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Yuri [45]
2 years ago
14

A sector of a circle makes a 127° angle at its centre. If the arc of the sector has length 36 mm, find

Mathematics
1 answer:
Veseljchak [2.6K]2 years ago
8 0

Answer:

Approximately 68.5\; \rm mm.

Step-by-step explanation:

Convert the angle of this sector to radians:

\begin{aligned}\theta &= 127^{\circ} \\ &= 127^{\circ} \times \frac{2\pi}{360^{\circ}} \\ &\approx 2.22\end{aligned}.

The formula s = r\, \theta relates the arc length s of a sector of angle \theta (in radians) to the radius r of this sector.

In this question, it is given that the arc length of this sector is s = 36\; \rm mm. It was found that \theta = 2.22 radians. Rearrange the equation s = r\, \theta to find the radius r of this sector:

\begin{aligned} r&= \frac{s}{\theta} \\ &\approx \frac{36\; \rm mm}{2.22} \\ &\approx 16.2\; \rm mm\end{aligned}.

The perimeter of this sector would be:

\begin{aligned}& 2\, r + s \\ =\; & 2 \times 16.2\; {\rm mm} + 36\; {\rm mm} \\ =\; & 68.5\; \rm mm\end{aligned}.

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The thumb length of fully grown females of a certain type of frog is normally distributed with a mean of 8.59 mm and a standard
PilotLPTM [1.2K]

Answer:

21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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 problem, we have that:

\mu = 8.59, \sigma = 0.63

Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

This is 1 subtracted by the pvalue of Z when X = 9.08. So

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

Z = \frac{9.08 - 8.59}{0.63}

Z = 0.78

Z = 0.78 has a pvalue of 0.7823

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21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

8 0
3 years ago
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