Let's break down the problem step by step to find the final cost of the dress with the given sticker price and the applied discount, coupon, and mail-in rebate.
1. Starting with the sticker price:
[tex]\[
\text{Sticker Price} = \$30.00
\][/tex]
2. Applying the discount:
The discount is [tex]\( 25\% \)[/tex] of the sticker price. To find the discount amount, we calculate [tex]\( 25\% \)[/tex] of [tex]\( \$30.00 \)[/tex]:
[tex]\[
\text{Discount Amount} = \frac{25}{100} \times 30.00 = \$7.50
\][/tex]
Subtract the discount amount from the sticker price to get the price after the discount:
[tex]\[
\text{Price after Discount} = 30.00 - 7.50 = \$22.50
\][/tex]
3. Applying the coupon:
The coupon is worth [tex]\( \$5.00 \)[/tex]. Subtract the coupon amount from the price after the discount:
[tex]\[
\text{Price after Coupon} = 22.50 - 5.00 = \$17.50
\][/tex]
4. Applying the mail-in rebate:
The mail-in rebate amount is [tex]\( \$3.00 \)[/tex]. Subtract the mail-in rebate from the price after the coupon:
[tex]\[
\text{Final Cost} = 17.50 - 3.00 = \$14.50
\][/tex]
Thus, the final cost of the dress is:
[tex]\[
\boxed{\$14.50}
\][/tex]
