing. The document should be double-spaced in Times New Roman font, which is no greater than 12 points in size. Use high-quality, credible, relevant sources to develop ideas that are appropriate for the discipline and genre of writing.