At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply:
A.) 0 < x ≤ 6
B.) 0 < x ≤ 3
C.) 4 ≤ x ≤ 6
D.) x ≤ 6
E.) |x - 5| ≤ 1
F.) |x - 2| ≤ 6

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cavs562 cavs562 · Answer 1 · 2017-07-25T18:48:34+02:00

The yogurt can weigh above or equal to 4 ounces or less or equal to 6 ounces.

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facundo3141592 facundo3141592 · Answer 2 · 2022-02-11T13:39:51+01:00

By writing an inequality and then converting it to an absolute value equation, we will see that the correct options are C and E.

To find the inequality, we need to find the lower and upper bounds.

First, we know that the machine fills the cups with 4 oz of yogurt, so this is the minimum value allowed, we will have:

4 ≤ x

Then we can add toppings to a maximum value of 6 ounces, this will be the maximum, then we have:

4 ≤ x ≤ 6

We can also write this an absolute value equation, we define:

Then the absolute value equation is:

|x - M| ≤ m

By replacing what we found before, we have:

So the absolute value equation is:

|x - 5| ≤ 1

Finally, we can conclude that the correct options are C and E.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/11234618