Jane Hilman went to her bank. She had a balance of $1,009.88 in her savings account. She withdrew $130.00 and the teller credite
1 answer:
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Answer:
(3x + 1)²
Step-by-step explanation:
Given
9x² + 6x + 1 ← is a perfect square of the form
(ax + b)² = a²x² + 2abx + b²
Compare like terms to find a and b
a²x² = 9x² ⇒ a² = 9 ⇒ a = = 3
b² = 1 ⇒ b = = 1
and 2ab = 2 × 3 × 1 = 6
Thus
9x² + 6x + 1 = (3x + 1)²
Answer:
27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.
Step-by-step explanation:
To solve this problem, it is important to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
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
In this problem, we have that:
What is the probability that the mean volume of a random sample of 144 bottles is less than 12 oz
This is the pvalue of Z when
By the Central Limit Theorem
has a pvalue of 0.2743.
So there is a 27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.