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Mathematics

1 answer:

VashaNatasha [74]2 years ago

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The average rate of change, of the function, between the intervals, x = 2 to x = 6 is: 180.

<h3>What is the Average Rate of Change of a Function?</h3>

Average rate of change = $\frac{f(b) - f(a)}{b - a}$ .

Given the function, $f(x)= 3^x + 25$ ,

The average rate of change using the intervals of, x = 2 to x = 6 would be solved as shown below:

a = 2

b = 6

f(a) = $f(2)= 3^2 + 25$ = 34

f(b) = $f(6)= 3^6 + 25$ = 754

Average rate of change = $\frac{754 - 34}{6 - 2} = \frac{720}{4}$

Average rate of change = 180

Therefore, the average rate of change, of the function, between the intervals, x = 2 to x = 6 is: 180.

Learn more about average rate of change on:

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Law Incorporation [45]

Using proportions, the number of 1/4 cup servings that she can make is given by:

B. 3 and 5/9.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, considering that Susie has 8/9 of a cup, the following <u>rule of three</u> is established:

1 serving - 1/4 cups

x servings - 8/9 cups

Applying cross multiplication:

$\frac{x}{4} = \frac{8}{9}$