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Vinvika [58]
3 years ago
10

The expression below is a sum of cubes. 125x3 + 169

Mathematics
2 answers:
diamong [38]3 years ago
7 0
125x^3 = (5x)^3
125x^3 is the cube of 5x.

169 = 13^2
169 is the square of 13, but not the cube of a rational number.

The statement is false.

Drupady [299]3 years ago
7 0

Answer:

\text{The expression }125x^3+169\text{ is not the sum of cube}

Step-by-step explanation:

Given the expression

125x^3+169

we have to tell the above expression is the sum of cube

The sum of cube is of the form

a^3+b^3   →  (1)

Expression: 125x^3+169

125 is the cube of 5 and 169 is the square of 13

125x^3+169

(5x)^3+13^2

Comparing above with equation (1), we see the given expression is not the sum of cube

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Lengths of full-term babies in the US are Normally distributed with a mean length of 20.5 inches and a standard deviation of 0.9
mash [69]

Answer:

66.48% of full-term babies are between 19 and 21 inches long at birth

Step-by-step explanation:

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.

Mean length of 20.5 inches and a standard deviation of 0.90 inches.

This means that \mu = 20.5, \sigma = 0.9

What percentage of full-term babies are between 19 and 21 inches long at birth?

The proportion is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19. Then

X = 21

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

Z = \frac{21 - 20.5}{0.9}

Z = 0.56

Z = 0.56 has a p-value of 0.7123

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

Z = \frac{19 - 20.5}{0.9}

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Z = -1.67 has a p-value of 0.0475

0.7123 - 0.0475 = 0.6648

0.6648*100% = 66.48%

66.48% of full-term babies are between 19 and 21 inches long at birth

5 0
2 years ago
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