If a state worked with a national government agency to solve a problem with large implications, such as a failing energy grid, it could be said that the problem is being solved through _______, 1. public-private partnership, 2. dual federalism, 3. the Dillon rule, 4. cooperative federalism, 5. joint government.

If a state worked with a national government agency to solve a problem with large implications, such as a failing energy grid, it could be said that the problem is being solved through _______, 1. public-private partnership, 2. dual federalism, 3. the Dillon rule, 4. cooperative federalism, 5. joint government.

4.  cooperative federalism
Problem 2 (25 Points) Given the following matrices: A = 5 !3 2 ” # $$$ % & ”’ , B = 4 !2 6 1 !5 3 ” # $$$ % & ”’ , C = 7 2 !1 !2 4 9 !3 2 1 ” # $$$ % & ”’ For each of the operations requested below, indicate whether or not the operation is valid. If not valid, indicate, and move on to the next operation. If valid, perform the requested operation, showing all of your work. Notation – ()T is the transpose of the matrix (), and det() is the determinant of the matrix (). Remember: Show all work and calculations (even if you check your final answer on a calculator). a. AB b. ATB c. BTC d. det(C)

Problem 2 (25 Points) Given the following matrices: A = 5 !3 2 ” # $$$ % & ”’ , B = 4 !2 6 1 !5 3 ” # $$$ % & ”’ , C = 7 2 !1 !2 4 9 !3 2 1 ” # $$$ % & ”’ For each of the operations requested below, indicate whether or not the operation is valid. If not valid, indicate, and move on to the next operation. If valid, perform the requested operation, showing all of your work. Notation – ()T is the transpose of the matrix (), and det() is the determinant of the matrix (). Remember: Show all work and calculations (even if you check your final answer on a calculator). a. AB b. ATB c. BTC d. det(C)

Solution: a. (5 points) Invalid multiplication. In the product AB, … Read More...
MECET 423: Mechanics of Materials Chap. 7 HW Chap. 7 Homework Set 1. Consider the beam shown in the image below. Let F1 = 2 kN and F2 = 3 kN. Assume that points A, B and C represent pin connections and a wire rope connects points B and C. Consider the dimensions L1, L2, L3 and L4 to be 2 m, 4 m, 6 m, and 10 m, respectively. The beam is made from HSS 152 X 51 X 6.4 (Appendix A-9) and the longer side of the rectangle is vertical. What is the maximum normal stress (units: MPa) experienced by the beam? 2. Consider the beam and loading shown below. The beam has a total length of 12 ft. and a uniformly distributed load, w, of 125 lb./ft. The cross section of the beam is comprised of a standard steel channel (C6 X 13) which has a ½ in. plate of steel attached to its bottom. Determine the maximum normal stress in tension and compression that is experienced by this beam due to the described loading. MECET 423: Mechanics of Materials Chap. 7 HW 3. Consider the cantilever beam shown in the image below. The beam is experiencing a linearly varying distributed load with w1 = 50 lb./ft. and w2 = 10 lb./ft. The beam is to be made from ASTM A36 structural steel and is to be 8 ft. in length. Select the smallest standard schedule 40 steel pipe size (Appendix A-12) which will ensure a factor of safety of at least 3. 4. The beam shown below has been fabricated by combining two wooden boards into a T-section. The dimensions for these sizes can be found in Appendix A-4. The beam is 9 ft. in length overall and dimension L1 = 3 ft. Assume the beam is made from a wood which has an allowable bending stress of 1500 psi (in both tension and compression). What is the largest value of the force which can be applied? MECET 423: Mechanics of Materials Chap. 7 HW 5. The image below shows a hydraulic cylinder which is being utilized in a simple press-fit operation. As can be seen the cylinder is being suspended over the work piece using a cantilever beam. Note from the right view that there is a beam on either side of the cylinder. You may assume that each will be equally loaded by the cylinder. The beams are to be cut from AISI 1040 HR steel plate which has a thickness of 0.750 in. The proposed design includes the following dimensions (units: inch): H = 2.00, h = 1.00, r = 0.08, L1 = 8, and L2 = 18. Evaluate the design by calculating the resulting factor of safety with respect to the yield strength of the material at the location of the step if the total force generated by the cylinder is 1,000 lb. Also state whether or not yielding is predicted to occur. You may assume that bending in the thickness direction of the beams is negligible. 6. Consider the cantilever beam shown below. The beam has a length of 4 ft. and is made from a material whose design stress, σd, is equal to 10,000 psi. It is to carry a load of 200 lb. applied at its free end. The beam is to be designed as a beam of constant strength where the maximum normal stress experienced at each cross section is equal to the design normal stress. To achieve this the height will be held constant at 1.5 in. while the base will vary as a function of the position along the length of the beam. Determine the equation which describes the required length of the base as a function of the position along the length of the beam. For consistency, let the origin be located at point A and the positive x axis be directed toward the right. MECET 423: Mechanics of Materials Chap. 7 HW 7. Consider the overhanging beam shown in the image below. Assume that L = 5 ft. and L1 = 3 ft. The beam’s cross section is shown below. The centerline marks the horizontal centroidal axis. The moment of inertia about this axis is approx. 0.208 in4. Due to the geometry of the cross section and the material, the beam has different maximum allowable normal stresses in tension and compression. The design normal stress in tension is 24,000 psi while the design normal stress in compression is 18,000 psi. Using this data determine the maximum force, F, which can be applied to the beam.

