An animal researcher randomly selected 98 dogs and cats and recorded if they napped between 2:00 p. m. and 2:30 p. m. The two-way table displays the data. A 4-column table with 3 rows. Column 1 has entries dog, cat, total. Column 2 is labeled nap with entries 15, 23, 38. Column 3 is labeled no nap with entries 32, 28, 60. Column 4 is labeled total with entries 47, 51, 98. The columns are titled napping habit and the rows are titled animal type.

Suppose an animal is randomly selected. Let event C = cat and let event N = nap. What is the value of P(C|N)?

StartFraction 38 Over 98 EndFraction
StartFraction 23 Over 51 EndFraction
StartFraction 47 Over 98 EndFraction
StartFraction 23 Over 38 EndFraction

  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.

b

step-by-step explanation:

1/2*qr*rs

step-by-step explanation:

i believe the answer is c.