The first step in solving the quadratic equation -5x2 + 8 = 133 is to subtract 8 from both sides of the equation.
For better understanding Let us solve this quadratic equation
The first step is to subtract 8 from both sides to isolate the variable.
-5x2 + 8 - 8 = 133 - 8
-5x2 = 125
x2 = 125/-5
x2 = - 25
x2 = - 25 = (5i)2
x = ± 5i
Therefore, from the above, we can say that The first step in solving the quadratic equation -5x2 + 8 = 133 is to subtract 8 from both sides of the equation.
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![\begin{array}{cccccc}{Mean} & {1.5} & {2} & {2.5} & {3} & {3.5}\ \\ {Probability} & {\frac{1}{6}} & {\frac{1}{6}} & {\frac{1}{3}} & {\frac{1}{6}} & {\frac{1}{6}}\ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccc%7D%7BMean%7D%20%26%20%7B1.5%7D%20%26%20%7B2%7D%20%26%20%7B2.5%7D%20%26%20%7B3%7D%20%26%20%7B3.5%7D%5C%20%5C%5C%20%7BProbability%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%5C%20%5Cend%7Barray%7D)
Explanation:
Given
![Cards = \{1,2,3,4\}](https://tex.z-dn.net/?f=Cards%20%3D%20%5C%7B1%2C2%2C3%2C4%5C%7D)
Required
The sampling distribution
The possible selection of 2 cards without replacement is as follows:
![S = \{(1,2) (1,3) (1,4) (2,1) (2,3) (2,4) (3,1) (3,2) (3,4) (4,1) (4,2) (4,3)\}](https://tex.z-dn.net/?f=S%20%3D%20%5C%7B%281%2C2%29%20%281%2C3%29%20%281%2C4%29%20%282%2C1%29%20%282%2C3%29%20%282%2C4%29%20%283%2C1%29%20%283%2C2%29%20%283%2C4%29%20%284%2C1%29%20%284%2C2%29%20%284%2C3%29%5C%7D)
Calculate the mean
![\begin{array}{cccccccccccc}{Selection} & {(1,2)} & {(1,3)} & {(1,4)} & {(2,1)} & {(2,3)} & {(2,4)}& {(3,1)} & {(3,2)} & {(3,4)} & {(4,1)} & {(4,2)} & {(4,3)} \ \\ {Mean} & {1.5} & {2} & {2.5} & {1.5} & {2.5} & {3} & {2} & {2.5} & {3.5} & {2.5} & {3} & {3.5}\ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccccccccc%7D%7BSelection%7D%20%26%20%7B%281%2C2%29%7D%20%26%20%7B%281%2C3%29%7D%20%26%20%7B%281%2C4%29%7D%20%26%20%7B%282%2C1%29%7D%20%26%20%7B%282%2C3%29%7D%20%26%20%7B%282%2C4%29%7D%26%20%7B%283%2C1%29%7D%20%26%20%7B%283%2C2%29%7D%20%26%20%7B%283%2C4%29%7D%20%26%20%7B%284%2C1%29%7D%20%26%20%7B%284%2C2%29%7D%20%26%20%7B%284%2C3%29%7D%20%5C%20%5C%5C%20%7BMean%7D%20%26%20%7B1.5%7D%20%26%20%7B2%7D%20%26%20%7B2.5%7D%20%26%20%7B1.5%7D%20%26%20%7B2.5%7D%20%26%20%7B3%7D%20%26%20%7B2%7D%20%26%20%7B2.5%7D%20%26%20%7B3.5%7D%20%26%20%7B2.5%7D%20%26%20%7B3%7D%20%26%20%7B3.5%7D%5C%20%5Cend%7Barray%7D)
List out the mean and the respective frequency
![1.5 \to 2](https://tex.z-dn.net/?f=1.5%20%5Cto%202)
![2 \to 2](https://tex.z-dn.net/?f=2%20%5Cto%202)
![2.5 \to 4](https://tex.z-dn.net/?f=2.5%20%5Cto%204)
![3 \to 2](https://tex.z-dn.net/?f=3%20%5Cto%202)
![3.5\to 2](https://tex.z-dn.net/?f=3.5%5Cto%20%202)
![Total \to 12](https://tex.z-dn.net/?f=Total%20%5Cto%2012)
Calculate the probability of each mean
![P(1.5) \to \frac{2}{12} \to \frac{1}{6}\\](https://tex.z-dn.net/?f=P%281.5%29%20%5Cto%20%5Cfrac%7B2%7D%7B12%7D%20%5Cto%20%5Cfrac%7B1%7D%7B6%7D%5C%5C)
![P(2) \to \frac{2}{12} \to \frac{1}{6}\\](https://tex.z-dn.net/?f=P%282%29%20%5Cto%20%5Cfrac%7B2%7D%7B12%7D%20%5Cto%20%5Cfrac%7B1%7D%7B6%7D%5C%5C)
![P(2.5) \to \frac{4}{12} \to \frac{1}{3}\\](https://tex.z-dn.net/?f=P%282.5%29%20%5Cto%20%5Cfrac%7B4%7D%7B12%7D%20%5Cto%20%5Cfrac%7B1%7D%7B3%7D%5C%5C)
![P(3) \to \frac{2}{12} \to \frac{1}{6}\\](https://tex.z-dn.net/?f=P%283%29%20%5Cto%20%5Cfrac%7B2%7D%7B12%7D%20%5Cto%20%5Cfrac%7B1%7D%7B6%7D%5C%5C)
![P(3.5) \to \frac{2}{12} \to \frac{1}{6}](https://tex.z-dn.net/?f=P%283.5%29%20%5Cto%20%5Cfrac%7B2%7D%7B12%7D%20%5Cto%20%5Cfrac%7B1%7D%7B6%7D)
So, the table of sampling distribution is:
![\begin{array}{cccccc}{Mean} & {1.5} & {2} & {2.5} & {3} & {3.5}\ \\ {Probability} & {\frac{1}{6}} & {\frac{1}{6}} & {\frac{1}{3}} & {\frac{1}{6}} & {\frac{1}{6}}\ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccc%7D%7BMean%7D%20%26%20%7B1.5%7D%20%26%20%7B2%7D%20%26%20%7B2.5%7D%20%26%20%7B3%7D%20%26%20%7B3.5%7D%5C%20%5C%5C%20%7BProbability%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%26%20%7B%5Cfrac%7B1%7D%7B6%7D%7D%5C%20%5Cend%7Barray%7D)