Sagot :
Answer: Only j = 2
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Explanation:
Let's solve for j
[tex]\frac{96}{j} \ge 40\\\\96 \ge 40j\\\\\frac{96}{40} \ge j\\\\2.4 \ge j\\\\j \le 2.4[/tex]
In the second step, I multiplied both sides by j. If j is a positive number, then the inequality sign will not flip. All of the answer choices are positive numbers, so we don't have to worry about the inequality sign flipping.
The last step shows that j = 2.4 or j < 2.4
So j is 2.4 or smaller.
Of the list given to us, only j = 2 fits the description, since something like j = 8 is not 2.4 or smaller.
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If j = 2, then,
[tex]\frac{96}{j} \ge 40\\\\\frac{96}{2} \ge 40\\\\48 \ge 40\\\\[/tex]
which is a true statement since 48 is larger than 40. This shows that j = 2 is a solution.
Something like j = 8 does not work because
[tex]\frac{96}{j} \ge 40\\\\\frac{96}{8} \ge 40\\\\12 \ge 40\\\\[/tex]
which is false because 12 is not equal to 40 or larger than 40. This means j = 8 is not a solution. You should find that j = 12 and j = 3 lead to similar false statements.
Of the list given, j = 2 is the only solution.
Answer:
[tex]\boxed{\boxed{\sf{j=2}}}[/tex]
Solution Steps:
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1.) Solve using j = 12:
- Plug in 12: [tex]\frac{96}{12}[/tex] ≥ [tex]40[/tex]
- Divide 96 by 12: [tex]=8[/tex]
- Compare: [tex]8[/tex] ≥ [tex]40[/tex]
So this is False.
2.) Solve using j = 8:
- Plug in 8: [tex]\frac{96}{8}[/tex] ≥ [tex]40[/tex]
- Divide 96 by 8: [tex]=12[/tex]
- Compare: [tex]12[/tex] ≥ [tex]40[/tex]
So this is False.
3.) Solve using j = 2:
- Plug in 2: [tex]\frac{96}{2}[/tex] ≥ [tex]40[/tex]
- Divide 96 by 2: [tex]=48[/tex]
- Compare: [tex]48[/tex] ≥ [tex]40[/tex]
So this is True.
4.) Solve using j = 3:
- Plug in 3: [tex]\frac{96}{3}[/tex] ≥ [tex]40[/tex]
- Divide 96 by 3: [tex]=32[/tex]
- Compare: [tex]32[/tex] ≥ [tex]40[/tex]
So this is False.
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