answer:1. The taxable income is calculated as the sum of ordinary income and interest income minus the payment made: {eq}text{Taxable Income} = 175,000 + 150,000 - 50,000 = 275,000 {/eq} With a flat 33% tax rate: {eq}text{Taxes Paid} = 0.33 * 275,000 = 90,750 {/eq} After-tax profits: {eq}text{After-Tax Profits} = 275,000 - 90,750 = 184,250 {/eq} 2. Applying the tax brackets: Income Bracket | Taxable Income | Tax Rate | Amount of Tax --- | --- | --- | --- 0 to 35,000 | 35,000 | 5% | 1,750 35,001 to 85,000 | 49,999 | 10% | 4,999.90 85,001 to 110,000 | 24,999 | 15% | 3,749.85 110,001 to 155,000 | 44,999 | 25% | 11,249.75 >155,001 | 119,999 | 42% | 50,399.58 Total taxes paid: {eq}text{Total Tax Paid} = 1,750 + 4,999.90 + 3,749.85 + 11,249.75 + 50,399.58 = 72,149.08 {/eq} 3. The marginal tax rate is the tax rate applied to the last dollar earned, which in this case is 42%. To calculate the average tax rate, divide the total taxes by the taxable income: {eq}text{Average Tax Rate} = frac{72,149.08}{275,000} times 100 = 26.24% {/eq} Based on these calculations, the Jaguars would prefer the bracketed tax structure, as it results in a lower tax liability than the flat rate.

answer:-frac{20 x^2}{2}+frac{32 x}{2}+frac{4}{2} = -10 x^2+16 x+2 Explanation: To find the sum of two polynomials, we simply add the coefficients of like terms. Therefore, we have: p(x) + q(x) = (-frac{9 x^2}{2}+frac{25 x}{2}-5) + (-frac{11 x^2}{2}+7 x+frac{9}{2}) = -frac{9 x^2}{2}-frac{11 x^2}{2}+frac{25 x}{2}+7 x-5+frac{9}{2} = -frac{20 x^2}{2}+frac{32 x}{2}+frac{4}{2} = -10 x^2+16 x+2

answer:a) The derivative of ( f(x) ) is: [ f'(x) = 1 - frac{1}{x} ] Setting the derivative to zero gives us the critical number: [ 0 = 1 - frac{1}{x} ] [ x = 1 ] b) The derivative of ( f(x) ) is: [ f'(x) = frac{1}{3} cdot frac{4x - 1}{x^{2/3}} ] Setting the derivative to zero gives us the critical number: [ 0 = frac{1}{3} cdot frac{4x - 1}{x^{2/3}} ] [ x = frac{1}{4} ] c) For this piecewise function, there are no critical numbers because the derivative does not change sign at the points where the function changes its form. d) The derivative of ( f(x) ) is: [ f'(x) = (x - 1)(x + 3) + |x - 1| ] Setting the derivative to zero gives us: [ 0 = (x - 1)(x + 3) + |x - 1| ] This equation yields two critical numbers: [ x = -1 ] Note that ( x = 1 ) is not a critical number because it results in a removable discontinuity in the derivative. In summary, the critical numbers are: a) ( x = 1 ) b) ( x = frac{1}{4} ) c) No critical numbers d) ( x = -1 )

answer:First, we must assume that [hat{B}, hat{C}] = 0 as well, so its eigenvalues in any representation must be constants. Then, we can use Dirac's "standard ket" |varpirangle to define our representation as f(a) = langle a| F(hat{A}) | varpi rangle, where F is the power series of f. From this, we can derive that [hat{B}, F(hat{A})] = -iC F'(hat{A}), where F' is the derivative of F. Since B|varpirangle = 0, we have langle a| hat{B} F(hat{A}) | varpi rangle = -iC partial_a f(a). Therefore, hat{B} f(a) = -iC partial_a f(a).