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Answer :
Let's solve the inequality step-by-step:
We have the inequality:
[tex]\[ 12 + \frac{40}{f} > 44 \][/tex]
We need to determine which value of [tex]\( f \)[/tex] makes this inequality true from the options given: [tex]\( f = 5 \)[/tex], [tex]\( f = 10 \)[/tex], [tex]\( f = 1 \)[/tex], [tex]\( f = 8 \)[/tex].
Let's evaluate the expression for each value of [tex]\( f \)[/tex]:
1. When [tex]\( f = 5 \)[/tex]:
[tex]\[ 12 + \frac{40}{5} = 12 + 8 = 20 \][/tex]
This value is not greater than 44, so [tex]\( f = 5 \)[/tex] does not satisfy the inequality.
2. When [tex]\( f = 10 \)[/tex]:
[tex]\[ 12 + \frac{40}{10} = 12 + 4 = 16 \][/tex]
This value is not greater than 44, so [tex]\( f = 10 \)[/tex] does not satisfy the inequality.
3. When [tex]\( f = 1 \)[/tex]:
[tex]\[ 12 + \frac{40}{1} = 12 + 40 = 52 \][/tex]
This value is greater than 44, so [tex]\( f = 1 \)[/tex] does satisfy the inequality.
4. When [tex]\( f = 8 \)[/tex]:
[tex]\[ 12 + \frac{40}{8} = 12 + 5 = 17 \][/tex]
This value is not greater than 44, so [tex]\( f = 8 \)[/tex] does not satisfy the inequality.
The only value of [tex]\( f \)[/tex] that makes the inequality true is [tex]\( f = 1 \)[/tex].
We have the inequality:
[tex]\[ 12 + \frac{40}{f} > 44 \][/tex]
We need to determine which value of [tex]\( f \)[/tex] makes this inequality true from the options given: [tex]\( f = 5 \)[/tex], [tex]\( f = 10 \)[/tex], [tex]\( f = 1 \)[/tex], [tex]\( f = 8 \)[/tex].
Let's evaluate the expression for each value of [tex]\( f \)[/tex]:
1. When [tex]\( f = 5 \)[/tex]:
[tex]\[ 12 + \frac{40}{5} = 12 + 8 = 20 \][/tex]
This value is not greater than 44, so [tex]\( f = 5 \)[/tex] does not satisfy the inequality.
2. When [tex]\( f = 10 \)[/tex]:
[tex]\[ 12 + \frac{40}{10} = 12 + 4 = 16 \][/tex]
This value is not greater than 44, so [tex]\( f = 10 \)[/tex] does not satisfy the inequality.
3. When [tex]\( f = 1 \)[/tex]:
[tex]\[ 12 + \frac{40}{1} = 12 + 40 = 52 \][/tex]
This value is greater than 44, so [tex]\( f = 1 \)[/tex] does satisfy the inequality.
4. When [tex]\( f = 8 \)[/tex]:
[tex]\[ 12 + \frac{40}{8} = 12 + 5 = 17 \][/tex]
This value is not greater than 44, so [tex]\( f = 8 \)[/tex] does not satisfy the inequality.
The only value of [tex]\( f \)[/tex] that makes the inequality true is [tex]\( f = 1 \)[/tex].
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