Question

SOMEONE HELP ME! MATH

Answer 1

50%

Explanation:

The end goal here is to find the total area of the entire figure from the center to the outer radius D. Then take the ratio of region B with respect to the total area, which will give you the probability of landing in the area B.

Circle A has a radius of 4. Circle B has a radius of 8. Circle C has a radius of 12. Circle D has a radius of 16. Therefore, the total area of the dartboard is given by:

`A_(total)=\pi r^2=\pi (16)^2=256\pi`

The area of the region B can be found by thinking of region B as a shaded region between two concentric circles A and C. The area of the circle C is given by:

`A_C=\pi r^2=\pi (12)^2=144\pi`

The area of circle A is given by:

`A_A=\pi r^2=\pi (4)^2=16\pi`

Therefore the area of region B would be:

`A_B=144\pi -16\pi =128\pi`

Finally, the probability of landing in region B would be:

`P=A_B/A_(total)=128\pi /256\pi =0.5`