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.
First, distribute the (1/2) into (4x+12) by multiplying them.
The equation becomes:
2x + 6 + 5x = 30
On the left side, combine “like terms” through addition.
7x + 6 = 30
Subtract 6 from both sides:
7x = 24
Finally, get x alone by dividing both sides by 7:
x = 24/7, or if you wanted to round the decimal answer, it’s about 3.429.
Answer:
1. r=anything
2. d=6
3. b=4
Step-by-step explanation:
ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.
Formula of the Pythagorus Theorem :
⇒ a² + b² = c²
⇒ AD² + CD² = AC²
The value of AD is 54 and the value of AC is 90:
54² + CD² = 90²
Solve for CD:
54² + CD² = 90²
CD² = 90² - 54²
CD² = 5184
CD = √5184
CD = 72
ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.
Formula of the Pythagorus Theorem :
⇒ a² + b² = c²
⇒ BD² + CD² = BC²
The value of CD is 72 and the value of BC is 97:
BD² + 72² = 97²
Solve for BD:
BD² = 97² - 72²
BD² = 4225
BD = √4225
BD = 65
Answer: The length of BD is 65 units.
