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To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, [tex]\( c \)[/tex], that Elisa uses to make one vase of either size?

A. [tex]\( 4.5 \ \textless \ c \ \textless \ 12 \)[/tex]
B. [tex]\( 4.5 \leq c \leq 12 \)[/tex]
C. [tex]\( c \ \textless \ 4.5 \)[/tex] or [tex]\( c \ \textgreater \ 12 \)[/tex]
D. [tex]\( c \leq 4.5 \)[/tex] or [tex]\( c \geq 12 \)[/tex]

Sagot :

GinnyAnsweridn
To determine the correct compound inequality representing the number of ounces of clay, [tex]\( c \)[/tex], that Elisa uses to make one vase of either size, let's carefully examine the conditions provided for the small and large vases:

1. For a small vase, Elisa uses no more than 4.5 ounces of clay.
- This means [tex]\( c \)[/tex] is at most 4.5, or [tex]\( c \leq 4.5 \)[/tex].

2. For a large vase, Elisa uses at least 12 ounces of clay.
- This means [tex]\( c \)[/tex] is at least 12, or [tex]\( c \geq 12 \)[/tex].

We need to combine these two conditions using "or" because the amount of clay used to make a vase can fall into either category (small or large). Thus, the compound inequality should represent [tex]\( c \leq 4.5 \)[/tex] or [tex]\( c \geq 12 \)[/tex].

Combining these inequalities, we get:
[tex]\[ c \leq 4.5 \text{ or } c \geq 12 \][/tex]

So, the correct compound inequality is:
[tex]\[ c \leq 4.5 \text{ or } c \geq 12 \][/tex]
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