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The image contains a mathematical problem related to income tax, with a tax formula given in piecewise form. Let's solve the questions based on the given information.

### Tax formula:
\[
T(x) = 
\begin{cases} 
0 & \text{if } 0 \leq x \leq 15,000 \\
0.1x - 1500 & \text{if } 15,000 < x \leq 180,000 \\
0.13x - 6900 & \text{if } x > 180,000
\end{cases}
\]

Where:
- $x$ is the income in dollars.
- $T(x)$ is the tax on income $x$.

### 1. Dakota has an income of $300,000. How much will they pay in taxes?

Since Dakota's income is $300,000, which is greater than $180,000, we use the third formula:
\[
T(300,000) = 0.13(300,000) - 6900
\]
Let's calculate:
\[
T(300,000) = 39,000 - 6900 = 32,100
\]
Dakota will pay **$32,100** in taxes.

### 2. Aliyah has an income of $10,000. How much will they pay in taxes?

Aliyah's income is $10,000, which is less than $15,000. According to the formula:
\[
T(10,000) = 0
\]
Aliyah will pay **$0** in taxes.

### 3. Enrique has an income of $70,000. How much will they pay in taxes?

Enrique's income falls in the range $15,000 < x \leq 180,000$, so we use the second formula:
\[
T(70,000) = 0.1(70,000) - 1500
\]
Let's calculate:
\[
T(70,000) = 7,000 - 1500 = 5,500
\]
Enrique will pay **$5,500** in taxes.

### 4. A politician proposes increasing the tax rate to 19% for those making more than $330,000. How much more will Enrique pay?

Since Enrique earns $70,000, this tax increase proposal does not affect him, as the new tax rate is for incomes over $330,000. Therefore, Enrique will pay **$0 more** in taxes.

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

Here are some related questions for practice:
1. What would be the tax for someone earning $200,000?
2. If Dakota earned $150,000 instead, how much would the tax be?
3. Calculate the tax for an income of $20,000.
4. What would happen if the tax rate for those earning more than $500,000 was increased to 25%?
5. How would the formula change if there was an additional tax deduction of $2,000?

**Tip**: Always check the range of the income carefully before applying the correct tax formula.

In a certain country, the amount of income tax T on earnings of x dollars is computed according to the formula: T(x) = { 0 for 0 ≤ x ≤ 15,000, 0.1x - 1500 for 15,000 < x ≤ 180,000, 0.13x - 6900 for x > 180,000 }. How much tax will Dakota, Aliyah, and Enrique pay given their respective incomes of $300,000, $10,000, and $70,000? How much more will Enrique pay if a politician proposes raising the tax rate to 19% for incomes over $330,000?

Solve income tax calculations using a piecewise function for different income brackets. Learn how to calculate taxes for incomes of $300,000, $10,000, and $70,000 using a piecewise tax formula, and understand how a proposed tax rate increase would affect the calculations.

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