Anumeha mows lawns. She charges an initial fee and a constant fee for each hour of work.F represents Anumeha's fee (in dollars) for working t hours. F = 6 + 12t How much does Anumeha charge for each hour of work?

To find the area of the resulting surface when the given curve y = 1/4x^2 - 1/2 ln(x) is rotated about the y-axis, we can use the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from a to b

Here, a = 3 and b = 5.

First, we need to find the derivative of y with respect to x (dy/dx):

y = 1/4x^2 - 1/2 ln(x)
dy/dx = (1/4 * 2x) - (1/2 * 1/x) = x/2 - 1/(2x)

Now, let's plug this into the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (x/2 - 1/(2x))^2)] dx from 3 to 5

We will now integrate the expression within the brackets with respect to x from 3 to 5. This might be challenging to solve analytically, so we may need to use a numerical integration method or a calculator to find the exact value.

Once the integration is completed, you will obtain the surface area of the curve when rotated about the y-axis.

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A measurement that is the best estimate of the area of the banner in square meters include the following: A. 6 m².

In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):

Area of trapezoid, A = ½ × (a + b) × h

Where:

Based on the information provided about the two congruent trapezoid, we can logically deduce that they both have the same base area of 1 m.

This Means the total base of the entire triangle will be;

Base area = 1 + 1 ¾ + 1 + 1 ¾

Base area = 1 + 1.75 + 1 + 1.75

Base area = 5.5 m

Height of main triangle = 2 m

Area of banner = ½ × 5.5 × 2 = 5.5 ≈ 6.0 m²

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Complete Question:

An advertising banner has four sections, as modeled below. Two sections are congruent trapezoids, and two sections are congruent right triangles. Which measurement is the best estimate of the area of the banner in square meters?

6 m²

15 m²

8 m²

10 m²

To sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we'll need to use a differential equation or system of differential equations. So, to sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we would first draw a slope or direction field for our differential equation. Then, we would start at the point (0, y(0)) and follow the direction of the slope or arrow to sketch the solution for each initial value.
To sketch three solutions with the given initial values, follow these steps:
1. Determine the differential equation you're working with. For example, let's consider the equation y'(t) = y(t). This is just an example, and the process will be similar for other differential equations.
2. Solve the differential equation to obtain a general solution. In our example, the general solution is y(t) = C * e^t, where C is an arbitrary constant.
3. Apply the initial values to find specific solutions:
  a. For y(0) > 0, choose a positive value for C, such as C = 1. The specific solution is y(t) = e^t.
  b. For y(0) = 0, choose C = 0. The specific solution is y(t) = 0.
  c. For y(0) < 0, choose a negative value for C, such as C = -1. The specific solution is y(t) = -e^t.
4. Sketch the three solutions on the same graph:
  a. For y(t) = e^t, draw a curve that starts at (0,1) and increases exponentially as t increases.
  b. For y(t) = 0, draw a horizontal line at y = 0.
  c. For y(t) = -e^t, draw a curve that starts at (0,-1) and decreases exponentially (toward 0) as t increases.
These three curves represent the solutions with the specified initial values. Note that this process assumes you have a specific differential equation in mind. If you have a different equation, just follow the same steps to find and sketch the solutions.

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"A transformation T is linear if and only if [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2)[/tex] for all v1 and v2 in the domain of T and for all scalars c1 and c2" is true.

To understand why this statement is true, we need to first define what it means for a transformation to be linear.

A linear transformation is a function that satisfies two properties:

Additivity and homogeneity.

Additivity means that [tex]T(u + v) = T(u) + T(v)[/tex]for all vectors u and v in the domain of T, while homogeneity means that [tex]T(cv) = cT(v)[/tex] for all vectors v in the domain of T and all scalars c.
Let's look at the given statement. It states that [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2)[/tex] for all v1 and v2 in the domain of T and for all scalars c1 and c2.

This is equivalent to saying that T is both additive and homogeneous, since we can rewrite the statement as [tex]T(c1v1 + c2v2) = T(c1v1) + T(c2v2) = c1T(v1) + c2T(v2).[/tex]
A transformation satisfies the given statement, it is both additive and homogeneous, and hence it is linear.

