Question

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

Answer 1

HI!!

Answer 2

it is the ratio of the area of the circle to the area of the rectangle

Answer 3

a picture would be really really helpful

Answer 4

ugh im trying to draw it buts its hard

Answer 5

there we go loll

Answer 6

??

Answer 7

ok now we can do it

Answer 8

what are the side lenghts

Answer 9

you are actually told the diameter of each circle? it is 28 right (not that it matters one bit, just checking)

Answer 10

yess

Answer 11

the base of your rectangle is therefore \(28\) and the height is \(4\times 28=112\)
so the area of the rectangle is ?

Answer 12

i get \[28\times 112=3136\] as the area

Answer 13

then you would subtract the area of the four circles from the area of the rectangle

Answer 14

each circle has radius \(14\) so area \(4*14^2\times \pi\) or about \(2463\)

Answer 15

theres no side lengths though thts the problem

Answer 16

lol no dear but we know it anyway, because the diameter is 28

Answer 17

and i get 673?

Answer 18

hmm no i get
\[28\times 112=3136\]

Answer 19

for the total area that is

Answer 20

no 3136-2463

Answer 21

ooh ok i see yes

Answer 22

so \[\frac{673}{3136}\] for your answer

Answer 23

thats not an answer

Answer 24

lol that is because i read it wrong the second time
it is not "outside of the circles" but "inside of the circles"
just \[\frac{2463}{3136}\]

Answer 25

hmm also not quite
lets do the numbers again
\[\frac{4\times 14^2\times \pi}{28\times 112}\]

Answer 26

http://www.wolframalpha.com/input/?i=%284*14%5E2*pi%29%2F%2828*4*28%29
\[.785\]

Answer 27

also known as \(\frac{\pi}{4}\)

Answer 28

thanks!!