Solve the Problem $\$ 60$ Per Ticket, That Is, the Cost Function Is

question 378

Multiple Choice

Solve the problem.
-The cost to buy tickets online for a dance show is $\$ 60$ per ticket, that is, the cost function is $C ( x ) =$ $60 x$ for $x$ tickets to the show. There is a sales tax of $4.5 \%$ and a processing fee of $\$ 7$ for a group of tickets, that is, $T ( x ) = 1.045 x + 7$ is the total cost for $x$ dollars spent on tickets.
(a) Find $( T \circ C ) ( x )$
(b) Find $( T \circ C ) ( 7 )$ and interpret its meaning in the context of the problem.

• A) (a) \(( T \circ C ) ( x ) = 62.7 x + 7\); (b) \(( T \circ C ) ( 7 ) = 445.9\); The total cost to purchase 7 tickets.
• B) (a) \(( T \circ C ) ( x ) = 62.7 x + 7\); (b) \(( T \circ C ) ( 7 ) = 445.9\); The average cost per ticket.
• C) (a) \(( T \circ C ) ( x ) = 62.7 x + 420\); (b) \(( T \circ C ) ( 7 ) = 858.9\); The total cost to purchase 7 tickets.
• D) (a) \(( T \circ C ) ( x ) = 62.7 x + 420\); (b) \(( T \circ C ) ( 7 ) = 858.9\); The average cost per ticket.

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Definitions:

Confidence Interval

A span of numerical values, obtained from sampled data, which is expected to encompass the value of a parameter yet to be known from a population.

Population Mean Score

The average score or value of a specific variable for the entire population of interest.

SAT

A standardized test widely used for college admissions in the United States, assessing mathematical, reading, and writing skills.

Confidence Interval

A range of values, derived from the statistics of the observed data, that is likely to contain the value of an unknown population parameter.