Answer:
-8
Step-by-step explanation:
you add 5 to -7 to get -2
7 x -1 is -7
so x = -1
8 x -1 = -8
A is the answer. Reflection and rotation.
Answer:
![x^\frac{21}{5}](https://tex.z-dn.net/?f=x%5E%5Cfrac%7B21%7D%7B5%7D)
Step-by-step explanation:
We are given an expression and we have to transform it into an expression with exponent.
5th root of x can be written as ![x^\frac{1}{5}](https://tex.z-dn.net/?f=x%5E%5Cfrac%7B1%7D%7B5%7D)
![(\sqrt[5]{x^7})^3\\\\((x^7)^\frac{1}{5} )^3](https://tex.z-dn.net/?f=%28%5Csqrt%5B5%5D%7Bx%5E7%7D%29%5E3%5C%5C%5C%5C%28%28x%5E7%29%5E%5Cfrac%7B1%7D%7B5%7D%20%29%5E3)
The powers outside will be multiplied as: ![(x^a)^b = x^{ab}](https://tex.z-dn.net/?f=%28x%5Ea%29%5Eb%20%3D%20x%5E%7Bab%7D)
![(x^\frac{7}{5} )^3\\x^\frac{7*3}{5}\\x^\frac{21}{5}](https://tex.z-dn.net/?f=%28x%5E%5Cfrac%7B7%7D%7B5%7D%20%29%5E3%5C%5Cx%5E%5Cfrac%7B7%2A3%7D%7B5%7D%5C%5Cx%5E%5Cfrac%7B21%7D%7B5%7D)
where the exponent is
and it is a rational number by definition of rational numbers
Answer:
The probability that the wait time is greater than 14 minutes is 0.4786.
Step-by-step explanation:
The random variable <em>X</em> is defined as the waiting time to be seated at a restaurant during the evening.
The average waiting time is, <em>β</em> = 19 minutes.
The random variable <em>X</em> follows an Exponential distribution with parameter
.
The probability distribution function of <em>X</em> is:
![f(x)=\lambda e^{-\lambda x};\ x=0,1,2,3...](https://tex.z-dn.net/?f=f%28x%29%3D%5Clambda%20e%5E%7B-%5Clambda%20x%7D%3B%5C%20x%3D0%2C1%2C2%2C3...)
Compute the value of the event (<em>X</em> > 14) as follows:
![P(X>14)=\int\limits^{\infty}_{14} {\lambda e^{-\lambda x}} \, dx=\lambda \int\limits^{\infty}_{14} {e^{-\lambda x}} \, dx\\=\lambda |\frac{e^{-\lambda x}}{-\lambda}|^{\infty}_{14}=e^{-\frac{1}{19} \times14}-0\\=0.4786](https://tex.z-dn.net/?f=P%28X%3E14%29%3D%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B14%7D%20%7B%5Clambda%20e%5E%7B-%5Clambda%20x%7D%7D%20%5C%2C%20dx%3D%5Clambda%20%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B14%7D%20%7Be%5E%7B-%5Clambda%20x%7D%7D%20%5C%2C%20dx%5C%5C%3D%5Clambda%20%7C%5Cfrac%7Be%5E%7B-%5Clambda%20x%7D%7D%7B-%5Clambda%7D%7C%5E%7B%5Cinfty%7D_%7B14%7D%3De%5E%7B-%5Cfrac%7B1%7D%7B19%7D%20%5Ctimes14%7D-0%5C%5C%3D0.4786)
Thus, the probability that the wait time is greater than 14 minutes is 0.4786.