cost to buy tickets online for the dance show Riverdance is $0 per Write a function that represents the cost C(x) (in S) for x tickets to Riverdance. There is a sales tax of 7.5% and a processing fee of $7 for a group of tickets. Write the total cost T (a) for a dollars spent on tickets. Evaluate (TC)(x). Find (TC) (5) and interpret its meaning in the context of this problem.
cost to buy tickets online for the dance show Riverdance is $0 per Write a function that represents the cost C(x) (in S) for x tickets to Riverdance. There is a sales tax of 7.5% and a processing fee of $7 for a group of tickets. Write the total cost T (a) for a dollars spent on tickets. Evaluate (TC)(x). Find (TC) (5) and interpret its meaning in the context of this problem.
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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![### Calculating Ticket Costs for Riverdance
The cost to buy tickets online for the dance show *Riverdance* is $70 per ticket. Use the following exercises to understand and analyze the total cost aspects.
#### Question (a)
**Write a function that represents the cost \( C(x) \) (in \$) for \( x \) tickets to *Riverdance*.**
To write this function, we recognize that the cost per ticket is $70. Hence, the cost function \( C(x) \) for \( x \) tickets can be represented as:
\[ C(x) = 70x \]
#### Question (b)
**There is a sales tax of 7.5% and a processing fee of $7 for a group of tickets. Write the total cost \( T(a) \) for \( a \) dollars spent on tickets.**
Sales tax adds an additional 7.5% to the total cost, and there's a fixed processing fee of $7. The total cost function \( T(a) \) can be calculated as:
\[ T(a) = a \times 1.075 + 7 \]
Here, \( a \) is the cost calculated using the function \( C(x) \) in part (a).
#### Question (c)
**Evaluate \( (T \circ C)(x) \).**
To evaluate \( (T \circ C)(x) \), we need to compose the functions \( T(a) \) and \( C(x) \). Therefore:
\[ (T \circ C)(x) = T(C(x)) \]
First, substitute \( C(x) \) into \( T(a) \):
\[ T(C(x)) = T(70x) \]
Using the \( T(a) \) function defined earlier:
\[ T(70x) = 70x \times 1.075 + 7 \]
\[ (T \circ C)(x) = 75.25x + 7 \]
#### Question (d)
**Find \( (T \circ C)(5) \) and interpret its meaning in the context of this problem.**
To find \( (T \circ C)(5) \), substitute \( x = 5 \) into the composed function \( (T \circ C)(x) \):
\[ (T \circ C)(5) = 75.25 \times 5 + 7 \]
\[ (T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff40007eb-8445-42f5-b44d-67d7da88f643%2F63d0c82e-0c88-426d-9c92-8df4f1769b9f%2F7gyzkhp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Ticket Costs for Riverdance
The cost to buy tickets online for the dance show *Riverdance* is $70 per ticket. Use the following exercises to understand and analyze the total cost aspects.
#### Question (a)
**Write a function that represents the cost \( C(x) \) (in \$) for \( x \) tickets to *Riverdance*.**
To write this function, we recognize that the cost per ticket is $70. Hence, the cost function \( C(x) \) for \( x \) tickets can be represented as:
\[ C(x) = 70x \]
#### Question (b)
**There is a sales tax of 7.5% and a processing fee of $7 for a group of tickets. Write the total cost \( T(a) \) for \( a \) dollars spent on tickets.**
Sales tax adds an additional 7.5% to the total cost, and there's a fixed processing fee of $7. The total cost function \( T(a) \) can be calculated as:
\[ T(a) = a \times 1.075 + 7 \]
Here, \( a \) is the cost calculated using the function \( C(x) \) in part (a).
#### Question (c)
**Evaluate \( (T \circ C)(x) \).**
To evaluate \( (T \circ C)(x) \), we need to compose the functions \( T(a) \) and \( C(x) \). Therefore:
\[ (T \circ C)(x) = T(C(x)) \]
First, substitute \( C(x) \) into \( T(a) \):
\[ T(C(x)) = T(70x) \]
Using the \( T(a) \) function defined earlier:
\[ T(70x) = 70x \times 1.075 + 7 \]
\[ (T \circ C)(x) = 75.25x + 7 \]
#### Question (d)
**Find \( (T \circ C)(5) \) and interpret its meaning in the context of this problem.**
To find \( (T \circ C)(5) \), substitute \( x = 5 \) into the composed function \( (T \circ C)(x) \):
\[ (T \circ C)(5) = 75.25 \times 5 + 7 \]
\[ (T
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