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tigry1 [53]
3 years ago
14

Let f(x)=x^2+2x+3 . What is the average rate of change for the quadratic function from x=−2 to x = 5?

Mathematics
1 answer:
miskamm [114]3 years ago
5 0
To find the average rate of change of  given function f(x) on a given interval (a,b):

Find f(b)-f(a), b-a, and then divide your result for f(b)-f(a) by your result for b-a:


f(b) - f(a)
------------
    b-a

Here your function is f(x) = x^2 - 2x + 3.  Substituting b=5 and a=-2,
f(5) = 5^2 -2(5)+3 =?                          and f(-2) = (-2)^2 - 2(-2) + 3 = ?


Calculate           f(5) - [ f(-2) ]
                         ------------------ using your results, above.
                              5 - [-2]

Your answer to this, if done correctly, is the "average rate of change of the function f(x) = x^2+2x+3 on the interval [-2,5]."
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5. The point (-7, 4) is reflected over the line x = -3. Then,
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(4,1)

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Solve x^2 + 5x + 6 = 0​
grigory [225]

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In a random sample of 74 women at a company, the mean salary is $39,902 with a standard deviation of $3270 in a random sample of
ValentinkaMS [17]
The correct answer is the first choice, ($1818.30, $5077.70.)

To find this, we first find the z-score based on the confidence level:
Convert 95% to a decimal:  95%=95/100 = 0.95
Subtract from 1:  1-0.95 = 0.05
Divide by 2:  0.05/2 = 0.025
Subtract from 1:  1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.

Next, we identify 
\overline{x_1}=39902; \overline{x_2}=36454; n_1=74; n_2=40; \sigma_1=3270; \sigma_2=4677

Next we find
(\overline{x_1}-\overline{x_2})=(39902-36454) = 3448

Next we find 
\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}
\\
\\=\sqrt{\frac{3270^2}{74}+\frac{4677^2}{40}}=\sqrt{\frac{10692900}{74}+\frac{21874329}{40}}
\\
\\=831.479

Next, we multiply this value by z:
1.96(831.479) = 1629.70

The confidence interval is given by
3448\pm1629.70
\\
\\=(3448-1629.70, 3448+1629.70)
\\
\\=(1818.30, 5077.70)
5 0
3 years ago
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