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...First we to evaluate what was given: Evaluating f(x): Following are the values shown in tabular form: x | f(x) | -1 | -9 | 0 | -1 | 1 | 7 | Recall the to get slope (m) between P1 with coordinates (x1,y1) and P2 with coordinates (x2,y2) we use the formula: m = (y2 – y1) / (x2 – x1) say P1 = (x1,y1) = (-1,-9) and P2 = (x2,y2) = (0,-1) then m = (-1 - -9)/ (0 - -1) negative of negative is positive so m = (-1+9)/(0+1) m = slope = 8 Recall that the intercept of the line is point when x=0 so from the table x=0 when f(x) = -1 Thus our y-intercept is (0,-1). Evaluating g(x): g(x) = 3x -2 Recall that for an equation in the form y = mx+b the value of m is the slope of the line and b is the y intercept. Thus m=slope = 3 Thus our y-intercept is ( 0 , -2) COMPARISONS Part A : Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). f(x) : slope = 8 g(x): slope = 3 From above we can deduce that f(x) has a bigger slope. Par B: Which function has a greater y-intercept? Justify your answer. f(x) : y-intercept is (0,-1). g(x) : y-intercept is ( 0 , -2) If our reference is the x-axis, then we can deduce that with g(x) y-intercept being further from the axis, g(x) has the greater y-intercept....
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...family groups are allowed but no difference in slope coefficients, versus an alternative hypothesis where also slopes are allowed to differ between family groups. What do you conclude?Perform a Chow test where the null hypothesis is that intercept differences between family groups are allowed but no difference in slope coefficients, versus an alternative hypothesis where also slopes are allowed to differ between family groups. What do you conclude?Perform a Chow test where the null hypothesis is that intercept differences between family groups are allowed but no difference in slope coefficients, versus an alternative hypothesis where also slopes are allowed to differ between family groups. What do you conclude?Perform a Chow test where the null hypothesis is that intercept differences between family groups are allowed but no difference in slope coefficients, versus an alternative hypothesis where also slopes are allowed to differ between family groups. What do you conclude?Perform a Chow test where the null hypothesis is that intercept differences between family groups are allowed but no difference in slope coefficients, versus an alternative hypothesis where also slopes are allowed to differ between family groups. What do you conclude?Perform a Chow test where the null hypothesis is that intercept differences between family groups are allowed but no difference in slope coefficients, versus an alternative hypothesis where also slopes are allowed to differ between family......
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...(2a,b) 7. To prove that lines are parallel their slopes must be equal. To find the slope you take the change in the y –coordinates and divide by the change of x-coordinates. 8. The slope of segment FG is given by ((b-2b)/(2a-a)). Which equals (-b/a). 9. The slope of segment EH is given by ((0-b)/(a-0)). Which equals (-b/a). 10. The slopes of segments FG and EH are equal, so the lines are parallel to each other. 11. The slope of segment FE is given by ((2b-b)/(a-0)). Which equals (b/a). 12. The slope of segment GH is given by ((b-0)/(2a-a). Which equals (b/a). 13. The slopes of FE and GH are equals so these two segments are parallel to each other. 14. By definition, a four sided figure with two set of opposite parallel sides is a parallelogram. Figure EFGH is a parallelogram. Part D The synthetic technique requires someone to know and understand geometric postulates. Someone with limited knowledge of geometry would find it difficult, if not impossible to proof figure EFGH is a parallelogram using synthetic techniques. However synthetic techniques are useful when you don’t have the luxury of a grid and coordinate system. The analytic technique is much more straight forward. You have two line segments and the endpoints have coordinates (x,y). Take the difference of the y-coordinates and divide by the difference in the x-coordinates and you have the slope of the line. If those slopes are equal, then the lines are parallel. With......
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...T5J 2R4 October 27 - 2011 City of Edmonton Drainage Branch Dear Madam / Sir, Request for Change Order: Regarding to our meeting dated July 30, 1993; WestBan Construction Limited needs City’s approval for extra time and cost to precede with additional scope of the construction work (changing slope in North and East banks, adding required shoring for stabilizing the soil, leaving shoring in the ground, pouring tank concrete walls instead of shotcrete), according to the option B for both North and East Slopes (Attachment F2), the chosen schemes for slope remedies are attached in this document. WestBan, due to the delays of City of Edmonton and UMA in providing requested services to this company, believed that the justifications in cost and schedule are necessary to complete the project within satisfactory quality. WestBan is proposing extra CAD$72,500 and additional 28 days to the original project duration according to general conditions to the contract clauses 410.1, 404.3 and 404.4. It is noteworthy that the total amount of money requested is additional to the insurance of North and South slopes which stipulated in Attachment G Section 1.2 (Course of Construction Insurance). The detailed cost breakdown and the revised schedules are attached for references. The revised milestone dates are as followed: Completion of Storage Tank: 17-Sept-1993 Completion of Mech./Piping: 08-Oct-1993 Completion of Electrical/Control:......
