The weights of adult women are approximately normally distributed about a mean of 142 lbs. with a standard deviation of 14 lbs. If Renee is at the 96 percentile in weight for adult women, then her weight, in lbs. is closest
to

166. 5

Step-by-step explanation:

Given the following :

Mean weight (m) = 142 lbs

Standard deviation (sd) = 14 lbs

Renne = 96 percentile, what is Renne's weight

Using the equation :

Zscore = (score - mean) / standard deviation

96 percentile = 0.96 is equivalent to a Zscore of

1.75

Hence,

1.75 = (score - 142) / 14

14 * 1.75 = score - 142

24.5 = score - 142

24.5 + 142 = score

Score = 166.5

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.