MECET 423: Mechanics of Materials Chap. 7 HW Chap. 7 Homework Set 1. Consider the beam shown in the image below. Let F1 = 2 kN and F2 = 3 kN. Assume that points A, B and C represent pin connections and a wire rope connects points B and C. Consider the dimensions L1, L2, L3 and L4 to be 2 m, 4 m, 6 m, and 10 m, respectively. The beam is made from HSS 152 X 51 X 6.4 (Appendix A-9) and the longer side of the rectangle is vertical. What is the maximum normal stress (units: MPa) experienced by the beam? 2. Consider the beam and loading shown below. The beam has a total length of 12 ft. and a uniformly distributed load, w, of 125 lb./ft. The cross section of the beam is comprised of a standard steel channel (C6 X 13) which has a ½ in. plate of steel attached to its bottom. Determine the maximum normal stress in tension and compression that is experienced by this beam due to the described loading. MECET 423: Mechanics of Materials Chap. 7 HW 3. Consider the cantilever beam shown in the image below. The beam is experiencing a linearly varying distributed load with w1 = 50 lb./ft. and w2 = 10 lb./ft. The beam is to be made from ASTM A36 structural steel and is to be 8 ft. in length. Select the smallest standard schedule 40 steel pipe size (Appendix A-12) which will ensure a factor of safety of at least 3. 4. The beam shown below has been fabricated by combining two wooden boards into a T-section. The dimensions for these sizes can be found in Appendix A-4. The beam is 9 ft. in length overall and dimension L1 = 3 ft. Assume the beam is made from a wood which has an allowable bending stress of 1500 psi (in both tension and compression). What is the largest value of the force which can be applied? MECET 423: Mechanics of Materials Chap. 7 HW 5. The image below shows a hydraulic cylinder which is being utilized in a simple press-fit operation. As can be seen the cylinder is being suspended over the work piece using a cantilever beam. Note from the right view that there is a beam on either side of the cylinder. You may assume that each will be equally loaded by the cylinder. The beams are to be cut from AISI 1040 HR steel plate which has a thickness of 0.750 in. The proposed design includes the following dimensions (units: inch): H = 2.00, h = 1.00, r = 0.08, L1 = 8, and L2 = 18. Evaluate the design by calculating the resulting factor of safety with respect to the yield strength of the material at the location of the step if the total force generated by the cylinder is 1,000 lb. Also state whether or not yielding is predicted to occur. You may assume that bending in the thickness direction of the beams is negligible. 6. Consider the cantilever beam shown below. The beam has a length of 4 ft. and is made from a material whose design stress, σd, is equal to 10,000 psi. It is to carry a load of 200 lb. applied at its free end. The beam is to be designed as a beam of constant strength where the maximum normal stress experienced at each cross section is equal to the design normal stress. To achieve this the height will be held constant at 1.5 in. while the base will vary as a function of the position along the length of the beam. Determine the equation which describes the required length of the base as a function of the position along the length of the beam. For consistency, let the origin be located at point A and the positive x axis be directed toward the right. MECET 423: Mechanics of Materials Chap. 7 HW 7. Consider the overhanging beam shown in the image below. Assume that L = 5 ft. and L1 = 3 ft. The beam’s cross section is shown below. The centerline marks the horizontal centroidal axis. The moment of inertia about this axis is approx. 0.208 in4. Due to the geometry of the cross section and the material, the beam has different maximum allowable normal stresses in tension and compression. The design normal stress in tension is 24,000 psi while the design normal stress in compression is 18,000 psi. Using this data determine the maximum force, F, which can be applied to the beam.

