4/5 = 8/10 = 12/15 = 16/20 = 20/25
Hope it helps
Answer:
slope = -6 and y intercept=0
Step-by-step explanation:
Step-by-step explanation: The cosecant function is graphed in the given figure. we are to find the period of the function.
The period of a function is the distance travelled by the curve of the function in one complete revolution.
We can see that in the given figure, the distance between two consecutive points is given by
Therefore, the period of the cosecant function is
Thus, the correct option is (B) \pi.
A.
This is because this is a base of which many different translations can occur. <span />
Answer:
![P(X](https://tex.z-dn.net/?f=P%28X%20%3C1.96%29%20%3D%200.975)
![P(X >1.64) = 0.0505](https://tex.z-dn.net/?f=P%28X%20%3E1.64%29%20%3D%200.0505)
![P(0.5 < X < 0.5) = 0](https://tex.z-dn.net/?f=P%280.5%20%3C%20X%20%3C%200.5%29%20%3D%200)
Step-by-step explanation:
Given
--- Mean
--- Variance
Calculate the standard deviation
![\sigma^2 = 1](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D%201)
![\sigma = 1](https://tex.z-dn.net/?f=%5Csigma%20%3D%201)
Solving (a): P(X < 1.96)
First, we calculate the z score using:
![z = \frac{X - \bar x}{\sigma}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cbar%20x%7D%7B%5Csigma%7D)
This gives:
![z = \frac{1.96 - 0}{1}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B1.96%20-%200%7D%7B1%7D)
![z = \frac{1.96}{1}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B1.96%7D%7B1%7D)
![z = 1.96](https://tex.z-dn.net/?f=z%20%3D%201.96)
The probability is then solved using:
![(X < 1.96) = P(z](https://tex.z-dn.net/?f=%28X%20%3C%201.96%29%20%3D%20P%28z%20%3C1.96%29)
From the standard normal distribution table
![P(z](https://tex.z-dn.net/?f=P%28z%20%3C1.96%29%20%3D%200.97500)
So:
![P(X](https://tex.z-dn.net/?f=P%28X%20%3C1.96%29%20%3D%200.975)
Solving (b): P(X > 1.64)
First, we calculate the z score using:
![z = \frac{X - \bar x}{\sigma}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cbar%20x%7D%7B%5Csigma%7D)
This gives:
![z = \frac{1.64 - 0}{1}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B1.64%20-%200%7D%7B1%7D)
![z = \frac{1.64}{1}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B1.64%7D%7B1%7D)
![z = 1.64](https://tex.z-dn.net/?f=z%20%3D%201.64)
The probability is then solved using:
![(X > 1.64) = P(z >1.64)](https://tex.z-dn.net/?f=%28X%20%3E%201.64%29%20%3D%20P%28z%20%3E1.64%29)
![P(z >1.64) = 1 - P(z](https://tex.z-dn.net/?f=P%28z%20%3E1.64%29%20%3D%201%20-%20P%28z%3C1.64%29)
From the standard normal distribution table
![P(z >1.64) = 1 - 0.9495](https://tex.z-dn.net/?f=P%28z%20%3E1.64%29%20%3D%201%20-%200.9495)
So:
![P(X >1.64) = 0.0505](https://tex.z-dn.net/?f=P%28X%20%3E1.64%29%20%3D%200.0505)
Solving (c): P(0.5 < X < 0.5)
This can be split as:
![P(0.5 < X < 0.5) = P(0.5](https://tex.z-dn.net/?f=P%280.5%20%3C%20X%20%3C%200.5%29%20%3D%20P%280.5%3CX%29%20-%20P%28X%3C0.5%29)
In probability:
![P(0.50.5)](https://tex.z-dn.net/?f=P%280.5%3CX%29%20%3D%201%20-%20P%28X%3E0.5%29)
![P(0.5](https://tex.z-dn.net/?f=P%280.5%3CX%29%20%3D%201%20-%20%5B1%20-%20P%28X%3C0.5%29%5D)
![P(0.5](https://tex.z-dn.net/?f=P%280.5%3CX%29%20%3D%201%20-%201%20%2B%20P%28X%3C0.5%29)
![P(0.5](https://tex.z-dn.net/?f=P%280.5%3CX%29%20%3D%20%20P%28X%3C0.5%29)
becomes
![P(0.5 < X < 0.5) = P(X](https://tex.z-dn.net/?f=P%280.5%20%3C%20X%20%3C%200.5%29%20%3D%20P%28X%3C0.5%29%20-%20P%28X%3C0.5%29)
![P(0.5 < X < 0.5) = 0](https://tex.z-dn.net/?f=P%280.5%20%3C%20X%20%3C%200.5%29%20%3D%200)