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Conrad and jill have a taxable income of 63,670. they discovered that they are able to receive $1,500 tax credit for purchasing an energy efficient furnace. How will this tax credit affect their taxes? A) the tax credit will increase their taxable income by $1,500 B) the tax credit will reduce their taxable income by $1,500 C) the tax credit is added to the tax owed, not the taxable income D) the tax credit is subtracted from the tax owed, not taxable income

2 months ago

Solution 1

Guest #495

2 months ago

The answer is letter D. The tax credit will be subtracted from the tax owed, not taxable income. This is because a tax credit is something that will be deducted or offset to your liability and that is the tax you owed based on your own taxable income.

📚 Related Questions

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Solve the equation: Sin2x - Sinx = 0

Solution 1

We know that sin2x=2sinxcosx
(search the net for proof if you wish)

So the original equation becomes

2sinxcosx-sinx=0
The two terms both have sinx that can be taken out to get:

sinx(2cosx-1)=0
This is true if sinx=0 or 2cosx-1=0 , rewritten: cosx=1/2

sinx=0 than x=2kπ
cosx=1/2 than x=π/3+2kπ
where k is an integer

Question

A jogger goes 1.5km west and then turns south.If the jogger finishes 1.7 km from the starting point,how far south did the jogger go?

Solution 1

Hello!

You can use the Pythagorean Theorem to solve this

$a^{2} + b^{2} = c^{2}$

c is the hypotenuse
a and b are the legs

Put in the values you know

$1.5^{2} + b^{2} = 1.7^{2}$

Square the numbers

$2.25+ b^{2} =2.89$

Subtract 2.25 from both sides

$b^{2} =0.64$

Take the square root of both sides

b = 0.8

The answer is 0.8km

Hope this helps!

Question

Prostokat ma wymiary 2m×5dm .Jego pole wynosi÷ A.10dm kwadratowych B.100dm kwadratowych

Solution 1

Odpowiedź to A. 10dm kwadratowych

Question

Two events are independent when the following is true: a. the outcome of one event determines the outcome of the other event b. there is no correlation between the two events c. the outcome of one event does NOT determine the outcome of the other event d. The outcome of the event is determined by the theoretical probability of the event

Solution 1

Solution:

Independent Events:

Consider an experiment of Rolling a die, then getting an even number and multiple of 3.

Total favorable outcome = {1,2,3,4,5,6}=6

A=Even number = {2,4,6}

B=Multiple of 3 = {3,6}

A ∩ B={6}

P(A)= $\frac{3}{6}=\frac{1}{2}$ , P(B)= $\frac{2}{6}=\frac{1}{3}$

P(A ∩ B)= $\frac{1}{6}$

So, P(A)× P( B)= $\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$ =P(A ∩ B)

Hence two events A and B are independent.

Option (c). the outcome of one event does NOT determine the outcome of the other event

Solution 2

Answer:

C on edge or the outcome of one event does NOT determine the outcome of the other event

Step-by-step explanation:

Question

All the points equidistant to a given point would form ______? A. an eclipse B. a circle C. a parabola D. a line

Solution 1

B since a circle is all the points equidistant to a given point called the center of the circle.

Question

One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. let p represent the number of female insects in a population and s the number of sterile males introduced each generation. let r be the per capita rate of production of females by females, provided their chosen mate is not sterile. then the female population is related to time t by t = p + s p[(r − 1)p − s] dp. suppose an insect population with 10,000 females grows at a rate of r = 1.2 and 400 sterile males are added. evaluate the integral to give an equation relating the female population to time. (note that the resulting equation can't be solved explicitly for p. remember to use absolute values where appropriate.)

Solution 1

To be clear, the given relation between time and female population is an integral:
$t = \int { \frac{P+S}{P[(r - 1)P - S]} } \,
dP$

The problem says that r = 1.2 and S = 400, therefore substituting:
$t = \int { \frac{P+400}{P[(1.2 - 1)P - 400]}
} \, dP$

= $
\int { \frac{P+400}{P(0.2P - 400)} } \, dP$

In order to evaluate this integral, we need to write this rational function in a simpler way:
$\frac{P+400}{P(0.2P - 400)} = \frac{A}{P} +
\frac{B}{(0.2P - 400)}$

where we need to evaluate A and B. In order to do so, let's calculate the LCD:
$\frac{P+400}{P(0.2P - 400)} = \frac{A(0.2P -
400)}{P(0.2P - 400)} + \frac{BP}{P(0.2P - 400)}$

the denominators cancel out and we get:
P + 400 = 0.2AP - 400A + BP
= P(0.2A + B) - 400A

