The long-run rate of unemployment to which an economy always gravitates is the

*************************Optional Problem [25 points] *************************   Find   where using eigenvalue decomposition of A.    

If aggregate demand equals output,

The quantity theory of inflation indicates that if the aggregate output is growing at 3% per year and the growth rate of money is 5%, then inflation is

[25 Points] Consider the following nonlinear system of equations: Use two iterations of Newton’s method to approximate a solution of this system with the initial guess (x0 , y0)T = (1, 1).  

BONUS:  Suppose you have a linear correlation coefficient of either 1 or -1 (which indicates perfect linear correlation, or that the response variable is wholly determined by a linear polynomial based on the predictor variable). What would be the corresponding value of the test statistic given a test to determine whether r shows positive or negative correlation? Explain your answer in writing below, using relevant formula and mathematical analysis. 

BONUS:  Suppose you have a linear correlation coefficient of either 1 or -1 (which indicates perfect linear correlation, or that the response variable is wholly determined by a linear polynomial based on the predictor variable). What would be the corresponding value of the test statistic given a test to determine whether r shows positive or negative correlation? Explain your answer in writing below, using relevant formula and mathematical analysis. 

Geography and geographical features  Indicate whether each geographical term refers to water (agua) or land (tierra). las cataratas [1] la colina [2] la cordillera [3] el lago [4] la llanura [5] el mar [6] la meseta [7]

Affirmative informal commands Match the phrases on the right with those on the left to create logical commands for someone traveling to Mexico City.  

Numbers 1,000 and higher Write the numbers (digits) following the model. Do not add any periods or commas in your answers. Model: You see → mil trescientos cincuenta y ocho   ;   You write → 1358 dos mil cuarenta [1] cuarenta mil seiscientos setenta [2] tres mil quinientos [3] mil quinientos [4] dos mil  [5] diez mil doscientos uno [6] dos millones [7] un millón cuatrocientos mil setecientos cincuenta [8] doscientos mil novecientos [9] setecientos mil [10]