Category: Mathematics

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I need chapter 10 to be completed the test and also my final. I also need the notes by Monday because my last day of class is Tuesday and I need to submit the notes by Monday.

3 assignments. Need by end of day today or tomorrow if possible. Please let me know price and how many assignments you can do. Thanks!

Assignment 1 :Discussion Post
In this assignment, you will acquire the skills and knowledge to identify logarithmic and exponential functions.
Up to this point, in your exploration of higher-order polynomials, you’ve likely grasped that these functions don’t consistently exhibit linear growth or decay. Instead, their growth or decline can manifest in diverse patterns. You can gain a deeper understanding of these varied growth and decay phenomena through the lens of exponential and logarithmic functions. You will understand the applications of these functions in practical situations, including the growth of populations, compound interest, radioactive decay, and in pH levels in chemical solutions, etc.
You are required to complete all questions in this assignment, answer the following questions, and show stepwise calculations.
Task 1. 
Earthquakes are complex phenomena, and we do not intend to provide an exhaustive discussion of the scientific principles behind them. We will present a simplified explanation of the Richter scale, The Richter scale measures the magnitude of an earthquake by comparing the amplitude of the seismic waves of the given earthquake to those of a “magnitude 0 event”, which was chosen to be a seismograph reading of 0.001 millimeters recorded on a seismometer 100 kilometers from the earthquake’s epicenter.
Specifically, the magnitude of an earthquake is given by 
where x represents the seismograph reading in millimeters of the earthquake recorded 100 kilometers from the epicenter.
Using the above data, answer the following questions:
(a) Calculate the earthquake reading on the seismograph (using the M(x) function) when the magnitude of earthquake on the Richter scale 7.7 and 5.7. Compare the readings and conclude on the magnitudes of earthquakes based on the calculations obtained for both scale readings.
(b) In finding the magnitude of the earthquake, the experts have used the logarithmic function. In your opinion, discuss why this logarithmic function is used in describing this situation, and why not any other polynomial or exponential function used in describing the earthquake situation.
(c) Locate a new article discussing a recent earthquake in your country providing Richter scale magnitudes (You can also use an article that discuss country close to yours if there hasn’t been an earthquake in your country recently). Determine the seismograph reading by the magnitude of the earthquake registered in your country. Discuss the situation in brief. 
Your Discussion should be a about 250 in length. Please include a word count. Following the APA standard, use references and in-text citations for the textbook and any other sources
Assignment 2: Math assignment
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).
Submission Settings: 
Please complete all the 3 tasks in this assignment.
You may use a word document that addresses the questions mentioned above. Read the rubric on how you are going to be graded on this assignment.    
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.    
PLEASE COMPLETE THE 2 ASSIGNMENTS SEPARATELY ( SEPARATE DOCUMENTS)WITH  A REFERENCE PAGE ON BOTH OF THEM. THEY WON’T BE HANDED IN TOGETHER.

