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)<∞
0 less-than-or-equal-to f left parenthesis w right parenthesis less than infinity
0<f(w)<1,050
. 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)<∞
0 less-than-or-equal-to f left parenthesis w right parenthesis less than infinity
0<f(w)<1,050
Answers
GPT-4o mini
To find the appropriate inequality representing Dorian's earnings from dog walking, we need to consider the constraints:
1. Dorian earns $15 for each dog he walks, so his earnings, represented by \( f(w) \), is given by the equation \( f(w) = 15w \).
2. Since \( w \) (the number of dogs walked) must be a non-negative integer, the lowest value for \( f(w) \) is $0 (if he doesn't walk any dogs).
3. We must also consider a maximum earning limit. Since the problem specifies a maximum of $1,050, we can derive the number of walks by:
\[
15w \leq 1,050
\]
which implies
\[
w \leq \frac{1,050}{15} = 70.
\]
This means the maximum number of dogs Dorian can walk is 70, leading to a maximum earning of $1,050.
Given this context, the correct inequality that shows the range of his earnings would be:
\[
0 \leq f(w) \leq 1,050.
\]
Thus, the final answer is:
**0 ≤ f(w) ≤ 1,050**
1. Dorian earns $15 for each dog he walks, so his earnings, represented by \( f(w) \), is given by the equation \( f(w) = 15w \).
2. Since \( w \) (the number of dogs walked) must be a non-negative integer, the lowest value for \( f(w) \) is $0 (if he doesn't walk any dogs).
3. We must also consider a maximum earning limit. Since the problem specifies a maximum of $1,050, we can derive the number of walks by:
\[
15w \leq 1,050
\]
which implies
\[
w \leq \frac{1,050}{15} = 70.
\]
This means the maximum number of dogs Dorian can walk is 70, leading to a maximum earning of $1,050.
Given this context, the correct inequality that shows the range of his earnings would be:
\[
0 \leq f(w) \leq 1,050.
\]
Thus, the final answer is:
**0 ≤ f(w) ≤ 1,050**