SERE
RE
a.
Which of the following equations correctly describes how to calculate gross profit?
gross profit = (net sales) - (cost of goods sold)
b. gross profit = (cost of goods sold) - (net sales)
gross profit = (net income) - (operating expenses)
d. gross profit = (operating expenses) - (net income)
C.

We know, point on a line segment which cut a line into the ratio m : n is given by :

\([(\dfrac{mx_1+nx_2}{m+n}),(\dfrac{my_1+ny_2}{m+n}) ]\)

Putting value of point A and B and m =2 and n = 5 .

We get :

\([(\dfrac{2(2)+5(18)}{2+5}),(\dfrac{2(6)+5(12)}{2+5}) ]\\\\(\dfrac{94}{7},\dfrac{72}{7})\)

Hence, this is the required solution.

Answer:

\(z=\frac{3 (28 + 17p)}{p + D}\)

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

Here is your answer!

Answer:

Rectangle B has a length of 4 inches.

Step-by-step explanation:

Rectangle A has a width of 3 inches and a length of 5 inches.

Let us find its perimeter:

Perimeter = 2(L + W)

where L = length

W = width

Its perimeter is therefore:

P = 2(5 + 3)

P = 2 * 8 = 16 inches

Rectangle B has the same perimeter as Rectangle A. Let us find the length of B.

Its width is 4 inches, therefore, perimeter is:

P = 2(L + W)

16 = 2(L + 4)

16 = 2L + 8

16 - 8 = 2L

8 = 2L

=> L = 8 / 2 = 4 inches

Rectangle B has a length of 4 inches.

Answer:

(-4,0)

Step-by-step explanation:

Answer:

A = 1

B = 5

Step-by-step explanation:

Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.

To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.

First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:

6x + 4(0) + 0 = 24

6x = 24

x = 4

So, the plane intersects the x-axis at (4, 0, 0).

Similarly, to find the y-intercept, we set x = 0 and z = 0:

6(0) + 4y + 0 = 24

4y = 24

y = 6

So, the plane intersects the y-axis at (0, 6, 0).

To find the z-intercept, we set x = 0 and y = 0:

6(0) + 4(0) + z = 24

z = 24

So, the plane intersects the z-axis at (0, 0, 24).

We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).

To find the volume of this tetrahedron, we can use the formula:

Volume = (1/3) * base area * height

The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.

The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.

Plugging these values into the volume formula:

Volume = (1/3) * 12 * 24

= 96 cubic units

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Answer:

- 21

Step-by-step explanation:

The minimum value occurs at the vertex of the function

The equation of a parabola 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

f(x) = x² - 6x - 12

add/ subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 - 12

     = (x - 3)² - 21

with vertex = (3, - 21 )

The minimum is the value of k, that is minimum value = - 21

The equation of the tangent line to the curve y = 16x sin(x) at the point (π/2, 8π) is y = 16x.

To find the equation of the tangent line to the curve y = 16x sin(x) at the point (π/2, 8π), we need to determine the slope of the tangent line and use the point-slope form of a linear equation.

The slope of the tangent line at a specific point on a curve can be found by taking the derivative of the function at that point.

Given y = 16x sin(x), let's find its derivative:

dy/dx = d/dx (16x sin(x))

      = 16 (sin(x) + x cos(x))

To find the slope of the tangent line at (π/2, 8π), substitute x = π/2 into the derivative:

dy/dx = 16 (sin(π/2) + (π/2) cos(π/2))

      = 16 (1 + (π/2) * 0)

      = 16

Therefore, the slope of the tangent line at (π/2, 8π) is 16.

Now, using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the point (π/2, 8π), and m is the slope of the tangent line.

Substituting the values, we have:

y - 8π = 16(x - π/2).

Simplifying:

y - 8π = 16x - 8π.

Rearranging the terms, we get the equation of the tangent line:

y = 16x.

Therefore, the equation of the tangent line to the curve y = 16x sin(x) at the point (π/2, 8π) is y = 16x.

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Question:

Solution:

Consider the following functions:

and

a) f(-3):

if we evaluate the function f at x = -3, we get:

so that, the correct answer is:

b) g(4):

if we evaluate the function g at x = 4, we get:

so that, the correct answer is:

c) f(3)*g(3):

Step 1: evaluate f at x = 3:

Step 2: evaluate g at x = 3:

Step 3: multiply f(3) and g(3):

so that, we can conclude that the correct answer is:

We have

w = 60 (cos(1.7) + i sin(1.7)) = 60 exp(1.7i)

z = 71 (cos(4.4) + i sin(4.4)) = 71 exp(4.4i)

so then

wz = 60•71 exp(1.7i + 4.4i)

wz = 4260 exp(6.1i)

wz = 4260 (cos(6.1) + i sin(6.1))

Answer:

4x² + 8x - 8

Step-by-step explanation:

We are given these following functions:

f(x) = 8x²+3x-1

g(x) = 4x² - 5x + 7

We have to do: f(x) - g(x)

