Answer:
Step-by-step explanation:
For a standard normal distribution of mean 
and 
the statistic 
In this problem we look for the value of X that is 2 standard deviations above the mean.
If there are two standard deviations above the mean, then, in the standard normal distribution, the statistic 
.
Then, we clear X.
Where:
Answer:
See below.
Step-by-step explanation:
4x^2-24x
Find the GCF.
4 - 1, 2, 4
24 - 1, 2, 3, 4, 6, 8, 12, 24
The GCF of x^2 and x is x.
The complete GCF is 4x.
4x(x-6)
-hope it helps
For example,area = a, length = l, width = w
First we write two equations. The easier equation is the area equation, which we know to be
a = l x w
So that the first equation is :
<span>96 = l x w </span>
we make the second equation of the following statements :
<em>The length of a rectangle is 2 foot less than 3 times its width.</em>
<span>so it becomes :
l = 3w - 2
</span>
<span>To solve, we can use the substitution method.
</span>
![96 = l \times w\\96=(3w-2) \times w\\96=3w^{2}-2w\\3w^{2}-2w-96=0~~~~~~[now\ factor\ the\ equation]\\ (3w+16)(w-6)=0](https://tex.z-dn.net/?f=96%20%3D%20l%20%5Ctimes%20w%5C%5C96%3D%283w-2%29%20%5Ctimes%20w%5C%5C96%3D3w%5E%7B2%7D-2w%5C%5C3w%5E%7B2%7D-2w-96%3D0~~~~~~%5Bnow%5C%20factor%5C%20the%5C%20equation%5D%5C%5C%20%283w%2B16%29%28w-6%29%3D0)
<span><em>So if our width is 6, Now substitute the value of w = 6 into equation 2 </em></span>
So "w" = 6 and "l" = 16, and if we multiply them together, we get the correct area, 96. So our dimensions are 6 by 16.
Answer:
Axis of symmetry:
Vertex:
Step-by-step explanation:
The given quadratic equation is
By comparing to the general quadratic function;
We have a=4,b=5,c=-1
The equation of the axis of symmetry is given by the formula;
We got this formula by completing the square on the general quadratic function.
We substitute a=4 and b=5 to obtain;
is the axis of symmetry.
To find the y-value of the vertex, we put
into the function to obtain;
The vertex of the given function is
X + 4/3 = - 2
x = - 10/3
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