QuestionCalculate the income tax $h(x)$ for the following incomes: (a) $1260$ , (b) $7160$ , (c) $49070$ . Round to the nearest cent.

Studdy Solution

STEP 1

Assumptions1. The function h(x) is defined as a piecewise function, where x is the taxable income of a single person. . The function h(x) is divided into three parts based on the range of x.
3. The tax rate varies depending on the range of x.

STEP 2

To find the value of h(1260), we need to identify which range1260 falls into. Looking at the function, we can see that1260 falls into the first range0 ≤ x <6000.

STEP 3

Now that we know which part of the function to use, we can substitute1260 into the function for x.
$h(1260) =0.02 \times1260$

STEP 4

Calculate the value of h(1260).
$h(1260) =0.02 \times1260 = \$25.20$ This means that a single person with a taxable income of \$1260 would owe \$25.20 in state income tax.

STEP 5

Next, we find the value of h(7160). Again, we need to identify which range7160 falls into. Looking at the function, we can see that7160 falls into the second range6000 ≤ x <11,000.

STEP 6

Now that we know which part of the function to use, we can substitute7160 into the function for x.
$h(7160) =120 +0.03 \times (7160 -6000)$

STEP 7

Calculate the value of h(7160).
$h(7160) =120 +0.03 \times (7160 -6000) = \$147.80$ This means that a single person with a taxable income of \$7160 would owe \$147.80 in state income tax.

STEP 8

Finally, we find the value of h(49,070). Again, we need to identify which range49,070 falls into. Looking at the function, we can see that49,070 falls into the third range x ≥11,000.

STEP 9

Now that we know which part of the function to use, we can substitute49,070 into the function for x.
$h(49,070) =270 +.04 \times (49,070 -11,000)$

STEP 10

Calculate the value of h(49,070).
$h(49,070) =270 +0.04 \times (49,070 -,000) = \$,812.80$ This means that a single person with a taxable income of \$49,070 would owe \$,812.80 in state income tax.

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QuestionCalculate the income tax $h(x)$ for the following incomes: (a) $1260$ , (b) $7160$ , (c) $49070$ . Round to the nearest cent.

Studdy Solution

STEP 1

Assumptions1. The function h(x) is defined as a piecewise function, where x is the taxable income of a single person. . The function h(x) is divided into three parts based on the range of x.
3. The tax rate varies depending on the range of x.

STEP 2

To find the value of h(1260), we need to identify which range1260 falls into. Looking at the function, we can see that1260 falls into the first range0 ≤ x <6000.

STEP 3

Now that we know which part of the function to use, we can substitute1260 into the function for x.
$h(1260) =0.02 \times1260$

STEP 4

Calculate the value of h(1260).
$h(1260) =0.02 \times1260 = \$25.20$ This means that a single person with a taxable income of \$1260 would owe \$25.20 in state income tax.

STEP 5

Next, we find the value of h(7160). Again, we need to identify which range7160 falls into. Looking at the function, we can see that7160 falls into the second range6000 ≤ x <11,000.

STEP 6

Now that we know which part of the function to use, we can substitute7160 into the function for x.
$h(7160) =120 +0.03 \times (7160 -6000)$

STEP 7

Calculate the value of h(7160).
$h(7160) =120 +0.03 \times (7160 -6000) = \$147.80$ This means that a single person with a taxable income of \$7160 would owe \$147.80 in state income tax.

STEP 8

Finally, we find the value of h(49,070). Again, we need to identify which range49,070 falls into. Looking at the function, we can see that49,070 falls into the third range x ≥11,000.

STEP 9

Now that we know which part of the function to use, we can substitute49,070 into the function for x.
$h(49,070) =270 +.04 \times (49,070 -11,000)$

STEP 10

Calculate the value of h(49,070).
$h(49,070) =270 +0.04 \times (49,070 -,000) = \$,812.80$ This means that a single person with a taxable income of \$49,070 would owe \$,812.80 in state income tax.

