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Answer:
6. 60°
7. 5.19559
8. 7.96011
Step-by-step explanation:
6. The sum of angles in a triangle is 180°, so the remaining angle is ...
180° -40° -80° = 60°
7. The lengths of sides are proportional to the sine of the opposite angle (Law of Sines).
a = c·sin(A)/sin(C) = 7·sin(40°)/sin(60°) ≈ 5.19559
8. Same explanation as 7.
b = c·sin(B)/sin(C) = 7·sin(80°)/sin(60°) ≈ 7.96011
Answer:
0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years
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.
A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year
This means that
What is the probability that a given battery will last between 2.3 and 3.6 years?
This is the p-value of Z when X = 3.6 subtracted by the p-value of Z when X = 2.3. So
X = 3.6
has a p-value of 0.8849
X = 2.3
has a p-value of 0.0808
0.8849 - 0.0808 = 0.8041
0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years