Drag another vector

. Compare the sx and sy values to the values from questions #10 and #11. What do you notice about these values? Comparing the four tables, we see that

We can imagine a right-angled triangle from the vector. a. Use Pythagoras theorem to show that | | 2 = ax 2 + ay 2

Now think of a vector with a magnitude of | | = 28 and an angle of θ = 45o

2. A model airplane is flying North with a velocity of 15 m/s. A strong wind is blowing East at 12 m/s. a. What is the airplane’s resultant speed (magnitude of velocity vector)? The resultant speed is given by |

Describe the difference between simple interest and compound interest. Why does it make sense that the interest rate r is divided by n in the compound interest formula?

Question 

The Basic Four-Step Problem-Solving Procedure

Assessment Description
In your own words, describe the basic four-step problem-solving procedure. Explain why each step is important. Create a simple problem that could be used in a classroom and demonstrate how you would use each of the four steps to solve this problem. How would you teach this process in the classroom?

Scenario

Smart businesses in all industries use data to provide an intuitive analysis of how they can get a competitive advantage. The real estate industry heavily uses linear regression to estimate home prices, as the cost of housing is currently the largest expense for most families. Additionally, in order to help new homeowners and home sellers with important decisions, real estate professionals need to go beyond showing property inventory. They need to be well versed in the relationship between price, square footage, build year, location, and so many other factors that can help predict the business environment and provide the best advice to their clients.

Selling Price and Area Analysis for D.M. Pan National Real Estate Company

Prompt

You have been recently hired as a junior analyst by D.M. Pan Real Estate Company. The sales team has tasked you with preparing a report that examines the relationship between the selling price of properties and their size in square feet. You have been provided with a Real Estate Data spreadsheet that includes properties sold nationwide in recent years. The team has asked you to select a region, complete an initial analysis, and provide the report to the team.

Note: In the report you prepare for the sales team, the response variable (y) should be the listing price, and the predictor variable (x) should be the square feet.

Specifically, you must address the following rubric criteria using the Module Two Assignment Template:

• Generate a Representative Sample of the Data
  • Select a region and generate a simple random sample of 30 from the data.
  •  Report the mean, median, and standard deviation of the listing price and the square foot variables.
• Analyze Your Sample
  • Discuss how the regional sample created is or is not reflective of the national market.
    • Compare and contrast your sample with the population using the National Statistics and Graphs document.
  • Explain how you have made sure that the sample is random.
    • Explain your methods to get a truly random sample.
• Generate Scatterplot
  • Create a scatterplot of the x and y variables noted above and include a trend line and the regression equation

Recall that samples are used to generate statistics, which businesses use to estimate population parameters. You have learned how to take samples from populations and use them to produce statistics. For two quantitative variables, businesses can use scatterplots and the correlation coefficient to explore a potential linear relationship. Furthermore, they can quantify the relationship in a regression equation.

Housing Price Prediction Model for D.M. Pan Real Estate Company

Prompt

This assignment picks up where the Module Two assignment left off and will use components of that assignment as a foundation.

You have submitted your initial analysis to the sales team at D.M. Pan Real Estate Company. You will continue your analysis of the provided Real Estate Data spreadsheet using your selected region to complete your analysis. You may refer back to the initial report you developed in the Module Two Assignment Template to continue the work. This document and the National Statistics and Graphs spreadsheet will support your work on the assignment.

Shaver Manufacturing, Inc., offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.
a. What fraction of the employees cost more than $1,500 per year for dental expenses?

Analysis of Annual Dental Insurance Costs for XYZ Employees

To find the portion of employees at XYZ Company who cost more than $1,500 per year for dental expenses, we need to calculate the z-score and then find the corresponding percentage using the standard normal distribution table. The information for XYZ Company’s dental expenses is as follows:

Mean (μ) = $1,280

Standard Deviation (σ) = $420

Hypothesis Testing – The Mean Salary for Engineering Managers at XYZ Company

In order to test the claim that the mean salary for engineering managers at XYZ Company is at least $170,000, a one-tailed hypothesis test with a significance level of 0.05 was conducted. The null hypothesis (H0) and alternative hypothesis (Ha) are the following.

• Null Hypothesis (H0): The mean salary for engineering managers at XYZ Company (μ (mu)) is greater than or equal to $170,000.

Based on the provided salary data for male and female employees, we will test whether there are significant differences in the salaries of the employees at the company based on their genders. Assuming that the samples are independent and their variances are not known but assumed to be equal, the calculated mean salaries for the employees are as follows:

Conclusion

How does the test decision relate to the hypothesis, and are your conclusions statistically significant?

