answer:Based on the profitability index, the projects should be selected in the following order: 1. Project C (Profitability index = 0.35) 2. Project B (Profitability index = 0.33) 3. Project A (Profitability index = 0.31) Oxford Company should invest in Project C first, which requires an investment of 510,000. Then, they should invest in Project B, which requires an investment of 650,000. Finally, they should invest in Project A, which requires an investment of 810,000. This selection would allow Oxford Company to invest a total of 1,970,000, which exceeds their budget of 1,500,000. However, since Project D has the lowest profitability index (0.22), it should not be selected for investment.

answer:Using the substitution ln x - ln y = u iff x = ye^u, the differential equation becomes: ue^u,du=-dfrac{dy}{y} Solving for y, we get: y=Be^{-u(u+1)} Substituting back for u, we obtain: y=Be^{-(ln x - ln y)(ln x - ln y +1)} Simplifying and solving for xe^{-x/y}, we get: xe^{-x/y}=dfrac{B}{y}e^{frac{x}{y}}=g(y)

answer:To find the mode, we determine the number that appears most frequently in the sequence. After sorting the sequence, we can count the occurrences of each number: -7 appears once, -frac{20}{3} appears four times, -frac{17}{3} appears once, -frac{13}{3} appears four times, -frac{4}{3} appears three times, 4 appears four times, frac{16}{3} appears eight times, frac{29}{3} appears twice. The mode is the number with the highest count, which is frac{16}{3}, appearing eight times. Therefore, the mode of the sequence is frac{16}{3}.

answer:The second derivative of f(x) can be found by applying the chain rule twice. First, we find the first derivative: f'(x) = frac{d}{dx}left(6 - frac{15 x^3}{2}right)^2 = 2left(6 - frac{15 x^3}{2}right) cdot frac{d}{dx}left(6 - frac{15 x^3}{2}right) f'(x) = 2left(6 - frac{15 x^3}{2}right) cdot left(-frac{45 x^2}{2}right) f'(x) = -frac{45}{2} left(6x - frac{15x^3}{2}right) = -frac{270}{2} x + frac{675}{2} x^3 Now, we find the second derivative: f''(x) = frac{d}{dx}left(-frac{270}{2} x + frac{675}{2} x^3right) f''(x) = -frac{270}{2} + frac{2025}{2} x^2 f''(x) = -135 + 1012.5x^2 Simplifying further, we get: f''(x) = 135x^2 - 135 So, the second derivative of the function is f''(x) = 135x^2 - 135.