Question

question-
calculate the weighted average of \a = f \b = in each of the following cases:
a: when the weight of a is 3 f the weight of b is 2.
w₁=
w₂=
x₁=
x₂=
b: when the weight of b is three times the weight of a.
w₁=
w₂=
x₁=
x₂=

Explanation:

Step1: Determine the values of \(A\) and \(B\)

From the number - line, \(A=-7\) and \(B = 2\).

Step2: Calculate the weighted - average for case A

The formula for the weighted average \(\bar{x}=\frac{w_1x_1 + w_2x_2}{w_1 + w_2}\). Here, \(w_1 = 3\), \(x_1=-7\), \(w_2 = 2\), \(x_2 = 2\).

$$
LATEXBLOCK0
$$

Step3: Calculate the weights for case B

Let the weight of \(A\) be \(w_1=k\), then the weight of \(B\) is \(w_2 = 3k\).

$$
LATEXBLOCK1
$$

Answer:

For case A: The weighted average is \(-3.4\). For case B: The weighted average is \(-0.25\).