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...Pipeline Routes For Delivery Of US North Slope Natural Gas to Lower-48 Markets [pic] Economics 494 March 2, 2005 By: Etienne Snyman Pipeline Routes for Delivery of US North Slope Natural Gas to Lower-48 Markets Table of Contents 1.0 Introduction 1.1 Over-the-Top Route 1.2 Alaska Highway Route 2.0 Part 1 2.1.0 Economic Impacts of the Alaska Highway and “Over-The-Top” Routes on Various Stakeholders 2.1.1 Natural Gas Producers in Alaska 2.1.2 Natural Gas Producers in the Beaufort Sea-Mackenzie Delta 2.1.3 Mackenzie Valley Corridor Producers 2.1.4 Producers in the Western Canadian Sedimentary Basin 2.1.5 Producers in the Supply Regions of the Lower 48 US States 2.1.6 The Global Liquefied Natural Gas Sector 2.1.7: Natural Gas End-use Consumers 2.1.8: Pipeline Operating Companies 2.1.9: American Taxpayer Perspective of the Alaska Highway Route 2.1.10: Canadian Taxpayer Perspective of the Alaska Highway Route 2.1.11: American Taxpayer Perspective of the “Over-the-Top” Route 2.1.12: Canadian Taxpayer Perspective of the “Over-the-Top” Route 2.1.13: Aboriginal Interests 2.2.0: Potential Environmental Impacts of the Alaska Highway and the “Over-The-Top” Routes 2.2.1: Overview 2.2.2: Environmental Impacts According To The Yukon Conservation Society 2.2.3: Environmental......
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...two tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) The degrees of freedom as shown in the output is 33 The critical value at =0.05 is 2.035 (d) What is your conclusion about the slope? The t-statistic exceeds the critical value so slope is significantly different from zero (2.889>2.035) (e) Interpret the 95 percent confidence limits for the slope. It can be said with 95% confidence that true slope falls between 0.0101 and 0.0584. (f) Verify that F = t2 for the slope. t=2.889 (as shown in the output) 2=8.346321≈8.35 F=8.35 (as shown in the output) Therefore =2 (g) In your own words, describe the fit of this regression. 2=0.202=20.2% (As shown in the output) While using x as predictor variable only explains 20.2%of the variability in y, the slope is significantly different from 0, so the model is informative. 12.50 In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation. The regression equation is: =6.5763+0.0452 (b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at α = .05. The degrees of freedom as shown in the output is 62 The critical value at =0.05 is 1.999 (c) What is your conclusion about the slope? The t-statistic greatly exceeds the critical value so slope is significantly......
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... QUESTION FOUR: skiing down a slope Rosemary skis down a slope in a straight line, as shown in the diagram below. At the bottom of the slope, her speed is 8 ms-1. The combined mass of Rosemary and her skis is 80 kg. [pic] a) Rosemary was stationary before she started skiing down the slope, and it took her 36.7 s to travel 110 m. Calculate her average speed down the slope. Average speed = ms-1 g) Calculate the kinetic energy of Rosemary and her skis as she reaches the bottom of the slope when she is moving at 8 ms-1. Give an appropriate unit for your answer. Kinetic energy = h) The kinetic energy gained by Rosemary when she reached the bottom of the slope does not equal the energy she had when she was stationary at the top of the slope. Explain using the principles of physics why her energy at the top of the slope and her energy at the bottom of the slope are not equal. In your answer, you should: • name the type of energy Rosemary has at the top of the slope • calculate the difference between her kinetic energy at the bottom of the slope and her energy at the top of the slope • justify the difference between her kinetic energy at the bottom of the slope and her energy at the top of the......
