Answer:
a) 0.96
b) 0.016
c) 0.018
d) 0.982
e) x = 2
Step-by-step explanation:
We are given with the Probability density function f(x)= 2/x^3 where x > 1.
<em>Firstly we will calculate the general probability that of P(a < X < b) </em>
P(a < X < b) =
=
=
{ Because
}
=
=
=
=
a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }
Comparing with general probability we get,
P(1 < X < 5) =
=
= 0.96 .
b) P(X > 8) = P(8 < X < ∞) = 1/
- 1/∞ = 1/64 - 0 = 0.016
c) P(6 < X < 10) =
=
= 0.018 .
d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)
=
+ (1/
- 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
e) We have to find x such that P(X < x) = 0.75 ;
⇒ P(1 < X < x) = 0.75
⇒
= 0.75
⇒
= 1 - 0.75 = 0.25
⇒
=
⇒
= 4 ⇒ x =
Therefore, value of x such that P(X < x) = 0.75 is 2.
The algebra tiles show two equal factors. They are (x + 4).
Then, the perfect square is the product of the two equal factors, (x + 4) * (x +4).
That is (x + 4)^2.
Then develop that perfect square to find the constant term.
(x + 4)^2 = x^2 + 8x + 16.
That means that the constant term needed to complete the trinomial is 16.
Answer: 16
Quadratic equation which has no solution gives zero for the value of d.
d = b² - 4ac
0 = 3² +- 4(-1)c
-9 = +_ 4c
c = -9/-4 pr 9/-4
c = 9/4 or -9/4
In short, Your Answers would be Option C & E
Hope this helps!