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3 years ago

PLEASE HELP GIVING 30 POINTS!!!! 1 6 ≥ 6 + x/2

Mathematics

2 answers:

DENIUS [597]3 years ago

4 0

Answer:

x ≤ 20

Step-by-step explanation:

Subtract 66 from both sides.

16 − 6 ≥ x/2.

Simplify 16 − 6 = 10.

10 ≥ x/2.

Multiply both sides by 22.

10 × 2 ≥ x.

Simplifiy 10 x 2 = 20.

20 ≥ x.

Switch sides.

x ≤ 20.

Temka [501]3 years ago

3 0

The answer is x<20. Hope that helps.

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First of all, we will find z-score corresponding to 38 and 56.

$z=\frac{x-\mu}{\sigma}$

$z=\frac{38-38}{6}=\frac{0}{6}=0$

Now we will find z-score corresponding to 56.

$z=\frac{56-38}{6}=\frac{18}{6}=3$

We know that according to Empirical rule approximately 68% data lies with-in standard deviation of mean, approximately 95% data lies within 2 standard deviation of mean and approximately 99.7% data lies within 3 standard deviation of mean that is $-3\sigma\text{ to }3\sigma$ .

We can see that data point 38 is at mean as it's z-score is 0 and z-score of 56 is 3. This means that 56 is 3 standard deviation above mean.

We know that mean is at center of normal distribution curve. So to find percentage of data points 3 SD above mean, we will divide 99.7% by 2.

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Therefore, approximately $49.85\%$ of lightbulb replacement requests numbering between 38 and 56.

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