In a right angled triangle we can use Pythagoras theorem to determine third side in case two sides are given.
The formula of Pythagoras theorem is given by:

Where x , y and z are sides of triangle , z is hypotenuse.
Now we use this formula to find hypotenuse.
Plugging other two sides which are 5 in. and 12 in.



Taking square root on both sides
square root of 169 is 13
so we have z=13
Hypotenuse is 13 inches.
Answer:
5%
Step-by-step explanation:
Hospital A (with 50 births a day), because the more births you see, the closer the proportions will be to 0.5.
Hospital B (with 10 births a day), because with fewer births there will be less variability.
The two hospitals are equally likely to record such an event, because the probability of a boy does not depend on the number of births
Answer:
The answer is below
Step-by-step explanation:
The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places.
(a) What is the probability that more than three aircraft arrive within an hour?
(b) If 30 separate one-hour intervals are chosen, what Is the probability that no interval contains more than three arrivals?
(c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.1.
Solution:
a) A poisson distribution is given by the formula:

λ = 1 hour
Therefore:
P(X > 3) = 1 - P(X < 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(x = 3)]




P(X > 3) = 1 - [0.3679+0.3679 + 0.1839 + 0.0613] = 0.019
b) Assuming 30 1 hour intervals, hence:
![P(X \leq 3)^{30}=[1-P(X\geq 30)]^{30}=(1-0.019)^{30}=0.5624](https://tex.z-dn.net/?f=P%28X%20%5Cleq%203%29%5E%7B30%7D%3D%5B1-P%28X%5Cgeq%2030%29%5D%5E%7B30%7D%3D%281-0.019%29%5E%7B30%7D%3D0.5624)
c) mean = 1 hour
mean = 1 / λ
1 = 1 / λ
λ = 1
The cumulative distribution function of a continuous variable is:


Answer:
60
Step-by-step explanation:
if it went down one more it would be 30