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...horizontal and vertical number lines are called the x-axis and the y-axis, respectively. These axes divide the plane into four regions, called quadrants, which are numbered as shown below. What is the slope of a line? Identify the possible values of the slope and the relation to the line they pass through. For example, if the slope of a line is 3 / 2, it means that the rise is 3, the run is 2, and the line rises from left to right. (6/28) The slope is the rate of change (steepness of line). Slope is also termed as ratio of rise above run.The slope of the line is calculated by dividing the difference of the y-coordinates of a point on a line by the difference of the x-coordinates. The formula is as shown below. For this reason, if the slope is 3⁄2 then the equation will be 3⁄2 = (Y_2-Y_1)⁄(X_2-X_1 ) Hence, if we had the values of one of the coordinates, we would possibly calculate the value of the other coordinate. Answer to Kenneth Great Post! One of the most important properties of a straight line is in how it angles away from the horizontal. This is what is commonly referred to as the slope of the line. To calculate the slope of a line, one needs two points on that line (Seber & Lee, 2012). The greater the slope of the line the steeper the line will be. The slope of a line characterizes the general direction in which a line points. Seber, G. A. F., & Lee, A. J. (2012). Linear Regression Analysis. Hoboken: Wiley. Answer to Laura The methods used......
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...of soil that are on slight slopes or hillsides. a. Alternatively, you could look for patches of the same soil type with different amounts of plant cover, for example, bare soil and a grassy area. b. Alternatively, you could compare different degrees of slope with the same soil type and plant cover. c. Choose a sufficient number of sites so that you can compare the variable of interest as the sole change between sites. For example, if you wanted to investigate degree of slope, you should select at least three sites with similar soil types and plant cover but different slopes. If you want to investigate the effect of plant cover, select at least three sites with similar slope and soil type, but different amounts (or types) of cover. 2. For each test site, make 3 sampling containers. d. Cut the tops off plastic bottles such as soda bottles or milk jugs. Use the utility knife safely: keep your fingers away from the path of the blade. e. Use the same size bottle for all sites. f. Bury each container so the lip is even with or slightly below the soil surface. 3. Weigh the soil that collects in the containers after each rain. Dry the soil in an oven before you weigh it; you don't want to weigh the water, just the soil. 4. Keep records in your lab notebook. g. You'll want to have a description of each test site, including information about the slope (see Bibliography for a good method for measuring slope), soil type and plant......
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...linear equation (slope-intercept form). y 3x 4 Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 6 48) Graph the linear equation (slope-intercept form). 3 y x 1 2 49) Graph the linear equation (slope-intercept form). y 2 x 50) Graph the linear inequality (slope-intercept form). 1 y x2 3 51) Graph the linear inequality (slope-intercept form). y x3 52) Graph the linear equation. y4 Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 7 53) Graph the linear equation. x 2 54) Graph the linear equation (standard form). 6x 2 y 8 55) Graph the linear equation (standard form). 3x 6 y 12 56) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form_________________________ Standard form_________________________ Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 8 57) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form_________________________ Standard form_________________________ 58) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form_________________________ Standard form_________________________ 59) Determine the slope of the line that goes through the points. 5,6 & 2,15 60) Determine the slope of the line......
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...STUDY OF SLOPE STABILITY IN LIGNITE MINES By Mamta Jaswal (090610122047) Nilay J. Patel (090610122029) Ashish D. Patel (090610122026) Satish B. Patel (090610122013) Supervised by: Prof. Rajesh Arora M. Tech. A project part-1 submitted to Gujarat Technological University In partial fulfilment of The Requirements for the Degree of Bachelor of Engineering In Mining Engineering October 2012 CERTIFICATE This is to certify that Ms. Mamta Jaswal of BE. Semester VII (Mining engineering) has completed her one full semester on project work Titled “STUDY OF SLOPE STABILITY IN LIGNITE MINES” Satisfactorily in partial fulfilment of requirement of Bachelor of Engineering In Mining Engineering, Gujarat Technology University, Ahmedabad in the year 2012. Date: / / 2012 Place: Palanpur Internal Guide Prof. V.J. Sharma Prof. Rajesh Arora Head of Department (Mining engineering) Seal of institute CERTIFICATE This is to certify that Mr. Nilay J. Patel of BE. Semester VII (Mining engineering) has completed his one full semester on project work Titled “STUDY OF SLOPE STABILITY IN LIGNITE MINES” Satisfactorily in...
