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Answer :
Sure! Let's tackle each part of the question step by step.
1. First Inequality: The weight is less than [tex]\( 8 \frac{1}{6} \)[/tex] pounds.
- The problem states that the weight is less than [tex]\( 8 \frac{1}{6} \)[/tex] pounds. In mathematical terms, this is expressed as:
[tex]\[
w < 8 \frac{1}{6}
\][/tex]
- To make it easier to work with, we convert the mixed number [tex]\( 8 \frac{1}{6} \)[/tex] to an improper fraction. However, the relevant information indicates this would be approximately 8.166666666666666, so we can consider it directly:
[tex]\[
w < 8.1667 \quad (\text{rounded value})
\][/tex]
- The variable [tex]\( w \)[/tex], representing weight, must be a positive number, which means:
- Type of numbers [tex]\( w \)[/tex] can represent: Positive numbers (greater than 0).
2. Second Inequality: There must be at least 67 police officers on duty.
- The word "at least" tells us that the number can be 67 or more. Mathematically, this is:
[tex]\[
p \geq 67
\][/tex]
- The variable [tex]\( p \)[/tex], representing the number of police officers, is required in this situation, typically as whole numbers since you can't have a fraction of a police officer on duty.
- Type of numbers [tex]\( p \)[/tex] can represent: Whole numbers (including and above 67).
By the end, we have:
- An inequality for the weight as [tex]\( w < 8.1667 \)[/tex], where [tex]\( w \)[/tex] is a positive number.
- An inequality for the police officers as [tex]\( p \geq 67 \)[/tex], where [tex]\( p \)[/tex] represents whole numbers.
1. First Inequality: The weight is less than [tex]\( 8 \frac{1}{6} \)[/tex] pounds.
- The problem states that the weight is less than [tex]\( 8 \frac{1}{6} \)[/tex] pounds. In mathematical terms, this is expressed as:
[tex]\[
w < 8 \frac{1}{6}
\][/tex]
- To make it easier to work with, we convert the mixed number [tex]\( 8 \frac{1}{6} \)[/tex] to an improper fraction. However, the relevant information indicates this would be approximately 8.166666666666666, so we can consider it directly:
[tex]\[
w < 8.1667 \quad (\text{rounded value})
\][/tex]
- The variable [tex]\( w \)[/tex], representing weight, must be a positive number, which means:
- Type of numbers [tex]\( w \)[/tex] can represent: Positive numbers (greater than 0).
2. Second Inequality: There must be at least 67 police officers on duty.
- The word "at least" tells us that the number can be 67 or more. Mathematically, this is:
[tex]\[
p \geq 67
\][/tex]
- The variable [tex]\( p \)[/tex], representing the number of police officers, is required in this situation, typically as whole numbers since you can't have a fraction of a police officer on duty.
- Type of numbers [tex]\( p \)[/tex] can represent: Whole numbers (including and above 67).
By the end, we have:
- An inequality for the weight as [tex]\( w < 8.1667 \)[/tex], where [tex]\( w \)[/tex] is a positive number.
- An inequality for the police officers as [tex]\( p \geq 67 \)[/tex], where [tex]\( p \)[/tex] represents whole numbers.
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