Research suggests that about 24% of 12 year olds in the United States can pick out the stats of Colorado on a map. What is the probability that you mist sample 5 twelve year olds to find the first one who can pick out Colorado on a map?

The probability that I mist sample 5 12-year-olds to find the first one who can pick out Colorado on a map is 1.  

Step-by-step explanation:

The research suggests that about 24% of 12-year-olds in the US can pick out the state of Colorado on a map. The probability always exceeds the probabilities of picking out 1 over 5 12-year-olds, which is 20%, in a sample is well-represented the 12-year-old population of the US. Hence, the answer is 1 (or 100%).

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

true

explanation: