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Gennadij [26K]
3 years ago
10

A class of 30 is divided into 2 groups such that the size of the smaller group is 2/3 the size of the larger group. How large is

the smaller group?
Mathematics
1 answer:
pogonyaev3 years ago
6 0

Answer:

I kinda did a lil of this in my head so i might not be 100% correct, but i would say the bigger group is 20 and the smaller group is 10

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What is the best approximation for the area of this circle?
Svetradugi [14.3K]
Area of circle = πr² = 3.14×4² = 50.24m²

The best approximation is C.
6 0
3 years ago
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The Office of Student Services at a large western state university maintains information on the study habits of its full-time st
Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20 hours, standard deviation of 6:

This means that \mu = 20, \sigma = 6

Sample of 150:

This means that n = 150, s = \frac{6}{\sqrt{150}}

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}

Z = 2.04

Z = 2.04 has a p-value of 0.9793

X = 19.5

Z = \frac{X - \mu}{s}

Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}

Z = -1.02

Z = -1.02 has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

3 0
3 years ago
Which of the following is equivalent to the sum of
barxatty [35]
Answer:I think it’s A sorry if it’s wrong.
4 0
2 years ago
-73 greater than or equal to 15 + 11x
Alecsey [184]
-73 ≥ 15 + 11x 
so the first thing you should do is to add -15 on both sides of the equation so you will have:
-73 -15 ≥ 11x 
- 88 ≥ 11x 
so the answer is:
-88/11 ≥ x or -8 ≥ x :)))
i hope this is helpful
have a nice day 
5 0
3 years ago
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Factor by grouping.......
Gekata [30.6K]

Answer:

A. (7n-1) (8n-1)

Step-by-step explanation:

56n^2 -8n-7n+1

56n^2 -8n       -7n+1

Factor out 8n from the first group   and -1 from the second group

8n (7n-1)     -1(7n-1)

Factor out the (7n-1)

(7n-1) (8n-1)

7 0
3 years ago
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