So

f(x) - g(x) = 8x² + 3x - 1 - (4x² - 5x + 7)

The minus means that the signal of everything inside the parenthesis is changed. So

8x² + 3x - 1 - (4x² - 5x + 7) = 8x² + 3x - 1 - 4x² + 5x - 7

Now we combine the like terms:

With x²: 8x² - 4x² = 4x²

With x: 3x + 5x = 8x

Independent: -1 - 7 = -8

The answer is:

4x² + 8x - 8

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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Answer:

30(D)

Step-by-step explanation:

38.48-26.94=11.54

11.54÷38.48×100

≈30

Image vertices are :R' = (-20 , 28) ; S' = (8 ,24) ; T' = (20, -12) ; V' = (-16, 0)

Dilation usually refers to the transformation of a geometric figure by multiplying its coordinates by a constant factor, thereby making the figure larger or smaller. In two-dimensional Euclidean space, dilation involves multiplying the x- and y-coordinates of a point by a constant factor, which results in a new point that is either larger or smaller than the original point, depending on the value of the dilation factor.

Given :

Scale Factor = 4

Vertices given in the above graph :

R = (-5 , 7) ; S = (2 ,6) ; T = (5 , -3) ; V = (-4, 0)

Calculation :

We must multiply the vertices by the scale factor 4 in order to determine the picture vertices for a dilatation with centre (0, 0).

So the image vertices are :

R' = (-20 , 28) ; S' = (8 ,24) ; T' = (20, -12) ; V' = (-16, 0)

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Answer:

Equation of this line is y = 1

Step-by-step explanation:

We have to write an equation of a line passing through (0,1) and slope 0.

Standard equation of a line in slope form is y = mx + c

Where m = slope and c = y intercept.

Since m = 0

so y = c is the equation.

This line passes through (0,1)

so equation will be Y = 1

Equation of this line is y = 1

Step-by-step explanation:

Hope this helps:)

Answer:

y = 1

Step-by-step explanation:

\(\sf y =\dfrac{2}{5}x-4\)

Step-by-step explanation:

        To find the equation of the required line, first we need to find the slope of the given line in the graph.

          Choose two points from the graph.

         (0 ,4)    x₁ = 0 & y₁ = 4

         (2,-1)     x₂ = 2 & y₂ = -1

\(\sf \boxed{\sf \bf Slope=\dfrac{y_2-y_1}{x_2-x_1}}\)

           \(\sf = \dfrac{-1-4}{2-0}\\\\=\dfrac{-5}{2}\)

       \(\sf m_1=\dfrac{-5}{2}\)

\(\sf \text{Slope of the perpendicular line m = $\dfrac{-1}{m_1}$}\)

                                                    \(\sf = -1 \div \dfrac{-5}{2}\\\\=-1 * \dfrac{-2}{5}\\\\=\dfrac{2}{5}\)

\(\boxed{\sf slope \ intercept \ form \ : \ y = mx + b}\)

Here, m is slope and b is y-intercept.

Substitute the m value in the above equation,

                    \(\sf y =\dfrac{2}{5}x + b\)

    The line is passing through (5 , -2),

                     \(\sf -2 = \dfrac{2}{5}*5+b\)

                     -2 =  2 + b

                -2 - 2 = b

                      b = -4

Slope-intercept form:

                \(\sf y = \dfrac{2}{5}x-4\)

Formula for the Slope: (y2 - y1) / (x2 - x1)

You can use any two points to find the slope, as long as those two points are on the line.

Point 1 = (-2, 8)

Point 2 = (0, 0)

Slope = (0 - 8) / (0 - - 2)

Slope = -8 / 2

Slope = -4

Hope this helps!

Answer:

-4

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: -3 --> -2 --> -1 --> 0 --> 1

y value: 12 --> 8 --> 4 --> 0 --> -4

When y changed from 12 to 8, the x changed from -3 to -2.

y: 12 --> 8

x: -3 --> -2

There was a difference of -4 in the y and a difference of 1 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -4 and 1 we found, we can say that the slope is -4/1.

If we simplify this answer, we end up with -4.

So -4 is the slope of the data.

By using the concept of LCM, it can be concluded that

It is necessary to find the LCM of polynomials to divide polynomials

What is LCM ?

LCM means least common  multiple. LCM of two numbers a and b is the least number which is divisible by both a and b.

LCM means least common multiple

As there is a question of multiple here, so there will be a concept of division into question

So it is necessary to find the LCM of polynomials to divide polynomials

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The polar equation r = -8 represents a circle centered at the origin with a radius of 8 units. In rectangular form, the equation can be written as x^2 + y^2 = 64, where (x, y) are the Cartesian coordinates.

In polar coordinates, r represents the distance from the origin, and the angle θ represents the direction from the positive x-axis. The equation r = -8 means that the distance from the origin is always -8, regardless of the angle θ. Since distance cannot be negative, this implies that the circle is centered at the origin and has a radius of 8 units.

