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3 years ago

9

A car travelling at 90km/h is 500m behind another car travelling at 70km/h in the same direction. How long will it take the firs

t car to catch the second?

1 answer:

MAXImum [283]3 years ago

6 0

Relative speed: 90 - 70 = 20 km/h

s = d ÷ t

t = d ÷ s

t = 500 m ÷ 20 km/h x 1000 m/h x 1 ÷ 60 hr/mins

t = 1.5 minutes.

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3 years ago

The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resista

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Answer:

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Problems of normally distributed samples are solved using the z-score formula.

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

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.

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This means that when X = 10.634, Z has a pvalue of 1-0.1 = 0.9. So when X = 10.634, Z = 1.28.

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

$1.28 = \frac{10.634 - \mu}{\sigma}$

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$9.7565 - \mu = -1.96\sigma$

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$\mu = 10.634 - 1.28\sigma$

So

$10.634 - 1.28\sigma = 9.7565 + 1.96\sigma$

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3 years ago

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