The first equation
6x^2 -18x-24=0
-the graph opens up
6(x^2 -3x -4)=0
6(x^2 -3x +9/4-4-9/4)=0
6(x-3/2)-25x6/4=
6(x-3/2)-75/2
-Vertex is at (3/2, -75/2)
-Axis of symmetry is x=3/2
Second equation
3r^2 -16r -12=0
-the graph opens up
...
Answer:
48
Step-by-step explanation:
Given that:
![A \ score \ of \ 60 \ falls \ two \ standard \ deviations \ above \ the \ mean \\ \\ A \ score \ of \ 42 \ falls \ one \ standard \ deviation \ below \ the \ m ean](https://tex.z-dn.net/?f=A%20%20%5C%20score%20%20%5C%20of%20%5C%20%2060%20%20%5C%20falls%20%5C%20%20two%20%20%5C%20standard%20%20%20%5C%20deviations%20%5C%20%20above%20%5C%20%20the%20%5C%20mean%20%5C%5C%20%5C%5C%20A%20%5C%20%20score%20%5C%20of%20%5C%2042%20%20%5C%20falls%20%5C%20%20one%20%20%5C%20standard%20%20%5C%20deviation%20%5C%20below%20%20%5C%20the%20%5C%20m%20ean)
The interval for score = 60 - 42 = 18
If we divide it by the 3 standard deviations; the interval result into
= 18/3
= 6
So, the standard deviation is 6, and the mean = 42 + 6
= 48
Answer:
8.08 %
Step-by-step explanation:
Let us denote :
score X follows a normal distribution with mean
and standard deviation ![=1.5](https://tex.z-dn.net/?f=%3D1.5)
Step 2
The probability that someone scored 21.9 or less is :
![\mathrm{P}(\mathrm{X} \leq 21.9)](https://tex.z-dn.net/?f=%5Cmathrm%7BP%7D%28%5Cmathrm%7BX%7D%20%5Cleq%2021.9%29)
![=\mathrm{P}\left(\mathrm{Z} \leq \frac{21.9-24}{1.5}\right)](https://tex.z-dn.net/?f=%3D%5Cmathrm%7BP%7D%5Cleft%28%5Cmathrm%7BZ%7D%20%5Cleq%20%5Cfrac%7B21.9-24%7D%7B1.5%7D%5Cright%29)
![=\mathrm{P}(\mathrm{Z} \leq-1.4)](https://tex.z-dn.net/?f=%3D%5Cmathrm%7BP%7D%28%5Cmathrm%7BZ%7D%20%5Cleq-1.4%29)
![=0.0808](https://tex.z-dn.net/?f=%3D0.0808)
![=8.08%](https://tex.z-dn.net/?f=%3D8.08%25)
Answer : ![8.08 %](https://tex.z-dn.net/?f=8.08%20%25)
I think 12 might be the second one, I'm not sure though!
Answer:
1/12
Step-by-step explanation:
1/3 times 1/4 is 1/12