Question

find the weighted average. if necessary, round your answer to the nearest tenth. what is the weighted average? round to the tenth if necessary.

Explanation:

Step1: Recall weighted - average formula

The weighted - average formula is $\bar{x}=\frac{\sum_{i = 1}^{n}w_ix_i}{\sum_{i = 1}^{n}w_i}$, where $x_i$ are the values and $w_i$ are the weights. Here, we assume the values on the number - line are $x_1 = 4$ and $x_2=10$, and the weights are $w_1 = 4$ and $w_2 = 3$.

Step2: Calculate the numerator

$\sum_{i = 1}^{2}w_ix_i=w_1x_1 + w_2x_2=4\times4+3\times10=16 + 30=46$.

Step3: Calculate the denominator

$\sum_{i = 1}^{2}w_i=w_1 + w_2=4 + 3=7$.

Step4: Calculate the weighted average

$\bar{x}=\frac{46}{7}\approx6.6$.

Answer:

$6.6$