The circle on the right has center O. Its radius is 3 yd., and the central angle a measures 130°. What is the area of the shaded
region? Give the exact answer in terms of π, and be sure to include the correct unit in your answer.
1 answer:
Answer:
area of the sector = 3.25π yard²
Step-by-step explanation:
The radius of the circle is 3 yards . The central angle is 130° let us say it is the sector angle of the circle. The angle is 130°. If the shaded area of the circle is the sector area of the circle the area of the sector can be computed below.
area of a sector = ∅/360 × πr²
where
∅ = center angle
r = radius
area of the sector = 130/360 × π × 9
area of the sector = 1170π/360
area of the sector = 3.25π yard²
If the shaded area is segment. The shaded area can be solved with the formula.
Area of segment = area of sector - area of the triangle
Area of segment = ∅/360 × πr² - 1/2 sin∅ r²
The picture demonstrate the area of sector and the segment of a circle with illustration on how to compute the area of the triangle
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Answer:
The probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work is 0.3046.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the travel times to get to work.
The expected travel time is, <em>μ</em> = 38.3 minutes.
The distribution of random variable <em>X</em> can be defined as the distribution of time interval between which a person reaches their work place at a constant average rate.
This implies that <em>X</em> follows an Exponential distribution with parameter, .
The probability density function of <em>X</em> is:
Compute the probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work as follows:
Thus, the probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work is 0.3046.