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kenny6666 [7]
3 years ago
11

Given that f(x) = −x 4 and g(x) = −2x − 3, solve for f(g(x)) when x = 2. −14 −7 7 11

Mathematics
1 answer:
Rudiy273 years ago
7 0
F(x) = -x + 4
g(x) = -2x - 3

f(g(x)) = -(-2x - 3) + 4 = 2x + 3 + 4 = 2x + 7
f(g(2)) = 2(2) + 7 = 4 + 7 = 11
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An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est
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Answer:

The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).

Step-by-step explanation:

We have to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.95}{2} = 0.025

Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a p-value of 1 - 0.025 = 0.975, so Z = 1.96.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96\frac{3.7}{\sqrt{582}} = 0.3

The lower end of the interval is the sample mean subtracted by M. So it is 24.1 - 0.3 = 23.8

The upper end of the interval is the sample mean added to M. So it is 24.1 + 0.3 = 24.4.

The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).

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