On the other hand, if a transformation is linear, it must satisfy the given statement by definition.

The statement "A transformation T is linear if and only if [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2[/tex]) for all v1 and v2 in the domain of T and for all scalars c1 and c2" is true.

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Identify the predictor and response variables, then create a scatterplot in Minitab. Characterize the association between the variables as linear or nonlinear and negative, none, or positive.

In exploratory data analysis, the first step is to identify the research question and the two variables of interest. The predictor variable (also known as the explanatory variable or independent variable) is the one that is used to explain or predict the outcome of the response variable (also known as the dependent variable).

After identifying the two variables, one can use software such as Minitab to create a scatterplot of the data. The scatterplot helps to visualize the relationship between the two variables.

To characterize the association between the two variables, we would first determine if the relationship appears to be linear or nonlinear. If the relationship is roughly linear, we would then determine if it is negative (meaning that as one variable increases, the other tends to decrease), positive (meaning that as one variable increases, the other tends to increase), or none (meaning that there is no clear trend).

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the value of f(6) is -972.To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:

4, -12, 36, -108, 324, -972, ...

How to solve the question?

We can use the recursive formula given to find the value of f(6). Let's start by calculating f(2):

f(2) = -3f(1) = -3(4) = -12

Next, we can calculate f(3) using the same formula:

f(3) = -3f(2) = -3(-12) = 36

We can continue this process for f(4) and f(5):

f(4) = -3f(3) = -3(36) = -108

f(5) = -3f(4) = -3(-108) = 324

Finally, we can use the formula to find f(6):

f(6) = -3f(5) = -3(324) = -972

Therefore, the value of f(6) is -972.

To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:

4, -12, 36, -108, 324, -972, ...

Each term in the sequence is obtained by multiplying the previous term by -3. We can see that the sequence alternates between positive and negative values, with the magnitude of each term growing rapidly. By the time we reach f(6), the magnitude has grown to 972, and the negative sign indicates that the term is negative. Thus, f(6) is equal to -972.

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If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.

To factor is to identify the terms that make up an expression when they are multiplied together.

Given quadratic equation:

p² + 14p + 48 = 0

Find the factors of 48 such that on addition 14 will come:

48 = 6*8

So,

p² + 6p + 8p + 48 = 0

Taking p common first two terms:

p(1 + 6) + 8p + 48 = 0

Now, taking 8 common from last two terms

p(p + 6) + 8(p + 6) = 0

taking (p + 6) from both .

(p + 6)(p + 8) = 0

Now,

p + 6 = 0

p = -6 and

p + 8 = 0

p = -8

Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.

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Correct question:

Solve the given quadratic equation using the factorization method:

p² + 14p + 48 = 0

Answer:

the value of x ia 7/2 and y is 5/2

There are two real solutions if the radicand is positive.

There is one real solution if the radicand is zero.

There are no real solutions if the radicand is negative.

In mathematics, the radicand refers to the value inside a square root (√) symbol. In the given equations and solutions, we can see that there are square root symbols involved, and we can determine the nature of the solutions based on the sign of the radicand.

For the first equation, y = -16x² + 32x - 10, the solutions for x are given as x = (-32 ± √384) / -32. The radicand in this case is 384. Since 384 is positive, greater than 0, there will be two real solutions for x.

For the second equation, y = 4x² + 12x + 9, the solutions for x are given as x = (-12 ± √0) / 8. The radicand in this case is 0. Since the square root of 0 is 0, there is only one real solution for x in this case.

Therefore, For the third equation, y = 3x² - 5x + 4, the solutions for x are given as x = (5 ± √(-23)) / 6. The radicand in this case is -23. Since the square root of a negative number is not a real number, there are no real solutions for x in this case.

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See full text below

Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is 1. y = negative 16 x squared + 32 x minus 10. x = StartFraction negative 32 plus-or-minus StartRoot 384 EndRoot Over negative 32 EndFraction. 2. y = 4 x squared + 12 x + 9. x = StartFraction negative 12 plus-or-minus StartRoot 0 EndRoot Over 8 EndFraction. 3. y = 3x squared minus 5 x + 4. x = StartFraction 5 plus-or-minus StartRoot negative 23 EndRoot Over 6 EndFraction.

