Quadrilateral ABCD has vertices AC-3.6), B(6,0), C(9. -9), and D(0, -3). Prove that ABCD is a) a parallelogram
1 answer:
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Explanation:
The quadrilateral will be a parallelogram if the diagonals bisect each other. That will be the case if the sums of their end-point coordinates are the same.
A + C = (-3, 6) +(9, -9) = (6, -3)
B + D = (6, 0) +(0, -3) = (6, -3)
Both diagonals have their midpoint at (3, -1.5), so the diagonals are mutual bisectors. The figure ABCD must be a parallelogram.
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The midpoint of AC is (A+C)/2 = (6, -3)/2 = (3, -1.5).
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Answer:
The z-score for the trainee is of 2.
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 mean of the test scores is 72 with a standard deviation of 5.
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Find the z-score for a trainee, given a score of 82.
This is Z when X = 82. So
The z-score for the trainee is of 2.
Answer: (i) This angle is 33.41% of the full rotation.
(ii) 120.38°
Step-by-step explanation:
GIven: Measure of full rotation = 2π radians
Measure of an angle = 2.1 radians.
The percent of this angles of a full rotation =
i.e. This angle is 33.41% of the full rotation.
In degrees,