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(D) The given function is $f(x) = x^3 - 16x^2 + 20x - 5$. To find the interval where the function is strictly decreasing,we find its derivative: $f'(x

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$\frac{1}{6}$

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(D) The given function is $f(x) = x^3 - 16x^2 + 20x - 5$. To find the interval where the function is strictly decreasing,we find its derivative: $f'(x) = 3x^2 - 32x + 20$. Setting $f'(x) Factoring the quadratic: $(3x - 2)(x - 10) This inequality holds for $x \in (\frac{2}{3}, 10)$. The set of numbers is $S = \{1, 3, 5, \dots, 59\}$. The number of elements in $S$ is $n(S) = 30$. We need to find the numbers from the set $S$ that lie in the interval $(\frac{2}{3}, 10)$. These numbers are $E = \{1, 3, 5, 7, 9\}$. The number of favorable outcomes is $n(E) = 5$. The probability is $P = \frac{n(E)}{n(S)} = \frac{5}{30} = \frac{1}{6}$.

If a number is drawn at random from the set {$1, 3, 5, 7, \dots, 59$},then the probability that it lies in the interval in which the function $f(x) = x^3 - 16x^2 + 20x - 5$ is strictly decreasing,is

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