Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the regular hexagon.

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

step 1

Find the probability that a point chosen randomly inside the rectangle is in the circle

Find the area of the rectangle

Find the area of the circle

In this problem we have

substitute

step 2

Find the probability that a point chosen randomly inside the rectangle is in the regular hexagon

Find the area of the regular hexagon

In this problem we have

substitute

step 3

Find the probability that a point chosen randomly inside the rectangle is  either in the circle or in the regular hexagon

Is the sum of the two probabilities

Round to the nearest hundredth

the diameter is 16 cm. are you a teacher?

step-by-step explanation:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°