Caitlin wants to draw n line segments, without lifting her pencil off the paper and without retracing her path, so that each segment crosses exactly one other segment (not counting intersections at vertices) and she ends up back where she started.A. Show how she can do this for n = 6. B. For which n can it be done, and for which n is it impossible?

11.25

step-by-step explanation:

juan's ratio of violin to cello is

3/2.5

he practices the violin for 9 hours; this gives us the ratio

9/x

for his cello practice.

together we have the proportion

3/2.5 = 9/x

cross multiplying, 3(x) = 9(2.5)

3x = 22.5

divide both sides by 3:

3x/3 = 22.5/3

x = 7.5

juan practices his cello for 7.5 hours.

nina's ratio of viola to cello is

3/2

since she practiced the cello for the same amount of time as juan, that means she practices 7.5 hours.   this gives us the ratio

x/7.5

and the proportion

3/2 = x/7.5

cross multiplying,

3(7.5) = 2(x)

22.5 = 2x

dividing both sides by 2,

22.5/2 = 2x/2

11.25 = x