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Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

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Critical Reflection Assignment (Essay 5) Goals: • As the name implies, the hope is you will reflect on your writing choices, which may in turn get you to rethink some of them and perhaps give you ideas for further revision. • Reflecting also gives you opportunity to reinforce good choices you made and hence remember them to do again when you write future papers. • This further provides you the opportunity to take credit for some good choices and hopefully bolster your confidence. • It allows you to point out why your paper demonstrates your competency in writing academic essays to justify a passing grade in English 111. • It also is a last ditch effort to show your thinking!!! If you explain why you made the choices you did in your synthesis essay, and you truly share your thinking, it helps you meet top box expectations yet again. Directions: 1. Choose either essay 3 or 4 to write about. 2. Take some time to reflect on how your idea for that essay came about, why you picked that idea to go with, what questions came to mind, and what pre-writing strategies you went through to get started. 3. Get out one of your copies of the English 111 Rubric. Go over it. Make sure you know what each box is looking for. 4. Plan an essay that helps you show that you have met the expectations of each box. Stress your thinking and reasoning. For any idea you include – explain why you did those things. Emphasize what you believed the job was, why you chose to approach it the way you did, the options you considered, and what you ended up doing after revising. 5. Be sure to include a discussion of effective thinking, complexity, source selection, source use, synthesis, and revision. 6. As you have teachers in your audience, it would likely be a good choice to include what you learned and how you’ll use that in your future writing. Rough Draft should be completed Tuesday Week 14. Final (REVISED) Copy due at your meeting week 14/15.

Critical Reflection Assignment (Essay 5) Goals: • As the name implies, the hope is you will reflect on your writing choices, which may in turn get you to rethink some of them and perhaps give you ideas for further revision. • Reflecting also gives you opportunity to reinforce good choices you made and hence remember them to do again when you write future papers. • This further provides you the opportunity to take credit for some good choices and hopefully bolster your confidence. • It allows you to point out why your paper demonstrates your competency in writing academic essays to justify a passing grade in English 111. • It also is a last ditch effort to show your thinking!!! If you explain why you made the choices you did in your synthesis essay, and you truly share your thinking, it helps you meet top box expectations yet again. Directions: 1. Choose either essay 3 or 4 to write about. 2. Take some time to reflect on how your idea for that essay came about, why you picked that idea to go with, what questions came to mind, and what pre-writing strategies you went through to get started. 3. Get out one of your copies of the English 111 Rubric. Go over it. Make sure you know what each box is looking for. 4. Plan an essay that helps you show that you have met the expectations of each box. Stress your thinking and reasoning. For any idea you include – explain why you did those things. Emphasize what you believed the job was, why you chose to approach it the way you did, the options you considered, and what you ended up doing after revising. 5. Be sure to include a discussion of effective thinking, complexity, source selection, source use, synthesis, and revision. 6. As you have teachers in your audience, it would likely be a good choice to include what you learned and how you’ll use that in your future writing. Rough Draft should be completed Tuesday Week 14. Final (REVISED) Copy due at your meeting week 14/15.

