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:
∠ XZY ≈ 23.6°
Step-by-step explanation:
Using the sine ratio in the right triangle, that is
sinXZY =
=
=
, then
∠ XZY =
(
) ≈ 23.6° ( to 1 dec. place )
Answer:
D. 18.68
Step-by-step explanation:

Applying PEMDAS as order of operations.
Solving the exponents first ![[(\frac{2}{5})^2=\frac{4}{25}]](https://tex.z-dn.net/?f=%5B%28%5Cfrac%7B2%7D%7B5%7D%29%5E2%3D%5Cfrac%7B4%7D%7B25%7D%5D)

Multiplying ![[53\times \frac{4}{25}=8.48]](https://tex.z-dn.net/?f=%5B53%5Ctimes%20%5Cfrac%7B4%7D%7B25%7D%3D8.48%5D)

Dividing ![[27\div \frac{5}{3}=16.2]](https://tex.z-dn.net/?f=%5B27%5Cdiv%20%5Cfrac%7B5%7D%7B3%7D%3D16.2%5D)

Adding and subtracting.

Answer:
y>-5-3x
Step-by-step explanation:
Answer:
Pretty Simple!
Step-by-step explanation:
So, according to similar triangles, all the measures of their corresponding angles are equal.
According to the picture, <A corresponds to <D. Thus:
m<D=32 degrees
Hope this helps!