Question
15. A tuxedo rental company charges a flat fee of $200 plus a $50 per day fee to rent one of their tuxedos. The function that models the cost to rent a tuxedo is t(d)=50d+200, where d represents the number of days in which the tuxedo is rented and t represents the total cost of the rental.
Select all reasonable scales for the vertical axis.(3 points)
$1
$1
$5
$5
$25
$25
$50
$50
$100
$100
$400
Select all reasonable scales for the vertical axis.(3 points)
$1
$1
$5
$5
$25
$25
$50
$50
$100
$100
$400
Answers
Answered by
GPT-4o mini
To determine reasonable scales for the vertical axis (cost) of the function \( t(d) = 50d + 200 \), we can analyze the function based on the values of \( d \) (the number of days).
1. **Minimum Cost**: When \( d = 0 \):
\[
t(0) = 50(0) + 200 = 200
\]
The minimum cost is $200.
2. **For various values of \( d \)**:
- \( d = 1 \): \( t(1) = 50(1) + 200 = 250 \)
- \( d = 2 \): \( t(2) = 50(2) + 200 = 300 \)
- \( d = 3 \): \( t(3) = 50(3) + 200 = 350 \)
- \( d = 4 \): \( t(4) = 50(4) + 200 = 400 \)
- And so on...
Given the range of values (starting from $200 and increasing), the reasonable scales for the vertical axis (the cost) would be those that make sense within this context and that can fit above $200.
Let's evaluate the options:
- **$1**: Not reasonable, since the minimum cost is $200.
- **$5**: Not reasonable, since the minimum cost is $200.
- **$25**: Not reasonable, since the minimum cost is $200.
- **$50**: Not reasonable, since the minimum cost is $200.
- **$100**: Not reasonable, since the minimum cost is $200.
- **$400**: Reasonable, as it falls within the expected range of costs (e.g., for 4 days).
### Therefore, the only reasonable scale for the vertical axis is:
- **$400**
1. **Minimum Cost**: When \( d = 0 \):
\[
t(0) = 50(0) + 200 = 200
\]
The minimum cost is $200.
2. **For various values of \( d \)**:
- \( d = 1 \): \( t(1) = 50(1) + 200 = 250 \)
- \( d = 2 \): \( t(2) = 50(2) + 200 = 300 \)
- \( d = 3 \): \( t(3) = 50(3) + 200 = 350 \)
- \( d = 4 \): \( t(4) = 50(4) + 200 = 400 \)
- And so on...
Given the range of values (starting from $200 and increasing), the reasonable scales for the vertical axis (the cost) would be those that make sense within this context and that can fit above $200.
Let's evaluate the options:
- **$1**: Not reasonable, since the minimum cost is $200.
- **$5**: Not reasonable, since the minimum cost is $200.
- **$25**: Not reasonable, since the minimum cost is $200.
- **$50**: Not reasonable, since the minimum cost is $200.
- **$100**: Not reasonable, since the minimum cost is $200.
- **$400**: Reasonable, as it falls within the expected range of costs (e.g., for 4 days).
### Therefore, the only reasonable scale for the vertical axis is:
- **$400**
Answer
that is a multiple choice question
Answered by
GPT-4o mini
I apologize for misunderstanding your request! Given that we are dealing with a multiple-choice question regarding reasonable scales for the vertical axis based on the cost function \( t(d) = 50d + 200 \), let's re-evaluate the options provided:
- **$1**: Not reasonable (too low).
- **$5**: Not reasonable (too low).
- **$25**: Not reasonable (too low).
- **$50**: Not reasonable (too low).
- **$100**: Not reasonable (too low).
- **$400**: Reasonable (within the calculated cost for multiple days of rental).
### Therefore, the **reasonable scale for the vertical axis** is:
- **$400**
I hope this helps clarify! If you have any more questions or need further assistance, feel free to ask.
- **$1**: Not reasonable (too low).
- **$5**: Not reasonable (too low).
- **$25**: Not reasonable (too low).
- **$50**: Not reasonable (too low).
- **$100**: Not reasonable (too low).
- **$400**: Reasonable (within the calculated cost for multiple days of rental).
### Therefore, the **reasonable scale for the vertical axis** is:
- **$400**
I hope this helps clarify! If you have any more questions or need further assistance, feel free to ask.