Category: Algebra

Solution: Rearranging terms, we have:
12m2 – 4m2 + 5m – 9m – 7m + 10
= (12 – 4) m2 + (5 – 9 – 7) m + 10
= 8m2 + (– 4 – 7) m + 10
= 8m2 + (–11) m + 10
= 8m2 –11 m + 10

Solution: Rearranging terms, we have:
12m2 – 4m2 + 5m – 9m – 7m + 10
= (12 – 4) m2 + (5 – 9 – 7) m + 10
= 8m2 + (– 4 – 7) m + 10
= 8m2 + (–11) m + 10
= 8m2 –11 m + 10

In a company of CE, ME and EE, the sum of their ages is 2160 and ave is 36. The average age of CE and ME is 39, of CE and EE is 110/3 and EE &ME is 360/11. If the ages of CE is increased by 1 of ME is increased by 6, and of EE increased by 7, the average of all their ages increased by 5. How many CE are there?

In your own words, write two arguments , one that is valid and one that is not valid. Make sure not to specify which is argument is valid.
EXAMPLE:
Hi Class,
I wanted to share how we write arguments using symbols, and how it can be made clear when an argument is valid or not.
Here’s an example:
Cats don’t like swimming. Tom does not like swimming. Therefore, Tom is a cat.
To write the argument using logic symbols:
Let c = being a cat
s = like to swim
T = being Tom
So, the argument “Cats don’t like swimming. Tom does not like swimming. Therefore, Tom is a cat” would be written:
?⟶∼? (If you’re a cat, then you don’t like swimming.
?⟶∼? (If you’re Tom, then you don’t like swimming.)
____________
∴T⟶? (Therefore, if you’re Tom, then you are a cat.)
So, we know only 1 thing about Tom, that Tom doesn’t like swimming.
And, we know only 1 thing about cats, that cats don’t like swimming.
We have not proven that Tom is a cat! It is possible that some people (and dogs and pigs, etc.) don’t like swimming…

Please use the assignment to submit your first project.
If your project was done in class, please submit an explanation.
Please detail what sections in the book your project covered and what you learned by working on your project.
Description
Projects can take various forms, such as Zines, lecture videos, exams with solutions manuals/grading rubrics, and more. These projects allow you to demonstrate your mastery of the material in ways that suit your learning style.
Zines: Create a visually engaging zine that explains key concepts from a selected section. Use illustrations, diagrams, and concise explanations to convey the material.
Lecture Videos: Develop a series of short lecture videos covering specific topics within a section. Explain concepts, provide examples, and guide viewers through problem-solving. (Most strongly recommended)
Exams with Solutions Manuals and Grading Rubrics: Design a comprehensive exam that tests understanding of a particular section. Include a solutions manual with detailed explanations and a grading rubric for self-assessment. (Strongly recommended)
Interactive Online Modules: Create interactive online modules using platforms like HTML, CSS, or JavaScript. Include animations, quizzes, and simulations to illustrate concepts from various sections.
Graphical Representations: Develop graphical representations, such as infographics or posters, to visually explain the relationships and applications of concepts within a section.
Educational Board Games: Create an educational board game centered around calculus concepts. Include rules, game pieces, and questions that reinforce learning through play. (Strongly recommended)
Peer Teaching Sessions: Organize and lead a peer teaching session on a specific topic. Prepare materials, examples, and engage your classmates in the learning process. (Strongly recommended)
Mathematical Modeling Project: Develop a mathematical model for a real-world problem, applying the principles of calculus. Present your model, assumptions, and conclusions. (Strongly recommended)
Data Analysis Project: Collect and analyze data, applying calculus concepts to draw conclusions. Present your findings and explain how calculus contributes to the interpretation of data.
Artistic Expression: Express calculus concepts through art, whether it’s through paintings, sculptures, or digital art. Use creativity to convey mathematical ideas.
Programming Project: Develop a computer program or script that simulates a calculus concept. Showcase your coding skills in solving mathematical problems. (Strongly recommended)
Effort
An individual project should take you about 1 day of work (3-6 hours). If a project takes more work, please let me know and we can consider counting it for more.
Sharing
Your project will require a presentation unless it is a video. Also, all projects will be shared with the class.
Examples
Here is a great video explaining one of the more interesting topics later in the semester.

Second, here is a more fun and creative project.

This assignment serves as an opportunity to assess your ability to identify exponential and logarithmic functions. Among the various functions you’ve studied, exponential and logarithmic functions hold particular significance when it comes to representing practical situations marked by non-linear and rapid changes. Recognizing logarithms as the inverse of exponential functions will enable you to solve equations involving exponential functions using logarithmic properties.
Within this assignment, you will delve into the properties of logarithms and acquire the skill to express scenarios using either exponential or logarithmic functions.
You are required to complete all the 3 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 for drawing the graphs.
Task 1.
Please answer the following questions related to exponential and logarithmic functions:
(i)What are exponential and logarithmic functions? How are they related? What are their key factors (Explain the variables used in the definitions of these functions)? Discuss their domain and range.
(ii) What is the difference between exponential, logarithmic, and power functions? Provide one mathematical example for each and illustrate the differences of growth patterns and any special points (such as asymptotes, intercepts, and zeros), if applicable. Graph the examples.
(iii)How to explain if a function has exponential growth?
(iv)Between exponential and logarithmic functions, which one grows faster? Provide an explanation for your answer.
(v) Write the observations of growth patterns and special points (if any) by drawing the graphs for the examples given
Task 2. Before working on task 2, please read the following reading: 
Reading section 4.1- Exponential Growth and Decay of the following textbook will help you in understanding the concepts better.
Yoshiwara, K. (2020). Modeling, functions, and graphs. American Institute of Mathematics. https://yoshiwarabooks.org/mfg/frontmatter.html
Write the logarithmic properties at each step to solve the following questions:
(i) Simplify using logarithmic properties,
(ii) Condense the complex logarithm into single term
(iii) Solve:
Task 3. A research laboratory has been conducting experiments on the rapid increase of cancer cells in an animal. They have observed that cancer cell growth increases by 2% every year with certain medication. Initially, in the year 2018, there were 232.26 units of these cells in the animal.
Using the above data, answer the following questions:
(i) Create a table to illustrate the yearly increase in cancer cells up to the year 2023.
(ii) Examine the table of values and identify the mathematical function that represents this growth pattern, specifying the key factors of the mathematical function.
(iii) Utilize this mathematical function to project the level of cancer cells in 10 years, assuming the growth rate continues at the same pace.
(iv) Illustrate the growth pattern by plotting a graph (Take scale 100units on X and Y-axes).

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.

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.

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

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