Answer:

D

Step-by-step explanation:

given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the turning point ( vertex ) is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = 2x² + 4x - 3 ← is in standard form

with a = 2, b = 4 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{4}{2(2)}[/tex] = - [tex]\frac{4}{4}[/tex] = - 1

substitute x = - 1 into the equation for corresponding y- coordinate

y = 2(- 1)² + 4(- 1) - 3 = 2(1) - 4 - 3 = 2 - 7 = - 5

turning point = (- 1, - 5 )

Answer:

The Correct answer is D

(-1,-5)

Answer: The sequence modeling the amount of money in Samuel’s savings account is a recursive sequence. Each term in the sequence is determined by adding $75 to the previous term. The first term in the sequence is $100, representing Samuel’s initial deposit. After n months, the amount of money in Samuel’s savings account can be calculated using the formula An = An-1 + 75, where An represents the amount of money in his account after n months and An-1 represents the amount of money in his account after n-1 months.

For example, after 1 month, the amount of money in Samuel’s savings account will be A1 = A0 + 75 = 100 + 75 = $175. After 2 months, the amount of money in his account will be A2 = A1 + 75 = 175 + 75 = $250. And so on.

The quadratic formula x = (-b ± √ ( [tex]b^2[/tex] - 4ac)  / (2a) is used to find the solutions (or roots) of a quadratic equation of the form [tex]ax^2[/tex] + bx + c = 0.

In this formula, "a", "b", and "c" are coefficients of the quadratic equation, and the ± symbol indicates that there are two possible solutions, one with a positive square root and one with a negative square root. By plugging in the values of "a", "b", and "c" from the given quadratic equation, one can use the quadratic formula to calculate the solutions for x that satisfy the equation.

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x = (-b ± √(b² - 4ac)) / (2a) is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.

The formula x = (-b ± √(b² - 4ac)) / (2a) is known as the Quadratic Formula, used to find the solutions to a quadratic equation of the form ax² + bx + c = 0.

The formula x=-b± b2 -4ac2a, is called the quadratic formula, which is used to find the solutions (or roots) to a quadratic equation of the form ax2+bx+c=0,

where a, b, and c are coefficients of the equation.

The term under the square root sign (b2-4ac) is called the discriminant and can tell you whether the quadratic equation has two real solutions (if the discriminant is positive), one real solution (if the discriminant is zero), or two complex conjugate solutions (if the discriminant is negative).

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Answer:

for the following question the answer will be

1/5=0.2 given as example

60%=0.6

50%=1/2

3/4=0.75

for 1/6 there os no answer for it the answer is 0.166

The resulting histogram would show the distribution of the grades on the exam, with the bins and frequency of data points clearly displayed. The title, axis labels, and scales would provide context for the graph and make it easy to interpret the data.

In mathematics and computer science, a graph is a collection of points, called vertices or nodes, that are connected by lines, called edges or arcs. Graphs can be used to model and analyze relationships between objects or data, such as social networks, transportation systems, or web pages.

Here,

Part A:

The best graphical representation to display the given data is a histogram. A histogram is a bar graph-like representation of data that divides the data into intervals or bins and shows the frequency of each interval. Histograms are appropriate for displaying continuous data, which the grades on the exam can be considered as, and can also show the distribution of the data.

Part B:

To create a histogram of the given data, follow these steps:

Choose the number of bins or intervals. In this case, we can choose a reasonable number of bins, such as 6-8, to display the distribution of the grades.

Determine the range of the data. The lowest grade is 60 and the highest is 99, so the range is 99-60 = 39.

Calculate the bin size. The bin size is calculated by dividing the range by the number of bins. For example, if we choose 6 bins, the bin size would be 39/6 ≈ 6.5. Since it is difficult to have bins that are fractions of a point, we can round the bin size up to the nearest whole number to get a bin size of 7.

Create the bins. Starting from the lowest grade, create intervals or bins of size 7 that cover the range of the data. For example, the first bin would be 60-66, the second bin would be 67-73, and so on.

Count the frequency of data points that fall into each bin. For example, there are 2 data points in the first bin, 3 data points in the second bin, and so on.

