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2 years ago

X = 0.045 Prove algebraically that x can be written as 1/22

Mathematics

2 answers:

kenny6666 [7]2 years ago

8 0

Answer:

Lets suppose this number is recurring, then we can prove.

x=0.045 (45 is recurring)

$10x=0.45$ (45 is recurring)

=> $100x =4.54$ (54 is recurring)

=> $1000x= 45.45$ (45 is recurring)

We will subtract 1000x-10x to get rid of the decimals:

$1000x-10x = 45.45-0.45$

$990x =45$

=> $x =45/990$

Dividing by 5

=> $x= 9/198$

Now dividing by 9

$x =1/22$

Hence, proved.

blagie [28]2 years ago

7 0

The least decimal place in 0.045 is found in the thousandths place. Thus, if expressed as a fraction, it would be 45/1000. Let's substitute this to the equation:

x = 45/1000
1000x = 45
(1000/45)x = 1

When you divide 1000 by 45, the quotient would be 22.2222222... This could be round to the nearest whole number which is 22. Then,

22x = 1
x = 1/22

I hope I was able to answer your question. Have a good day.

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Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below

Kay [80]

Answer:

Due to the higher z-score, Cade should be offered the job.

Step-by-step explanation:

Z-score:

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.

If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?

Whoever had the higher z-score.

Reyna:

Reyna got a score of 75.3; this version has a mean of 69.3 and a standard deviation of 12.

This means that $X = 75.3, \mu = 69.3, \sigma = 12$

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

$Z = \frac{75.3 - 69.3}{12}$

$Z = 0.5$

Kaitlyn:

Kaitlyn got a score of 228.4; this version has a mean of 206 and a standard deviation of 28.

This means that $X = 228.4, \mu = 206, \sigma = 28$

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

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Cade got a score of 7.88; this version has a mean of 7.2 and a standard deviation of 0.4. This means that $X = 7.88, \mu = 7.2, \sigma = 0.4$

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Answer:

Margin of Error = 1.0% to the nearest tenth of a percent.

Step-by-step explanation:

Margin of Error is the width of the confidence interval about the mean.

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Margin of Error = (Critical value) × (standard Error)

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