The two sides must be equal to each other, bringing the system:
$\left \{ {{0.2A + B = 1} \atop {-400A =
400}} \right.$

Which can be easily solved:
$\left \{ {{B=1.2} \atop {A=-1}} \right.$

Therefore, our integral can be written as:
$t = \int { \frac{P+400}{P(0.2P - 400)} } \,
dP = \int {( \frac{-1}{P} + \frac{1.2}{0.2P-400} )} \, dP$
= $- \int { \frac{1}{P} \, dP +
1.2\int { \frac{1}{0.2P-400} } \, dP$
= $- \int { \frac{1}{P} \, dP +
6\int { \frac{0.2}{0.2P-400} } \, dP$
= - ln |P| + 6 ln |0.2P - 400| + C

Now, let’s evaluate C by considering that at t = 0 P = 10000:
0 = - ln |10000| + 6 ln |0.2(10000) - 400| + C
C = ln |10000| - 6 ln |1600|
C = ln (10⁴) - 6 ln (2⁶·5²)
C = 4 ln (10) - 36 ln (2) - 12 ln (5)
Therefore, the equation relating female population with time requested is:
t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln (2) - 12 ln (5)

Question

After the booster club sold 40 hot dogs at a football game, it had $90 in profit. After the next game, it had sold a total of 80 hot dogs and had a total of $210 in profit. Which equation models the total profit,y,based on the number of hotdogs sold,x

Solution 1

Answer:

Required equation $y = 3x-30$

Step-by-step explanation:

Given : After the booster club sold 40 hot dogs at a football game, it had $90 in profit. After the next game, it had sold a total of 80 hot dogs and had a total of $210 in profit.

To find : Which equation models the total profit,y,based on the number of hot dogs sold,x ?

Solution :

Let x = total number of hot dogs sold

y = total profit from total sales of hot dogs

We can model the equation: $y = m x + b$ ......[A]

where, y is the total profit and x is the number of hot dogs sold.

Profit for 40 hot dogs = $90 profit

The system of equation form is

$90 =40m + b$ ......[1]

Profit for 80 hot dogs = $210 profit

The system of equation form is

$210 =80m + b$ .......[2]

The solution of equations [1] and [2]

Subtract equation [1] and [2]

$210-90 = 80m-40m + b-b$

$120 = 40m$

$\frac{120}{40} = m$

$3 = m$

Substitute in equation [1]

$90 =40(3) + b$

$90 =120+ b$

$b=-30$

Substitute the values in equation [A]

$y = 3x-30$

This is the required equation models the total profit based on number of hot dogs.

Solution 2

The correct answer would be: y-90=3(x-40)

Question

Work out the area of a triangle of base 5cm and height 6 cm? Please been stuck on this for ages x

Solution 1

The area of triangle = 1/2 b h

where b = base and h = height
so b = 5 cm and h = 6 cm

Now you can find A = 1/2 (5)(6) = 1/2 (30) = 15

answer
A = 15 cm^2

hope that helps

Question

Find the work done by the force field f(x,y,z)=3xi+3yj+7kf(x,y,z)=3xi+3yj+7k on a particle that moves along the helix r(t)=3cos(t)i+3sin(t)j+3tk,0≤t≤2π

Solution 1

Call the path $\mathcal C$ . Then the work done by $\mathbf f(x,y,z)$ along $\mathcal C$ is given by the line integral, $\displaystyle\int_{\mathcal C}\mathbf f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=2\pi}\mathbf f(x(t),y(t),z(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt$
Swapping the $\mathbf{ijk}$ notation out for ordered component notation, I'll write
$\mathbf r(t)=(x(t),y(t),z(t))=(3\cos t,3\sin t,3t)$
so that
$\dfrac{\mathrm d\mathbf r}{\mathrm dt}=(-3\sin t,3\cos t,3)$
The line integral reduces to $\displaystyle\int_0^1(9\cos t,9\sin t,7)\cdot(-3\sin t,3\cos t,3)\,\mathrm dt$ $=\displaystyle\int_0^1(-27\cos t\sin t+27\sin t\cos t+21)\,\mathrm dt$ $=\displaystyle21\int_0^1\mathrm dt=21$

Question

Round 0.246 to the nearest tenth

Solution 1

.2 is the correct answer to this question

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