Rewrite the function by completing the square f(x) =4x2+12x+9
1 answer:
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = 4x² + 12x + 9
The coefficient of the x² term must be 1 so factor out 4 from the first 2 terms
f(x) = 4(x² + 3x) + 9
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² + 3x
f(x) = 4(x² + 2()x +
-
) + 9
= 4(x + )² - 9 + 9
= 4(x + )²
Thus
f(x) = 4x² + 12x + 9 = 4(x + )²
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Answer:
Ninety-five percent of consumers in the U.S. consumed less than 63.59 gallons.
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:
The standard deviation is the square root of the variance, so
Also, the mean is 42.2, so
Ninety-five percent of consumers in the U.S. consumed less than how many gallons?
The 95th percentile, which is the value of X when Z has a pvalue of 0.95. So X when
Ninety-five percent of consumers in the U.S. consumed less than 63.59 gallons.