Draw the histogram. On the horizontal axis, label and scale the bins. On the vertical axis, label and scale the frequency of data points in each bin. Draw a rectangle above each bin with a height equal to the frequency of data points in that bin.

Title: Grades on Recent 8th Grade Mathematics Exam

X-axis label: Grades

Y-axis label: Frequency

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Answer:

Vertical translation

Step-by-step explanation:

Let's compare each point to its corresponding point in the image.

First, look at point A. Look at point A'.

With respect to the shapes ABCD and A'B'C'D', they are in the same position (in between B/B' and D/D'; across from C/C').

If you look at the image again, you'll find that the shape A'B'C'D' is not a rotated version of ABCD.

Thus, we can rule out the option "90° clockwise rotation."

A reflection across the x-axis indicates that A'B'C'D' and ABCD would be symmetrical across the x-axis (a horizontal line).

Because ABCD and A'B'C'D' are not symmetrical across a horizontal line, we can also rule out "Reflection across the x-axis."

Now, look at the position of A'B'C'D' with respect to ABCD. It's directly next to ABCD. In other words, it was shifted sideways.

Translations are basically just shifts.

Recall that horizontal means up and down, while vertical means side to side.

Since this is a sideways shift, we can conclude that the translation was:

a vertical translation.

If a circle graph were created using the findings, A. Kayaking would be the lake activity with a central angle of 54°.

A central angle is one having endpoints on the perimeter and a vertex in the centre of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle.

Lake Activity             Number              Degrees

                             of Campers

Kayaking                     15                         (15/100 x 360°) = 54°

Wakeboarding            11                        (11/100 x 360°) =  40°

Windsurfing                 7                        (7/100 x 360°) = 25°

Waterskiing                13                        (13/100 x 360°) = 47°

Paddleboarding        54                         (54/100 x 360°) = 194°

Total number             100

Thus, Kayaking hence has a 54° central degree when viewed proportionately.

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Therefore, we can say: limit sin(x) as x approaches pi/2 does not exist lim sin(x) as x approaches 0 = 0.

Although the function (sin x)/x is not defined at zero, it approaches 1 arbitrarily close as x approaches zero. In other words, when x gets closer to zero, the limit of (sin x)/x = 1.

We can put g(x) equal to -1/x and h(x) equal to 1/x because sin(x) is always between -1 and 1. As x approaches either positive or negative infinity, we know that the limit of both -1/x and 1/x is zero, and as a result, the limit of sin(x)/x is also zero.

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The solution to the equation -2/(x - 8) = (x - 1)/(x + 2) is x = 3 after checking for extraneous solutions.

To solve the equation

-2/(x - 8) = (x - 1)/(x + 2)

We can start by cross-multiplying to eliminate the fractions

-2(x + 2) = (x - 1)(x - 8)

Simplifying both sides, we get

-2x - 4 = x² - 9x + 8

Bringing all the terms to one side, we get

x² - 7x + 12 = 0

Now we can factor the quadratic equation to get

(x - 3)(x - 4) = 0

So the solutions are x = 3 and x = 4. However, we need to check for any extraneous solutions that may have been introduced by the original equation.

Plugging in x = 3 to the original equation, we get

-2/(3 - 8) = (3 - 1)/(3 + 2)

Which simplifies to

2/5 = 2/5

Therefore, x = 3 is a valid solution.

Plugging in x = 4 to the original equation, we get

-2/(4 - 8) = (4 - 1)/(4 + 2)

Which simplifies to

1/2 = 3/6

Therefore, x = 4 is not a valid solution.

So the only solution to the equation is x = 3.

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Answer:

We can start by using the Pythagorean identity to simplify the expression for cos J:

cos^2(J) + sin^2(J) = 1

Since we are given the value of sin J, we can substitute and solve for cos J:

cos^2(J) + (4/√82)^2 = 1

cos^2(J) + 16/82 = 1

cos^2(J) = 66/82

cos(J) = ±√(66/82)

We want to express cos J in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:

cos(J) = ±√[(2311)/(2*41)]

cos(J) = ±(√2/2) * (√33/√41)

Since J is in the first or second quadrant (based on the given value of sin J), we know that cos J is positive, so we can drop the negative sign:

cos(J) = (√2/2) * (√33/√41)

Therefore, the exact value of cos J in simplest radical form is (√2/2) * (√33/√41).

