Question
Dorian earns $15 every time he walks a dog. He models the total amount of money he makes walking dogs with the equation f(w)=15w
. Which inequality shows the range of his earnings given the real-world constraints?(1 point)
Responses
0≤f(w)<∞
0 less-than-or-equal-to f left parenthesis w right parenthesis less than infinity
0<f(w)<1,050
0 less than f left parenthesis w right parenthesis less than 1,050
0≤f(w)≤1,050
0 less-than-or-equal-to f left parenthesis w right parenthesis less-than-or-equal-to 1,050
−∞<f(w)≤1,050
. Which inequality shows the range of his earnings given the real-world constraints?(1 point)
Responses
0≤f(w)<∞
0 less-than-or-equal-to f left parenthesis w right parenthesis less than infinity
0<f(w)<1,050
0 less than f left parenthesis w right parenthesis less than 1,050
0≤f(w)≤1,050
0 less-than-or-equal-to f left parenthesis w right parenthesis less-than-or-equal-to 1,050
−∞<f(w)≤1,050
Answers
GPT-4o mini
To find the appropriate inequality that shows the range of Dorian's earnings from walking dogs, we need to consider the constraints:
1. He cannot earn negative money, so his earnings must be greater than or equal to zero: \(f(w) \geq 0\).
2. The total earnings are also constrained by a maximum, which in this example will be \(1,050\) based on the implication that he may have a limit to the number of dog walks he can do.
Based on these constraints, the correct inequality that describes the range of his earnings is:
\[ 0 \leq f(w) \leq 1,050 \]
Thus, the final answer is:
**0≤f(w)≤1,050**
(0 less-than-or-equal to f left parenthesis w right parenthesis less-than-or-equal to 1,050)
1. He cannot earn negative money, so his earnings must be greater than or equal to zero: \(f(w) \geq 0\).
2. The total earnings are also constrained by a maximum, which in this example will be \(1,050\) based on the implication that he may have a limit to the number of dog walks he can do.
Based on these constraints, the correct inequality that describes the range of his earnings is:
\[ 0 \leq f(w) \leq 1,050 \]
Thus, the final answer is:
**0≤f(w)≤1,050**
(0 less-than-or-equal to f left parenthesis w right parenthesis less-than-or-equal to 1,050)