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The image shows a question about U.S. federal income tax calculations based on tax brackets for the year 2011. It asks you to write formulas for calculating income tax at different income levels and to calculate the tax on a specific income. Here's how you can approach it:

### a. Income between $0 and $8,500
For incomes in this range, the tax rate is **10%**. So, the formula for calculating the tax $ T $ when income $ x $ is between $0 and $8,500 is:

\[
T = 0.10 \times x
\]

### b. Income between $8,500 and $34,500
For incomes in this range, the tax is **$850** plus **15%** of the amount exceeding $8,500. So, the formula for calculating the tax $ T $ when income $ x $ is between $8,500 and $34,500 is:

\[
T = 850 + 0.15 \times (x - 8,500)
\]

### c. Income between $34,500 and $83,600
For incomes in this range, the tax is **$4,750** plus **25%** of the amount exceeding $34,500. So, the formula for calculating the tax $ T $ when income $ x $ is between $34,500 and $83,600 is:

\[
T = 4,750 + 0.25 \times (x - 34,500)
\]

### d. Tax for income of $159,000
For an income of $159,000, the tax is calculated based on the bracket between **$83,600 and $174,400**. According to the table, the tax is **$17,025** plus **28%** of the amount exceeding $83,600.

So for an income of $159,000, the tax is:

\[
T = 17,025 + 0.28 \times (159,000 - 83,600)
\]

Let's calculate this:

\[
T = 17,025 + 0.28 \times 75,400 = 17,025 + 21,112 = 38,137
\]

So, the tax on an income of $159,000 is **$38,137**.

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Would you like any further details on any of these calculations or clarifications?

### Additional Practice Questions:
1. What is the tax on an income of $90,000?
2. Calculate the tax for an income of $50,000.
3. How would the formula change for an income over $174,400?
4. What would be the tax on an income of $83,600 exactly?
5. How does the marginal tax rate affect tax calculations in each bracket?

**Tip**: Always remember that for incomes in higher brackets, you only apply the higher tax rate to the portion of income that exceeds the previous bracket's limit!

Workers in the U.S. pay several types of taxes on income. The lesson discussed the FICA taxes. You also have to pay federal income tax. Your federal income tax rate is based on the amount of money you make. Income is broken into levels called tax brackets. The table below shows the tax brackets for 2011.
 a) Assume your income x is $0 < x ≤ $8,500, write a formula to calculate the amount of tax you owe.
 b) Write a formula for the income tax for a person earning income where $8,500 < x ≤ $34,500.
 c) Write a formula for the income tax for a person earning income where $34,500 < x ≤ $83,600.
 d) The amount of tax you owe on a $159,000 income is $____.

Learn how to calculate federal income tax using 2011 tax brackets. Includes formulas for different income ranges: $0 to $8,500, $8,500 to $34,500, $34,500 to $83,600, and tax calculation on a $159,000 income.

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