Answer:
4 hours
Step-by-step explanation:
Given
Car 1:
![Speed = 26mph](https://tex.z-dn.net/?f=Speed%20%3D%2026mph)
![Time = h](https://tex.z-dn.net/?f=Time%20%3D%20h)
Car 2:
![Speed = 52mph](https://tex.z-dn.net/?f=Speed%20%3D%2052mph)
--- i.e. 2 hours after car 1
Required
Determine the time car 1 will meet car 2
To do this, we calculate the distance of both cars using:
![Distance = Speed * Time](https://tex.z-dn.net/?f=Distance%20%3D%20Speed%20%2A%20Time)
For Car 1:
![Distance = 26 * h](https://tex.z-dn.net/?f=Distance%20%3D%2026%20%2A%20h)
![Distance = 26h](https://tex.z-dn.net/?f=Distance%20%3D%2026h)
For Car 2:
![x^{2} Distance = 52 * (h - 2)](https://tex.z-dn.net/?f=x%5E%7B2%7D%20Distance%20%3D%2052%20%2A%20%28h%20-%202%29)
Open bracket
![Distance = 52h - 104](https://tex.z-dn.net/?f=Distance%20%3D%2052h%20-%20104)
When car 2 meets up with car 1, they are at the same distance.
So:
![26h = 52h - 104](https://tex.z-dn.net/?f=26h%20%3D%2052h%20-%20104)
Collect Like Terms
![26h - 52h = -104](https://tex.z-dn.net/?f=26h%20-%2052h%20%3D%20-104)
![-26h = -104](https://tex.z-dn.net/?f=-26h%20%3D%20-104)
Solve for h
![h = \frac{-104}{-26}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B-104%7D%7B-26%7D)
![h = 4](https://tex.z-dn.net/?f=h%20%3D%204)
<em>Car 2 will catch car 1; 4 hours from the start</em>
' 8 ' is the numerical coefficient.
' x ' is the literal coefficient.
You have
Multiply both sides by 20:
![20\cdot\dfrac{x}{20}=\dfrac{4}{5}\cdot 20](https://tex.z-dn.net/?f=20%5Ccdot%5Cdfrac%7Bx%7D%7B20%7D%3D%5Cdfrac%7B4%7D%7B5%7D%5Ccdot%2020)
The equation becomes
![x=16](https://tex.z-dn.net/?f=x%3D16)
The null hypothesis is that the mean is 83 out of 100. The alternative hypothesis is that the mean is less than 83.
Answer:
![\frac{2a-2b}{5a+5b} =\frac{2}{5c}](https://tex.z-dn.net/?f=%5Cfrac%7B2a-2b%7D%7B5a%2B5b%7D%20%3D%5Cfrac%7B2%7D%7B5c%7D)
Step-by-step explanation:
![\frac{a+b}{a-b} =c](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2Bb%7D%7Ba-b%7D%20%3Dc)
![\Longleftrightarrow \frac{a-b}{a+b} =\frac{1}{c}](https://tex.z-dn.net/?f=%5CLongleftrightarrow%20%5Cfrac%7Ba-b%7D%7Ba%2Bb%7D%20%3D%5Cfrac%7B1%7D%7Bc%7D)
![\Longleftrightarrow \frac{2}{5} \times \frac{a-b}{a+b} =\frac{2}{5} \times \frac{1}{c}](https://tex.z-dn.net/?f=%5CLongleftrightarrow%20%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20%5Cfrac%7Ba-b%7D%7Ba%2Bb%7D%20%3D%5Cfrac%7B2%7D%7B5%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7Bc%7D)
![\Longleftrightarrow \frac{2\times(a-b)}{5\times(a+b)} = \frac{2\times1}{5\times c}](https://tex.z-dn.net/?f=%5CLongleftrightarrow%20%20%5Cfrac%7B2%5Ctimes%28a-b%29%7D%7B5%5Ctimes%28a%2Bb%29%7D%20%3D%20%5Cfrac%7B2%5Ctimes1%7D%7B5%5Ctimes%20c%7D)
![\Longrightarrow \frac{2a-2b}{5a+5b} =\frac{2}{5c}](https://tex.z-dn.net/?f=%5CLongrightarrow%20%5Cfrac%7B2a-2b%7D%7B5a%2B5b%7D%20%3D%5Cfrac%7B2%7D%7B5c%7D)