Answer:
Step-by-step explanation:
5x + 7x - 1/2x + 1/4 = 6
move x to one side move numbers to the other side
5x + 7x - 1/2 x = 6 - 1/4
add x and numbers
23/2x = 23/4
divide both side by 23/2
x = (23/4)/(23/2)
= 1/2
plug it in to check the answer
5/2 + 7/2 - 1/4 + 1/4 = 6
12/2 = 6
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.
----------------------------
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.
THE ANSWER FOR THIS IS 5^1
Answer:
d. The interval contains only negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.
Step-by-step explanation:
Hello!
You have the data of the chemical measurements in two independent regions. The chemical concentration in both regions has a Gaussian distribution.
Be X₁: Chemical measurement in region 1 (ppm)
Sample 1
n= 12
981 726 686 496 657 627 815 504 950 605 570 520
μ₁= 678
σ₁= 164
Sample mean X[bar]₁= 678.08
X₂: Chemical measurement in region 2 (ppm)
Sample 2
n₂= 16
1024 830 526 502 539 373 888 685 868 1093 1132 792 1081 722 1092 844
μ₂= 812
σ₂= 239
Sample mean X[bar]₂= 811.94
Using the information of both samples you have to determina a 90% CI for μ₁ - μ₂.
Since both populations are normal and the population variances are known, you can use a pooled standard normal to estimate the difference between the two population means.
[(X[bar]₁-X[bar]₂)±
* 
]
[(678.08-811.94)±1.648*
]
[-259.49;-8.23]ppm
Both bonds of the interval are negative, this means that with a 90% confidence level the difference between the population means of the chemical measurements of region 1 and region 2 may be included in the calculated interval.
You cannot be sure without doing a hypothesis test but it may seem that the chemical measurements in region 1 are lower than the chemical measurements in region 2.
I hope it helps!
Multiply 30 by 30%.
=30 * 30%
convert % to decimal (30% ÷ 100)
=30 * 0.30
=9
ANSWER: 9 is 30% of 30.
Hope this helps! :)
