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HACTEHA [7]
2 years ago
6

You have decided to purchase a car for $19,000. The credit union requires a 10% down payment and will finance the balance with a

9% annual interest loan for 36 months. The sales tax in your city is 8.3%, and the license and title charges are $75. What is the total purchase price of the car including tax, license, and title?
Please select the best answer from the choices provided
A. $19,075.00
B. $18,594.30
C. $20,652.00
D. $20,577.00
Mathematics
1 answer:
Lady_Fox [76]2 years ago
6 0
<h2>○=> <u>Correct option</u> :</h2>

\color{plum} \bold{ \tt \:  \bold{C.  \$20,652.00}}

<h3>○=> <u>Steps to derive correct option</u> :</h3>

Selling price of a car = $19,000

Percentage of sales tax in the city = 8.3%

Sales tax :

= \tt  \frac{8.3}{10 \times 100}  \times 1900

= \tt  \frac{8.3 \times 19000}{1000}

= \tt  \frac{1577000}{1000}

\color{plum} = \tt  \$1577

Thus, the sales tax on the car = $1577

Cost of license and title = $75

Total price of car :

= Cost price of car + Sales tax + cost of license/title

=  \tt19000 + 1577 + 75

\color{plum} = \tt  \$20652

Thus, the total purchase price of the car = $20,652.00

Therefore, the correct option is <em>(C) $20,652.00</em>

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Step-by-step explanation:

<h3>Need to FinD :</h3>

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\red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

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As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

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\red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}}

\rule{200}{3}

\sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}}

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