There are 100 students in 11th grade at john d'obryant school of math & science in boston. 60 like basketball and 70 like te
1 answer:
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Answer:
a) 3 kilograms
b) 5.7 kilograms
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
We have to find X for both values of Z.
a) z = -1.35
3 kilograms
b) z = 2.64
5.7 kilograms
Answer:
(x + 3)² + (y + 1)² = 100
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center of the circle and r is the radius.
The center is on the line x − 4y = 1, so:
h − 4k = 1
h = 1 + 4k
(x − 1 − 4k)² + (y − k)² = r²
Two points on the line are (3, 7) and (5, 5), so:
(3 − 1 − 4k)² + (7 − k)² = r²
(5 − 1 − 4k)² + (5 − k)² = r²
Set the equations equal:
(3 − 1 − 4k)² + (7 − k)² = (5 − 1 − 4k)² + (5 − k)²
(2 − 4k)² + (7 − k)² = (4 − 4k)² + (5 − k)²
4 − 16k + 16k² + 49 − 14k + k² = 16 − 32k + 16k² + 25 − 10k + k²
4 − 16k + 49 − 14k = 16 − 32k + 25 − 10k
53 − 30k = 41 − 42k
12k = -12
k = -1
h = 1 + 4k
h = -3
(3 − 1 − 4k)² + (7 − k)² = r²
(3 − 1 + 4)² + (7 + 1)² = r²
6² + 8² = r²
r = 10
Therefore, the equation of the circle is:
(x + 3)² + (y + 1)² = 10²
