A natural number is selected at random from the set x = { x : 1 ≤ x ≤ 100 }. The probability that the number satisfies the inequality x 2 - 13x ≤ 30 is?

Q: A natural number is selected at random from the set x = { x : 1 ≤ x ≤ 100 }. The probability that the number satisfies the inequality x 2 - 13x ≤ 30 is?

x2 - 13 x - 30 ≤ 0 ⇒ (x + 2) (x - 15) ≤ 0 ⇒ -2 ≤ x ≤ 15 But x is a natural number. ∴ 1 ≤ x ≤ 15 ∴ Reqd. Probability P = 15/100 = 3/20

5/9
9/50
3/20
7/9

Correct Answer: 3/20

Explanation:

x² - 13 x - 30 ≤ 0
⇒ (x + 2) (x - 15) ≤ 0
⇒ -2 ≤ x ≤ 15
But x is a natural number.
∴ 1 ≤ x ≤ 15
∴ Reqd. Probability P = 15/100 = 3/20

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