A student earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests. She scored 78% on the final exam and 86% on
1 answer:
Her weighted mean grade is 81.2% if the student earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests.
<h3>What is mean?</h3>It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have a student who earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests. She scored 78% on the final exam and 86% on her class projects.
The weighted mean can be calculated as:
After calculating, we get:
= 81.2%
Thus, her weighted mean grade is 81.2% if the student earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests.
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All the answers to the given parts are mentioned below -
<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.
We can write the proportional relationship as -
y = kx
Now, from the given information, we can write -
2 scoops need 0.5 gallon of water
6 scoops need 1.5 gallon of water
So -
k = 2/0.5
k = 2/(1/2)
k = 2 x 2 = 4
Equations that represents the relationship can be written as -
y = 4x + c
Now, 2 scoops need 0.5 gallon of water.
2 = 4 x 1/2 + c
2 = 2 + c
c = 0
So, the equation will be y = 4x.
Graph of y = 4x is attached at the end.
For 10 scoops of water -
10 = 4x
x = 2.5 gallons of water is needed.
Therefore, all the answers to the given parts are mentioned above.
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