What are the answer choices
Nice
area=pir^2
the areas are
pir^2+pi(2r)^2
they add to 8pi
8pi=pir^2+pi(2r)^2
undistribute pi
8pi=pi(r^2+(2r)^2)
divide both sides by pi
8=r^2+(2r)^2
expand
8=r^2+4r^2
add
8=5r^2
divide by 5
8/5=r^2
sqrt both sides
√(8/5)=r
double since it is double
2√(8/5) is radius of bigger aka (4√10)/5
radius=(4√10)/5
Answer: 15/91 which is choice B
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There are two methods to find this answer.
Method 1) We have 6 girls and 8+6 = 14 students. The probability of picking a girl is 6/14 = 3/7. After the first girl is chosen, we have 5 girls left out of 14-1 = 13 students overall. The probability of picking another girl (assuming the first selection was a girl) is 5/13. Multiply these probabilities: (3/7)*(5/13) = (3*5)/(7*13) = 15/91
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Method 2) We can use the nCr combination formula. Order does not matter.
We have nCr = 6 C 2 = 15 ways to pick 2 girls. See the attached image below for the steps (figure 1)
Out of nCr = 14 C 2 = 91 ways to pick 2 students. See the attached image below for the steps (figure 2)
So that's another way to get the answer 15/91.
Answer:
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