answer:First, we can multiply the entire expression by frac{4}{4} to get rid of the fractions: -7x^2 + frac{7x}{4} + frac{105}{8} = -7x^2 + frac{7x}{4} cdot frac{4}{4} + frac{105}{8} cdot frac{4}{4} = -7x^2 + 7x + frac{105}{2} Now, we can factor the quadratic expression using the quadratic formula: x = frac{-b pm sqrt{b^2 - 4ac}}{2a} where a, b, and c are the coefficients of the quadratic equation. In this case, we have: a = -7, quad b = 7, quad c = frac{105}{2} Substituting these values into the quadratic formula, we get: x = frac{-7 pm sqrt{7^2 - 4(-7)left(frac{105}{2}right)}}{2(-7)} = frac{-7 pm sqrt{49 + 1470}}{-14} = frac{-7 pm sqrt{1519}}{-14} = frac{-7 pm 39}{-14} There are two possible solutions: x = frac{-7 + 39}{-14} = -frac{32}{-14} = frac{16}{7} x = frac{-7 - 39}{-14} = -frac{46}{-14} = frac{23}{7} Therefore, the factors of the quadratic expression are: (x - frac{16}{7})(x - frac{23}{7}) Multiplying these factors together, we get: (x - frac{16}{7})(x - frac{23}{7}) = x^2 - frac{39x}{7} + frac{368}{49} = x^2 - frac{39x}{7} + frac{105}{8} = -7x^2 + 7x + frac{105}{8} = -7 left(x + frac{5}{4}right) left(x - frac{3}{2}right) Therefore, the factors of the quadratic expression -7x^2 + frac{7x}{4} + frac{105}{8} are -7 left(x + frac{5}{4}right) left(x - frac{3}{2}right). The answer is -7 left(x + frac{5}{4}right) left(x - frac{3}{2}right)

answer:The sorted numbers in ascending order are: -frac{26}{3}, -5, 0, 1, 2, 3 sqrt{2}, 7, 8.

answer:** The calculated internal rate of return (IRR) on the given investment is **8%**. **Explanation:** The net annual cash inflows are calculated as follows: Net annual cash inflows = Annual cash inflows - Annual cash outflows = 382,550 - 154,990 = 227,560 The IRR is the discount rate that makes the net present value (NPV) of the investment equal to zero. The NPV is calculated as follows: NPV = -Initial investment + Present value of future cash flows The present value of future cash flows is calculated using the following formula: PV = CF / (1 + r)^n where: * CF is the cash flow * r is the discount rate * n is the number of years Using the given information, we can calculate the NPV as follows: NPV = -2,000,045 + 227,560 / (1 + 7%)^1 + 227,560 / (1 + 7%)^2 + ... + 227,560 / (1 + 7%)^12 + 716,870 / (1 + 7%)^12 NPV = 0 Solving for r using trial and error or a financial calculator, we find that the IRR is 8%. This means that the investment is expected to generate an annual return of 8%.

answer:The demand for gasoline in Japan is inelastic, meaning that it is not very sensitive to changes in the market price of gasoline. However, the demand for gasoline is cross-price elastic, meaning that it is sensitive to changes in the prices of substitute goods, such as electric-powered cars. Therefore, a fall in the price of electric-powered cars would lead to an increase in the demand for electric-powered cars and a decrease in the demand for gasoline-powered cars. This is because consumers would substitute away from gasoline-powered cars to electric-powered cars, which are now relatively cheaper. As a result, the overall demand for gasoline in Japan would decrease. In summary, even though the demand for gasoline in Japan is inelastic with respect to its own price, it is still responsive to changes in the prices of substitute goods, such as electric-powered cars.