Answer:
We need more info.
Step-by-step explanation:
Answer:
3164.56
Step-by-step explanation:
5*5*5*5(2*1000)/400-5
625(2000)/395
1250000/395
3164.56
Answer:
The probability that another accident will occur that same month = 0.44907
Step-by-step explanation:
Let consider X to be the random variable that follows an exponential distribution with a mean of 52.
The mean of the exponential distribution ![\dfrac{1}{\lambda } = 52 \implies \lambda = \dfrac{1}{52}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Clambda%20%7D%20%3D%2052%20%5Cimplies%20%5Clambda%20%3D%20%5Cdfrac%7B1%7D%7B52%7D)
Thus, the probability distribution of X is:
![f(x) = \lambda e ^{-\lambda x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Clambda%20e%20%5E%7B-%5Clambda%20x%7D)
![f(x) =\dfrac{1}{52} e ^{-x/52} \ \ \ \ x \geq 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%5Cdfrac%7B1%7D%7B52%7D%20e%20%5E%7B-x%2F52%7D%20%20%20%20%20%5C%20%5C%20%5C%20%5C%20x%20%5Cgeq%200)
Suppose X represents the time interval between the accident that happened in October 1 and the following accident.
Then, the probability that another accident will occur in the same month is the same as the event that the time between the two accidents are less than 31 (given that the month of October have 31 days)
Thus, we can calculate the required probability as follows:
![P(X \leq 31) = \int ^{31}_{0} \ f(x) \ dx](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2031%29%20%3D%20%5Cint%20%5E%7B31%7D_%7B0%7D%20%5C%20f%28x%29%20%5C%20dx)
![P(X \leq 31) = \int ^{31}_{0} \ \dfrac{1}{52} \ e^{-x/52} \ dx](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2031%29%20%3D%20%5Cint%20%5E%7B31%7D_%7B0%7D%20%5C%20%5Cdfrac%7B1%7D%7B52%7D%20%5C%20e%5E%7B-x%2F52%7D%20%5C%20dx)
![P(X \leq 31) = 1 - e^{-31/52}](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2031%29%20%3D%201%20-%20e%5E%7B-31%2F52%7D)
![\mathbf{P(X \leq 31) = 0.44907}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28X%20%5Cleq%2031%29%20%3D%200.44907%7D)
Thus, the probability that another accident will occur that same month = 0.44907
Two of the three side lengths are given. To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle. Use the Law of Cosines for this task.
a^2 = b^2 + c^2 - 2ac*cosA
Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or
a^2 = 250000 + 572500 - 750000(-0.1736), or
= 692264
Then a = +sqrt(692264) = 832 yds
Use Heron's Formula to find the area of the land.
First, calculate s=(a+b+c)/2: (500+750+832)/2 = 1041=s
According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )
Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )
I will leave this calculation to you to complete.
Suppose the area of the land is A square yards. Convert this to acres, using the fact that 1 acre = 4840 yd^2.
In acres, the area is
1 acre
A* ---------------- = (A/4840) acres
4840 yd^2
How much will this cost? Recall that the unit cost of the land is $2300/acre.
Then the total cost will be:
$2300
(A/4840) acres * ------------- = 0.475*A dollars. (Substitute your value for A)
1 acre