Factor the expression. 9b2 – 25
2 answers:
Answer: (3b + 5)(3b - 5)
Because both terms, 9b² and 25, are perfect squares, you can factor by taking the square roots of both terms.
The square root of 9b² is 3b (3b × 3b = 9b²).
The square root of 25 is 5 (5 × 5 = 25).
9b² - 25 has a negative, so the factored expression would be
(3b + 5)(3b - 5). The signs (+ and -) alternate in this case because the expression, 9b² - 25, has no middle term.
You can check your work by using FOIL. See the attachment below.
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Answer:
3.67% probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.
Step-by-step explanation:
To solve this question, we need 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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
Find the probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.
This is the pvalue of Z when X = 0.809.
By the Central Limit Theorem
has a pvalue of 0.0367
3.67% probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.
Answer:
Step-by-step explanation:
This should help I hope
Step-by-step explanation:
Answer is in the picture.