Assessment task: An essay EITHER on a mathematical topic of your choice, OR on one of the designated essay topics; see below.
Designated Essay Topics:
Note that our advice and the Criteria for Marking apply to these topics exactly as they do to the choose-your-own topics. In particular, there is room to move in the topics below, and you are permitted to and must choose a suitably narrow aspect of the topic, which will permit you to focus. Try to get properly into the ideas, and read properly scholarly articles so you can do so. A thin overview based on slight rewording of Wikipedia pages will not score well. No particular references are suggested: it’s part of your job to hunt. But if you are really stuck, you can ask for advice. 
My chosen topic  Why are soap bubbles round?
Word limit: 1500 +/- a little.
The essay should be approximately 1500 words, excluding the references. You should have a title page, which includes a word count (and your name and student number!). We are not overly fussy about the word count, but if you are edging over 1700 words, then that is probably excessive. In the other direction, you will find that 1500 words is really not a lot, and it is difficult to stay under 1500 words. Below 1400 words suggests a pretty thin essay.
Generative AI tools cannot be used in this assessment task
POINTERS TO WRITING A GREAT MATHS ESSAY
Pointer Number 1: Do not be boring
The world is flooded with bad mathematics and science writing: don’t add to the flood. Try to choose a topic that genuinely interests you and that you’d genuinely like to learn more about. Then, your enthusiasm can come through in the essay.
Your essay can be along the lines of a mathematical exposition or it can be more philosophical in nature. In any case, your goal is for your essay to be clear and engaging for non-experts. Think of your audience as your fellow Nature and Beauty students; your aim is to explain some cool mathematics in a manner enjoyable to them. 
Pointer Number 2: Do not be too technical
Yes, Marty will be able to understand the technicalities and jargon, but Marty is not your audience. Write for your fellow students, and if you need to take time to gently explain some ideas or language, then do so. 
Pointer Number 3: Avoid trendy and done-to-death and lecture topics
The world is full of pseudomathematics, so be careful to avoid such topics, or approach them with a very critical eye. Past essays on fractals, chaos, the golden ratio, sports, Rubik’s cube, RSA and music have tended to be poor and to have scored poorly. If you suggest a topic along these lines it may well be rejected, and you’ll have to think again. If in doubt, just ask me or Marty.
Pointer Number 4: Choose a small topic
1500 words is not a lot, particularly when you have to explain technical concepts to a non-expert reader. It is much better to choose a very small topic and to explore it properly than to give a sky-high overview of some large terrain. Make every word count. 
Pointer Number 5: Wikipedia is a good place to start and a bad place to end
General resources such as Wikipedia are great places to get going, but you’re aiming for something a lot more interesting and original than a reproduction of Wikipedia. Electronic databases such as Jstor (available via Monash library) are much better resources.
Popular maths books and articles, and the references they contain, are also a good place to get going. There are many such books, and many are very good. Some of our favourites are 
*) The Heart of Mathematics: An Invitation to Effective Thinking by M. Starbird and E. Burger, 
*)The Parsimonious Universe by S. Hildebrandt and A. Tromba, 
*)The Shape of Space by Jeffrey Weeks, Why do buses come in threes by Rob Eastaway and Jeremy Wyndham, 
*) Anything by Martin Gardner
*) The archive of Function magazine.
Pointer Number 6: Choose clear and sensible style and formatting
The essay must be typed, and you must include a full list of references and reasonable footnoting, but other than that the format is largely up to you. Just try to be clear. Headings and subheadings are very helpful. Diagrams – hand-drawn is fine – are very helpful (and they don’t contribute to the word count!) Boldface and italics and colours are good.
A good format to keep in mind is that of an article written for Plus magazine. Also, check out Burkard and Marty’s past maths column for The Age. 
Pointer Number 7: Be accurate
Needless to say, everything you write should be correct (not only the individual facts, but also the logical arguments that connect them!). Before you hand in your masterpiece, you should have at least two thoughtful friends proofread it and provide you with feedback. Even if your native language is not English I expect you to produce an essay that is grammatically correct. Use a spellchecker to weed out spelling mistakes.
Pointer Number 8: Enjoy it!
Writing a very good mathematics essay is not easy. It is a lot of work. But it can also be really rewarding, to figure out how some piece of mathematics works so well that you can explain it to basically anybody. If you are doing it right, the essay should be tiring but a lot of fun.
The maximum number of marks for the essay will be 32. Deductions from these 32 marks are based on the rough essay rubric reproduced below. In general, it is comparatively easy to avoid deductions in terms of “clarity” and “nuts and bolts”. It is harder to avoid deductions in terms of “making sense”. It is VERY hard to avoid deductions in terms of maths and originality, particularly for the designated essay topics.
The only way anybody will get full marks for their essay is if we consider it to be publishable in a magazine like New Scientist or the Plus magazine website.

Complete the following:
Research applications of logarithmic functions as mathematical models. Some ideas include but are not limited to: pH (acidity of solutions), intensity of sound (decibels), brightness of stars, human memory, progress over time in a sport, and profit over time. Choose an area of interest from above or provide one of your own, and explain how logarithmic functions are used.
Provide at least one example. The initial post of your discovery should be at least 250–500 words in length. Use current APA format to cite your sources (e.g., from library books, textbooks, and the Web). Your post must contain some of your own thoughts and reactions, in addition to any citations you make.

Pick ONE of the problems from this collection “Advanced Functions Questions” that has not already been solved. Pretend that you are tutoring someone who has never seen these problems before and give a detailed demonstration of its solution.
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate. The math problem that needs to be solved is in the photo attached and the answer is aswell

i have a bunch of precal quizzes that need to be done before may 8 at 11:59pm. questions are similar to the one below.

