The Area of a rectangle is represented by​ ​and its length is represented by .What is the width of the rectangle?If you double the length of the rectangle but keep the same width, what is the new area of the rectangle?2. Consider the following expression:Subtract the rational expressionsGiven the equation ​, solve the equation using your solution from part a.Solve the equation using LCD.Compare the methods used to solve the equation in parts c and d. Which method do you think is better and why?3. The average cost of electricity used for an 18 cubic ft. refrigerator that is 10 years old is $128 per year. A new refrigerator the same size costs about $81 per year for electricity. (Source: ​https://www.efficiencyvermont.com)Suppose a new refrigerator costs $500. Determine the total cost of having either refrigerator for 12 years, assuming the only costs associated with the refrigerator are its purchase cost and electricity.Determine the total annual cost for a new refrigerator that lasts 12 years, assuming the only costs associated with the refrigerator are its purchase cost and electricity.Write a function that gives the annual cost of a new refrigerator as a function of the number of years you own the refrigerator.What are the asymptotes of the rational function in part d? What does the horizontal asymptote mean in the context of this problem?Sketch the graph of the rational function from part c.If you plan on owning your refrigerator for 12 years, would it be more cost effective to keep your old refrigerator or purchase a new one? Explain.

In 2002, Boholst constructed a Life Position Scale for the purpose of finishing his dissertation. The construct life position was one of the variables he studied in his doctoral dissertation titled, The Influence of Life Scripts and Life Positions on Psychopathology and Positive Mental Health: A Structural Equation Modeling. He had to construct this scale because there was no available one at the time. In 2005, he and two other authors wrote another article that found modest correlations between Life Positions and Attachment Styles—validating the scale by establishing the relationship between life positions and a variable that was theoretically argued to have conceptual parallels or to be “similar” with it. In 2012, Isgor and two other authors translated the Life Position Scale into Turkish and established its reliability and validity.This is often a realistic scenario where a tool slowly attains credibility by a gradual validation process across the years—often by different authors. For example, in 2004, Weisner wrote his doctoral dissertation in the University of North Texas on the relationship between Affective Traits and Life Positions. Hadzi-Pesic and others more recently (2014) validated the Life Position Scale and found correlations with alcohol addicts’ personality. For this task, write a paper that addresses the following:Discuss the different types of validity that have been employed—whether implicitly or explicitly to validate the life position scale. It is ideal therefore to read articles in chronological order starting with the A Life Position Scale, Life Positions and Attachment: A Canonical Correlation Analysis, and Life Positions Scale Language Equivalence, Reliability and Validity Analysis.Length: 7-10 pages, not including title and reference pagesYour assignment should demonstrate thoughtful consideration of the ideas and concepts presented in the course by providing new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Upload your document and click the Submit to Dropbox button

The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The variables in the survey can be found in the file CODING.In this exercise, some of the estimation techniques presented in the module will be applied to the Springfield Shopping survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community, and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results.Managers associated with shopping areas like these find it useful to have point estimates regarding variables describing the characteristics and behaviors of their customers. In addition, it is helpful for them to have some idea as to the likely accuracy of these estimates. Therein lies the benefit of the techniques presented in this module and applied here. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement. Determine the point estimate, and then construct the 95% confidence interval for µ7 = the average attitude toward Springdale Mall. Repeat part (a) for µ8 and µ9, the average attitudes toward Downtown and West Mall, respectively. Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate, and then construct the 95% confidence interval for p26 = the population proportion of males. Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate, and then construct the 95% confidence interval for p28 = the population proportion in the “single or other” category. Assume the managers have requested estimates of the mean attitudes towards each mall with a margin of error of 0.05 for each. If the managers want to have 95% confidence that the sample mean will fall within this margin of error, how large should the sample size be for each mall?Items that should be included, at a minimum, are a title page, an introduction, a body that answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment response.Note: You must submit your Excel file with your report.