Homer Simpson finds himself in a panic attempting to meet the April 15th tax deadline. If Homer and his wife have an income of $60,000, earned $1200 in interest, invested $2500 in a tax-deferred savings plan, and have a total of $12,000 in exemptions and deductions, what would be his taxable income?

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Answer:

y = 3x - 11

Step-by-step explanation:

(3, -2) and (5, 4)

m = 4+2/5-3

m = 6/2

m = 3

y = 3x + b

4 = 3(5) + b

4 = 15 + b

b = -11

y = 3x - 11

The absolute value equation that has the solution set  is |x + 6| = 2

From the question, we have the following parameters that can be used in our computation:

Solution set = -4 and -8

The midpoint of the above solution is

c = (-4 - 8)/2

So, we have

c = -6

So, we have

|x + 6| = d

Using any of the points, we have

|-4 + 6| = d

Evaluate

d = 2

So, we have

|x + 6| = 2

Hence, the absolute value equation that has the solution set  is |x + 6| = 2

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Therefore, the solutions to x³ = -2 - 2i in polar form are x₁ = √6 + √2i, x₂ = -√2 + √6i, and x₃ = -√6 - √2i.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1. The real part of the complex number is a, and the imaginary part is bi. Complex numbers are often used in mathematics and engineering to represent quantities that involve both a real part and an imaginary part, such as electrical impedance, wave functions, and solutions to polynomial equations. Complex numbers can be added, subtracted, multiplied, and divided using rules similar to those for real numbers, and they can be plotted in a two-dimensional coordinate system called the complex plane, with the real part along the x-axis and the imaginary part along the y-axis.

Here,

To find the solutions to the equation x³ = -2 - 2i in polar form, we first convert the complex number -2 - 2i to polar form:

|-2 - 2i| = sqrt((-2)^2 + (-2)^2) = 2*sqrt(2)

arg(-2 - 2i) = tan⁻¹((-2)/(-2)) = tan⁻¹(1) = π/4 (in the second quadrant)

So, -2 - 2i in polar form is 2√2∠(π/4).

Next, we can write x³ in polar form as |x³|∠(3θ), where |x³| = |x|³ and 3θ is the angle formed by rotating θ three times. So we have:

|x³| = |-2 - 2i| = 2*sqrt(2)

3θ = arg(-2 - 2i) + 2kπ, where k is an integer

Substituting the value of arg(-2 - 2i), we have:

3θ = π/4 + 2kπ

Dividing both sides by 3, we get:

θ = π/12 + (2kπ)/3

So the three solutions in polar form are:

x₁ = 2√2∠(π/12)

x₂ = 2√2∠(5π/12)

x₃ = 2√2∠(9π/12)

Simplifying, we have:

x₁ = √6 + √2i

x₂ = -√2 + √6i

x₃ = -√6 - √2i

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The number of steps they climbed can be represented by positive

From the question, we understand that they climbed up

Upward movements are usually represented by the positive sign

This means that:

Steps = 125 or +125

Hence, the number of steps they climbed can be represented by positive

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The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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Answer:

vertex = (- 10, - 10 )

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

h(x) = x² + 20x + 90

add/subtract ( half the coefficient of the x- term )²

h(x) = x² + 2(10)x + 100 - 100 + 90

      = (x + 10)² - 10 ← in vertex form

with (h, k ) = (- 10, - 10 )

The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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Answer:

Read explanation

Step-by-step explanation:

t is greater than -3. This means it doesn't include -3 itself. So place an open dot at -3 on the number line, with the arrow pointing right because the inequality is greater than [-3].

The probability density function (pdf) for the uniform distribution has the basic formula: f(x) = 1/ (B-A) for A x B.

A continuous probability distribution, the uniform distribution is concerned with equally likely outcomes. It is referred to as having a rectangular distribution on the interval [a,b] or having a uniform distribution for the continuous random variable X. Above is a representation of the probability density function of a continuous uniform distribution. The probability of drawing a heart, club, diamond, or spade is equally likely; hence, the area under the curve is 1, which makes sense given that the total of all probabilities in a probability distribution is 1.

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Answer:

3/5x - 3/7

Do let me know if you need any clarification :)

The required area of the sculpture that is shaped like a circle is \(78.5m^2\).

Given that,

Jessie designed a sculpture that is shaped like a circle,

The circumference of the sculpture is 10π meters.

We have to determine,

Which measurement is closest to the area of the sculpture in square meters.

According to the question,

Circumference of the circle = \(2\pi r\)

Where, circumference = \(10\pi\)

Then,

\(10\pi =2\pi r\)

\(r=\frac{10\pi }{2\pi }\)

\(r=5m\)

Therefore,

Jessie designed a sculpture that is shaped like a circle.