Dr. Megan Zobb, a key researcher within the North Luna University Medical Center, has been studying a new variant of a skin disease virus that seems to be surfacing among the North Luna University population. This variant (which has been tentatively named Painful Rash or PR), leads to the formation of surface lesions on an individual’s body. These lesions are very similar to small boils or isolated shingles sores. These PR lesions are not necessarily clustered as shingles lesions but are isolated across the body.
Insights From Initial Interviews
Megan is initiating some efforts at a preliminary analysis. She has seen 20 initial patients and made several observations about the skin disease. She wants to analyze this initial data before structuring and recommending a more encompassing study.
The signs and symptoms of this disorder usually affect multiple sections of the patient’s body. These signs and symptoms may include:
Pain, burning, numbness, or tingling, but pain is always present.
Sensitivity to touch.
A red rash that begins a few days after the pain.
Fluid-filled blisters that break open and crust over.
Itching.
Some people also experience:
Fever.
Headache.
Sensitivity to light.
Fatigue.
Pain is always the first symptom of PR. For some, it can be intense. Depending on the location of the pain, it can sometimes be mistaken for a symptom of problems affecting the heart, lungs, or kidneys. Some people experience PR pain without ever developing the rash. The degree of pain that the individual experiences is seemingly proportional to the number of lesions.
Dr. Zobb is extremely concerned that this new variant is especially challenging to the younger population, who are active and like to be outdoors. She has asked you as an analyst and statistician for some assistance in analyzing her initial data. She is not a biostatistician, so she requests that you explain the process you use and your interpretation of the results for each task.
Initial Data Analysis
Dr. Zobb has accumulated some data on an initial set of 20 patients across multiple age groups. She believes that the data suggests younger individuals are affected more than others. She wants you to complete the tasks shown here based on the data below.
For each of the following, provide a detailed explanation of the process you used along with your interpretation of the results. Submit the response in a Word document and attach your Excel spreadsheet to show your calculations (where applicable). Be sure to number each response (e.g., 1.a, 1.b,…).
Develop an equation to model the data using a regression analysis approach and explain your calculation process in Excel.
Calculate the r-square statistic using Excel. Interpret the meaning of the r-square statistic in this case.
Determine three conclusions that address the initial observations and are supported by the regression analysis.
Regression Analysis Initial Data
Patient Number  Age of Patient  Number of Lesions
1 24 16
2 63 7
3 45 12
4 17 24
5 21 20
6 72 4
7 32 13
8 36 16
9 26 21
10 47 10
11 31 15
12 23 18
13 51 8
14 24 22
15 26 18
16 25 19
17 31 12
18 19 29
19 18 25
20 21 17
Effects of Sunlight Analysis
In her initial observations, Dr. Zobb notices that the number of lesions that appear on a patient seems to be dependent on the amount of direct sunlight exposure that the patient receives. She is uncertain at this point why this would be the case, but she is a good experimentalist and is trying to establish some observations that have statistical validity. She has taken a limited amount of data on 8 patients and wants you to complete the appropriate analysis based on the data below (be sure to show your work):
Develop an equation to model the data using a regression analysis approach and explain your calculation process, using Excel.
Megan has a small group of three additional patients that are the same age that she wants to examine for lesions. She knows the number of minutes of continuous exposure to direct sunlight that each has experienced. Predict the number of lesions that each of these patients will have based on the regression analysis that you completed in your initial data analysis:
Patient 9 – 193 minutes.
Patient 10 – 219 minutes.
Patient 11 – 84 minutes.
Determine three conclusions based on the correlation of the number of lesions to minutes of sunlight exposure, using regression analysis.
Sunlight Exposure Regression Data
Patient Number Time of Continuous Exposure to Direct Sunlight(Minutes) Number of Lesions
1 225 24
2 184 16
3 220 20
4 240 26
5 180 14
6 184 16
7 186 20
8 215 22
Over-the-Counter Medication Effectiveness Analysis
Dr. Zobb wants to test several over-the-counter lotions—that is, lotions available without a prescription—that can be applied directly to the lesions. She wants to determine whether there is a difference in the mean length of time it takes these three types of pain lotions to provide relief from the pain caused by these lesions. Megan is hoping that one of these lotions might be more promising than the others. Several sufferers (with roughly the same number of lesions) are randomly selected and given one of the three medications. Each sufferer records the time (in minutes) it takes the medication to begin working. The results are shown in the table below. She asks you to answer these questions (be sure to show your work).
State the null hypothesis and the alternative hypothesis for this situation.
At α = 0.01, can you conclude that the mean times are different? Assume that each population of relief times is normally distributed and that the population variances are equal. Hint: Use a one-way ANOVA to solve this problem. Be certain to show your calculations and describe the process you used to solve this problem.
Determine three conclusions on the effectiveness of the medication by addressing observations or hypotheses regarding these initial tests.
Effectiveness of Over-the-Counter Medications
Medication 1 (Minutes) Medication 2 (Minutes) Medication 3 (Minutes)
12 16 14
15 14 17
17 21 20
12 15 15
19
Summary of Data Analysis
Now that you have all of your data analysis:
Provide a three-paragraph summary of the findings you learned through the analysis.
Provide three data-driven suggestions for further exploration.

PROJECT – DESCRIPTION
The project contains two parts. Please complete both parts and upload the full project in Canvas by 4/23/24.
Do an internet and library search and then describe/critique at least four types of mortgages in your own words. Please describe any necessary conditions a borrower should meet to apply for them.  The project must include the headings given in the rubrics below and at least two references from the internet. It can be hand-written or typed with double space and a 12-size font and should be at most four pages.
Rubrics: 
Names of the mortgages: 2 pts
Description of the mortgages: 4 pts
Which mortgage do you think is the best and why: 2 pts.
References: 2 pts
You must follow the following Submission Format.
Format for question a:
Title: Names of the mortgages
Answer: ………………………………..
Format for question b:
Description of mortgages
Description …………………………………………………………, and so on for the remaining parts.
Write down the Binomial Probability Formula and define all the terms in it.  And then solve the following problem using the formula.
A family has five children. The probability of having a girl is (1/2).  What is the probability of having exactly 2 girls and 3​ boys? (Give your answer to four decimal places.)
Rubrics:
Binomial Probability Formula:2 pts.
Definition of terms in the formula: 2 pts.
Calculating the probabilities of success (p) and failure (q) in the formula: 2 pts.
Solution and Final Answer: 4 pts.