1. Write as a single power of 2. Carefully show each step of your work.2. Police departments find it very useful to be able to approximate driving speeds in skidding accidents. If the road surface is wet concrete the function is S(x) = is used, where S(x) is the speed of the car in miles per hour and x is the distance skidded in feet.a. Fill out the table for each of the distances shown below. Round to the nearest whole number:b. Find the distance the car will skid if the speed of the car is 60 miles per hour.Round to two decimal places.3. Complex numbers are used by engineers and physicists to measure electrical circuits. To measure voltage, they use the formula E = I • Z, where E is voltage in volts, I is the current in amps, and Z is impedance, or resistance, in ohms.a. Find the voltage for an electrical circuit if the current is 3 - 4i amps and the impedance is 2 + i ohms. Simplify your answer completely. b. Find the Impedance for an electrical circuit if the voltage is 18 - 24i and the current is 6 - 3i amps. Simplify your answer completely.

Data Analysis: Hypothesis Testing Use the Sun Coast Remediation data set to conduct a correlation analysis, simple regression analysis, and multiple regression analysis using the correlation tab, simple regression tab, and multiple regression tab respectively. The statistical output tables should be cut and pasted from Excel directly into the final project document. For the regression hypotheses, display and discuss the predictive regression equations.  Correlation: Hypothesis Testing  Restate the hypotheses: Example: Ho1: There is no statistically significant relationship between height and weight. Ha1: There is a statistically significant relationship between height and weight. Enter data output results from Excel Toolpak here. Interpret and explain the correlation analysis results below the Excel output. Your explanation should include: r, r2, alpha level, p value, and rejection or acceptance of the null hypothesis and alternative hypothesis.  Example: The Pearson correlation coefficient of r = .600 indicates a moderately strong positive correlation. This equates to an r2 of .36, explaining 36% of the variance between the variables. Using an alpha of .05, the results indicate a p value of .023 < .05. Therefore, the null hypothesis is rejected, and the alternative hypothesis is accepted that there is a statistically significant relationship between height and weight. Note: Excel data analysis Toolpak does not automatically calculate the p value when using the correlation function. As a workaround, the data should also be run using the regression function. The Multiple R is identical to the Pearson r in simple regression, R Square is shown, and the p value is generated. Be sure to show your results using both the correlation function and simple regression function.  Simple Regression: Hypothesis Testing Restate the hypotheses: Ho2:  Ha2:  Enter data output results from Excel Toolpak here. Interpret and explain the simple regression analysis results below the Excel output. Your explanation should include: multiple R, R square, alpha level, ANOVA F value, accept or reject the null and alternative hypotheses for the model, statistical significance of the x variable coefficient, and the regression model as an equation with explanation. Multiple Regression: Hypothesis Testing Restate the hypotheses: Ha3:    Ha3: Enter data output results from Excel Toolpak here. Interpret and explain the simple regression analysis results below the Excel output. Your explanation should include: multiple R, R square, alpha level, ANOVA F value, accept or reject the null and alternative hypotheses for the model, statistical significance of the x variable coefficients, and the regression model as an equation with explanation.

Week 5 Assignment - Case Study: Statistical Forecasting 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 are, 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 DataPatient NumberAge of PatientNumber of Lesions124162637345124172452120672473213836169262110471011311512231813518142422152618162519173112181929191825202117 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 hours 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 hours. Patient 10 – 219 hours. Patient 11 – 84 hours. Determine three conclusions based on the correlation of the number of lesions to hours of sunlight exposure, using regression analysis.  Sunlight Exposure Regression DataPatient NumberTime of Continuous Exposure to Direct Sunlight (Minutes)Number of Lesions122524218416322020424026518014618416718620821522Over 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 ? = 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 MedicationsMedication 1 (Minutes)Medication 2 (Minutes)Medication 3 (Minutes)121614151417172120121515 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. This course requires the use of Strayer Writing Standards. For assistance and information, please refer to the Strayer Writing Standards link in the left-hand menu of your course. Check with your professor for any additional instructions.  The specific course learning outcome associated with this assignment is: Recommend a course of action utilizing quantitative methods for health services including biostatistics, forecasting, and the modeling of predictive functions.