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QuestionCalculate the income tax h(x)h(x)h(x) for the following incomes: (a) 126012601260, (b) 716071607160, (c) 490704907049070. Round to the nearest cent.

Studdy Solution

STEP 1

Assumptions1. The function h(x) is defined as a piecewise function, where x is the taxable income of a single person. . The function h(x) is divided into three parts based on the range of x.3. The tax rate varies depending on the range of x.

STEP 2

To find the value of h(1260), we need to identify which range1260 falls into. Looking at the function, we can see that1260 falls into the first range0 ≤ x <6000.

STEP 3

Now that we know which part of the function to use, we can substitute1260 into the function for x.h(1260)=0.02×1260h(1260) =0.02 \times1260h(1260)=0.02×1260

STEP 4

Calculate the value of h(1260).h(1260)=0.02×1260=$25.20h(1260) =0.02 \times1260 = \$25.20h(1260)=0.02×1260=$25.20This means that a single person with a taxable income of \$1260 would owe \$25.20 in state income tax.

STEP 5

Next, we find the value of h(7160). Again, we need to identify which range7160 falls into. Looking at the function, we can see that7160 falls into the second range6000 ≤ x <11,000.

STEP 6

Now that we know which part of the function to use, we can substitute7160 into the function for x.h(7160)=120+0.03×(7160−6000)h(7160) =120 +0.03 \times (7160 -6000)h(7160)=120+0.03×(7160−6000)

STEP 7

Calculate the value of h(7160).h(7160)=120+0.03×(7160−6000)=$147.80h(7160) =120 +0.03 \times (7160 -6000) = \$147.80h(7160)=120+0.03×(7160−6000)=$147.80This means that a single person with a taxable income of \$7160 would owe \$147.80 in state income tax.

STEP 8

Finally, we find the value of h(49,070). Again, we need to identify which range49,070 falls into. Looking at the function, we can see that49,070 falls into the third range x ≥11,000.

STEP 9

Now that we know which part of the function to use, we can substitute49,070 into the function for x.h(49,070)=270+.04×(49,070−11,000)h(49,070) =270 +.04 \times (49,070 -11,000)h(49,070)=270+.04×(49,070−11,000)

STEP 10

Calculate the value of h(49,070).h(49,070)=270+0.04×(49,070−,000)=$,812.80h(49,070) =270 +0.04 \times (49,070 -,000) = \$,812.80h(49,070)=270+0.04×(49,070−,000)=$,812.80This means that a single person with a taxable income of \$49,070 would owe \$,812.80 in state income tax.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCalculate the income tax $h(x)$ for the following incomes: (a) $1260$ , (b) $7160$ , (c) $49070$ . Round to the nearest cent.

Assumptions1. The function h(x) is defined as a piecewise function, where x is the taxable income of a single person. . The function h(x) is divided into three parts based on the range of x.
3. The tax rate varies depending on the range of x.

Now that we know which part of the function to use, we can substitute1260 into the function for x.
$h(1260) =0.02 \times1260$

Calculate the value of h(1260).
$h(1260) =0.02 \times1260 = \$25.20$ This means that a single person with a taxable income of \$1260 would owe \$25.20 in state income tax.

Now that we know which part of the function to use, we can substitute7160 into the function for x.
$h(7160) =120 +0.03 \times (7160 -6000)$

Calculate the value of h(7160).
$h(7160) =120 +0.03 \times (7160 -6000) = \$147.80$ This means that a single person with a taxable income of \$7160 would owe \$147.80 in state income tax.

Now that we know which part of the function to use, we can substitute49,070 into the function for x.
$h(49,070) =270 +.04 \times (49,070 -11,000)$

Calculate the value of h(49,070).
$h(49,070) =270 +0.04 \times (49,070 -,000) = \$,812.80$ This means that a single person with a taxable income of \$49,070 would owe \$,812.80 in state income tax.