Mathematics: Rose and Jack plan to study together for the Math test. They decide to meet at the library between 8:00pm and 8:30pm. Assume that they each arrive (independently) at a random time (uniformly) in this interval. It is possible that someone has to wait up to 30 minutes for the other to arrive. (a). What is the probability that someone (Rose or Jack, whichever arrives ﬁrst) must wait more than 20 minutes until the other one arrives? What is the probability that Joe waits more than 20 minutes? (b). What

Rose and Jack plan to study together for the Math

Ответ:

sr814952

22.01.2022

Mathematics

(a) 1/3

(b) 1/15

Step-by-step explanation:

(a)Let X denote the waiting time in minutes. It is given that X follows a uniform distribution, and since the variable being measured is time, we assume it to be a continuous uniform distribution.

$f_X(x) =\begin{cases} \frac{1}{30} & 0\leqx\leq 30\\ 0 & otherwise \end{cases}$

Now

$P(X20) = \int_{20}^{30}f_X(x) = \frac{1}{30} \times 10 = \frac{1}{3}$ .

Jack or Rose arriving first is equally likely, therefore the probability of Jack waiting is just the half of the above obtained probability i.e $\frac{1}{6}$

(b)Using the formula for the expectation of a uniform continuous distribution,

$E(X) = \frac{30+0}{2} = 15$

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Ответ:

avablankenship

03.04.2023

Mathematics

Earth diameter = 12,750 km
Earth radius = 6,375 km
Sphere Surface Area =   4 • π • r²
Sphere Surface Area =    4 * 3.14159 * 6375^2
Sphere Surface Area =    4 * 3.14159 * 40,640,625
Earth's Entire Surface Area =    510,704,724 square kilometers
Surface NOT covered by water = 510,704,724 * .3
Surface NOT covered by water = 153,211,417 square kilometers

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