Let ‘s’ be the son’s age 12 years ago.
Let ‘f’ be the father’s current age.
4 years ago, the son was:
s-4
So, his father is currently:
3(s-4)
=
3s-12
Therefore:
f = 3s-12
In twelve years, the son will be:
s+12
And the father will be:
f+12
This can also be written as:
3s-12+12 as the fathers younger age would be f = 3s+12
=
3s
So, we know that s+12 is half the fathers current age, meaning the father is currently 2(s+12) which is equivalent to 2s+24. Also, we know that the father is currently 3 times the sons age 12 years ago, so 3s (proven by the calculations we made above). Therefore, 2s+24=3s which means 24=s. We can then substitute this, and we will receive 24+12 = 36
Son’s current age: 36
We then substitute the son’s age 12 years ago into 2s+24 to give us the father’s age.
2(24)+24 = 72
Father’s current age: 72
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:
11 3/5*9*12 1/2=1,305
1,305 cubic meters
Hope I helped.
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
