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EastWind [94]
3 years ago
11

Given the function f(x) = 4x + 1, EXPLAIN and show how to find the average rate of change between x = 1 and x = 3.

Mathematics
2 answers:
Tasya [4]3 years ago
7 0
Average rate of change is another word for the slope. The function you have is presented in slope-intercept form (y=mx+b), where m=your slope. This means that you already know the slope, which is 4.

Just in case you need to show why the slope = 4, I’ll leave how to find it here:

To find the slope, use the formula: y2-y1/x2-x1

First, you need to find the y-values at x=1 and x=3. To do this, plug the x-values into the equation. The value you end up with is your y-value.

f(1) = 4(1) + 1 = 5
f(3) = 4(3) + 1 = 13

So your two points are (1, 5) and (4, 13). Now plug these points into the slope formula

m = (13-5)/(3-1) = 8/2. 8 divided by two is 4, so your average rate of change is 4. You can double check this by graphing.
11Alexandr11 [23.1K]3 years ago
4 0

The average rate of change is calculated as the slope of the line between the two points on the graph. Since at x = 1, y = -3, and at x = 3, y = 1, these are the two points which we calculate the slope from. Using the formula

m = (y2 - y1)/(x2 - x1)

m = (1 - (-3))/(3 - 1)

m = 4/2

m = 2

Therefore the slope, or the average rate of change, between these points is 2.

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Using the normal distribution, it is found that 58.97% of students would be expected to score between 400 and 590.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
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The proportion of students between 400 and 590 is the <u>p-value of Z when X = 590 subtracted by the p-value of Z when X = 400</u>, hence:

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Z = \frac{590 - 502}{115}

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X = 400:

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0.7764 - 0.1867 = 0.5897 = 58.97%.

58.97% of students would be expected to score between 400 and 590.

More can be learned about the normal distribution at brainly.com/question/27643290

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