Complete the square.


Use de Moivre's theorem to compute the square roots of the right side.


Now, taking square roots on both sides, we have


Use de Moivre's theorem again to take square roots on both sides.



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Stuck on the same question and it looks like nobody cares to answer on this website
Step-by-step explanation:
gallons to quarts have the ratio 1:4.
there are 4 quarts in a gallon (hence the name of quarts by the way).
so, the question is really, which order pair have also a 1:4 ratio between x and y ?
(1, 4)
(2, 8)
(3, 12)
the (4, 1) would represent a 4:1 ratio.
and as you know, 4/1 is different to 1/4.
a ratio is nothing else than a fraction. just the "whole" is different.
the pure fraction 1/4 means that the whole is 4/4, has 4 times 1/4.
a ratio 1:4 (you can also write as 1/4) means that the whole has 5 (1+4) parts.
other than that they are compared and calculated with the same way as normal fractions.
Answer:
P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.
Step-by-step explanation:
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:

Find P(X > 1.05).
This is 1 subtracted by the pvalue of Z when X = 1. So:



has a pvalue of 0.8413
So P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.