Answer:
C. It has been stretched horizontally.
Step-by-step explanation:
According to the diagram, the parabola has not been reflected in any way, nor has it been translated, since the parabola is pointing up in a smile, and the vertex is still at the origin.
The parabola does appear to be stretched, since the parent function had points at (1, 1), and (2, 4), but this parabola does not contain those points.
Since the parabola appears to be flatter than the parent function, we can say that C. It has been stretched horizontally.
Hope this helps!
F(x) = x³ + 3x² - 10x - 24
The root factors must be the factors of 24.
1 x 24 ; 2 x 12 ; 3 x 8 ; 4 x 6.
The most probable roots would be -4, -3, -2, -1, 1, 2, 3, or 4.
Using synthetic division, one can find that the smallest root is -3.
(x - 3)(x² - 6x - 8). The quadratic can now be factored as (x + 2)(x - 4) and further factored as (x - 3)(x + 2)(x - 4).
The correct factors are: (x - 3) (x + 2) (x - 4)
Answer:
The mean and standard deviation for the z-scores in this distribution are 0 and 1 respectively.
Step-by-step explanation:
Let the random variable <em>X</em> follow a Normal distribution with mean <em>μ </em>and standard deviation <em>σ.</em>
The <em>z</em>-scores are standardized form of the raw scores <em>X</em>. It is computed by subtracting the mean (<em>μ</em>) from the raw score <em>x</em> and dividing the result by the standard deviation (<em>σ</em>).

These <em>z</em>-scores also follow a normal distribution.
The mean is:
![E(z)=E[\frac{x-\mu}{\sigma} ]=\frac{1}{\sigma}\times [E(x)-\mu] =\frac{1}{\sigma}\times [\mu-\mu]=0](https://tex.z-dn.net/?f=E%28z%29%3DE%5B%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%3D%5Cfrac%7B1%7D%7B%5Csigma%7D%5Ctimes%20%5BE%28x%29-%5Cmu%5D%20%3D%5Cfrac%7B1%7D%7B%5Csigma%7D%5Ctimes%20%5B%5Cmu-%5Cmu%5D%3D0)
The standard deviation is:
![Var(z)=Var[\frac{x-\mu}{\sigma} ]=\frac{1}{\sigma^{2}}\times [Var(x)-Var(\mu)] =\frac{\sigma^{2}-0}{\sigma^{2}}=1\\SD(z)=\sqrt{Var(z)}=1](https://tex.z-dn.net/?f=Var%28z%29%3DVar%5B%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%3D%5Cfrac%7B1%7D%7B%5Csigma%5E%7B2%7D%7D%5Ctimes%20%5BVar%28x%29-Var%28%5Cmu%29%5D%20%3D%5Cfrac%7B%5Csigma%5E%7B2%7D-0%7D%7B%5Csigma%5E%7B2%7D%7D%3D1%5C%5CSD%28z%29%3D%5Csqrt%7BVar%28z%29%7D%3D1)
Thus, the mean and standard deviation for the z-scores in this distribution are 0 and 1 respectively.

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Factorise a² - b² :
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Crossed out common factors, (x + a) :
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Answer: A
Step-by-step explanation:
Nothing you a bum