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matrenka [14]
2 years ago
9

How do you solve this?

Mathematics
2 answers:
Radda [10]2 years ago
8 0

Answer:

1 and 9

Step-by-step explanation:

5-\sqrt{16}

5+\sqrt{16\\

Kobotan [32]2 years ago
3 0

Answer:

Well one do the square root of 16

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Area of Square ABCD = 10m * 10m = 100m².

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The Oriental Pearl Tower in Shanghai, China, is a 468-meter high tower with 11 spheres along the tower. Two spheres are larger t
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The approximate total volume of the two largest spheres on the Oriental Pearl Tower 113105.45 m³.

<h3 /><h3>How to find the volume of a sphere</h3>

The volume of the sphere is calculated as follows:

volume = 4 / 3 πr³

where

  • r = radius

The lower two larger spheres in the tower has a radius of 25 meters and 22.5 meters. Therefore, the total volume of the two largest sphere is as follows:

volume of lower sphere = 4 / 3 × 3.14 × 25³

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volume of higher sphere = 4 / 3 × 3.14 × 22.5³

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2 years ago
Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 o
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Answer:

27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.

Step-by-step explanation:

To solve this problem, it is important to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, 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 random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 12.01, \sigma = 0.2, n = 144, s = \frac{0.2}{\sqrt{144}} = 0.0167

What is the probability that the mean volume of a random sample of 144 bottles is less than 12 oz

This is the pvalue of Z when X = 12

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

By the Central Limit Theorem

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

Z = \frac{12 - 12.01}{0.0167}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743.

So there is a 27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.

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