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...CITY OF ATLANTA BUREAU OF DRINKING WATER Water Service Adjustment Request DATE: Dear Customer Service: We have received a high water bill for service at Account Number: leak was discovered which has been repaired by I understand that it is my responsibility to furnish proof that the leak existed and that repairs have been made. Date of repair(s) Location of repair(s) I have enclosed a purchase receipt and/or statement from repair person. a plumber’s receipt report A/an ; Please approve the maximum credit to adjust my account. Name: Mailing Address: Service Address: Phone Street Street City City State State Zip Zip Work: Home: OFFICE USE ONLY: Cycle Customer Service Personnel Date City of Atlanta Department of Watershed Management 55 Trinity Avenue, S.W Atlanta, Georgia 30303 Phone # 404-658-6500 Fax 404-602-4402 CITY OF ATLANTA BUREAU OF DRINKING WATER Water & Sewer Appeals Request Date: Name: Service Address: Mailing Address: City: Home Phone: Billing Date(s) of Disputed Bill NATURE OF APPEAL State: Business Phone: Zip Account No.: Note: All current charges and any past due amount that is not in dispute must be paid in order to avoid interruption of water service. Please return this form within ﬁve (5) days of receipt to: Bureau of Drinking Water Attn: Water & Sewer Appeals Request Customer Service Division 651-14th Street N.W Atlanta, Georgia 30318 City of Atlanta Department of Watershed Management 55 Trinity Avenue SW Atlanta,......
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...CJ340 Applied Criminal Justice Ethics Unit 4 Essay The Slippery slope is a term used to describe events that cannot be controlled once started. Gratuities is what pushes officers down the slippery slope path. Delattre (2011) stated “that the slippery slope of corruption begins with any gratuity, including the well-known free cup of coffee” (p.87). Gratuities sometimes lead officers to a lifetime of corruption. It was said that society plays a major role in police corruption. The three theories regarding pubic corruption are Society-at-Large Hypothesis, Structural or Affiliation Hypothesis and the Rotten Apple Hypothesis. Officers are held to a higher standard because they took an oath to protect and serve. When policeman accept gratuities it is seen as morally wrong. Gratuities can come in many forms such as free stuff like coffee, flowers, and other items given for a job well done. Some restaurant owners give a free cup of coffee to officers with the mindset of I scratch your back you scratch mine. “Some clearly want the police presence, but others want illegally parked customers to be left alone, and so on” (Delattre, 2011, p. 87). It was said that “Once an officer gets in the habit of receiving things for free, it is easier to accept a large bribe” (Petrocelli, 2006, p.1). Some officer’s try to justify that accepting a small gratuity is not a conflict in interest when it deals with morals. They say it’s......
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... • The slope-intercept formula for a line is y = mx + b, where m is the slope of the line and b is the y-intercept. • The point-slope formula for a line is y – y1 = m (x – x1). This formula uses a point on the line, denoted by (x1, y1), and the slope of the line, denoted by m, to calculate the slope-intercept formula for the line. Also, there is some information from Calculus you must use: Recall: • The first derivative is an equation for the slope of a tangent line to a curve at an indicated point. • The first derivative may be found using: A) The definition of a derivative : lim h →0 f (x + h ) − f ( x ) h B) Methods already known to you for derivation, such as: • Power Rule • Product Rule • Quotient Rule • Chain Rule (For a complete list and description of these rules see your text) With these formulas and definitions in mind you can find the equation of a tangent line. Consider the following problem: Find the equation of the line tangent to f ( x ) = x 2 at x = 2. Having a graph is helpful when trying to visualize the tangent line. Therefore, consider the following graph of the problem: 8 6 4 2 -3 -2 -1 1 2 3 The equation for the slope of the tangent line to f(x) = x2 is f '(x), the derivative of f(x). Using the power rule yields the following: f(x) = x2 f '(x) = 2x (1) Therefore, at x = 2, the slope of the tangent line is f '(2). f '(2) = 2(2) =4 (2) Now , you know the slope of the......
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...related to economic inequality? • • The poor take their place in the lower extremes of the distribution of income and wealth Poverty and inequality share causal factors http://www.pewsocialtrends.org/2015/12/09/4-middle-class-incomes-fall-further-behind-uppertier-incomes/ http://www.pewsocialtrends.org/2015/12/09/the-american-middle-class-islosing-ground/ Using graphs: a review • Slope of straight line – Ratio of vertical change “rise” over horizontal change “run” – Slope of straight line: Same numerical value (constant) – Negative slope: One variable falls, other rises – Positive slope: Both variables rise Using graphs: a review • Zero slope: Y value doesn’t change • Infinite slope: X value doesn’t change Using graphs: a review • How to measure slope Y Y C 11 C 9 8 Slope = 1/10 B A 0 8 3 13 (a) A X 0 Slope = 3/10 B 13 3 (b) X Using graphs: a review • Slope of a curved line – Different numerical value (not constant) Using graphs: a review • How to measure slope at a point on a curved graph: Slope of tangent (straight line) Using graphs: a review • Indifference curves – Axes - quantities of two goods consumed that produce some level of satisfaction (utility) – Curve - given quantity of satisfaction • Points on curve = quantities of two goods consumed that produce some level of satisfaction (utility) ...
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