Answers:
The z scores are approximately:
- Care of Magical Creatures: z = 0.333
- Defense Against the Dark Arts: z = 0.583
- Transfiguration: z = -0.263
- Potions: z = -0.533
From those scores, we can say:
- Best grade = Defense Against the Dark Arts
- Worst grade = Potions
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Further Explanation:
We'll need to convert each given score to a corresponding standardized z score.
The formula to use is
z = (x - mu)/sigma
where,
- x = given grade for each class
- mu = mean
- sigma = standard deviation
Let's find the z score for the Care of Magical Creatures class
z = (x - mu)/sigma
z = (3.80 - 3.75)/(0.15)
z = 0.333 approximately
Repeat this process for the Defense Against the Dark Arts score.
z = (x - mu)/sigma
z = (3.60 - 3.25)/(0.60)
z = 0.583 approximately
And for the Transfiguration class as well
z = (x - mu)/sigma
z = (3.10 - 3.20)/(0.38)
z = -0.263 approximately
The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.
Now do the final class (Potions) to get this z score
z = (x - mu)/sigma
z = (2.50 - 2.90)/(0.75)
z = -0.533 approximately
This grade is below average as well.
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To summarize, we have these z scores
- Care of Magical Creatures: z = 0.333
- Defense Against the Dark Arts: z = 0.583
- Transfiguration: z = -0.263
- Potions: z = -0.533
Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.
Answer:
Step-by-step explanation:
The reciprocal of a number is 1 / the number,
so the reciprocal of x is 
.
Hope this helps, let me know if you have any questions! :)
Find the volume of the candle using the formula for volume of a cylinder:
V = PI x r^2 x h = 3.14 x 3.4^2 x 6 = 217.79 cubic cm. Round to 217.8
Find the volume of the block: V = l x w x h = 15 x 12 x 18 = 3,240 cubic cm.
Now divide the volume of the block by the volume of a candle:
3240 / 217.8 = 14.88
Round to the nearest tenth = 14.9 candles.
Answer:
y = 9x - 11
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, - 38) and (x₂, y₂ ) = (8, 61)
m = 
= 
= 9, thus
y = 9x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 61), then
61 = 72 + c ⇒ c = 61 - 72 = - 11
y = 9x - 11 ← equation of lie
