Part A:
An example of a system of inequalities that would only have D and F as solutions is 
and 
. These would both be dotted lines since its not greater than or equal to, and they would be shaded in the upper region since its greater than.
Part B:
You can verify by plugging in the coordinates of D and F into both inequalities. If the coordinates are true for both inequalities, then they are in the overlapping shaded region.
D = (2,4)
F = (-2,3)
true
true
Part C:
You can either plug the inequality into a graph. If the coordinate is in the shaded region, in this context it would be able to raise chickens in that farm.
The other option is plugging in the coordinates of each farm into the inequality. If the inequality is true for those coordinates, then that farm can raise chickens.
Answer:
Heights of 29.5 and below could be a problem.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches.
This means that 
There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.
Heights at the 5th percentile and below. The 5th percentile is X when Z has a p-value of 0.05, so X when Z = -1.645. Thus
Heights of 29.5 and below could be a problem.
Area of the triangle = (1/2)(base)(height) = (1/2)(4)(5) = 10 square units.
The correct answer is A.
V = 180 cm3
l = 10 cm
w = 4 cm
h = ?
V=lwh, so to get h, divide equation by lw, to get h=V/(lw).
h = 180/(10*4) = 4.5 cm
Initially, the point (-3,4) is in the second quadrant of the cartesian plane. If the rotation is about point (-3,0) at 90 degrees, you find a point that when connected to (-3,4) makes two lines perpendicular to each other. Since the direction is counterclockwise, you move 3 points to the left, then 4 points down. That would be (-7,0). The answer is A.
