A number x is chosen at random from the set { | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We are given the inequality $\frac{(x-10)(x-50)}{(x-30)} \ge 0$. Using the wavy curve method (sign scheme) for the expression $f(x) = \frac{(x-10)

Vedclass · Accepted Answer

$0.71$

Vedclass · Answer

(A) We are given the inequality $\frac{(x-10)(x-50)}{(x-30)} \ge 0$. Using the wavy curve method (sign scheme) for the expression $f(x) = \frac{(x-10)(x-50)}{(x-30)}$,the critical points are $x = 10, 30, 50$. The sign of $f(x)$ in different intervals is: - For $x - For $10 \le x - For $30 - For $x \ge 50$: $f(x) \ge 0$ Since $x \in \{1, 2, \dots, 100\}$,we look for integers $x$ in the intervals $[10, 30)$ and $[50, 100]$. In the interval $[10, 30)$,the integers are $\{10, 11, \dots, 29\}$. The number of such integers is $29 - 10 + 1 = 20$. In the interval $[50, 100]$,the integers are $\{50, 51, \dots, 100\}$. The number of such integers is $100 - 50 + 1 = 51$. The total number of favorable outcomes is $20 + 51 = 71$. The total number of possible outcomes is $100$. Therefore,$P(A) = \frac{71}{100} = 0.71$.

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, \dots, 100\}$. Define the event: $A =$ the chosen number $x$ satisfies $\frac{(x - 10)(x - 50)}{(x - 30)} \ge 0$. Then $P(A)$ is

Similar Questions

$A$ coin is tossed three times. Consider the following events:
$A$: 'No head appears',
$B$: 'Exactly one head appears',
$C$: 'At least two heads appear'.
Do they form a set of mutually exclusive and exhaustive events?

$A$ coin is tossed again and again. If tail appears on the first three tosses, then the chance that head appears on the fourth toss is

$A$ bag contains $5$ distinct Red,$4$ distinct Green,and $3$ distinct Black balls. If balls are drawn one by one without replacement,what is the probability of getting a particular red ball in the fourth draw?

$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

Two dice are thrown together. The probability that at least one will show its digit $6$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module