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guapka [62]
3 years ago
15

Find the perimeter and area of the figure to the nearest hundredth use 3.14 for pi.

Mathematics
1 answer:
ZanzabumX [31]3 years ago
3 0

Answer:

Perimeter = 36.84 ft

Area = = 64.26 ft²

Step-by-step explanation:

✔️Perimeter of the figure = the length of the surrounding border the rectangle + surrounding border of circle

Length for surrounding border of the rectangle = 3 + 3 + 3 + 3 + 3 + 3 = 18 ft

Surrounding border of a circle = circumference of a full circle (two half circle makes 1 full circle)

Circumference of the circle = πd

diameter (d) = 12 - (3 + 3) = 6 ft

π = 3.14

Circumference = 3.14*6

= 18.84 ft

✅Perimeter = 18 + 18.84 = 36.84 ft

✔️Area = area if the rectangle + area of the full circle

= L*W + πr²

L = 12 ft

W = 3 ft

π = 3.14

r = ½(6) = 3 ft

Plug in the values

Area = 12*3 + 3.14*3²

= 36 + 28.26

= 64.26 ft²

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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

c) 86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

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

1 - 0.7533 = 0.2467

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

C. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?

Z = 1.5 has a pvalue of 0.9332

Z = -1.5 has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

6 0
3 years ago
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