The equation in the image contains summations and weights, suggesting a form similar to a weighted average or linear combination. Here's a transcription and explanation of the mathematical expressions from the image:

1. $W = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}$

This is a weighted average formula, where:

• $W$ is the weighted average.
• $w_i$ represents the weights for each item.
• $x_i$ represents the values for each item.
• $n$ is the total number of items.
• The numerator, $\sum_{i=1}^{n} w_i x_i$, represents the sum of the product of weights and values.
• The denominator, $\sum_{i=1}^{n} w_i$, represents the sum of the weights.

2. $\sum_{i=1}^{n} w_i = 1$

This indicates that the sum of all the weights $w_i$ equals 1. This condition typically appears in probability or statistical contexts, ensuring that the weights are normalized.

Breakdown:

• The equation calculates a weighted average $W$ where each value $x_i$ is multiplied by its corresponding weight $w_i$.
• The sum of the weights equals 1, which ensures that the weighted average is normalized.

Would you like more details or further explanations?

Here are 5 related questions to deepen understanding:

1. What is the significance of a normalized sum of weights (i.e., when $\sum w_i = 1$)?
2. How does a weighted average differ from a simple average?
3. In what practical scenarios are weighted averages commonly used?
4. How does changing the weights $w_i$ affect the overall weighted average?
5. What other methods can be used to combine values besides weighted averages?

Tip: When working with weighted averages, ensure the sum of the weights is 1, or else the result will need to be rescaled accordingly.