The analysis aimed to test whether the salesperson’s average cost per house is above the region’s average in order to validate or refute the claim in the research. The analysis indicates the p-value, which is the test statistic, is less than the level of significance selected for the analysis (p=0.05). Since the decision rule was an upper-tail, we accept the null hypothesis and conclude that the salesperson’s average cost per square foot price is equal to the Pacific region average. This implies that the average cost per square foot of his home sales is not $275, as the advertisement claims. Therefore, it is recommended to review the model used to arrive at the value of $275 and correct the biasedness before publishing the advertisement.

References

Salkind, N. (2015). Excel Statistics: A Quick Guide. Third Edition. SAGE Publications.

Turner, D. P. (2020). Sampling Methods in Research Design. Headache: The Journal of Head and Face Pain, 60(1), 8–12

Hypothesis Testing for Regional Real Estate Company

Introduction

The Regional Real Estate Company needs an analysis of real estate data to inform critical decisions. One of the Company’s salespersons within the Pacific region has recently returned to the office with a newly designed advertisement. The advertisement claims that the average cost per square foot of his home sales is above the average cost per square foot in the Pacific Region. The company has hired me as a statistical analyst to test the claim before he can approve the advertisement for use. The claim indicates that the average cost per square foot of his home sales is $275. Therefore, the current analysis tests the hypothesis to offer a basis for the decision.

Hypothesis Testing for Regional Real Estate Company

Introduction

The Regional Real Estate Company needs an analysis of real estate data to inform critical decisions. One of the Company’s salespersons within the Pacific region has recently returned to the office with a newly designed advertisement. The advertisement claims that the average cost per square foot of his home sales is above the average cost per square foot in the Pacific Region. The company has hired me as a statistical analyst to test the claim before he can approve the advertisement for use. The claim indicates that the average cost per square foot of his home sales is $275. Therefore, the current analysis tests the hypothesis to offer a basis for the decision.

Question 

Discussion – Variables Concept

In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they can be used to create an algebraic expression.

To Infinity… And Beyond!, Investing and Saving, Exploring the World of Numbers

Exploring the World of Numbers

In conclusion, the linear regression equation Y = 79.11x +166649 is a model that will allow you to predict a house’s potential listing price based on its size in square feet. Although there are other factors that contribute to the price of the listing, the correlation is so strong that the use of this model makes sense. The results of this analysis met my expectations. If you are interested in developing a model to make better predictions, it would be helpful to use a larger set of data. Developing models for specific areas that are interested in making predictions is also an innovative idea. A regression model would be best suited for a less variability data set. For example, in the analysis I made of a single region earlier, r and r2 were much closer to 1. This means that more price variability could be predicted by size

Scenario

You have been hired by the D. M. Pan National Real Estate Company to develop a model to predict housing prices for homes sold in 2019. The CEO of D. M. Pan wants to use this information to help their real estate agents better determine the use of square footage as a benchmark for listing prices on homes. Your task is to provide a report predicting the housing prices based on square footage. To complete this task, use the provided real estate data set for all U.S. home sales as well as national descriptive statistics and graphs provided.

Directions

Using the Project One Template located in the What to Submit section, generate a report including your tables and graphs to determine if the square footage of a house is a good indicator of what the listing price should be. Reference the National Statistics and Graphs document for national comparisons and the Real Estate Data spreadsheet (both found in the Supporting Materials section) for your statistical analysis.

Note: Present your data in a clearly labelled table and using clearly labelled graphs.

Specifically, include the following in your report:

Introduction

1. Describe the report: Give a brief description of the purpose of your report.
   1. Define the question your report is trying to answer.
   2. Explain when using linear regression is most appropriate.
      1. When using linear regression, what would you expect the scatterplot to look like?
   3. Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.

Random Number Generation: How do Computers Generate Random Numbers?

1. Marks are only awarded for the final answer, so indicate this answer clearly. (a) [5 marks] Find the limit limx→9 x − 9 √ x + 7 − 4 . (b) [5 marks] Find the slope of the curve 4y 4 + 5x 8 = 3y + 6x at the point (1, 1). (c) [5 marks] Determine the point(s) at which the function f(x) = 9 csc(6x) is continuous. (d) [5 marks] Use the relation limθ→0 sin θ θ = 1 to find the limit limx→0 6x + 6x cos(6x) sin(6x) cos(6x)