Math Snap

STEP 1

Assumptions1. The cost per ticket is $40. The sales tax is3.5%
3. There is a processing fee of $6 for a group of tickets4. The cost function$C(x)$represents the cost for$x$tickets5. The total cost function$(a)$represents the total cost for$a$ dollars spent on tickets

STEP 2

(a) We need to write a function that represents the cost $C(x)$ for $x$ tickets. Since each ticket costs $40, the cost for$x$tickets will be$40x$.
$$C(x) =40x$$

STEP 3

(b) We need to write the total cost function $(a)$ for $a$ dollars spent on tickets. The total cost includes the cost of the tickets, the sales tax, and the processing fee. The sales tax is3.5% of the cost of the tickets, and the processing fee is a flat rate of $6.
$$(a) = a +0.035a +6$$

STEP 4

(c) We need to evaluate the composition of the functions $$ and $C$, denoted as $( \circ C)(x)$. This means we substitute $C(x)$ into $(a)$.
$$(C(x)) = C(x) +0.035C(x) +6$$

STEP 5

Substitute $C(x)$ from Step2 into the equation from Step4.
$$(C(x)) =40x +0.035(40x) +$$

STEP 6

implify the equation from Step5.
$$(C(x)) =40x +1.4x +6$$

STEP 7

Combine like terms in the equation from Step6.
$$(C(x)) =41.4x +6$$

STEP 8

(d) We need to find $( \circ C)(4)$, which means we substitute $4$ for $x$ in the equation from Step7.
$$(C(4)) =41.4(4) +6$$

Calculate $( \circ C)(4)$.
$$(C(4)) =41.4(4) +6 =165.6 +6 =171.6$$The total cost for4 tickets, including the sales tax and processing fee, is $171.6. This means that if you buy4 tickets to Riverdance online, you will spend a total of$171.6.