answer:To multiply these polynomials, we use the distributive property twice: [ p(x) cdot q(x) = (-2e x^2 - 5e x + 2e) cdot (-5e x^2 - e x) ] Expanding: [ = (-2e x^2) cdot (-5e x^2) + (-2e x^2) cdot (-e x) + (-5e x) cdot (-5e x^2) + (-5e x) cdot (-e x) + 2e cdot (-5e x^2) + 2e cdot (-e x) ] Simplify each term: [ = 10e^2 x^4 + 2e^2 x^3 + 25e^2 x^3 + 5e^2 x^2 - 10e^2 x^2 - 2e^2 x ] Combine like terms: [ = 10e^2 x^4 + (2e^2 + 25e^2) x^3 + (5e^2 - 10e^2) x^2 - 2e^2 x ] [ = 10e^2 x^4 + 27e^2 x^3 - 5e^2 x^2 - 2e^2 x ]

answer:The probability that fewer than 3 customers are in default is approximately 0.8455. To compute this, we can use the cumulative binomial distribution. In Excel, the formula "BINOM.DIST" is utilized with the following inputs: number of successes (2), number of trials (10), probability of success (0.14), and "True" for a cumulative probability. {eq}P(X le 2) = BINOM.DIST(2,10,0.14,True) approx 0.8455 {/eq} Alternatively, we can calculate it mathematically using the binomial probability formula: {eq}P(X) = dfrac{n!}{(X! cdot (n- X)!)} cdot p^X cdot (1-p)^{(n-X)} {/eq} Where: - n = 10 (number of trials) - X = 2 or 1 or 0 (number of successes, as we want fewer than 3) - p = 0.0014 (probability of default) Calculating for each possible value of X (0, 1, 2) and summing the probabilities: {eq}P(X le 2) = left( dfrac {10!}{(2! cdot 8!)} cdot 0.0014^2 cdot 0.9986^8 right) + left( dfrac {10!}{(1! cdot 9!)} cdot 0.0014^1 cdot 0.9986^9 right) + left( dfrac {10!}{(0! cdot 10!)} cdot 0.0014^0 cdot 0.9986^{10} right) = 0.8455 {/eq}

answer:To determine the reaction order for each reactant, we compare the initial rates of experiments where the concentration of one reactant changes while the other remains constant. For reactant A: {eq}rm{dfrac{rate_2}{rate_1} = dfrac{k[A]_2^m[B]_2^n}{k[A]_1^m[B]_1^n} = dfrac{0.10}{0.05} = left(dfrac{0.40}{0.20}right)^m} rm{2 = 2^m} rm{m = 1} {/eq} Therefore, the reaction is first-order with respect to A. For reactant B: {eq}rm{dfrac{rate_3}{rate_2} = dfrac{k[A]_3^m[B]_3^n}{k[A]_2^m[B]_2^n} = dfrac{0.20}{0.10} = left(dfrac{0.20}{0.10}right)^n} rm{2 = 2^n} rm{n = 1} {/eq} Therefore, the reaction is also first-order with respect to B. Overall reaction order: The overall reaction order is the sum of the individual reaction orders, which is 1 + 1 = 2.

answer:The directivity of a parabolic reflector is a measure of its ability to concentrate electromagnetic energy in a particular direction. It is defined as the ratio of the power radiated in the desired direction to the power that would be radiated by an isotropic antenna (an antenna that radiates equally in all directions). The directivity of a paraboloid reflector is given by the following formula: D = 4πA/λ^2 where: D is the directivity A is the area of the reflector λ is the wavelength of the electromagnetic radiation The area of a paraboloid reflector is given by the following formula: A = πD^2/4 Substituting this expression for A into the formula for directivity, we get: D = 4π(πD^2/4)/λ^2 Simplifying this expression, we get: D = πD^2/λ^2 This formula shows that the directivity of a paraboloid reflector is proportional to the square of its mouth diameter. The directivity of a paraboloid reflector is proportional to the square of its mouth diameter (D).