Option 1 - Work IndependentlyPrintPrint these directions."We interrupt your regular programming to bring you a special report. This is Carl Sterns, news anchor for Channel 1. Thirty minutes ago, the notorious crime syndicate Acute Perps struck again at the world-famous Wright Bank. Street reporter Stuart Olsen is live on the scene in Geo City. Let's go to Stuart now to find out more about these breaking developments. Stuart, what can you tell us?""Well, Carl, at approximately 8:30 this morning, a trio of masked men overwhelmed security forces here at the Wright Bank in Geo City and robbed the bank of all its cash. This is the third robbery in as many days orchestrated by Acute Perps. According to police sources, the gang robs three locations in three days and then goes unseen for weeks before they strike again. Because this is their third robbery, officials expect the robbers will go underground for the next few weeks. However, the police need the help of Geo City citizens in the meantime.""This gang traditionally hits the three locations during each crime spree using the same pattern. Police are asking citizens to predict the next three locations Acute Perps will attack. They will use the information to stake out these locations in the coming weeks and bring Acute Perps to justice. Back to you, Carl.""Thanks, Stuart. It looks like the city has some important work to do!"Step 1: Pick a TransformationYou have been asked by the police to find one of the three locations the Acute Perps gang is likely to hit in the coming weeks. Because the gang sticks to a triangular pattern, the locations could be a translation, reflection, or rotation of the original triangle. Choose one of the following scenarios to help locate the gang:Obtuse Scalene Triangle Translation to prove SSS CongruenceIsosceles Right Triangle Reflection to prove ASA CongruenceEquilateral Equiangular Triangle Rotation to prove SAS CongruenceAfter you have selected the one transformation you will be completing, go to step 2 for detailed directions.Step 2: Detailed DirectionsFirst, construct a triangle as indicated by your choice in step 1 on a coordinate plane. For example, if you chose to use an obtuse scalene triangle translation to prove SSS Congruence, then you will construct an obtuse scalene triangle. Make sure to measure your triangle's angles and sides. You can use the concept of distance and slope to ensure your triangle satisfies the criteria indicated by your choice. Write down the original coordinates of this triangle.Next, identify and label three points on the coordinate plane that are the transformation of your original triangle. Make sure you use the transformation indicated within the scenario you selected. For example, if you chose to use an obtuse scalene triangle translation to prove SSS Congruence, then you complete a translation of your triangle. Remember, you only need to complete one transformation on your triangle. Write down these new coordinates for this second triangle.If you chose Obtuse Scalene Triangle Translation to prove SSS Congruence, use the coordinates of your transformation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula and each corresponding pair of sides to receive full credit.If you chose Isosceles Right Triangle Reflection to prove ASA Congruence, use the coordinates of your reflection to show that the two triangles are congruent by the ASA postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. (Hint: Remember when you learned how to copy an angle?) You must show all work with the distance formula for the corresponding pair of sides, and your work for the corresponding angles to receive full credit.If you chose Equilateral Equiangular Triangle Rotation to prove SAS Congruence, use the coordinates of your rotation to show that the two triangles are congruent by the SAS postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. (Hint: Remember when you learned how to copy an angle?) You must show all work with the distance formula for the corresponding pair of sides, and your work for the corresponding angles, to receive full credit.You must submit the construction of the original triangle and your transformation. You may create this graph using graphing technology. You may also print and use graph paper.Step 3: QuestionsProvide an answer to the questions that match your selected scenario. Because you only completed one scenario, only one group of questions should be answered in complete sentences and submitted with your work.Obtuse Scalene Triangle Translation to prove SSS CongruenceDescribe the translation you performed on the original triangle. Use details and coordinates to explain how the figure was transformed, including the translation rule you applied to your triangle.What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.Did your triangle undergo rigid motion? Explain why.Isosceles Right Triangle Reflection to prove ASA CongruenceAnswer the following questions:What line of reflection did you choose for your transformation?How are you sure that each point was reflected across this line?What reflection rule did you apply to your triangle?What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.Did your triangle undergo rigid motion? Explain why.Equilateral Equiangular Triangle Rotation to prove SAS CongruenceAnswer the following questions:How many degrees did you rotate your triangle?In which direction (clockwise, counterclockwise) did it move?What rotation rule did you apply to your triangle?What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.Did your triangle undergo rigid motion? Explain why.Step 4: What to SubmitSubmit the following to your instructor using a word processing document or by copying and pasting into the assignment box. You may scan, save, or take a digital picture of your construction.Your construction of your original triangle and your transformationThe three ordered pairs, with labels, of both the original and congruent triangles you created using your transformation (Make sure to indicate which scenario was chosen.)All work for any corresponding sides using the distance formula, and clear labelsAll work for any corresponding angles (shown by use of a compass and straightedge or the slope formula)The answer to the questions that match your scenarioNote: Please submit the written portion of this assignment using a word processing document or by copying and pasting into the assignment box.

1- Post your thoughts about Case 1.1 Entertainment on a Cruise Ship that you were asked to read this week. Comment on the open-ended questions associated with the case 2- Post your thoughts about this video lecture: The Best Stats You Have Ever Seen. To what extent do you think that the visual presentation of data (which is a strength of statistics) provides useful information for policy makers? Which part of the presentation did you find most personally informative and revealing?Please, each answer on a separate page.

Option 2: Probabilities of Graduation and PublicationInstructionsIn the following study, three different universities have been tracking a select group of professors over the course of their employment at that university to determine the number of students who are in a particular professor’s classes, how many of those students have graduated, and if any of them have had their work published. In the attached Excel file, Probabilities, are the totals for each of the professors at the three different universities that participated in the study.The purpose of this study is to find the probabilities of graduation and publication for the students in the different professors’ courses. While a causal relationship may not be found between a professor and student graduation or publication, we need to rank the professors based on the different probabilities found with the data sets as described below.Prepare a report (see below) with your ranking of the professors based on the probabilities and conditional probabilities as well as the analysis of each university. Include the following seven (7) items in table format which is provided in the Probabilities file to support your ranking.Note: Be sure to use five (5) decimal places for your probabilities in the table, as some of them will be quite small. Do not convert to percentages as we are interested in probabilities only here. The overall probability of students graduating at each of the three universities. The overall probability of students having a publication at each of the three universities. The overall probability of students having a publication, given that they graduated at each of the three universities. The probability of a student graduating for each professor. The probability of a student having a publication for each professor. The probability of a student having a publication given that they graduated for each professor. Rank the professors within each university for each of the probabilities in 4–6. Then find the sum of the ranks and determine an overall ranking for each professor. Paper Requirements Items that should be included, but are not limited Items that should be included, at a minimum, are a title page, an introduction, a body which 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. This will aid in grading with partial credit if errors are found in the report.