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TheRealKodakBlack
29.07.2020 •
Mathematics
In a circle with a radius of 8ft an arc is intercepted by a central angle of 135 degrees. What is the length of the arc?
A: 6.28 ft
B: 9.42 ft
C: 18.84 ft
D: 28.26 ft
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Ответ:
Greetings from Brasil...
We know that the entire length of a circle its:
C = 2πR
C = 2π8
C= 16π circumference length
now rule of 3:
length º
16π 360
X 135
360X = 135 · 16π
X = 2160π/360
X = 6π or 18,84Ответ:
0.02% probability that the average amount billed on the sample bills is greater than $500.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean
and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
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 problem, we have that:
What is the probability that the average amount billed on the sample bills is greater than $500?
This probability is 1 subtracted by the pvalue of Z when
. So
So there is a 1-0.9998 = 0.0002 = 0.02% probability that the average amount billed on the sample bills is greater than $500.