https://file.aiquickdraw.com/mathbot/file/17308315649620f5z5lm8.jpg

To solve this problem, let's analyze the discount process:

1. **Store Discount (40%)**: If the store offers a 40% discount, the price after this discount is 60% of the original price $ x $. Therefore, the function for the store discount $ s(x) $ can be written as:
   \[
   s(x) = 0.6x
   \]

2. **Employee Discount (10%)**: Employees receive an additional 10% discount, which means they pay 90% of the price. The function for the employee discount $ e(x) $ is:
   \[
   e(x) = 0.9x
   \]

The problem asks for the composite function that results from applying the employee discount first and then the store discount. This requires calculating $ s(e(x)) $.

### Step-by-Step Calculation of $ s(e(x)) $

1. First, apply the employee discount:
   \[
   e(x) = 0.9x
   \]

2. Then, apply the store discount to $ e(x) $:
   \[
   s(e(x)) = s(0.9x) = 0.6 \times 0.9x = 0.54x
   \]

So, the correct answer is:
\[
s(e(x)) = 0.54x
\]

### Answer:
The correct choice is:
\[
\text{Option 1: } s(e(x)) = 0.54x
\]

Would you like further details or have any other questions?

Here are five related questions for further practice:
1. What would the composite discount be if the store discount was 30% instead of 40%?
2. How would the final price change if the employee discount was applied after the store discount?
3. If the original price was $100, what would be the final price after both discounts?
4. How would you express the composite function if both discounts were variable percentages?
5. How would you calculate the final price if an additional fixed discount was added after both discounts?

**Tip:** When dealing with composite discounts, remember to multiply the remaining percentages sequentially to find the effective discount factor.

A store offers a discount of 40% off any one regular-price item. The price paid after this discount is represented by s(x). Employees also receive 10% off any purchases; the price paid after this discount is represented by e(x). Which of the following represents the composite function of applying the employee discount first, and the store discount second?

Explore a composite discount problem where a store offers 40% off, and employees receive an additional 10% off. Learn to calculate the final price using composite functions. Suitable for students in Grades 9-10.

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