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.
Hello.
The answer is choice A. angle 1 = 118, angle 2 = 118
Explanation:
The four angles above are congruent (meaning the same) to the ones beneath.
Angles 1 and 2 are also congruent, so they will measure the same.
Lets label the angles above A, B, C, D. B being the known angle, which is 118°. The angles beneath can be labelled E, F, G, H.
∠B ≅ ∠D
∠ABCD ≅ ∠EFGH
∠BD ≅ ∠FH
FH (or 1 and 2) equal 118.
Answer:
5:2
Step-by-step explanation:
Start with what the question is asking for, which is the ratio of math problems to minutes.
With ratios "to" also means ":", so you can change it to math problems : minutes.
Then, substitute the numbers for the labels. Math problems = 10 and minutes = 4, so now you have 10:4
Lastly, to simplify the ratio, find the greatest common factor, in this case 2, and divide both sides, which gives you your answer 5:2
First either add or subtract the number in the parenthesis (3^2-4) which equals to 5
90/[10+5) add the number in the parenthesis again (always do the parenthesis first) [10+5]= 15.
lastly divide 90/15 which equals to 6
always remember (PEMDAS)