Given f(x) = x^2 - 5x + 4. If a number x is c | vedclass

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(C) We are given the function $f(x) = x^2 - 5x + 4$. We need to find the probability that $f(x) > 10$ for $x \in \{1, 2, 3, \dots, 20\}$.Solving the i

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$\frac{7}{10}$

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(C) We are given the function $f(x) = x^2 - 5x + 4$. We need to find the probability that $f(x) > 10$ for $x \in \{1, 2, 3, \dots, 20\}$.Solving the inequality $x^2 - 5x + 4 > 10$:$x^2 - 5x - 6 > 0$$(x - 6)(x + 1) > 0$Since $x$ is a natural number,$x + 1$ is always positive. Thus,we need $x - 6 > 0$,which implies $x > 6$.The natural numbers from $1$ to $20$ that satisfy $x > 6$ are $\{7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}$.The number of such values is $20 - 7 + 1 = 14$.The total number of natural numbers is $20$.The probability is $\frac{14}{20} = \frac{7}{10}$.

Given $f(x) = x^2 - 5x + 4$. If a number $x$ is chosen at random from the first $20$ natural numbers,then the probability that the chosen $x$ satisfies the inequality $f(x) > 10$ is

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