Among the most famous of all meteor showers are the Perseids, which occur each year in early August. In some areas the frequency of visible Perseids can be as high as 40 per hour. What is the probability that an observer who has just seen a meteor will have to wait at least 5 minutes before seen another.

the required probability is 0.0357

Step-by-step explanation:

Given the data in the question;

X-Exp( λ = 40/60 = 0.6667

Pdf: f( x ) = λe^(-λx), 0 < x

so

Cdf: P( X < x ) = 1 - e^(-λe)

( X ≤ x ) = 1 - e^(-λe), for x > 0 ⇒ p( X > x ) = e^(-λe)

now to wait at least 5 minutes before seen another

p(X  > 5 ) = e^(-λe)

we substitute

p(X  > 5 ) = e^(-0.6667 × 5)

p(X  > 5 ) = e^(-3.3335)

p(X  > 5 ) = 0.035668 ≈ 0.0357

Therefore,  the required probability is 0.0357

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

just sum

10 + 10 = 20