Please see attachment to help. I really need it.

Mathematics

1 answer:

telo118 [61]3 years ago

6 0

(fg)(x) = (x^3 -4x+2)(x^2+2)
(fg)(x) = x^5 - 4x^3 + 2x^2 + 2x^3 -8x + 4
(fg)(x) =x^5 - 2x^3 + 2x^2 -8x + 4

answer
x^5 - 2x^3 + 2x^2 -8x + 4

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A manufacturer knows that their items have a normally distributed length, with a mean of 15.4 inches, and standard deviation of

Masteriza [31]

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .