(7)^2-4(5)(-6)=
49+120=169 is the answer
We want to find an equation for the given solutions and the multiplicity of each solution.
The equation is:
![0 = (x - 2)*(x + 1)^2](https://tex.z-dn.net/?f=0%20%3D%20%28x%20-%202%29%2A%28x%20%2B%201%29%5E2)
First, assume that we have a given equation and we know that we have solutions {x₁, x₂, ..., xₙ}, each one with multiplicity {m₁, ..., mₙ}.
The equation, of a polynomial that meets these requirements, is given by:
![0 = A*(x - x_1)^{m_1}*...*(x - x_n)^{m_n}](https://tex.z-dn.net/?f=0%20%3D%20A%2A%28x%20-%20x_1%29%5E%7Bm_1%7D%2A...%2A%28x%20-%20x_n%29%5E%7Bm_n%7D)
Where A is the leading coefficient and can be any real number.
Now that we know that, here we have the solutions:
- x = 2 with multiplicity 2
- x = -1 with multiplicity 2
We don't have information about the leading coefficient, so we assume it is equal to 1.
Then the equation is:
![0 = (x - 2)*(x + 1)^2](https://tex.z-dn.net/?f=0%20%3D%20%28x%20-%202%29%2A%28x%20%2B%201%29%5E2)
If you want to learn more, you can read:
brainly.com/question/11536910
Answer:
a) The mean is 0.15 and the standard error is 0.056.
b) 1. Yes
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportions p, in samples of size n, the mean is
and the standard error is
. The Central Limit Theorem applies is np > 5 and np(1-p)>5.
In this question:
![n = 40, p = 0.15](https://tex.z-dn.net/?f=n%20%3D%2040%2C%20p%20%3D%200.15)
So
(a) Find the mean and the standard error of the distribution of sample proportions.
![\mu = 0.15, s = \sqrt{\frac{0.15*0.85}{40}} = 0.056](https://tex.z-dn.net/?f=%5Cmu%20%3D%200.15%2C%20s%20%3D%20%5Csqrt%7B%5Cfrac%7B0.15%2A0.85%7D%7B40%7D%7D%20%3D%200.056)
So the mean is 0.15 and the standard error is 0.056.
(b) Is the sample size large enough for the Central Limit Theorem to apply?
np = 40*0.15 = 6 > 5
np(1-p) = 40*0.15*0.85 = 5.1>5
So yes
Answer:
x = 3
Step-by-step explanation:
-14x+14=4x-40
−14x+14=4x−40
Answer:
A
Step-by-step explanation:
surface area = length x width x depth
so 5x5x7=175.