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.
Answer:
B. 6 inches
Step-by-step explanation:
To find how wide it is, multiply the length by 3/4
8(3/4)
= 6
The width of the rectangle in 6 inches.
So, the correct answer is B. 6 inches
1/2, because 3/10 + 1/5 = 5/10. that means that the other part of 1 is 5/10 or 1/2
The table models an exponential relationship, and the equation of the table is 
<h3>How to analyze the table of values?</h3>
The table of values is given as:
x 0 1 2 3 4
y 4 2 1 1/2 1/4
The above table shows an exponential model
An exponential model is represented as:

When x = 0 and y = 4, we have

Evaluate
a = 4
When x = 1 and y = 2, we have

Evaluate

Substitute 4 for a
4b = 2
Divide both sides by 4
b = 1/2
Substitute 4 for a and 1/2 for b in 

Hence, the equation of the table is 
Read more about exponential models at:
brainly.com/question/11464095
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