Answer:
G7. (2√3)/3
G8. -2+√7
G9. (6 +2√2 -3√3 -√6)/7
Step-by-step explanation:
G7.

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G8.

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G9.

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<em>Comment on the problems</em>
In most cases, these expressions are the simplest possible (take the least amount of ink to draw, and take the fewest math operations to evaluate). What seems to be intended is that the denominator be made a rational number. This is done by multiplying the given fraction by a fraction equal to 1 that has the same denominator but with the sign of the radical reversed (unless, as in the first case, the radical is by itself).
The purpose of doing this is to take advantage of the fact that (a-b)(a+b) = a²-b², so if "a" or "b" is a square root, that root will not be seen in the product. In problem G9, we see this can make the numerator quite messy--not exactly a simpler form--but all the irrational numbers are in the numerator.
Answer: 1:5
Step-by-step explanation:
i think you can just divide by 4
Use photo math shows step by step! So much easier than relying on other people!
Hey!
In order to simplify this equation, we'll first have to multiply both sides of the equation by v. This will give us v on its own.
<em>Original Equation :</em>

<em>New Equation {Added Multiply Both Sides by V} :</em>

<em>Solution {New Equation Solved} :</em>

Now we'll switch sides to get v on the left side of the equation which is generally where we always want the variables to be located in these types of equations.
<em>Old Equation :</em>

<em>New Equation {Switched} :</em>

Now we'll divide both sides by v to get v on its own.
<em>Old Equation :</em>

<em>New Equation {Added Divide Both Sides by V} :</em>

<em>Solution {New Equation Solved} :</em>

<em>So, this means that in the equation

,</em>

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Hope this helps!
- Lindsey Frazier ♥
The variance is the total of the squared distances of the given data from the mean.
This can be calculated through the equation,
σ² = summation of X² / N - μ²
where σ² is the variance X's are the data, N is the number of terms, and μ is the mean.
summation of X² = 100² + 100² + 120² + 120² + 180² = 81200
N = 5
μ = (100 + 100 + 120 + 120 + 180) / 5
μ = 124
Substituting these values to the equation for variance,
σ² = (81200/5) - 124² = 864
Thus, the variance is equal to 864.