Add or subtract the following:  

USE THE QUADRATIC  FORMULA TO SOLVE THE QUADRATIC EQUATION:  

Add the following radical:  

Rewrite the following:  

Contrast negative and positive freedom (and rights), and make sure to discuss the role of government envisioned by each of these concepts of freedom.

Long Response.   Please analyze the 2024 presidential election, and in the analysis provide a paragraph about each of these three items: What happened in 2020; The 2024 Electoral College landscape for the candidates; and  Expectations about each candidate’s performance among demographic groups, including the campaigns’ tactics for reaching their goals.

Please discuss controversies surrounding voter ID laws, and indicate the significance of the Crawford v. Marion County decision of the Supreme Court.

Please address the significance of the Electoral Count Act, as revised after 2020.

Information for questions 5-7 The following figure shows three isoquants for a firm that produces candy, with units of labor on the horizontal axis, and units of capital on the vertical axis. Each isoquant is labeled with the output of candy that its combinations of labor and capital produce. Note that each grid spacing is 0.25 on both axes. Also shown are some auxiliary lines in solid black. The steepest line has slope = 2, and the three flattest lines all have slope = 1 (all of these slopes are in absolute value). Note that each of the auxiliary lines is tangent to an isoquant, and that its tangency point is marked with a dot.   Starting from the wage of w=50 and the rental rate of r=25, suppose that the rental rate increases to 50. Calculate the change in the amount of capital that the firm employs, in order to keep producing 15 units of candy at minimum cost. This can be an increase or a decrease, make sure to enter a positive number for an increase, and a negative number for a decrease.

Information for questions 16-17 A firm has short-run production function given by . Note that in the short run, we can replace K in the production function f(L,K) by whatever constant value K has in the short run, and so the production function becomes effectively only a function of L. Here, the firm is using 10 units of capital in the short-run. This firm’s short-run (total) cost function is given by .   Calculate the rental rate. Only the exact answer is accepted. Write 0 if the exact answer cannot be calculated with the information given.