1. what is the area of a parallelogram whose vertices are a(−1, 12) , b(13, 12) , c(2, −5) , and d(−12, −5) ? 2. each small square on the grid is 1 ft². which estimate best describes the area of this figure? 25 ft² 35 ft² 50 ft² 65 ft²

1. 238 2. 50 ft² The area of a parallelogram is bh where b is the base, and h is the height. Since line segments AB and CD are conveniently horizontal, I'll use the length of line segment CD as the base (which is 14), and the distance between line segments AB and CD as the height (which is 17). So 14 * 17 = 238 So the area of the parallelogram is 238. As for estimating the area of the polygon in the drawing, first, look at the overall length and width. The figure covers an area 8 units wide and 8 units tall except for the corners. So the upper limit on it's size is 64. Now look at the upper left hand corner. A bit over 3 square units isn't covered. So the new upper limit to your estimate is 64 - 3 = 61 units. Look at the upper right corner. Looks like about 3.5 units aren't covered there. So the new estimate becomes 61-3.5 = 57.5. Looking at the lower left corner let's us subtract another 4 units giving 57.5 - 4 = 53.5. Lower right corner shows another 4 units or so uncovered, so 53.5 - 4 = 49.5. Now look at the available choices of 25, 35, 50, and 65 to see what's closest. And that's obviously 50. So the answer is 50 ft².

See below:)

Step-by-step explanation:

a)

mean = 63.6 , s.d = 2.5. We need to compute Pr(58 <= X <= 80)

The corresponding z-values needed to be computed

z1 = (58 - 63.6)/2.5 = -2.24

z2 = (80 - 63.6)/2.5 = 6.56

Therefore, we get:

Pr(58 <= X <= 80) = Pr( (58 - 63.6)/2.5 <= Z <= (80-63.6)/2.5 ) = Pr(-2.24 <= Z <= 6.56)

= 1 - 0.0125 = 0.9875

98.75 % of the women meet the requirements,Hence not too many women are being denied the opportunity to join this branch of the millitary.

b)

z value for lower 1% = -2.3263

corresponding x value = 63.6 - (2.5X2.3263) = 57.78

Z value for upper 2% = 2.0537

corresponding x value = 63.6 + (2.5X2.0537) = 68.73

The new height requirements is between 57.78 and 68.73 inch