Answer: 228.8cm

Step-by-step explanation:

Hope this helps! :)

If the noon class has a symmetric distribution, the median would be 15.

From the given table,

a) Evening class has the highest average age, that is 22 years.

b) Morning class has age that are the most spread out, that is 2.4.

c) If the noon class has a symmetric distribution, the median would be 15 (which is equal to the mean).

Therefore, if the noon class has a symmetric distribution, the median would be 15.

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Answer:       This is called percent error this is how i solve.

                    8     20%

                    3     100%

          800. 60 =               48000          

An iterated integral for the given function f and region d is  [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex].

What is integral?

An integral is the continuous equivalent of a sum in mathematics, where sums are used to compute areas, volumes, and their generalizations. One of the two basic operations in calculus, along with differentiation, is integration, which is the process of computing an integral.

Here, we have

Given: Consider the following F(x, y) = x + y YA (1,1) D 0 2 x

Equation of line passes through (2,0),(1,1)

= (y - y₁)/(y₂ - y₁) =  (x - x₁)/(x₂ - x₁)

=  (y - 0)/(1 - 0) =  (x - 2)/(1 - 2)

= y/1 = (x-2)/(-1)

y = -x + 2

x = 2-y

∫∫F(x,y)dA = [tex]\int\limits^0_1 \int\limits^2_y {f(x,y)} \, dx dy[/tex]

∫∫F(x,y)dA = [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex]

Hence,  an iterated integral for the given function f and region d is  [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex].

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Answer: a=2 b= -2 c= -2

Step-by-step explanation: you replace y with a and you plug the x for them in so a= -1^2 -3 (-1) - 2 and you solve that to equal 2 then you solve for the others

The thief stole 22 oranges using algebraic equations.

To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.

According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.

We also know that the thief was left with only 9 oranges. So we can set up the equation:

x - [(1/2)x + 2] = 9

Simplifying this equation:

(1/2)x - 2 = 9
(1/2)x = 11
x = 22

Therefore, the thief stole 22 oranges.

The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.

To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.

In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.

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Answer:

a) What is her GROSS pay for a week? 1,400

b) What is her GROSS pay for a year? 67,200

c) What are her TOTAL DEDUCTIONS for a week? 351.39

d) What is her NET pay for a week? 1,048.61

e) What is her NET pay for a year? 50,333.28

f) What does she pay in Income Tax per YEAR? 13,535.52

g) What does she pay in CPP contributions per YEAR? 2,537.28

h) What does she pay in El contributions per YEAR? 793.92

i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%

Step-by-step explanation:

 GROSS

 NET

 There are 4 weeks in a month, 52 weeks in a year.

a) What is her GROSS pay for a week? 1,400

b) What is her GROSS pay for a year? 67,200

c) What are her TOTAL DEDUCTIONS for a week? 351.39

d) What is her NET pay for a week? 1,048.61

e) What is her NET pay for a year? 50,333.28

f) What does she pay in Income Tax per YEAR? 13,535.52

g) What does she pay in CPP contributions per YEAR? 2,537.28

h) What does she pay in El contributions per YEAR? 793.92

i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%

An equation which shows how to find p, the price Mrs. Merson paid for the car include the following: B) 5500/p = 55/100.

In Mathematics and Science, a price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about the amount of money that Mersin paid for the car, an equation which shows how to find the price (p) is given by;

55% of p = 5500

55/100 × p = 5500

5500/p = 55/100

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Complete Question:

Mrs. Merson is selling her car. Her research shows that the car has a current value of $5,500,

which is 55% of the amount Mrs. Merson paid for the car. A buyer wants to know the price

Mrs. Merson paid for the car.

• Which equation shows how to find p, the price Mrs. Merson paid for the car?

A) 55/p = 5500/100

B) 5500/p = 55/100

C) p/5500 = 55/100

D) p/5 = 5500/100

Answer:

Step-by-step explanation: