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
−∞<f(w)≤1,050
negative infinity less than f left parenthesis w right parenthesis less-than-or-equal-to 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
0<f(w)<1,050
0 less than f left parenthesis w right parenthesis less than 1,050
0≤f(w)<∞
0 less-than-or-equal-to f left parenthesis w right parenthesis less than infinity
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. Which inequality shows the range of his earnings given the real-world constraints?(1 point)
Responses
−∞<f(w)≤1,050
negative infinity less than f left parenthesis w right parenthesis less-than-or-equal-to 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
0<f(w)<1,050
0 less than f left parenthesis w right parenthesis less than 1,050
0≤f(w)<∞
0 less-than-or-equal-to f left parenthesis w right parenthesis less than infinity
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Answers
GPT-4o mini
To determine the range of Dorian's earnings while walking dogs, we first need to consider the equation given: \( f(w) = 15w \), where \( w \) represents the number of dogs walked.
1. Dorian earns $15 per dog.
2. If we assume he has a maximum number of dogs he can walk, for example, if he can walk up to 70 dogs, his maximum earnings would be \( 15 \times 70 = 1,050 \).
3. Therefore, his earnings, \( f(w) \), must be between $0 (if he walks no dogs) and his maximum allowed amount, which in this case is $1,050.
Considering these points, the correct inequality that shows the range of his earnings, given these constraints, is:
**0 ≤ f(w) ≤ 1,050**
This means Dorian can earn at least $0 (if he walks no dogs) and at most $1,050.
1. Dorian earns $15 per dog.
2. If we assume he has a maximum number of dogs he can walk, for example, if he can walk up to 70 dogs, his maximum earnings would be \( 15 \times 70 = 1,050 \).
3. Therefore, his earnings, \( f(w) \), must be between $0 (if he walks no dogs) and his maximum allowed amount, which in this case is $1,050.
Considering these points, the correct inequality that shows the range of his earnings, given these constraints, is:
**0 ≤ f(w) ≤ 1,050**
This means Dorian can earn at least $0 (if he walks no dogs) and at most $1,050.