ENG 111 M05 14 Apr. 15   Forest Gump and … Read More...
CAUSAL ANALYSIS GUIDELINES: According to John J. Ruskiewicz and Jay T. Dolmage, “We all analyze and explain things daily. Someone asks, ‘Why?’ We reply, ‘Because . . .’ and then offer reasons and rationales” (138). This type of thinking is at the core of the causal analysis. You will write a causal analysis which explores, through carefully examined research and logical analysis, certain causes or factors which contribute to an issue or problematic situation, based on the topic you choose to write on. Your causal analysis should explore more than one type of cause, such as necessary causes, sufficient causes, precipitating causes, proximate causes, remote causes, reciprocal causes, contributing factors, and chains of causes, as outlined in our course text in the chapter devoted to Causal Analyses. Your project should also reflect significant critical thinking skills. In addition to the actual causal analysis essay, you will be also create an annotated bibliography. These process elements will help you organize and focus your ideas and research in a beneficial way. The following is an organizational structure that outlines the chronology and content of your Causal Analysis: I. Introduction: In one (or at the most two) paragraph(s) introduce your topic. Give a brief overview of your topic and thesis in a few sentences. your evaluative claim and your causal claim. It should be specific, logical, and clear. II. History/Background to Current Situation: This section should take as much space as needed—a few to several paragraphs. Discuss the significant and relevant history of your topic up to the current situation and how it came to be. Use research as needed to give precise and accurate background for context in making your later causal argument. Comment on your research as well, so that you don’t lose your voice. As you explore other points of view, your own point of view will evolve in significant ways. III. Evaluative Claim: Once you have given a brief history/background of the current situation, evaluate the situation, the topic, as it is at present. Again, use research as appropriate to support your judgments. While this section of your essay could run anywhere from one to three paragraphs, typically one paragraph is the norm, as you are basically passing judgment on the situation, arguing evaluatively. This is an argument of pathos and logos, predominantly. IV. Causal Argument: This is the longest portion of your essay, the “meat,” the heart of your work. Once you have detailed the history/background to current situation and evaluated the current situation, you are ready to present your causal analysis. Demonstrate a link between the current situation and the causes for its negative condition. Of course, you will use current significant and relevant research to support your causal claim, and you will want to find the most dominant and pervasive logical causes, utilizing research, for the current situation as possible. These will connect forward as well to your proposal. Remember to use specific supporting detail/examples, and to analyze all of your research causally, thoroughly, and with clarity. NOTE: SECTIONS THREE AND FOUR ABOVE ARE INTERCHANGEABLE. IN OTHER WORDS, IF YOU FEEL YOU CAN PRESENT A BETTER ARGUMENT BY SHOWING CAUSES FIRST AND THEN EVALUATING THE CURRENT SITUATION, THAT CAN WORK JUST AS WELL AS THE ORDER OUTLINED ABOVE. I WILL LEAVE IT UP TO YOU AS THE WRITER TO ESTABLISH WHICH ORDER WORKS MOST EFFECTIVELY. V. Counterargument/Conditions of Rebuttal and Rebuttal: There will be those who disagree with you so you will want to acknowledge their points of view. What are their assumptions about this topic? What questions do they raise for consideration? Acknowledging other points of view gives your essay credibility and shows that you have been fair and broad in your inquiry and presentation. (You will need at least one credible source to represent at least one counterargument.) Then explain how you have considered this counterargument, but still find your own analysis to be more logical and accurate; this is your rebuttal. VI. Conclusion: Summarize the meaningful conclusions you have drawn clearly and precisely, remembering to resummarize your thesis. Give your specific proposal here as well. This will become your transition paragraph between the causal analysis and the proposal, so you must state your proposal precisely to pave the way for the proposal argument in full to come. Keep in mind these critical thinking outcomes: • Pursue the best information via reliable research (no Internet web sites should be used—Use the library electronic databases, such as ____, for academic research. • Engage in broad and deep inquiry • Analyze different points of view • Examine and challenge your own underlying assumptions as you undergo this exciting journey in scholarship. Please also reflect on these questions as you progress through your research and project work: About yourself: • What assumptions (beliefs) did you have about this topic coming into the project? • Have some of those assumptions been challenged? Have some been validated? • What questions do you still have about your issue? • What questions have you been able to answer through your research? About your audience: • What questions might your audience have about your topic? What points of view do they represent? • What information do you want to provide to help answer those questions? • How can you address a diverse audience so that its members will be moved to see your own point of view as significant and worth consideration? • How has pursuing the best information in a fair and honest, ethical, and logical manner allowed you to show respect for your audience as well as yourself as a thinker? Documentation Style: MLA format for paper format, in-text citations, works cited page, and annotated bibliography format. Paper Length: 6-8 double-spaced pages. Annotated Bibliography: At least 4 sources, formatted in MLA style. List of Sources Page: At least 5-8 sources used; formatted in MLA style. Warning: Plagiarism is punishable with an “F,” so be sure to document your research carefully. Causal Analysis Topics Choose one: • Causes of bullying • Causes of gun violence in schools • Causes of obesity in children • Causes of lying / Reasons why people lie • Causes of the fear of darkness Write in the 3rd-person point of view (using pronouns such as he, she, they, etc.). Do not write in the 1st- person (I, me, etc.) or 2nd-person (you, your) point of view.

