Question

question 10 (multiple choice worth 4 points) (04.03 mc) find the weighted average of the numbers 1 and 8, with a weight of $\frac{2}{5}$ on the first number and $\frac{3}{5}$ on the second number. 5.2 3.5 4.8 1.6

Explanation:

Step1: Apply weighted - average formula

The weighted - average formula is $w_1x_1 + w_2x_2$, where $w_1$ and $w_2$ are weights and $x_1$ and $x_2$ are values. Here, $x_1 = 1$, $w_1=\frac{2}{5}$, $x_2 = 8$, and $w_2=\frac{3}{5}$.
\[

$$\begin{align*} \text{Weighted average}&=\frac{2}{5}\times1+\frac{3}{5}\times8\\ \end{align*}$$

\]

Step2: Calculate each product

First, calculate $\frac{2}{5}\times1=\frac{2}{5}=0.4$ and $\frac{3}{5}\times8=\frac{24}{5} = 4.8$.
\[

$$\begin{align*} \frac{2}{5}\times1&=0.4\\ \frac{3}{5}\times8&=4.8 \end{align*}$$

\]

Step3: Sum the products

Add the two results together: $0.4 + 4.8=5.2$.
\[
0.4+4.8 = 5.2
\]

Answer:

5.2