Answer:
![P(x) = x^3 - 10x^2+ 34x-40](https://tex.z-dn.net/?f=P%28x%29%20%3D%20x%5E3%20-%2010x%5E2%2B%2034x-40)
Step-by-step explanation:
Given
-- Leading coefficient
![Zeros: 4\ and\ 3 - i](https://tex.z-dn.net/?f=Zeros%3A%204%5C%20and%5C%203%20%20-%20i)
Required
Determine the polynomial
Represent the zeros with a and b
Such that
![a = 4](https://tex.z-dn.net/?f=a%20%3D%204)
![b = 3 - i](https://tex.z-dn.net/?f=b%20%3D%203%20-%20i)
The polynomial is:
![P(x) = p * (x - a) * (x - b)](https://tex.z-dn.net/?f=P%28x%29%20%3D%20p%20%2A%20%28x%20-%20a%29%20%2A%20%28x%20-%20b%29)
![P(x) = 1 * (x - 4) * (x - (3 - i))](https://tex.z-dn.net/?f=P%28x%29%20%3D%201%20%2A%20%28x%20-%204%29%20%2A%20%28x%20-%20%283%20-%20i%29%29)
However, to solve further: We need to symmetrise over 3-i and its conjugate
![P(x) = 1 * (x - 4) * (x - (3 - i))* (x - (3 + i))](https://tex.z-dn.net/?f=P%28x%29%20%3D%201%20%2A%20%28x%20-%204%29%20%2A%20%28x%20-%20%283%20-%20i%29%29%2A%20%28x%20-%20%283%20%2B%20i%29%29)
![P(x) = (x - 4) * (x - (3 - i))* (x - (3 + i))\\\\](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%28x%20-%204%29%20%2A%20%28x%20-%20%283%20-%20i%29%29%2A%20%28x%20-%20%283%20%2B%20i%29%29%5C%5C%5C%5C)
To define a suitable function, the expression becomes
![P(x) = (x - 4) * ((x - 3)^2+1)](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%28x%20-%204%29%20%2A%20%28%28x%20-%203%29%5E2%2B1%29)
![P(x) = (x - 4) * ((x - 3)(x - 3)+1)](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%28x%20-%204%29%20%2A%20%28%28x%20-%203%29%28x%20-%203%29%2B1%29)
![P(x) = (x - 4) * (x^2 - 6x + 9+1)](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%28x%20-%204%29%20%2A%20%28x%5E2%20-%206x%20%2B%209%2B1%29)
![P(x) = (x - 4) * (x^2 - 6x +10)](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%28x%20-%204%29%20%2A%20%28x%5E2%20-%206x%20%2B10%29)
Open bracket
![P(x) = x^3 - 6x^2 +10x - 4x^2 + 24x-40](https://tex.z-dn.net/?f=P%28x%29%20%3D%20x%5E3%20-%206x%5E2%20%2B10x%20-%204x%5E2%20%2B%2024x-40)
![P(x) = x^3 - 6x^2 - 4x^2+10x + 24x-40](https://tex.z-dn.net/?f=P%28x%29%20%3D%20x%5E3%20-%206x%5E2%20%20-%204x%5E2%2B10x%20%2B%2024x-40)
![P(x) = x^3 - 10x^2+ 34x-40](https://tex.z-dn.net/?f=P%28x%29%20%3D%20x%5E3%20-%2010x%5E2%2B%2034x-40)
Answer:
(3.442 ; 6.558)
Step-by-step explanation:
Given :
Mean score after patient is given the magnet treatment :
Mean score, xbar = 5
Standard deviation, s = 2.4
Sample size, n = 20
The confidence interval :
Mean ± margin of error
Margin of Error = Tcritical * standard error
The critical value at 95%, df = 20 - 1 = 19
Tcritical = 2.093 (T-student distribution)
The standard error = s/√n = 2.4 / √20 = 0.5367
The margin of error = 2.903 * 0.5367 = 1.558
The confidence interval :
Xbar ± Margin of error
5 ± 1.558
(3.442 ; 6.558)
3/11, all you have to do is add both numbers and put one of them over the sum, that will get you the probability of drawing that color.
Answer:
x=-4
Step-by-step explanation:
x+12=8
x=8-12
Andre did not multiple both by four to get the exact whole number. He also, didnt subtract 12 which is not possible due to it being multiplied by 1/4.