.3333 is considered a rational number. What makes this number rational? Explain your reasoning.

1 answer:

7 0

It’s a rational number when you round it to any place value, if you don’t round, it’s not rational.

Rational numbers are fractions and decimals that don’t go on and on forever, and no fractions that are over 0.

Since .3333 doesn’t go on forever, it’s rational.

It’s rounded to the Ten Thousandths.

Examples:
Rational: 4/5 .35 6/8
Not Rational: .3333333 (forever) 4/0 6/0 .555555 (forever).

Hope this helps :)

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Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use t

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Answer:

$\mu = 11$

$\sigma = 2.08$

Step-by-step explanation:

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.

Middle 85%.

Values of X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to 0.5 + 0.85/2 = 0.925

Above the interval (8,14)

This means that when Z has a pvalue of 0.075, X = 8. So when $Z = -1.44, X = 8$ . So