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4 years ago

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A circle has a radius of 555 inches (\text{in})(in)(, start text, i, n, end text, )and a central angle that intercepts an arc wi

th a length of 30\text{ in}30 in30, start text, space, i, n, end text. What is the measure, in radians, of this central angle?

2 answers:

lukranit [14]4 years ago

4 0

datnis nod the roight acojfnflnnjnfrn Step-by-step explanation:

leva [86]4 years ago

3 0

Answer:

Central angle = 0.0003π

Step-by-step explanation:

Radius of circle = r = 555 in = 14.097 m

Arc length = s = 30 in = 0.762 m

Using formula

$s=r\theta\\\\\theta=\frac{s}{r}\\\\\theta=\frac{0.762}{14.097}\\\\\theta=0.05408$

Converting θ to radians

$\theta=0.05408\frac{\pi}{180}\\\\\theta=0.0003\pi$

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Required

A histogram to show the most likely outcome

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This is represented as:

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$P(X = 2) = ^5C_2 * 0.826^2 * (0.174)^{3}$

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$P(X = 3) = ^5C_3 * 0.826^3 * (0.174)^2$

$P(X = 3) = 10 * 0.5636 * 0.030276 \approx 0.1706$

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$P(X = 4) = 5 * 0.4655 * 0.174 \approx 0.4050$

$P(X = 5) = ^5C_5 * 0.826^5 * (1 - 0.826)^{5-5}\\$

$P(X = 5) = ^5C_5 * 0.826^5 * (0.174)^0$

$P(X = 5) = 1 * 0.3845 * 1 \approx 0.3845$

From the above computations, we have:

$P(X = 0) \approx 0.0002$

$P(X = 1) \approx 0.0038$

$P(X = 2) \approx 0.0359$

$P(X = 3) \approx 0.1706$

$P(X = 4) \approx 0.4050$

$P(X = 5) \approx 0.3845$

See attachment for histogram

<em>From the histogram, we can see that the most likely outcome is at: x = 4</em>

<em>Because it has the longest vertical bar (0.4050 or 40.5%)</em>

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3 years ago

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