What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? all of the circles are congruent, and the diameter of each circle is 28 cm. a. 0.112 b. 0.196 c. 0.697 d. 0.785

option D. 0.785

Explanation:

1) the probability will be equal to the area of the shaded region divided by the area of the rectangle:

                      area of the shaded region
probability =
                        area of the rectangle

2) call r the radius of the circles (all are equal)

area of one circle = π (r^2)

area of the four circles = 4π(r^2) = area of the shaded region

3) area of the rectangle

length of the rectangle: 2r
height of the rectangle: 8r

area of the rectgangle = (2r)(8r) = 16 r^2

4) probability = 4π(r^2) /[(16)(r^2)] = π / 4

use π = 3.1416

probability = 3.1416 / 4 = 0.785

And you do not need to use the diameter given. The answer does not depend on this number.

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.