A certain country uses a progressive tax system. The amount of tax consists of a linear part proportional to the income and a nonlinear part depending on the income by a power law. The total amount of tax is determined by the formula T(W)=aW+(bW+c)p, where W is the income; p is the exponent, a,b,c are some positive numbers. At what level of income the tax rate will be minimal?

1.4 Which of the following equations are linear? (iii) x = -7y + 3z (i) x + 5xy – 2z = 1 1 (v) VTx + v2y + (ii) x + 3y + z = 2 (iv) e" – z = 4 z = 71/3 (a) (i), (iii) and (v) (b) (iii) and (iv) (c) (ii), (iii) and (v) (d) (ii) and (iii) (e) None of the above.

4. Linearize the following nonlinear functions: a. Mä + b(x² – 1) + kx = 0 k and b are positive values and greater than zero. b. The following couples function x +y– 2y² = -4 x² + y² = 8 undefined

1 4. Which of the following equations gives the data in the table above ? (A) y = x+ 1 (B) y= (x + 1) (C) y = x2 +1 (D) y = x2 + x (E) y = (x + 1)² + x X O H m5

1. Regression analysis was applied to return rates of sparrow hawk colonies. Regression analysis was used to study the relationship between return rate (x: % of birds that return to the colony in a given year) and immigration rate (y: % of new adults that join the colony per year). The following regression equation was obtained. ! = 31.9 – 0.34x Based on the above estimated regression equation, if the return rate were to decrease by 10% the rate of immigration to the colony would:  a. increase by 34%  b. increase by 3.4%  c. decrease by 0.34%  d. decrease by 3.4%ood alcohol by exactly 0.018/   2. In regression analysis, the variable that is being predicted is the  a. response, or dependent, variable  b. independent variable  c. intervening variable  d. is usually x   3. The correlation coefficient is used to determine:  a. A specific value of the y-variable given a specific value of the x-variable  b. A specific value of the x-variable given a specific value of the y-variable  c. The…

Write down the linear equation where the standard error in the parentheses below the coefficients. Estimate a real GDP per capita regression of Malaysia from 1970 to 2019 as follows:ln RGDPCt = a + b1 ln PDEBTt + b2 ln HCt + b3 ln INFLATIONt + b4 ln TRADEt + e (1) where the determinants are:PDEBT – public debtHC – human capitalINFLATION – inflationTRADE – total tradeRegression result is displayed on the table provided. Please . Asap. Thanks!

5. The table below shows the height, in feet, of a rock thrown from the top of a building each second after it was thrown. Which model would fit this data best: linear, quadratic, or cubic? Use the model to write a best-fit equation, then estimate the height of the rock at 5 seconds. Time Height 0 250 1 280 2 284 249 202 3 4

Create a quadratic model for the data shown in the table 1 -1 X -1 -1 y Oy=0.85r² +0.11 - 1.78 y = 0.98x² -0.74 - 0.82 y = 0.112²1.78x +.9998 X y = -0.85x² -0.11x +1.78 2 2 5 20

A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.