If the endpoints of the diameter of a circle are (−6, 6) and (6, −2), what is the standard form equation of the circle? A) x2 +
(y + 2)2 = 36 B) x2 + (y + 2)2 = 52 C) x2 + (y − 2)2 = 36 D) x2 + (y − 2)2 = 52
1 answer:
Answer:
D) x² + (y − 2)² = 52
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so is the average of the end points:
(h, k) = ((-6, 6) +(6, -2))/2 = (0, 4)/2 = (0, 2)
Then the distance between the center and an end point is the radius. It is found using the distance formula:
r = √((x2 -x1)² +(y2 -y1)²) = √((-6 -0)² +(6 -2)²) = √(36 +16) = √52
Putting these values into the standard form equation for a circle ...
(x -h)² +(y -k)² = r²
gives ...
(x -0)² +(y -2)² = (√52)²
x² +(y -2)² = 52 . . . . . matches choice D
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Answer:
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals
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.
Mean 490 mg and variance of 400.
This means that
What is the probability that a randomly selected pill contains at least 500 mg of minerals?
This is 1 subtracted by the p-value of Z when X = 500. So
has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals