This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution to your questions: Part 1: Solve the equation for س (x) Step 1: Write down the equation. س = (5)/(25) - 7 + 60 Step 2: Simplify the fraction. س = 0.2 - 7 + 60 Step 3: Perform the subtraction and addition. س = -6.8 + 60 س = 53.2 The value of س is 53.2. Part 2: Regression Analysis We are given the following data for Year (x) and Exports (y): | Year (x_i) | Exports (y_i) | x_i^2 | x_i y_i | | :----------: | :-------------: | :-----: | :-------: | | 2 | 0.15 | 4 | 0.30 | | 7 | 0.16 | 49 | 1.12 | | 11 | 0.17 | 121 | 1.87 | | 13 | 0.18 | 169 | 2.34 | | 16 | 0.19 | 256 | 3.04 | | Sum | 0.85 | 599 | 8.67 | Step 1: Calculate the sums. n = 5 x_i = 2 + 7 + 11 + 13 + 16 = 49 y_i = 0.15 + 0.16 + 0.17 + 0.18 + 0.19 = 0.85 x_i^2 = 4 + 49 + 121 + 169 + 256 = 599 x_i y_i = 0.30 + 1.12 + 1.87 + 2.34 + 3.04 = 8.67 Step 2: Calculate the slope (b) of the regression line y = a + bx. The formula for b is: b = (n( x_i y_i) - ( x_i)( y_i))/(n( x_i^2) - ( x_i)^2) Substitute the values: b = (5(8.67) - (49)(0.85))/(5(599) - (49)^2) b = (43.35 - 41.65)/(2995 - 2401) b = (1.7)/(594) b ≈ 0.00286195 Step 3: Calculate the y-intercept (a) of the regression line. The formula for a is: a = ( y_i - b( x_i))/(n) Substitute the values: a = (0.85 - (0.00286195)(49))/(5) a = (0.85 - 0.14023555)/(5) a = (0.70976445)/(5) a ≈ 0.14195289 Step 4: Write the regression equation. The regression equation is y = a + bx. y = 0.14195 + 0.00286x The regression equation is y = 0.14195 + 0.00286x. Part 3: Forecast exports for year 20 Step 1: Use the regression equation and substitute x = 20. y_20 = 0.14195289 + 0.00286195(20) y_20 = 0.14195289 + 0.057239 y_20 = 0.19919189 Step 2: Round the forecast to an appropriate number of decimal places. y_20 ≈ 0.19919 The forecast for exports for year 20 is 0.19919. 3 done, 2 left today. You're making progress.