Answer:
1. P(X=0)=0.135
2. P(T>1)=0.271
Step-by-step explanation:
1. Let X be the number of accidents in the next year. Find the distribution of X and calculate P(X=0).
The rigth distribution to describe this type of event as number of accidents per unit of time is the Poisson distribution.
![P(x=k)\frac{\lambda^ke^{-\lambdat}}{k!}](https://tex.z-dn.net/?f=P%28x%3Dk%29%5Cfrac%7B%5Clambda%5Eke%5E%7B-%5Clambdat%7D%7D%7Bk%21%7D)
In this case k=0 accidents, parameter λ=2 events/year and t=1 year:
![P(X=0)=\frac{2^0e^{-2}}{0!}=\frac{1*e^{-2}}{1} = 0.135](https://tex.z-dn.net/?f=P%28X%3D0%29%3D%5Cfrac%7B2%5E0e%5E%7B-2%7D%7D%7B0%21%7D%3D%5Cfrac%7B1%2Ae%5E%7B-2%7D%7D%7B1%7D%20%3D%200.135)
2. Let T be the amount of time until the next accident. Find the distribution of T and calculate P(T>1).
In this case, the time between events can be best described by an exponential distribution:
![P(X>t)=e^{-\lambda t}](https://tex.z-dn.net/?f=P%28X%3Et%29%3De%5E%7B-%5Clambda%20t%7D)
In this case parameter λ=2 events/year and t=1 year:
![P(X>1)= e^{-2}=0.271](https://tex.z-dn.net/?f=P%28X%3E1%29%3D%20e%5E%7B-2%7D%3D0.271)
I=PRT
interest=I
P=principal
R=rate in decimal
t=time in years
P=1500
T=1
R=5%=0.05
I=1500 times 0.05 times 1
I=75
interst is 75
total amount is 1500+75=$1575 total
Answer:
The trigonometric function that can be use to solve for the height (h) is tanФ = opposite / adjacent
The height of the kite is 221.72 feet
Step-by-step explanation:
The trigonometric function that can be use to solve for the height (h) is tanФ = opposite / adjacent
To solve for height h of the kite, we will follow the steps below;
We will use the trig. function
tanФ = opposite / adjacent
from the diagram given Ф = 29° opposite = h and adjacent = 400 feet
tan 29° = h / 400
cross-multiply
h = 400 tan 29°
h =221.72 feet
The height of the kite is 221.72 feet
Answer:
78
Step-by-step explanation:
6(2x² - 5) = [?] if x = -3
6(2(-3)² - 5)
6(2(9) - 5)
6(18 - 5)
6(13) = 78
eeeeeAnswer:
Step-by-step explanation: