In how many ways can you cover a 2 × n chessboard by 2 × 1 dominoes (placed horizontally or vertically)? Find a recurrence relation and initial values.

Discrete Mathematics

Homework 7

Solve the following problems. Justify your answers. Solutions without justification will
not receive full credit.

1. How many binary strings of length n do not contain 10?

2. Find a recurrence relation for the number of length-n ternary strings (strings using values 0, 1, 2) without two consecutive 0s.What are the initial values?

3. In how many ways can you cover a 2 × n chessboard by 2 × 1 dominoes (placed horizontally or vertically)? Find a recurrence relation and initial values.

4. How many subsets are there of the set {1, 2, . . . , n} that DO NOT contain three consecutive integers? Find a recurrence relation and initial values.

5. Which is larger 2100 or F100?

6. Use induction to prove
F2 + F4 + F6 + ···+ F2n= F2n+1 −1.

7. Prove (without using induction)
F 2n+1 −F 2n= Fn−1Fn+2.

How can you use probability and probability rules in arriving at the answer?What probability ideas does this demonstrate and use?

PROBABILITY PROJECT

The purpose of this Probability Project is to show your understanding of what you have learned in Module 3. You will watch a video and apply the appropriate probability concepts from this module. You will discuss your learnings in a 2-page paper as outlined below.

Instructions

This is a fun assignment to do. In chapter 5 you learned about basic probability and learned about conditional probability. Now, you get to see these two in action. You may have heard of the TV game: “Let’s Make a Deal,” where at the end of the show, contestants are presented with 3 doors and they are informed that behind one of the doors is a brand-new car. So, the contestant chooses one of three doors. Then the game show host (First one was Monty Hall), opens a door and reveals a goat. Then Monty asks if the contestant wants to switch or not. So, the question is, what is the probability of winning? Should stay, or should switch? What would you do?

Imagine that the set of Monty Hall’s game show Let’s Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn’t hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors. After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch? Think about what you think the answer is: stay or switch?

1. Watch a TEDEd video that explains the problem: “Should stay or should switch doors?”

2. Write a paper that includes:

What did you think the probability of winning the car was, before you watched the video? (3 points)

Information from the video what the answer really is (3 points)

How can you use probability and probability rules in arriving at the answer?What probability ideas does this demonstrate and use? Explain and give examples. You may use other sources as well but make sure to cite them (you may want to watch the extended version of the video if you are not sure, watch the Monty Hall Problem video. (15 points)

Are you surprised by the answer to the question “stay or switch”? Does it make sense? (3 points)

2 pages long, using size 12 font, double spaced, cover page, references included. (3 points) References Should I stay or should I switch doors? (n.d.). Retrieved from https://ed.ted.com/featured/PWb09pny

Explain the difference between joint(nonexclusive) events and disjoint(mutually exclusive) events.

Writing Assignment I MAT181

DUE (Midterm Exam Day)

Chapter 4

1. Explain the meaning of “Event with equally likely outcomes”. (4pts)

2. Explain the difference between joint(nonexclusive) events and disjoint(mutually exclusive) events. (4pts)

3. Explain the difference between P(A) and P(A|B). What does it mean if they are equal in value? What does it mean if they are unequal in value? (4pts)

4. Explain the difference between P(A|B) and P(B|A). Must they be equal in value? (4pts)

5. Explain the difference between Permutation and Combination. (4pts)

Chapter 5

1. Explain what a discrete random variable is. List examples.(4pts)

2. What are the requirements for a discrete probability distribution? (4pts)

3. Explain what binomial probability distribution is.

Explain the difference between descriptive statistics and inferential statistics.

Writing Assignment I MAT181

DUE (Midterm Exam Day)

For each Chapter, answer each question in your own words using no more than 2-3 properly constructed sentences (correct grammar, punctuation, spelling, etc.).

Be sure to include support for any “choice” answers. Use declarative sentences, citing factual information based on definitions, procedures, etc.

Chapter 1

1. Explain the difference between a population and a sample (from a statistical point of view). (4pts)

2. Explain the difference between quantitative variable and qualitative variable. (4pts)

3. Explain the difference between descriptive statistics and inferential statistics. (4pts)

Chapter 2

1. For a dataset, without constructing of the frequency distribution table; how to obtain the class width of frequency distribution table if the number of classes is given? (2pts)

Note: Use the formula in the slides; here frequency distribution table is not provided.