CAUSAL ANALYSIS GUIDELINES: According to John J. Ruskiewicz and Jay T. Dolmage, “We all analyze and explain things daily. Someone asks, ‘Why?’ We reply, ‘Because . . .’ and then offer reasons and rationales” (138). This type of thinking is at the core of the causal analysis. You will write a causal analysis which explores, through carefully examined research and logical analysis, certain causes or factors which contribute to an issue or problematic situation, based on the topic you choose to write on. Your causal analysis should explore more than one type of cause, such as necessary causes, sufficient causes, precipitating causes, proximate causes, remote causes, reciprocal causes, contributing factors, and chains of causes, as outlined in our course text in the chapter devoted to Causal Analyses. Your project should also reflect significant critical thinking skills. In addition to the actual causal analysis essay, you will be also create an annotated bibliography. These process elements will help you organize and focus your ideas and research in a beneficial way. The following is an organizational structure that outlines the chronology and content of your Causal Analysis: I. Introduction: In one (or at the most two) paragraph(s) introduce your topic. Give a brief overview of your topic and thesis in a few sentences. your evaluative claim and your causal claim. It should be specific, logical, and clear. II. History/Background to Current Situation: This section should take as much space as needed—a few to several paragraphs. Discuss the significant and relevant history of your topic up to the current situation and how it came to be. Use research as needed to give precise and accurate background for context in making your later causal argument. Comment on your research as well, so that you don’t lose your voice. As you explore other points of view, your own point of view will evolve in significant ways. III. Evaluative Claim: Once you have given a brief history/background of the current situation, evaluate the situation, the topic, as it is at present. Again, use research as appropriate to support your judgments. While this section of your essay could run anywhere from one to three paragraphs, typically one paragraph is the norm, as you are basically passing judgment on the situation, arguing evaluatively. This is an argument of pathos and logos, predominantly. IV. Causal Argument: This is the longest portion of your essay, the “meat,” the heart of your work. Once you have detailed the history/background to current situation and evaluated the current situation, you are ready to present your causal analysis. Demonstrate a link between the current situation and the causes for its negative condition. Of course, you will use current significant and relevant research to support your causal claim, and you will want to find the most dominant and pervasive logical causes, utilizing research, for the current situation as possible. These will connect forward as well to your proposal. Remember to use specific supporting detail/examples, and to analyze all of your research causally, thoroughly, and with clarity. NOTE: SECTIONS THREE AND FOUR ABOVE ARE INTERCHANGEABLE. IN OTHER WORDS, IF YOU FEEL YOU CAN PRESENT A BETTER ARGUMENT BY SHOWING CAUSES FIRST AND THEN EVALUATING THE CURRENT SITUATION, THAT CAN WORK JUST AS WELL AS THE ORDER OUTLINED ABOVE. I WILL LEAVE IT UP TO YOU AS THE WRITER TO ESTABLISH WHICH ORDER WORKS MOST EFFECTIVELY. V. Counterargument/Conditions of Rebuttal and Rebuttal: There will be those who disagree with you so you will want to acknowledge their points of view. What are their assumptions about this topic? What questions do they raise for consideration? Acknowledging other points of view gives your essay credibility and shows that you have been fair and broad in your inquiry and presentation. (You will need at least one credible source to represent at least one counterargument.) Then explain how you have considered this counterargument, but still find your own analysis to be more logical and accurate; this is your rebuttal. VI. Conclusion: Summarize the meaningful conclusions you have drawn clearly and precisely, remembering to resummarize your thesis. Give your specific proposal here as well. This will become your transition paragraph between the causal analysis and the proposal, so you must state your proposal precisely to pave the way for the proposal argument in full to come. Keep in mind these critical thinking outcomes: • Pursue the best information via reliable research (no Internet web sites should be used—Use the library electronic databases, such as ____, for academic research. • Engage in broad and deep inquiry • Analyze different points of view • Examine and challenge your own underlying assumptions as you undergo this exciting journey in scholarship. Please also reflect on these questions as you progress through your research and project work: About yourself: • What assumptions (beliefs) did you have about this topic coming into the project? • Have some of those assumptions been challenged? Have some been validated? • What questions do you still have about your issue? • What questions have you been able to answer through your research? About your audience: • What questions might your audience have about your topic? What points of view do they represent? • What information do you want to provide to help answer those questions? • How can you address a diverse audience so that its members will be moved to see your own point of view as significant and worth consideration? • How has pursuing the best information in a fair and honest, ethical, and logical manner allowed you to show respect for your audience as well as yourself as a thinker? Documentation Style: MLA format for paper format, in-text citations, works cited page, and annotated bibliography format. Paper Length: 6-8 double-spaced pages. Annotated Bibliography: At least 4 sources, formatted in MLA style. List of Sources Page: At least 5-8 sources used; formatted in MLA style. Warning: Plagiarism is punishable with an “F,” so be sure to document your research carefully. Causal Analysis Topics Choose one: • Causes of bullying • Causes of gun violence in schools • Causes of obesity in children • Causes of lying / Reasons why people lie • Causes of the fear of darkness Write in the 3rd-person point of view (using pronouns such as he, she, they, etc.). Do not write in the 1st- person (I, me, etc.) or 2nd-person (you, your) point of view.

