- A hip -hop dance group pays an hourly fee to rent a practice room. One month, they spend $1,232.25 to rent the room for 15.5 hours. What is the fee to rent the room for 1 hour?
- Complete the sentence or solve the problem.
a. When 0 < 1,=”” a=”” dilation=”” is=”” a(n)=””>
The correct answer and explanation is:
Problem 1: Rent Fee Calculation
We are given that a hip-hop dance group pays a total of $1,232.25 to rent a practice room for 15.5 hours. We need to determine the fee to rent the room for 1 hour.
To find the hourly rate, we divide the total cost by the number of hours rented: Hourly Fee=Total CostNumber of Hours=1232.2515.5\text{Hourly Fee} = \frac{\text{Total Cost}}{\text{Number of Hours}} = \frac{1232.25}{15.5}
Calculating this: Hourly Fee=79.5\text{Hourly Fee} = 79.5
So, the fee to rent the room for 1 hour is $79.50.
Problem 2: Dilation Description
The second part of your query appears to relate to geometry, specifically dilation. Let’s break it down.
a. When 0<k<10 < k < 1, a dilation is a(n) reduction.
Explanation:
In geometry, dilation refers to resizing a figure by a scale factor. A scale factor is a number that either enlarges or reduces the figure. It works in such a way that if the scale factor is greater than 1, the figure is enlarged (stretched). Conversely, if the scale factor is between 0 and 1 (i.e., 0<k<10 < k < 1), the figure is reduced (shrunk).
- Enlargement: If the scale factor k>1k > 1, every point in the figure moves farther from the center of dilation, making the image larger than the original. For example, if a scale factor of k=2k = 2 is used, the image is twice the size of the original.
- Reduction: If the scale factor 0<k<10 < k < 1, every point in the figure moves closer to the center of dilation, making the image smaller than the original. For example, if k=0.5k = 0.5, the image will be half the size of the original figure.
The key takeaway is that when the scale factor is between 0 and 1, the figure undergoes a reduction.
Let me know if you need further clarification or additional help!