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11Alexandr11 [23.1K]
2 years ago
5

There are 4 prime numbers between 10 and 20 11,13,17, and 19 are there always the same number of prime number between 2 consecut

ive multiples of 10 explain
​
Mathematics
2 answers:
Ann [662]2 years ago
7 0

Answer:

No

Step-by-step explanation:

For example between 50 and 60 there is only 2 primes: 53&59

Therefore this one contradiction proves that there is not going to be always 4 primes between two consecutive multiples of 10.

vivado [14]2 years ago
3 0

Answer:

No

Step-by-step explanation:

Given: There are 4 prime numbers between 10 and 20 i.e, 11,13,17, and 19.

To verify : If are there always the same number of prime numbers between 2 consecutive multiples of 10

Solution:

No, it is not so that there always the same number of prime numbers between 2 consecutive multiples of 10.

For example:

50 and 60 are multiples of 10 .

Prime numbers between 50 and 60 are 53 and 59 .

i.e, there are two prime numbers between 50 and 60.

Therefore, this contradicts the statement that there always the same number of prime number between 2 consecutive multiples of 10.

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So we do 21-9=12 so then we now know that the rectangle is 12 so then we do 12*8 units which is= 96 . Now the triangles. so the first one we know that its 8*3 and times it by 1/2 because two triangles is equal to a rectangle so the first triangle is 12 and now the second. its 9-3= 6 then its 6*8*1/2 which is equal to 24 so now the final answer is

96+12+24 which is equal to 132 so i'm guessing it 132 square units

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Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

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:

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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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

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This means that p = \frac{99}{99+78} = 0.5593

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\mu = p = 0.5593

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

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

By the Central Limit Theorem

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

Z = \frac{0.61 - 0.5593}{0.0373}

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1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

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