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(20 pts total) Continuous Probability Density a) (4 pts) Graph f when the density f(x) = k where k is a constant if −4≤?≤4 and 0 elsewhere b) (4 pts) What is the value of k? c) (4 pts) Graph F for the same functions d) (4 pts) What is the ?(0≤?≤4)? e) (4 pts) Find the interval ?(−?≤?≤?) where the probability is 95% 7) (20 pts total) Find the mean and variance of the random variable X with probability function f(x) a) (10 ???) ?(0)=0.512,?(1)=0.384,?(2)=0.096,?(3)=0.008 b) (10 ???) ?(?)=2? (0≤?≤1) 8) (20 pts total) Let X be normal with a mean of 80 and a variance of 9. Find: a) (5 pts) P(X>83) b) (5 pts) P(X<81) c) (5 pts) P(X<80) d) (5 pts) P(78<X<82)

(20 pts total) Continuous Probability Density a) (4 pts) Graph f when the density f(x) = k where k is a constant if −4≤?≤4 and 0 elsewhere b) (4 pts) What is the value of k? c) (4 pts) Graph F for the same functions d) (4 pts) What is the ?(0≤?≤4)? e) (4 pts) Find the interval ?(−?≤?≤?) where the probability is 95% 7) (20 pts total) Find the mean and variance of the random variable X with probability function f(x) a) (10 ???) ?(0)=0.512,?(1)=0.384,?(2)=0.096,?(3)=0.008 b) (10 ???) ?(?)=2? (0≤?≤1) 8) (20 pts total) Let X be normal with a mean of 80 and a variance of 9. Find: a) (5 pts) P(X>83) b) (5 pts) P(X<81) c) (5 pts) P(X<80) d) (5 pts) P(78

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