How many standard deviations above the mean is 14,500 hours 1.25 1.5 2.5 using the standard normal table the probability that Seth’s light bulb will last no more than 24,500 (P(z<1.25)) hours is about 89%.
Answer: {y∈R: y≤6} or [6,∞)
Explanation:
This problem doesn't require too much math. If you look at the equation given, you can see that it is a quadratic equation in the form of
. Since this is a quadratic equation, we have an idea of that the graph would look like. It either curves up or down. Since this is a positive equation,
, we know that this is going to curve up. In order to find the minimum of the curve, you would use
.
![\frac{-12}{2(3)}=-2](https://tex.z-dn.net/?f=%5Cfrac%7B-12%7D%7B2%283%29%7D%3D-2)
This means the x value of the parabola is -2. To find the y, you plug -2 into the original equation.
![f(2)=3(-2)^2+12(-2)+18](https://tex.z-dn.net/?f=f%282%29%3D3%28-2%29%5E2%2B12%28-2%29%2B18)
![f(2)=6](https://tex.z-dn.net/?f=f%282%29%3D6)
Now that we know the y value of the minimum/vertex is 6, and it is determined that the parabola curves up, the range is y≤6 because the range starts at 6 and goes off toward infinity.
Where is the rest of the info?
G(-30)=2(-30)/3+3
g(-30)=(-60/3)+3
g(-30)=-20+3
g(-30)=-17