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love history [14]
3 years ago
5

Maria Contrerras earned $53,000 in taxable income. She figured her tax from the single taxpayer table above.

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
7 0

Answer:

Tax= $ 7,173.5

Step-by-step explanation:

Her taxable income is $ 43,000 which lies in the tax category $ 31,850 to

$ 77,100.

Tax for $ 31,850 is $ 4,386

Plus 25% of the amount = ( $ 43,000- $ 31,850 )= $ 11,150 over

25 % of $ 11,150= $ 2,787.5

Total Tax= $ 4386 + $ 2787.5= $ 7,173.5

Step-by-step explanation:

yes

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A segment has an endpoint at (1,−2). The midpoint is at (−4,−2). What are the coordinates of the other endpoint?
vodka [1.7K]

Answer:

The other midpoint is located at coordinates (-9,-2) (Second option)

Step-by-step explanation:

<u>Midpoints</u>

If P(a,b) and Q(c,d) are points in \mathbb{R} ^2, the midpoint between them is the point exactly in the center of the line that joins P and Q. Its coordinates are given by

\displaystyle x_m=\frac{a+c}{2}

\displaystyle y_m=\frac{b+d}{2}

We are given one endpoint at P(1,-2) and the midpoint at M(-4,-2). The other endpoint must be at an equal distance from the midpoint as it is from P. We can see both given points have the same value of y=-2. This simplifies the calculations because we only need to deal with the x-coordinate.

The x-distance from P to M is 1-(-4)=5 units. This means the other endpoint must be 5 units to the left of M:

x (other endpoint)= - 4 - 5 = - 9

So the other midpoint is located at (-9,-2) (Second option)

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3 years ago
Distance from sun in au from mercury pls thanks
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Identify the domain, range, and codomain in each graph. Then use the codomain and range to determine whether the
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Step-by-step explanation:

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Solve 4(x + 6) = 2(2x + 12)
Andru [333]

Answer:

Infinitely many solutions

Step-by-step explanation:

4(x+6)=2(2x+12)

4(x+6)=2(2(x+6))

4(x+6)=4(x+6)

Infinitely many solutions

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The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,
uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right).

We need to solve it and obtain an expression for P(t) in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right).

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that k=0.04 and K=500 and the initial condition P(0)=100.

Notice that this equation is separable, then

\frac{dP}{P(1-P/K)} = kdt.

Now, intagrating in both sides of the equation

\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C.

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}.

So,

\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|.

We have obtained that:

-\ln\left| \frac{K-P}{P}\right| = kt +C

which is equivalent to

\ln\left| \frac{K-P}{P}\right|= -kt -C

Taking exponentials in both hands:

\left| \frac{K-P}{P}\right| = e^{-kt -C}

Hence,

\frac{K-P(t)}{P(t)} = Ae^{-kt}.

The next step is to substitute the given values in the statement of the problem:

\frac{500-P(t)}{P(t)} = Ae^{-0.04t}.

We calculate the value of A using the initial condition P(0)=100, substituting t=0:

\frac{500-100}{100} = A} and A=4.

So,

\frac{500-P(t)}{P(t)} = 4e^{-0.04t}.

Finally, as we want the value of t such that P(t)=200, we substitute this last value into the above equation. Thus,

\frac{500-200}{200} = 4e^{-0.04t}.

This is equivalent to \frac{3}{8} = e^{-0.04t}. Taking logarithms we get \ln\frac{3}{8} = -0.04t. Then,

t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325.

So, the population of rats will be 200 after 25 months.

6 0
3 years ago
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