QuestionAugust 25, 2025

Weighted Average: The coordinate -9 has a weight of (1)/(3) and the coordinate 27 has a weight of (2)/(3) Find the weighted average. square

Weighted Average: The coordinate -9 has a weight of (1)/(3) and the coordinate 27 has a weight of (2)/(3) Find the weighted average. square
Weighted Average: The coordinate -9 has a weight of (1)/(3) and the coordinate 27 has a weight of (2)/(3) Find the weighted average. square

Solution
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Answer

15 Explanation 1. Apply the Weighted Average Formula Use the formula for weighted average: \text{Weighted Average} = \frac{\sum (x_i \cdot w_i)}{\sum w_i}, where x_i are the coordinates and w_i are the weights. 2. Calculate the Numerator Compute (-9) \cdot \frac{1}{3} + 27 \cdot \frac{2}{3} = -3 + 18 = 15. 3. Calculate the Denominator The sum of the weights is \frac{1}{3} + \frac{2}{3} = 1. 4. Compute the Weighted Average Divide the numerator by the denominator: \frac{15}{1} = 15.

Explanation

1. Apply the Weighted Average Formula<br /> Use the formula for weighted average: $\text{Weighted Average} = \frac{\sum (x_i \cdot w_i)}{\sum w_i}$, where $x_i$ are the coordinates and $w_i$ are the weights.<br />2. Calculate the Numerator<br /> Compute $(-9) \cdot \frac{1}{3} + 27 \cdot \frac{2}{3} = -3 + 18 = 15$.<br />3. Calculate the Denominator<br /> The sum of the weights is $\frac{1}{3} + \frac{2}{3} = 1$.<br />4. Compute the Weighted Average<br /> Divide the numerator by the denominator: $\frac{15}{1} = 15$.
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