Answer:
x=1.89278
Step-by-step explanation:
change into a logmarith
log_3 8=x
use change of base formula
put in calculator
x= 1.89278
Answer:
16.2 kilograms
Step-by-step explanation:
30 300-gram cans = 9000 grams of soup
18 400-gram cans = 7200 grams of vegetables
9000 + 7200 = 16200 grams
1000 grams = 1 kilogram
16200 / 1000 = 16.2 kilograms
Answer:
For this case we want to find this probability:
![P(X>11)](https://tex.z-dn.net/?f=%20P%28X%3E11%29)
And we can use the cumulative distribution given by:
![F(x) = 1-e^{-\lambda x}](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%201-e%5E%7B-%5Clambda%20x%7D)
The mean is given by:
![\mu = \frac{1}{\lambda}](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%5Cfrac%7B1%7D%7B%5Clambda%7D)
And then ![\lambda = \frac{1}{\mu}= \frac{1}{6.5}= 0.1538](https://tex.z-dn.net/?f=%20%5Clambda%20%3D%20%5Cfrac%7B1%7D%7B%5Cmu%7D%3D%20%5Cfrac%7B1%7D%7B6.5%7D%3D%200.1538)
And replacing we got:
![P(X>11) = 1-P(X](https://tex.z-dn.net/?f=%20P%28X%3E11%29%20%3D%201-P%28X%3C11%29%20%3D%201-%20%5B1-%20e%5E%7B-0.1538%20%2A11%7D%5D%3D%20e%5E%7B-0.1538%2A11%7D%3D%200.18409)
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
![P(X=x)=\lambda e^{-\lambda x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%5Clambda%20e%5E%7B-%5Clambda%20x%7D)
Solution to the problem
For this case we can define the random variable X= "checkout times"
And the distribution for X is given by:
For this case we want to find this probability:
![P(X>11)](https://tex.z-dn.net/?f=%20P%28X%3E11%29)
And we can use the cumulative distribution given by:
![F(x) = 1-e^{-\lambda x}](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%201-e%5E%7B-%5Clambda%20x%7D)
The mean is given by:
![\mu = \frac{1}{\lambda}](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%5Cfrac%7B1%7D%7B%5Clambda%7D)
And then ![\lambda = \frac{1}{\mu}= \frac{1}{6.5}= 0.1538](https://tex.z-dn.net/?f=%20%5Clambda%20%3D%20%5Cfrac%7B1%7D%7B%5Cmu%7D%3D%20%5Cfrac%7B1%7D%7B6.5%7D%3D%200.1538)
And replacing we got:
![P(X>11) = 1-P(X](https://tex.z-dn.net/?f=%20P%28X%3E11%29%20%3D%201-P%28X%3C11%29%20%3D%201-%20%5B1-%20e%5E%7B-0.1538%20%2A11%7D%5D%3D%20e%5E%7B-0.1538%2A11%7D%3D%200.18409)
Answer: Mhm
Step-by-step explanation:
Fasle