Area of the circle = \(\pi r^2\)

Where, r = 5m

Then,

Area of the circle is given by,

\(=\pi r^2\)

\(=78.5m^2\)

Hence, The required area of the sculpture that is shaped like a circle is \(78.5m^2\).

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Answer:

A. A 180 degree rotation about the midpoints of AB.

Step-by-step explanation:

The rotation of a shape less than 360 degrees will carry the figure onto itself. A parallelogram is a rectangular shape which is slight diagonal shaped. The parallelogram will carry transformation when its rotation is about 180 degrees.

The equation of the line shown is y = 2x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2

Constant of proportionality, k = 2.

Therefore, the required equation is given by:

y = kx

y = 2x

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Answer:

$9.20 for 1 toy

Step-by-step explanation:

If it's $46 for 5 toys, we can divide both $46 and 5 to get $9.20 for 1 toy.

Answer:The combined functions W(x) and G(x) represent the amount of wood and glass required to produce a picture frame. Based on the information provided,

W(x)= 2[(f+g)(x)] and G(x) = (f-g)(x)

By looking at the values of the given table, it can be observed that the rate of change in the amount of glass required (G(x)) is not constant, it increases as x increases.

On the other hand, the rate of change in the amount of wood required (W(x)) is not constant as well, it increases as x increases too.

It's not mentioned any information about constant rate of change for f and g.

Therefore, the correct statement that describes the combined functions W(x) and G(x) is: "Neither the amount of wood required nor the amount of glass required has a constant rate of change."

It's important to mention that the problem provided does not have a unique solution, because the values for f and g are not defined so it's not possible to infer their behaviour over time.

It is only possible to infer the behaviour of the functions W(x) and G(x) given the information provided, and it is clear that the rate of change for both functions does not remain constant, but it increases as x increases.

Step-by-step explanation:

Step-by-step explanation:

which part of the question do you need

Given:

Required:

To find the second step in solving the given equation.

Explanation:

Consider

The first step is, subtract 7 on both side.

The second step is, multiply each side by 3.

Final Answer:

The second step is multiply each side by 3.

Answer:

60 in.²

Step-by-step explanation:

A = (B + b)h/2

A = (14 in. + 6 in.)(6 in.)(1/2)

A = 60 in.²

Answer:

60 in^2

Step-by-step explanation:

solution Given:

Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE

we have

Area of Rectangle ABCD= length* breadth =BC*AB=14*6=84 in^2

Area of Triangle CDE= 1/2* base*height=1/2*DE*CD=1/2*8*6=24 in ^2

Now

Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE

=84 in^2-24in^2

=60 in^2

Similarly, we have another way to calculate the area of the trapezoid;

Area = 1/2*h*(side1*side2)

=1/2*AB*(AE+BC)

=1/2*6*(6+14)

=60 in^2

Answer:

It is correct please I do not want yo sound rude can you give me brainliest answer.

Answer:

correct steps

Step-by-step explanation:

if asked to find angles in terms of the ratios, then don't forget to shift sin / cos / tan across the equal sign and change it to arc sin / cos / tan.

Answer:

-8b^2 + 4b

Step-by-step explanation:

To simplify the expression (-6b^2 2b-1) + (-2b^2 + 4b), we need to combine like terms.

First, let's distribute the negative sign to the terms inside the first set of parentheses:

(-6b^2) + (-2b^1) = -6b^2 - 2b^1

Now let's combine the terms inside the second set of parentheses:

(-2b^2) + (4b) = -2b^2 + 4b

Finally, let's add the two expressions:

(-6b^2 - 2b^1) + (-2b^2 + 4b) = -6b^2 - 2b^1 - 2b^2 + 4b

Simplifying, we get:

-8b^2 + 4b = -8b^2 + 4b

The final simplified expression is: -8b^2 + 4b.

The additional gas it will take to fill the tank is 16 gallons

From the question, we have the following parameters that can be used in our computation:

Capacity = 24 gallons

Current volume = 1/3 full

This means that

Remaning volume = 1 - 1/3

Evaluate

Remaning volume = 2/3

The additional gas it will take to fill the tank is

Additional = 2/3 * 24

Evaluate

Additional = 16

Hence, the additional gas it will take to fill the tank is 16 gallons

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The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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Answer:

f(-1) = 6

Explanation:

Looking at the piecewise function given, we see that

f(x) = -3x -5

for x different from -1

And

f(x) = 6

for x = -1

So, we choose the suitable one, since x = -1

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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Answer:

m=15/14

Step-by-step explanation:

Answer:

Step-by-step explanation: yes because when rewritten in standard form the x term will still be raised to the 2nd power.