To convert the polar equation to rectangular form, we can use the conversion formulas:

x = r * cos(θ)

y = r * sin(θ)

Substituting r = -8 into the formulas, we get:

x = -8 * cos(θ)

y = -8 * sin(θ)Simplifying further, we have:

x = -8cos(θ)

y = -8sin(θ)

In rectangular form, the equation becomes x^2 + y^2 = (-8cos(θ))^2 + (-8sin(θ))^2 = 64. This equation represents a circle centered at the origin with a radius of 8 units. Sketching its graph would yield a complete circle centered at (0, 0) with a radius of 8.

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The number of robberies reported in your city is a quantitative variable.

Quantitative variables are numerical in nature and represent quantities or amounts. They can be further classified as either discrete or continuous. In the case of the number of robberies reported, it is a discrete quantitative variable because it takes on a countable, whole number value. It represents a specific quantity or amount of robberies reported in the city, such as 0, 1, 2, and so on.

On the other hand, qualitative variables (also known as categorical variables) represent qualities or characteristics that do not have a numerical value. Examples of qualitative variables could be the type of crime (e.g., robbery, burglary, assault) or the color of a car (e.g., red, blue, green).

Therefore, the number of robberies reported in your city is a quantitative variable.

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Answer:

CB = 5, \(m\angle{BDA} = 23^\circ\)

Step-by-step explanation:

Assuming that the marks next to angle D mean that \(\angle{BDA} \cong \angle{BDC}\), then there is enough information to conclude that the two right triangles are congruent (HA theorem--hypotenuse/angle).

Then all the corresponding parts of the two triangles are congruent, including segments BA and BC, making them the same length.

4x + 1 = 9x - 4

Solving for x,

1 = 5x - 4

5 = 5x

1 = x

Pluggint x = 1 into the two expressions reveals that the length of segment CB is 5.

The two small angles at D are congruent, so \(m\angle{BDA}=23^\circ\).

8 Guidelines for Critically Evaluating a Statistical Study

1. Identify the Goal, Population, and Type of Study

2. Consider the Source

3. Examine the Sampling Method

4. Look for Problems in Defining or Measuring the Variables of

Interest

5. Watch Out for Confounding Variables

6. Consider the Setting and Wording of Any Survey

7. Check That Results Are Fairly Represented in Graphics or

Concluding Statements

8. Stand Back and Consider the Conclusions

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Answer:

\(74.1\)$

Step-by-step explanation:

\( \frac{x}{57} = \frac{30}{100} \)

\((x)100 = (30)57\)

\((x)100 = 1710\)

\( \frac{(x)100}{100} = \frac{1710}{100} \)

\(x = \frac{1710}{100} \)

\(x = 17.1\)

\(57 + 17.1 = 74.1\)

\(74.1\)$

There were 200 participants at the telematch.

The second degree is represented mathematically by a quadratic equation, where the highest power of the variable is 2.

It is expressed as ax² + bx + c = 0, where x is the variable and a, b, and c are the coefficients.

Let the total number of participants be P. Then, the number of children is (P-125), and the number of girls is (P-125) × (1-B/(P-125)), where B is the number of boys, put all values:

(P-125) × (1-B/(P-125)) = (P-B-125)/2

Simplifying the above equation, we get:

B² - 250B + (P-125)² = 0

We know the quadratic formula;

B = (250 ± √(250² - 4×(P-125)²))/2

Since B must be an integer, only the positive root is possible, and it must be a whole number.
Therefore, we can solve for P by trying out integer values for B until we find one that gives a whole number for P. Trying out values, we find that B = 100 gives P = 200, which is a whole number.
Therefore, there were 200 participants at the Telematch.

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Answer

SOLUTION

Problem Statement

The question asks us to insert the correct operator symbol depending on which number is greater, smaller or whether the two numbers are equal

The numbers given are:

Solution

To solve this problem, we need to ensure the two numbers are in the same form. Either they are both decimals or they are both fractions.

For this solution, we should make the fraction into a decimal and then compare the two numbers.

We should note that for negative numbers if a negative number is larger in magnitude than another negative number, then the negative number with the larger magnitude is actually the smaller number.

To illustrate this, take the following example:

Now that we understand the logic to use to solve the question, we can proceed to solve the question.

Let us now convert the fraction into a decimal:

After this, we can now compare the two numbers:

Therefore, the solution is:

Answer:

\(5000=5*10^3\)

Step-by-step explanation:

\(5000=5*10^3\)

Answer:

The answer is B or the 2nd option

Step-by-step explanation:

HAVE A GREAT DAY AND STAY SAFE!

The graph which shows the velocity of the particle at any time attached below.

The velocity of a particle modeled by the function,

         \(V(t)=\frac{1}{10}(3t-8)^{3} +2\)

It is observe that the given velocity function is cubic function.

The attached graph shows the velocity of the particle at any time.

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