answer:To avoid double counting, the value of intermediate goods is not directly included in the calculation of GDP. Since intermediate goods are used in the production of final goods, their value is already reflected in the value of the final goods. Including the value of intermediate goods separately would lead to an overestimation of economic output.

answer:To find the Taylor series expansion of the inverse of x^4 around x = 5, we first need to find the derivatives of the inverse function. Let y = x^{-4}. Then, y' = -4x^{-5} y'' = 20x^{-6} y''' = -120x^{-7} Evaluating these derivatives at x = 5, we get y'(5) = -4(5)^{-5} = -frac{4}{3125} y''(5) = 20(5)^{-6} = frac{20}{15625} y'''(5) = -120(5)^{-7} = -frac{120}{78125} Now, we can write the Taylor series expansion of y = x^{-4} around x = 5 as y = y(5) + y'(5)(x-5) + frac{y''(5)}{2!}(x-5)^2 + frac{y'''(5)}{3!}(x-5)^3 + cdots = 5^{-4} - frac{4}{3125}(x-5) + frac{20}{15625}frac{(x-5)^2}{2} - frac{120}{78125}frac{(x-5)^3}{6} + cdots = frac{1}{625} - frac{4}{3125}(x-5) + frac{10}{15625}(x-5)^2 - frac{20}{78125}(x-5)^3 + cdots Since we only want the third-order Taylor series expansion, we stop after the term involving (x-5)^3. Therefore, the third-order Taylor series expansion of the inverse of x^4 around x = 5 is frac{1}{625} - frac{4}{3125}(x-5) + frac{10}{15625}(x-5)^2 - frac{20}{78125}(x-5)^3 The answer is frac{7 (x-625)^3}{6250000000}-frac{3 (x-625)^2}{2500000}+frac{x-625}{500}+5

answer:To find the values of x, y, and z, we can solve this system of equations. First, we can multiply the second equation by 2 to eliminate z when we add the two equations together: begin{align*} -20x + 10y + 2z &= -10 end{align*} Now, add the first equation to this modified second equation: begin{align*} (5x + 9y - 2z) + (-20x + 10y + 2z) &= 2 - 10 5x - 20x + 9y + 10y - 2z + 2z &= -8 -15x + 19y &= -8 end{align*} Next, we can solve for x in terms of y: begin{align*} x &= frac{19y + 8}{15} end{align*} Substitute this expression for x into the first equation: begin{align*} 5left(frac{19y + 8}{15}right) + 9y - 2z &= 2 end{align*} Simplify and solve for y: begin{align*} frac{95y + 40}{15} + 9y - 2z &= 2 95y + 40 + 135y - 30z &= 30 230y - 30z &= 30 - 40 230y - 30z &= -10 10y - z &= -frac{1}{3} end{align*} Now, let's solve for z in terms of y: begin{align*} z &= 10y + frac{1}{3} end{align*} Substitute the expressions for x and z back into the second equation: begin{align*} -10left(frac{19y + 8}{15}right) + 5y + (10y + frac{1}{3}) &= -5 -38y - 16 + 5y + 10y + frac{1}{3} &= -5 -13y - frac{47}{3} &= -5 -39y - 47 &= -15 -39y &= -15 + 47 -39y &= 32 y &= -frac{32}{39} end{align*} Now, substitute y back into the expressions for x and z: begin{align*} x &= frac{19 left(-frac{32}{39}right) + 8}{15} x &= frac{-608 + 312}{585} x &= frac{-296}{585} z &= 10 left(-frac{32}{39}right) + frac{1}{3} z &= frac{-320}{39} + frac{13}{39} z &= frac{-287}{39} end{align*} However, the provided answer {17,13,100} is not correct. The correct solution is: begin{align*} x &= frac{-296}{585}, quad y = -frac{32}{39}, quad z = frac{-287}{39} end{align*}

answer:Direct materials cost per equivalent unit = Total cost of direct materials / Equivalent units for direct materials = 510,000 / 8,500 tons = 60 per ton Conversion cost per equivalent unit = Total conversion costs for the period / Equivalent units for conversion = 81,200 / 8,120 tons = 10 per ton Direct materials cost per equivalent unit: 60 per ton Conversion cost per equivalent unit: 10 per ton