Answer:
![y = \frac{1}{6}x - 4](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B6%7Dx%20-%204)
![y = \frac{x}{2} + 2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bx%7D%7B2%7D%20%2B%202)
![y = \frac{1}{8}x](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B8%7Dx)
![y = \frac{1}{6}x+ \frac{2}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B6%7Dx%2B%20%5Cfrac%7B2%7D%7B3%7D)
![y = 12x - 9](https://tex.z-dn.net/?f=y%20%3D%2012x%20-%209)
Step-by-step explanation:
Required
Represent in gradient intercept form
This means that the equation be in form: ![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
Solving (a): ![3y = \frac{1}{2}x - 12](https://tex.z-dn.net/?f=3y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20-%2012)
Divide through by 3
![\frac{3y}{3} = \frac{1}{3*2}x - \frac{12}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3y%7D%7B3%7D%20%3D%20%5Cfrac%7B1%7D%7B3%2A2%7Dx%20-%20%5Cfrac%7B12%7D%7B3%7D)
![y = \frac{1}{6}x - 4](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B6%7Dx%20-%204)
Solving (b): ![5x = 10y - 20](https://tex.z-dn.net/?f=5x%20%3D%2010y%20-%2020)
Make y the subject
![10y = 5x + 20](https://tex.z-dn.net/?f=10y%20%3D%205x%20%2B%2020)
Divide through by 10
![y = \frac{5x}{10} + \frac{20}{10}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B5x%7D%7B10%7D%20%2B%20%5Cfrac%7B20%7D%7B10%7D)
![y = \frac{x}{2} + 2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bx%7D%7B2%7D%20%2B%202)
Solving (c): ![x = 8y](https://tex.z-dn.net/?f=x%20%3D%208y)
Make y the subject
![8y= x](https://tex.z-dn.net/?f=8y%3D%20x)
Divide through by 8
![y = \frac{1}{8}x](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B8%7Dx)
Solving (d): ![\frac{1}{2}x = 3y - 2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%20%3D%203y%20-%202)
Make y the subject
![3y = \frac{1}{2}x+ 2](https://tex.z-dn.net/?f=3y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dx%2B%202)
Divide through by 3
![y = \frac{1}{2*3}x+ \frac{2}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%2A3%7Dx%2B%20%5Cfrac%7B2%7D%7B3%7D)
![y = \frac{1}{6}x+ \frac{2}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B6%7Dx%2B%20%5Cfrac%7B2%7D%7B3%7D)
Solving (d): ![\frac{2}{3}y - 8x = -6](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dy%20-%208x%20%3D%20-6)
Make y the subject
![\frac{2}{3}y = 8x -6](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dy%20%3D%208x%20%20-6)
Divide through by 3/2
![\frac{3}{2} * \frac{2}{3}y =\frac{3}{2} * ( 8x -6)](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%20%2A%20%5Cfrac%7B2%7D%7B3%7Dy%20%3D%5Cfrac%7B3%7D%7B2%7D%20%2A%20%28%208x%20%20-6%29)
![y =\frac{3}{2} * ( 8x -6)](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7B3%7D%7B2%7D%20%2A%20%28%208x%20%20-6%29)
![y =\frac{3}{2} * 8x -\frac{3}{2} * 6](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7B3%7D%7B2%7D%20%2A%208x%20%20-%5Cfrac%7B3%7D%7B2%7D%20%2A%206)
![y = 3 * 4x - 3 * 3](https://tex.z-dn.net/?f=y%20%3D%203%20%2A%204x%20-%203%20%2A%203)
![y = 12x - 9](https://tex.z-dn.net/?f=y%20%3D%2012x%20-%209)
From the question we are told that:
Sample size ![n=40](https://tex.z-dn.net/?f=n%3D40)
Generally Number of class (K) is Mathematically given as
![2^k \geq 40](https://tex.z-dn.net/?f=2%5Ek%20%5Cgeq%2040)
Therefore
![2^k \geq 2^6](https://tex.z-dn.net/?f=2%5Ek%20%5Cgeq%202%5E6)
![k=6](https://tex.z-dn.net/?f=k%3D6)
Generally with class interval of k
Class Width is mathematically given as
![W=\frac{highest\ score-lowest\ score}{k}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7Bhighest%5C%20score-lowest%5C%20score%7D%7Bk%7D)
![W=\frac{97-42}{6}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B97-42%7D%7B6%7D)
![W=10](https://tex.z-dn.net/?f=W%3D10)
The complete Table is attached below
2)
The complete Image of the Histogram is attached below
Answer:
SSA
Step-by-step explanation:
It can be seen that they have a common 90 degree angle and both of the sides are the same, therefore proving that these two triangles are congruent.
4х - 16 = 6 * (3 + х)
4х - 16 = 18 + 6х
4х - 6х = 18 + 16
- 2х = 34
х = 34 : (- 2)
х = - 17
-------------------------------------------
4 * (- 17) - 16 = 6 * (3 + (- 17))
- 68 - 16 = 6 * (- 14)
- 84 = - 84
A company has an annual electric bill of $495,000. Of that amount, 3/5 was billed during June, July, August, and September. On average, how much money was billed during each of those four months? A. $34,750 B. $74,250 C. $139,000 D. $417,000 so in conclusion just add up all those prices and you should get 7929$