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Jlenok [28]
3 years ago
9

Debra served 48 people in 3 hours. At this rate how many hours will it take to serve 80 people?

Mathematics
2 answers:
Norma-Jean [14]3 years ago
8 0

Answer:

5

Step-by-step explanation:

Use ratios.

\frac{3}{48} =\frac{x}{80}

Solve for x

x=5

Nadusha1986 [10]3 years ago
7 0

Answer:

5 hours

Step-by-step explanation:

Make a proportion

She served 48 people in 3 hours, and served 80 people in x hours

48/3=80/x

Cross multiply

48*x=80*3

48x=240

Divide both sides by 48 to isolate x

x=5

So, it will take 5 hours to serve 80 people

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A grading scale is set up for 1000 students' test scores. It assumes the
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Answer:

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

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.

It assumes the scores are normally distributed with a mean score of 75 and a standard deviation of 15.

This means that \mu = 75, \sigma = 15

How many students will score between 48 and 75?

First we find the proportion, which is the pvalue of Z when X = 75 subtracted by the pvalue of Z when X = 48. So

X = 75

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

Z = \frac{75 - 75}{15}

Z = 0

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

Z = \frac{48 - 75}{15}

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Z = -1.8 has a p-value of 0.0359

1 - 0.0359 = 0.4641

Out of 1000:

0.4641*1000 = 464

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

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