Answer:
a ≈ 21.8
Step-by-step explanation:
We require the third angle in the triangle
Subtract the sum of the 2 angles from 180
third angle = 180° - (75 + 31.8)° = 180° - 106.8° = 73.2°
Using the Sine rule, that is
=
( cross- multiply )
a × sin75° = 22 × sin73.2° ( divide both sides by sin75° )
a = ≈ 21.8 ( to the nearest tenth )
Answer:
The bulbs should be replaced each 1436.9 hours.
Step-by-step explanation:
Problems of normally distributed samples are 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:
How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?
This is the first percentile of hours. So it is X when Z has a pvalue of 0.01.
So it is X when Z = -2.33.
The bulbs should be replaced each 1436.9 hours.