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DochEvi [55]
2 years ago
6

Find n so that the number sentence below is true:

Mathematics
1 answer:
adell [148]2 years ago
6 0

Answer: n=6

Step-by-step explanation:

2^3 x 4^3 = 2^3 x 2^n = 2^9

(2×2×2) ×(4×4×4) = (2x2x2) ×2^n=(2x2x2x2x2x2x2x2x2)

8 x 64 = 8x 2^n = 512

512= 8x 2^n = 512

divide all through by 8 so that 2^n can stand alone

512/8 = (8x 2^n)/8 = 512/8

64 = 2^n = 64

express 64 as a base of 2

2^6 = 2^n = 2^6

since they all have same base, cancel out the base.

therefore,

6=n=6

n = 6

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A population has mean 187 and standard deviation 32. If a random sample of 64 observations is selected at random from this popul
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Answer:

11.51% probability that the sample average will be less than 182

Step-by-step explanation:

To solve this question, we have 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 = 187, \sigma = 32, n = 64, s = \frac{32}{\sqrt{64}} = 4

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This is the pvalue of Z when X = 182. So

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

By the Central Limit Theorem

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

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Z = -1.2 has a pvalue of 0.1151

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3 years ago
the length and width of a rectangle are in the ratio 5:3. The perimeter of the rectangle is 32 cm. Find the length and width.
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