Complete the following table by finding the net price factor, single equivalent discount, trade discount (in dollars), and net price (in dollars). Round the net price factor and single equivalent discount to five decimal places, and the trade discount and net price to the nearest cent, when necessary. List price $4.39 trade discount rate 13/10/10

To solve this problem, we need to calculate four values based on the list price of $4.39 and a trade discount series of 13%, 10%, and 10%. The values we are asked to calculate are:

1. **Net Price Factor (NPF):** This is the product of the complements of the trade discounts.
2. **Single Equivalent Discount (SED):** This is the overall discount rate, calculated as $ 1 - \text{NPF} $.
3. **Trade Discount (in dollars):** This is the dollar amount saved, calculated as $ \text{List Price} \times \text{SED} $.
4. **Net Price (in dollars):** This is the amount the customer actually pays, calculated as $ \text{List Price} - \text{Trade Discount} $.

Let's proceed step-by-step.

### Step 1: Net Price Factor (NPF)
The Net Price Factor is the product of the complements of each trade discount. The complement of a discount is $ 1 - \frac{\text{Discount Rate}}{100} $.

Given the trade discount series $ 13\% / 10\% / 10\% $:

\[
\text{NPF} = (1 - 0.13) \times (1 - 0.10) \times (1 - 0.10)
\]
\[
\text{NPF} = 0.87 \times 0.90 \times 0.90
\]

### Step 2: Single Equivalent Discount (SED)
The Single Equivalent Discount is:

\[
\text{SED} = 1 - \text{NPF}
\]

### Step 3: Trade Discount (in dollars)
The Trade Discount in dollars is:

\[
\text{Trade Discount} = \text{List Price} \times \text{SED}
\]

### Step 4: Net Price (in dollars)
The Net Price is:

\[
\text{Net Price} = \text{List Price} - \text{Trade Discount}
\]

Now, let me calculate these values.Here are the completed values for the table:

1. **Net Price Factor (NPF):** 0.70470
2. **Single Equivalent Discount (SED):** 0.29530
3. **Trade Discount (in dollars):** $1.30
4. **Net Price (in dollars):** $3.09

Would you like any further details on these calculations, or do you have any questions?

Here are five related questions:
1. How is the complement of a discount calculated?
2. What happens if one or more of the trade discount rates increase?
3. How would the calculation change if the list price were higher?
4. Can the single equivalent discount ever exceed 1?
5. Why do we multiply the complements of the trade discount rates?

**Tip:** When working with trade discounts, always apply the percentages in sequence to get the correct net price.

Learn how to calculate the net price factor, single equivalent discount, trade discount, and net price for a list price of $4.39 with trade discount rates of 13%, 10%, and 10%. This step-by-step guide includes key percentage calculations and real-world applications suitable for students in Grades 9-12.

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