B=x9 + 1
C=81x3 + 16x6
D=x6 + x3
E=27x9 + x12
F=9x3 + 27x9
Translating word problems to algebraic expressions: One number exceeds another by 24. The sum of the numbers is 58. What are the numbers?
solve for c
Answer:
Step-by-step explanation:
Given that you choose at random a real number X from the interval [2, 10].
a) Since this is a contnuous interval with all number in between equally likely
E = probability for choosing a real number is U(2,10)
pdf of E is
b) P(X>5) =
For
P(X<5 or x>7) = 1-P(5<x<7)
=
The density functionof a real number selected randomly within the range [2,10] is 1/8, with the probability of an event being the difference between the two values divided by 8. The probabilities that X is greater than 5, lies between 5 and 7 and that the inequality X^2 - 12X + 35 > 0 always holds are 5/8, 1/4 and 1 respectively.
The subject of this question is probability, particularly continuous uniform distribution. (a) A real number X selected from a certain interval [2, 10] has a continuous uniform distribution. Hence, the density function f(x) = 1/(b-a) = 1/8 for 2 ≤ x ≤ 10 and0otherwise. The probability of an event E, where E is [a,b], is the integral of f(x) from a to b, which is (b-a)/(10-2).
(b) Probability that X > 5 is the integral of f(x) from 5 to 10, which is (10-5)/8 = 5/8. Probability that 5 < X < 7 is the integral from 5 to 7, which is (7-5)/8 = 1/4. Lastly, the inequality X^2 - 12X + 35 > 0 factors out to (X-5)^2 + 10 > 0 which is always true as square number is always non-negative, thus the probability is 1.
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