Answer:
a) 3.47% probability that there will be exactly 15 arrivals.
b) 58.31% probability that there are no more than 10 arrivals.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
If the mean number of arrivals is 10
This means that 
(a) that there will be exactly 15 arrivals?
This is P(X = 15). So


3.47% probability that there will be exactly 15 arrivals.
(b) no more than 10 arrivals?
This is 














58.31% probability that there are no more than 10 arrivals.
Answer:
Step-by-step explanation:
<u><em>answer may vary sorry i could not seem to get this question sorry try asking someone else </em></u>
The position function of a particle is given by:

The velocity function is the derivative of the position:

The particle will be at rest when the velocity is 0, thus we solve the equation:

The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
![t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Substituting:
![\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81-4%282%29%28-18%29%7D%7D%7B2%282%29%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81%2B144%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B225%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm15%7D%7B4%7D%20%5Cend%7Bgathered%7D)
We have two possible answers:

We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
Answer:
(x-7)^2+(y-8)^2=121
Step-by-step explanation: