Question

1. fill in the blank 1 point
2. the weight of point j is \\(\frac{1}{2}\\) the weight of point i. the weight of h is 3 times the weight of i. find the weighted average

number line image: i at -10, j at -6, h at 1 (positions: -10, -8, -6, -4, -2, 0, 2)
the weighted average is type your answer...
give your answer rounded to the nearest tenth or as an improper fraction.

Explanation:

Step1: Identify values and weights

Let the weight of \( I \) be \( w \). Then weight of \( J \) is \( \frac{1}{2}w \), weight of \( H \) is \( 3w \).
From the number line: \( I = -10 \), \( J = -6 \), \( H = 1 \).

Step2: Apply weighted average formula

Weighted average \( = \frac{w_1x_1 + w_2x_2 + w_3x_3}{w_1 + w_2 + w_3} \)
Substitute \( w_1 = w \), \( x_1 = -10 \); \( w_2 = \frac{1}{2}w \), \( x_2 = -6 \); \( w_3 = 3w \), \( x_3 = 1 \):
\[

$$\begin{align*} \text{Weighted average} &= \frac{w(-10) + \frac{1}{2}w(-6) + 3w(1)}{w + \frac{1}{2}w + 3w} \\ &= \frac{-10w - 3w + 3w}{\frac{2w + w + 6w}{2}} \\ &= \frac{-10w}{\frac{9w}{2}} \\ &= \frac{-10w \times 2}{9w} \\ &= \frac{-20}{9} \approx -2.2 \end{align*}$$

\]

Answer:

\(-2.2\) (or \(\frac{-20}{9}\))