Answer:
slope = 4
Step-by-step explanation:
Calculate the slope m using the slope formula
m = ![\frac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (3, 12) ← 2 points on the line
m =
=
= 4
Answers:
- angle1 = 156 degrees
- angle2 = 24 degrees
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Explanation:
The two angles form a straight line, which is 180 degrees
Add up the angle expressions and set the sum equal to 180.
(angle1) + (angle2) = 180
(4x) + (x-15) = 180
(4x+x)-15 = 180
5x-15 = 180
5x = 180+15
5x = 195
x = 195/5
x = 39
We use that x value to find each missing angle
- angle1 = 4x = 4*39 = 156 degrees
- angle2 = x-15 = 39-15 = 24 degrees
Then notice how angle1+angle2 = 156+24 = 180 to verify the answer.
Side note: Angles that add to 180 are considered supplementary.
Solution :
Let :
X = number of overtime hours
S = total weekly salary
S = ![$12 \times 40 + 18 \times X$](https://tex.z-dn.net/?f=%2412%20%5Ctimes%2040%20%2B%2018%20%5Ctimes%20X%24)
S = 480 + 18X
E(S) = ![$480 + 18 \times E(X)$](https://tex.z-dn.net/?f=%24480%20%2B%2018%20%5Ctimes%20E%28X%29%24)
![$E(S) = 480 + 18 \times 15$](https://tex.z-dn.net/?f=%24E%28S%29%20%3D%20480%20%2B%2018%20%5Ctimes%2015%24)
= 750
Mean of S = 750
Var (S) = ![$18^2 \times Var(X)$](https://tex.z-dn.net/?f=%2418%5E2%20%5Ctimes%20Var%28X%29%24)
Var(S) = ![$18^2 \times 4^2$](https://tex.z-dn.net/?f=%2418%5E2%20%5Ctimes%204%5E2%24)
= 5184
Variance of S = 5184
The standard deviation equals square root of 5184 = 72