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Ghella [55]
3 years ago
10

Kent has a collection of pennies and nickels with a value of 1.98. The number of pennies he has is five less than twice the numb

er of nickels. How many of each coin does Kent have?
Mathematics
1 answer:
BaLLatris [955]3 years ago
7 0

Answer:

Kent has a collection of pennies and nickles with a value of $1.98. The number of pennies he has is five less than twice the number of nickles. How many of each coin does Kent have?

----

p + 5n = 198

p = 2n - 5

---

Sub for p

2n-5 + 5n = 198

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Answer:

a) 96.64% probability that maximum speed is at most 50 km/h

b) 24.67% probability that maximum speed is at least 48 km/h

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Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

\mu = 46.8, \sigma = 1.75

A. What is the probability that maximum speed is at most 50 km/h?

This is the pvalue of Z when X = 50. So

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

Z = \frac{50 - 46.8}{1.75}

Z = 1.83

Z = 1.83 has a pvalue of 0.9664

96.64% probability that maximum speed is at most 50 km/h.

B. What is the probability that maximum speed is at least 48 km/h?

This is 1 subtracted by the pvalue of Z when X = 48.

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

Z = \frac{48 - 46.8}{1.75}

Z = 0.685

Z = 0.685 has a pvalue of 0.7533

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