2. Explain the difference between a frequency distribution table and a relative frequency distribution table (4pts)

Chapter 3

1. Explain the difference between mean and median. Is mean always larger than median? (4pts)

2. Explain the difference between μ and x . How do you determine which is appropriate to use in a problem? (4pts)

3. Explain the difference between σ and s. How do you determine which is appropriate to use in a problem? (4pts)

4. What is the relationship between variance and standard deviation?

What did you think the probability of winning the car was, before you watched the video?

PROBABILITY PROJECT

The purpose of this Probability Project is to show your understanding of what you have learned in Module 3. You will watch a video and apply the appropriate probability concepts from this module. You will discuss your !earnings in a

2-page paper as outlined below.

Instructions

This is a fun assignment to do. In chapter 5 you learned about basic probability and learned about conditional probability. Now, you get to see these two in action. You may have heard of the TV game: “Let’s Make a Deal,” where at the end of the show, contestants are presented with 3 doors and they are informed that behind one of the doors is a brand-new car. So, the contestant chooses one of three doors. Then the game show host (First one was Monty Hall), opens a door and reveals a goat. Then Monty asks if the contestant wants to switch or not. So, the question is, what is the probability of winning? Should stay, or should switch? What would you do?

Imagine that the set of Monty Hall’s game show Let’s Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn’t hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors. After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch? Think about what you think the answer is: stay or switch?

1. Watch a TEDEd video that explains the problem: “Should stay or should switch doors?”

2. Write a paper that includes:

What did you think the probability of winning the car was, before you watched the video? (3 points)

Information from the video what the answer really is (3 points)

How can you use probability and probability rules in arriving at the answer? What probability ideas does this demonstrate and use? Explain and give examples.

You may use other sources as well but make sure to cite them (you may want to watch the extended version of the video if you are not sure, watch the Monty Hall Problem video. (15 points)

Are you surprised by the answer to the question “stay or switch”? Does it make sense? (3 points)

2 pages long, using size 12 font, double spaced, cover page, references included. (3 points) References Should I stay or should I switch doors? (n.d.). Retrieved from https://ed.ted.com/featured/PWb09pny

Explain the two different forecasting plans with pros and cons for each.

Investing for The Future

You are the owner of XYZ, Inc. You had a record year, and you want to invest the extra capital. After doing some research, you will write a project report detailing your financial considerations and findings to your business partners on your projected investment plan.

Post 1: Initial Thread

First, do some research at your local bank, through your retirement investment firm, or by reading articles on stock analysis. This can be done virtually. Investigate the financial terms of several investment options. What interest rate is being offered? Is the interest compounded daily, monthly, or yearly? Do your best to find out the financial details for at least two different investment options. You will be citing your references in APA style.

Second, do some investment calculations. You may use a scientific calculator. For your investment:

Choose an amount between $5,000 and $500,000 of extra capital for principal, P, the initial amount of money to invest.

Choose between 5 and 30 years for t, the number of years you will let the account grow.
Based on your research findings:

Use the rate for r, the investment growth rate per year.

If using the compound interest formula, use the appropriate value for n depending on if the compounding is performed on a daily, monthly, or yearly basis. If compounding is continuous, then you will use a different formula called the continuous compounding formula.

Compound Interest: Continuously Compounding Interest:

Two formulas: 1. Compound interest formula: A equals P times the quantity one plus r divided by n raised to the n times t power. 2. Continuously compounding interest formula: A equals P times e raised to the r times t power.

Third, reflect on your calculations and present your financial guidance in a project report. You will make two different plans based on an aggressive and conservative forecast of the market. (You may also make a combination of the two rates, allocating different investment amounts that total your initial capital.) Your project report should contain the following:

Introduction: One paragraph describing how investment could be beneficial to the company.

Three body paragraphs addressing each of the following:

Explain how compound interest works in your own words.

Explain the two different forecasting plans with pros and cons for each.

Present your calculations for each plan. Be sure to state the formula and outputs.

Conclusion: One paragraph summarizing your financial considerations and findings and their significance to the company.

Project Report Guide

Professional written reports should have an introduction, body, and conclusion. A good way to plan this project report is to write an introduction to the report. Next, write at least three body paragraphs and address each of the points listed above. End your report with a conclusion paragraph tying all of your ideas together. The report should be at least five paragraphs in length. A title page and reference page are also required.

You are expected to use at least one outside source for this report. Cite outside sources in proper APA format. You can find numerous APA resources in the Writing Center Writing Reference Library on the Research, Citation, and Plagiarism page.
Using Sources

Your report should include a highly developed purpose and viewpoint; it should also be written in Standard English and demonstrate exceptional content, organization, style, grammar, and mechanics. There should be no evidence of plagiarism. If you are unsure about what constitutes plagiarism, please review the plagiarism policy.

