Let's solve each part of the question step-by-step.
### Part a: Cost for 10 kids
To determine the cost for 10 kids, we will use the known cost per kid, which is [tex]$9.1. Therefore, the total cost for 10 kids is:
\[ a_{10} = 10 \times 9.1 = 91 \]
Thus, the cost for 10 kids is $[/tex]91.
### Part b: Cost for 17 kids
Similarly, for 17 kids, the total cost can be calculated as follows:
[tex]\[ a_{17} = 17 \times 9.1 \][/tex]
[tex]\[ a_{17} = 154.7 \][/tex]
Therefore, the cost for 17 kids is [tex]$154.7.
### Part c: Cost for 40 kids
Using the same method for calculating the total cost for 40 kids:
\[ a_{40} = 40 \times 9.1 \]
\[ a_{40} = 364 \]
Hence, the cost for 40 kids is $[/tex]364.
### Part 10: Number of kids to bring the total to [tex]$273
We are asked how many kids would bring the total cost to $[/tex]273. We already know that each kid costs [tex]$9.1. To find the number of kids, we divide the total cost by the cost per kid:
\[ \text{Number of kids} = \frac{273}{9.1} \]
\[ \text{Number of kids} = 30 \]
Therefore, 30 kids would bring the total cost to $[/tex]273.
### Part 11: Complete the table and graph the sequence
Let's fill in the provided table with the number of kids and their corresponding total costs. We already have the cost values for 1 to 5 kids.
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Number \\
of Kids \\
\end{tabular} & 1 & 2 & 3 & 4 & 5 \\
\hline
\begin{tabular}{l}
Total Cost \\
in Dollars \\
\end{tabular} & 9.1 & 18.2 & 27.3 & 36.4 & 45.5 \\
\hline
\end{tabular}
\][/tex]
To graph the sequence, you would plot the number of kids along the x-axis and the total cost in dollars along the y-axis. Each point on the graph corresponds to a pair (Number of Kids, Total Cost). For instance:
- (1, 9.1)
- (2, 18.2)
- (3, 27.3)
- (4, 36.4)
- (5, 45.5)
Connecting these points will show a linear relationship since the cost per kid remains constant at $9.1.
