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question:Mesquite Limited is considering an investment proposal with the following cash flows: Initial Investment: 270,000 Year 1: 100,000 Year 2: 100,000 Year 3: 100,000 Year 4: 100,000 What is the payback period of this investment?
answer:The payback period is the amount of time it takes for an investment to generate enough cash flow to cover its initial cost. To calculate the payback period, we need to divide the initial investment by the annual net cash flow. In this case, the initial investment is 270,000 and the annual net cash flow is 100,000. Therefore, the payback period is: Payback Period = Initial Investment / Annual Net Cash Flow Payback Period = 270,000 / 100,000 Payback Period = 2.7 years Therefore, the payback period of this investment is 2.7 years.
question:Write the Lewis structure for the bicarbonate ion, {eq}HCO_{3}^{-} {/eq}, including all valence electrons and the formal charges for each atom.
answer:The Lewis structure of the bicarbonate ion, {eq}HCO_{3}^{-} {/eq}, can be represented as follows: 1. Count the total valence electrons: - Carbon (C): 4 valence electrons - Oxygen (O): 6 valence electrons each (3 oxygens total) - Hydrogen (H): 1 valence electron - Plus one electron from the negative charge (-1) Total valence electrons: {eq}4 + (3 times 6) + 1 + 1 = 24 {/eq} 2. Draw the structure: - Carbon (C) is the central atom. - It forms one single bond with each of the two oxygen atoms and one bond with hydrogen. - One of the oxygen atoms has a double bond with carbon. - The negative charge is distributed on the single-bonded oxygen. The Lewis structure is: <img src="https://latex.codecogs.com/png.latex?rm%20large%20H%7CO%5E%7B%2B%7D%7CO%5E%7B-%7D" alt="H-C=O^- - O^-" title="H-C=O^- - O^-"/> 3. Calculate the formal charges: - Carbon (C): {eq}rm Formal%20charge%20=%204-%20(4%20+%200)%20=%200 {/eq} - Hydrogen (H): {eq}rm Formal%20charge%20=%201-%20(1%20+%200)%20=%200 {/eq} - Double-bonded oxygen: {eq}rm Formal%20charge%20=%206-%20(4%20+%202)%20=%200 {/eq} - Single-bonded oxygen (with H): {eq}rm Formal%20charge%20=%206-%20(1%20+%205)%20=%200 {/eq} - Single-bonded oxygen (with -1 charge): {eq}rm Formal%20charge%20=%206-%20(2%20+%204)%20=%20-1 {/eq} In summary, the bicarbonate ion's Lewis structure shows that all atoms except for one single-bonded oxygen atom have a formal charge of zero, and this oxygen atom has a formal charge of -1.
question:Find the roots of the quadratic polynomial -10x^2 + 7x + 12.
answer:The roots of the polynomial can be found by factoring or using the quadratic formula. Factoring, we have: -10x^2 + 7x + 12 = -(2x - 3)(5x + 4) Setting each factor equal to zero: 2x - 3 = 0 or 5x + 4 = 0 Solving for x in each equation: x = frac{3}{2} or x = -frac{4}{5} Thus, the roots are x = frac{3}{2} and x = -frac{4}{5}.
question:Calculate the new fare, rounded to the nearest penny, after applying a 12% increase to an initial fare of £2.90.
answer:To calculate the new fare, you can use either of these two methods: 1. Multiply the original fare by the percentage increase and add it to the original fare: ( 2.90 + 0.12 times 2.90 = 2.90 + 0.348 = 3.248 ) Rounded to the nearest penny, this is £3.25. 2. Multiply the original fare by the decimal equivalent of the percentage increase: ( 2.90 times 1.12 = 3.248 ) Again, rounded to the nearest penny, this is also £3.25. Both methods yield the same result.