answer:The probabilities are calculated using a standard normal distribution table, considering the standardized Z-score for each event. a. For the S&P 500: {eq}P(x>0) = 1 - P(Z<-frac{23.45}{20}) = 1 - P(Z<-1.1725) = 0.8795 b. For the S&P 500: {eq}P(x>10) = 1 - P(Z<-frac{10}{20}) = 1 - P(Z<-0.5) = 0.6915 c. For the S&P 500: {eq}P(x<-20) = P(Z<-frac{43.45}{20}) = P(Z<-2.1725) = 0.01491 d. For the S&P 500: {eq}P(x<-40) = P(Z<-frac{63.45}{20}) = P(Z<-3.1725) = 0.000756 e. For the NASDAQ: {eq}P(x>0) = 1 - P(Z<-frac{43.89}{30}) = 1 - P(Z<-1.463) = 0.9283 f. For the NASDAQ: {eq}P(x>10) = 1 - P(Z<-frac{33.89}{30}) = 1 - P(Z<-1.1297) = 0.8707 g. For the NASDAQ: {eq}P(x<-20) = P(Z<-frac{63.89}{30}) = P(Z<-2.13) = 0.0166 h. For the NASDAQ: {eq}P(x<-40) = P(Z<-frac{83.89}{30}) = P(Z<-2.796) = 0.00258 Note: The probabilities have been revised based on the correct calculation of Z-scores and standard normal distribution table lookups.

answer:c. decomposers Explanation: Decomposers are typically not depicted in Energy Pyramids, but they have an essential function in the ecosystem as they break down dead organisms and waste products, recycling nutrients back into the system.

answer:To differentiate the given function, we can use the product rule and the chain rule. The product rule states that if we have two functions f(x) and g(x), then the derivative of their product f(x)g(x) is given by: (fg)'(x) = f'(x)g(x) + f(x)g'(x) In this case, we can let f(x) = -(-7 x-8) and g(x) = sin left(8-8 x^3right). Then, we have: f'(x) = -(-7) = 7 g'(x) = cos left(8-8 x^3right) cdot (-8) = -8 cos left(8-8 x^3right) Substituting these values into the product rule, we get: (fg)'(x) = 7 sin left(8-8 x^3right) - (-7 x-8) cdot (-8) cos left(8-8 x^3right) Simplifying this expression, we get: f'(x) = 7 sin left(8-8 x^3right) + (7 x+8) cdot 8 cos left(8-8 x^3right) f'(x) = 7 sin left(8-8 x^3right) + 56 x cos left(8-8 x^3right) + 64 cos left(8-8 x^3right) f'(x) = 7 sin left(8-8 x^3right) + 56 x cos left(8-8 x^3right) + 64 cos left(8-8 x^3right) f'(x) = 7 sin left(8-8 x^3right) + 24 x^2 (7 x+8) cos left(8-8 x^3right) The answer is f'(x) = 7 sin left(8-8 x^3right)-24 x^2 (7 x+8) cos left(8-8 x^3right)

answer:1. Substitute x = -1 into the function f(x): f(-1) = (5(-1)^2 - frac{9}{2})^3 + log(3 - frac{5(-1)}{2}). 2. Simplify the expression inside the parentheses: f(-1) = left(frac{1}{2}right)^3 + logleft(3 - frac{5(-1)}{2}right). 3. Evaluate the cube of frac{1}{2}: f(-1) = frac{1}{8} + logleft(3 - frac{5(-1)}{2}right). 4. Evaluate the logarithm of frac{11}{2}: f(-1) = frac{1}{8} + logleft(frac{11}{2}right). 5. Use a calculator to approximate the value of logleft(frac{11}{2}right): f(-1) approx frac{1}{8} + 1.7328679 = 1.83. Therefore, the value of the function f(x) at the point x = -1 is approximately 1.83. The answer is f(-1) = left(5(-1)^2 - frac{9}{2}right)^3 + logleft(3 - frac{5(-1)}{2}right) = left(frac{1}{2}right)^3 + logleft(frac{11}{2}right) = frac{1}{8} + logleft(frac{11}{2}right) approx 1.83.