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ikadub [295]
3 years ago
6

Three numbers are in the ratio 3:4:5. If the sum of their cubes is 216000, find the largest of these three numbers.

Mathematics
1 answer:
Makovka662 [10]3 years ago
8 0

Answer:

50

Step-by-step explanation:

Let the numbers be 3x, 4x, 5x

(3x)^3 + (4x)^3 + (5x)^3 = 216000

27x^3 + 64x^3 + 125x^3 = 216000

216x^3 = 216000

x^3 = 1000

x = 10

5x = 5(10) = 50

Answer: 50

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Answer:

P(939.6 < X < 972.5) = 0.6469

Step-by-step explanation:

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

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

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

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that \mu = 965, \sigma = 113

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This means that n = 57, s = \frac{113}{\sqrt{57}} = 14.97

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

Z = \frac{972.5 - 965}{14.97}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

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

Z = \frac{939.6 - 965}{14.97}

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Z = -1.7 has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

So

P(939.6 < X < 972.5) = 0.6469

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