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

The acceptable range of weights is 4 ≤ x ≤ 6.
That is,
(a) 4 with no toppings
(b) 6 with toppings

Let us examine the given answers.
A) 0 < x ≤ 6
he lowest value of x is 4, so this answer not acceptable.
REJECT

B) 0 < x ≤ 3
Obviously, this does not satisfy 0 ≤ x ≤ 6.
REJECT

C) 4 ≤ x ≤ 6
This is exactly what we want.
ACCEPT

D) x ≤ 6
his does not satisfy x ≥ 4.
REJECT

E) |x - 5| ≤ 1
When x-5 ≤ 1, obtain
 x ≤ 6 (acceptable)
When 5 - x ≤ 1, obain
-x ≤ -4
x ≥ 4 (acceptable)
This is what we want.
ACCEPT

F) |x - 2 | ≤ 6
When x - 2 ≤ 6
x ≤ 8 (not acceptable)
REJECT

C and E

The correct answer is C.) 4 ≤ x ≤ 6

Step-by-step explanation:

Let the total weight of the cup be x ounces.

As given The cup is filled with 4 oz. of yogurt before any toppings are added.  

So, the initial weight of the cup be 4

⇒ 4 ≤ x (1)

When toppings are added, they are allowed up to a total weight of 6 oz.

So, the weight of the cup cannot exceed 6

⇒ x ≤ 6 (2)

By combining (1) and (2). We get,

4 ≤ x ≤ 6

This means that any weight between, and including, 4 and 6 oz. is acceptable.

Hence, The correct option is C.) 4 ≤ x ≤ 6

Based on what I know I would assume 15. However I would try and find a better answer (Also tell your teacher it's called Mushroom Kingdom not Mario Land)