Question

1. fill in the blank 1 point
2. the weight of point f is $\frac{1}{4}$ the weight of point g. find the weighted average.

the weighted average is type your answer..
give your answer rounded to the nearest tenth or as an improper fraction.

1. fill in the blank 1 point
2. quarter grades are calculated as shown below. what is the students average for the quarter?

	weight	category average
homework	15%	100%
quizzes	25%	82%

the students average for the quarter is type your answer.. %

Explanation:

3.

Step1: Let the weight of point G be $w_G = 4$ and the weight of point F be $w_F=1$. The value of point F is $x_F=- 2$ and the value of point G is $x_G = 6$.

The formula for weighted - average is $\bar{x}=\frac{\sum_{i = 1}^{n}w_ix_i}{\sum_{i = 1}^{n}w_i}$.
Here, $\sum_{i = 1}^{2}w_ix_i=w_Fx_F + w_Gx_G=1\times(-2)+4\times6=-2 + 24 = 22$, and $\sum_{i = 1}^{2}w_i=1 + 4=5$.

Step2: Calculate the weighted - average.

$\bar{x}=\frac{22}{5}=4.4$

Step1: Use the weighted - average formula $\bar{x}=\sum_{i = 1}^{n}w_ix_i$, where $w_i$ is the weight and $x_i$ is the category average.

For tests: $w_1 = 0.6$ and $x_1=0.7$; for homework: $w_2 = 0.15$ and $x_2 = 1$; for quizzes: $w_3=0.25$ and $x_3 = 0.82$.
$\bar{x}=0.6\times0.7+0.15\times1 + 0.25\times0.82$.

Step2: Calculate each product.

$0.6\times0.7 = 0.42$, $0.15\times1=0.15$, $0.25\times0.82 = 0.205$.

Step3: Sum up the products.

$\bar{x}=0.42+0.15 + 0.205=0.775$ or $77.5\%$

Answer:

$4.4$

4.