2. The Lorenz curve of a particular society is given by L(x) = Ax? + Bx. Suppose that the poorest half of the population receive only 35% of the society's income and that the Gini index of this society is 0.2 Find A and B.
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- Refresh your Math & Graphing Skills SOP-A D For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship. X-axis Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled The average grade received" and Y-axis should be labeled "The number of hours spent studying". Scenario As the number of hours spent studying rises, the average grade received rises. As the number of hours spent studying falis, the likelihood of getting an A falls. As the number of hours spent watching TV rises, the average grade received falls. True True or False: Line B has a slope of infinity. O False www Relationship Line YSolve the following problems by using the inverse of the matrix involved. (a) An automobile factory producess two models, A and B. Model A requires 1 labor hour to paint and 1 labor hour to polish; model B requires 1 labor hour for each 2 process. During each hour that the assembly line is operating, there are 80 labor hours available for painting and 65 labor hours for polishing. How many of each model can be produced each hour if all the labor hours available are to be utilized? (b) Suppose each model A requires 14 widgets and 10 shims and each model B requires 10 widgets and 7 shims. The factory can obtain 1050 widgets and 745 shims each hour. How many cars of each model can it produce while using all the parts available? (a) Model A: Model B: (b) Model A: Model B:The following graph contains four lines (A, B, C and D), each of which has a slope that is either positive, negative, zero, or infinite. Y-axisX-axisBDCA For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship. Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled “ ice-cream" and Y-axis should be labeled "The temperature". Scenario Relationship Line As the temperature rises, the demand for ice-cream rises. Negative As the temperature rises, the demand for hot cocoa falls. Positive As the temperature falls, the demand for popsicles falls. Negative True or False: Line B has a slope of infinity.…
- Suppose your worst enemy is standing over by the carnival games at (2,5) and wants to avoid you AT ALL COSTS. She takes a path that is parallel to yours and ends up at the roller coaster. What is an equation of the line representing your enemy's path?The following graph contains four lines (A, B, C and D), each of which has a slope that is either positive, negative, zero, or infinite. For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship. Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled “ The average grade received" and Y-axis should be labeled "The number of hours spent studying". Scenario: As the number of hours spent studying rises, the average grade received rises. Relationship: Positive or Negative Line: A, B, C, or D? Scenario: As the number of hours spent watching TV rises, the average grade received falls. Relationship: Positive or Negative Line: A, B, C, or D? Scenario: As the…The relationships between some economic variables w, y, and z and another economic variable, x, are shown in the graph above. Notice that the horizontal axis is labeled “x” since they are all functions of x but the vertical axis is not labeled. 1-1 Does the vertical axis need a label in order for you to be able to understand the graph?1-2What value of x minimizes w?
- Examine the product of the two matrices to determine if each is the inverse of the other. 1 - 1 1 - 5 5 2 - - 3 - 1 3 1 - 3 - 5 8 3 Are the matrices inverses of each other? Yes NoDetermine the shortest path of going from node 1 to node 6 using Dijkstra's Algorithm. Remember to indicate the length of the path and which arcs make up the shortest paths. Preserve all node labels (put newer labels to the right of earlier labels and indicate a permanent label by underlining it (see example node 7 and Monday Aug 31's class). If there are 2 paths that have the same length, please mention them both. 7 Graph: ∞, 12,7, 5, 3 2 3 2 4 4 5 3 1 6Draw a graph of the following function: y= e^x/(1+e^x)
- Mika earns $232 per week which she spends entirely at the grocery store, purchasing either food or alcohol. The price of food is $1/unit, while the price of alcohol is $3/unit. If Mika receives an additional $75/week in food stamps that can only be only be used to buy food at the grocery store (so, this money could be used to buy food but NOT alcohol), what is the vertical coordinate of the vertical intercept of Mika's budget constraint if she were to graph quantity of food on the horizontal axis and quantity of alcohol on the vertical axis? (Note: The answer may not be a whole number, so round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully).Could I get some help seeing the equation for L and an explanation on how to graph please?f(x1,x2) 4 2 0 -2 -4 −1 2 0 1 1 0 2 -1 X1 3-2 x2 Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3 Consider the following function: f(x1, x2) = 2x1 - x-x+3. - For your visual convenience, a portion of the function is depicted in Figure 2. (a) Compute the gradient vector of f. (b) Compute the Hessian matrix of f. (c) Determine all points that yield stationary values of f. (d) Use the second-order conditions to determine whether each of the stationary val- ues of f is a maximum, a minimum, or neither.