Answer:

Explanation:
A function f(x) is a Probability Density Function if it satisfies the following conditions:

Given the function:

(1)p(x) is greater than zero since the range of exponents of the Euler's number will lie in 
(2)
![\int_{0}^{\infty} p(x)=\int_{0}^{\infty} \dfrac{1}{r}e^{-x/r}\\=\dfrac{1}{r} \int_{0}^{\infty} e^{-x/r}\\=-\dfrac{r}{r}\left[e^{-x/r}\right]_{0}^{\infty}\\=-\left[e^{-\infty/r}-e^{-0/r}\right]\\=-e^{-\infty}+e^{-0}\\SInce \: e^{-\infty} \rightarrow 0\\e^{-0}=1\\\int_{0}^{\infty} p(x)=1](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20p%28x%29%3D%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20%5Cdfrac%7B1%7D%7Br%7De%5E%7B-x%2Fr%7D%5C%5C%3D%5Cdfrac%7B1%7D%7Br%7D%20%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20e%5E%7B-x%2Fr%7D%5C%5C%3D-%5Cdfrac%7Br%7D%7Br%7D%5Cleft%5Be%5E%7B-x%2Fr%7D%5Cright%5D_%7B0%7D%5E%7B%5Cinfty%7D%5C%5C%3D-%5Cleft%5Be%5E%7B-%5Cinfty%2Fr%7D-e%5E%7B-0%2Fr%7D%5Cright%5D%5C%5C%3D-e%5E%7B-%5Cinfty%7D%2Be%5E%7B-0%7D%5C%5CSInce%20%5C%3A%20e%5E%7B-%5Cinfty%7D%20%5Crightarrow%200%5C%5Ce%5E%7B-0%7D%3D1%5C%5C%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20p%28x%29%3D1)
The function p(x) satisfies the conditions for a probability density function.
The answer that is being described above is the ASTEROIDS. The one that we see floating between Mars and Jupiter is what we call the Asteroid Belt. The asteroid belt comprises of different rocky bodies and they also orbit within the solar system. Hope this helps.
Answer: The lower areas of the Atmosphere have a high temperature through the heats from the ground.
Explanation: High temperature experienced on the Earth surface is majorly caused by heats from the ground ( Earth crust).As a person ascend up to the Toposphere the temperature continues to reduce because because the heat from the ground is reduced as the heights increased.
It has been proven that as a person ascends into the Toposphere the amount of air and pressure reduces this will eventually lead to expansion of the gas particles which will then reduce the temperature.
Answer:
c. 2 m/s
Explanation:
The relationship between speed, frequency and wavelength of a wave is given by:

where
v is the speed of the wave
f is its frequency
is the wavelength
For the transverse wave in this problem, we have:
is the frequency
is the wavelength
Substituting these numbers into the equation, we find the speed of the wave:

Answer:
2 hours
Explanation:
The motorcycle travels 40 km per hour.
80km / 40km/h = 2 hours.