Writing With Integrity

Post 2: Reply to a Classmate

Choose one classmate’s post that you find interesting. Reply to their post in the role of one of the business partners.

Write a one-paragraph memo to state your opinion on whether the plan is too aggressive or not aggressive enough. Be sure to include your reasoning and a brief suggestion of some changes.

Post 3: Reply to Another Classmate

Choose another classmate’s response and reply to their post. Now you are playing the role of a customer of the business. You take pride in supporting businesses that have sound ethical and financial practices. You have the pleasure (and time) to read the financial project report.

Highlight one statement from your classmate’s report that resonates with you. Share your reason for highlighting this statement. Please remember to keep all math conversation positive and constructive.

Return to Unit 9 Discussion Instructions

Am looking forward to this discussion. Financial stability is one of the most applicable area for math for everyone. Let’s apply what we are learning and I hope you enjoy it. Take a little time to think through the questions and construct your thoughts before writing your essay.

A reminder that your Project Report should include a title page and of course APA formatted references. The report should be at least five paragraphs in length. Here is a reference for the APA formatting:

You will make two different plans based on an aggressive and conservative forecast of the market. Your project report should contain the following:

Introduction: One paragraph describing how investment could be beneficial to the company.

Three body paragraphs addressing each of the following:

Explain how compound interest works in your own words.

Explain the two different forecasting plans with pros and cons for each.

Present your calculations for each plan. Be sure to state the formula and outputs.

Conclusion: One paragraph summarizing your financial considerations and findings and their significance to the company.

What is the theoretical probability of the game?Is the game fair?

Probability Game

You will design your own game, which should be a game that could be played at a carnival, amusement park, or casino. You are encouraged to create a game that either doesn’t already exist, or exists but you add your own twist to the game. It cannot be an exact duplicate of an already existing game. The game does not have to be fair. You will be expected to explain the probability of your game.

You will submit a 1-2 page report that includes the following:

Introduction – Provide an overview of the game; what type of game is it? Where would this game be played?

Instructions – Step-by-Step instructions for how to play the game.

Game Description – What is needed to play the game? List all materials needed (dice, spinner, balls, etc). How many participants are needed to play, and is there a limit?

Probability Analysis – What is the theoretical probability of the game? (Include all outcomes). Is the game fair? If the game is not fair, how could the game be changed to make it so?

Individual Reflection

Your final submission includes written report as a Word doc format.

What is BIPV?How BIPV can be integrated into building design?

Electricity from solar energy that covers photovoltaic devices

Use this article for homework4. Incorporate Chapter 9 (Electricity from solar energy) that covers photovoltaic devices. Include the following:

1. What is BIPV?

2. How BIPV can be integrated into building design?

3. Overview of relevant PV Technologies (1st to 3rd generation).

4. Govt help including feed-in-tariff

5. Current state of BIPV and barriers to diffusion. Include citations. No citations including the in-text citation will result automatic deduction of 5 points.

Find an article that mentions a new drug that promises an improved survival rate.

This video focuses on when to use a mean and when to use a median. When data all have similar values, such as housing prices of similar-sized houses on the same block, then the mean is an appropriate measure, but if the value of one residence is 50 times as high as the others, then the median gives a better description of a typical value than the mean.

https://mediaplayer.pearsoncmg.com/assets/cWSUSyFyf2fjOGj5lEJQ_w73ZBZdo4JW

However, you want to get away from the idea that the data, and only the data, drives the choice of descriptive statistics. The example is given that, if you wanted to buy all the houses in Brooklyn, if you took the median, and multiplied by the number of houses, you wouldn’t have enough cash. So, the median is a useful descriptive statistic, but the mean is essential for planning and making decisions.

Option 1: Find an article that mentions a new drug that promises an improved survival rate.

Identify whether this rate represents the mean or the median of the data set.

Assess whether that is ideally what you’d want to know for this data.

Provide a specific reason for your answer.

Compare and contrast financial and managerial accounting.

Compare and contrast financial and managerial accounting

Write a 750 – 1250 word paper on the following topic:

Compare and contrast financial and managerial accounting. Provide one specific, real-life example of how either financial accounting helps external stakeholders make informed decisions or how managerial accounting helps managers to improve operational and financial performance.

Your paper must be formatted according to APA 6th edition guidelines, and you need to use at least three external references. Save your file as “LastnameFirstinitial-ACCT105-8.”