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Anna11 [10]
4 years ago
14

A=140° r=16 ft calculate the arc length s and area a for each of the sectors

Mathematics
1 answer:
Alisiya [41]4 years ago
4 0
\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180}~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=16\\
\theta =140
\end{cases}\implies s=\cfrac{(140)\pi (16)}{180}
\\\\\\
\textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=16\\
\theta =140
\end{cases}\implies A=\cfrac{(140)\pi (16)^2}{360}
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Answer:

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b) 0.0625

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Step-by-step explanation:

Let's start by first finding the probability a teacher orders 6 boxes. Since it is a four sided dice, the probability of getting a 1 is going to be 0.25.

Similarly, for any other number on the dice, the teacher orders 2 boxes. We can think of this as NOT rolling a 1. Using our previous answer, this comes out to be: 1 - 0.25 = 0.75

It should be remembered in the following answers that teachers ordering 6 or 2 boxes are not influenced by the results of other teachers. These are statistically independent events.

a) As given above, this probability is 0.75

b) The probability that both teachers order 6 boxes will be their individual probabilities multiplied. This comes out to be: 0.25 x 0.25 = 0.0625

c) Like in part (b), this is both of their probabilities multiplied:

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d) This is nearly the same as part (c), but with a little twist. The order matters. There are two scenarios:

  1.   First teacher gets 6 boxes, and the second gets 2.
  2.   First teacher gets 2 boxes, and the second gets 2.

Both of these events have a probability of 0.1875, as shown in (c). To get the total probability of this event happening, we must add these together:

0.1875 + 0.1875 = 0.375

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