Answer:
![Average\ Speed = 60 mi/hr](https://tex.z-dn.net/?f=Average%5C%20Speed%20%3D%2060%20mi%2Fhr)
Step-by-step explanation:
Given
![Distance = 345\ miles](https://tex.z-dn.net/?f=Distance%20%3D%20345%5C%20miles)
![Time = 5\ hours\ 45\ minutes](https://tex.z-dn.net/?f=Time%20%3D%205%5C%20hours%5C%2045%5C%20minutes)
Required
Determine the average speed
This is calculated as thus:
![Average\ Speed = \frac{Distance}{Time}](https://tex.z-dn.net/?f=Average%5C%20Speed%20%3D%20%5Cfrac%7BDistance%7D%7BTime%7D)
Convert time to hour:
![Time = 5\ hours\ 45\ minutes](https://tex.z-dn.net/?f=Time%20%3D%205%5C%20hours%5C%2045%5C%20minutes)
![Time = 5\ hours + \frac{45}{60}\ hour](https://tex.z-dn.net/?f=Time%20%3D%205%5C%20hours%20%2B%20%5Cfrac%7B45%7D%7B60%7D%5C%20hour)
![Time = 5\ hours + \frac{3}{4}\ hour](https://tex.z-dn.net/?f=Time%20%3D%205%5C%20hours%20%2B%20%5Cfrac%7B3%7D%7B4%7D%5C%20hour)
![Time = \frac{20 + 3}{4}\ hours](https://tex.z-dn.net/?f=Time%20%3D%20%5Cfrac%7B20%20%2B%203%7D%7B4%7D%5C%20hours)
![Time = \frac{23}{4}\ hours](https://tex.z-dn.net/?f=Time%20%3D%20%5Cfrac%7B23%7D%7B4%7D%5C%20hours)
![Time = 5.75\ hours](https://tex.z-dn.net/?f=Time%20%3D%205.75%5C%20hours)
![Average\ Speed = \frac{Distance}{Time}](https://tex.z-dn.net/?f=Average%5C%20Speed%20%3D%20%5Cfrac%7BDistance%7D%7BTime%7D)
![Average\ Speed = \frac{345}{5.75}](https://tex.z-dn.net/?f=Average%5C%20Speed%20%3D%20%5Cfrac%7B345%7D%7B5.75%7D)
![Average\ Speed = 60 mi/hr](https://tex.z-dn.net/?f=Average%5C%20Speed%20%3D%2060%20mi%2Fhr)
Answer:
The value is ![P(A) = 0.133617](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%200.133617)
Step-by-step explanation:
From the question we are told that
The mean is ![\mu = 7.5](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%207.5)
The standard deviation is ![\sigma = 0.2](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%200.2)
The safest water level is between 7.2 and 7.8
Generally the probability that the selected pool has a pH level that is not considered safe is mathematically represented as
![P(A) = 1 - P(7.2 \le X \le 7.8 )](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%201%20-%20P%287.2%20%5Cle%20X%20%20%5Cle%207.8%20%29)
Here
![P(7.2 < X < 7.8 ) = P(\frac{ 7.2 - \mu }{\sigma } < \frac{X - \mu }{ \sigma }](https://tex.z-dn.net/?f=P%287.2%20%3C%20X%20%20%3C%207.8%20%29%20%3D%20P%28%5Cfrac%7B%207.2%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%3C%20%20%5Cfrac%7BX%20-%20%5Cmu%20%7D%7B%20%5Csigma%20%7D%20%3C%5Cfrac%7B%207.8%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%20%29)
Generally ![\frac{X - \mu }{ \sigma } = Z (The \ standardized \ value \ of X )](https://tex.z-dn.net/?f=%5Cfrac%7BX%20-%20%5Cmu%20%7D%7B%20%5Csigma%20%7D%20%3D%20%20Z%20%28The%20%20%5C%20standardized%20%5C%20%20value%20%20%5C%20%20of%20%20X%20%29)
So
=>
From the z-table the probability of (Z < -1.5) and ( Z <1.5) are
![P(Z < 1.5) = 0.93319](https://tex.z-dn.net/?f=P%28Z%20%3C%20%201.5%29%20%3D%20%200.93319)
and
![P(Z < -1.5) = 0.066807](https://tex.z-dn.net/?f=P%28Z%20%3C%20%20-1.5%29%20%3D%20%200.066807)
So
So
![P(A) = 1 - 0.0866383](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%201%20-%200.0866383)
=> ![P(A) = 0.133617](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%200.133617)
Answer:
Given:
x+y=5, and
x=3
explanation:
Substituting the value of x in the given equation, we get
3+y=5
⇒y=2Step-by-step