a company manufactures and sells novelty Mugs. the manufacturing cost consist of a fixed cost of R8000 and a variable cost of R15 rand per mug. the mugs are sold at R35 each. assume a linear profit function. determine the profit function

Answers

Answer 1

Answer: ok so

8000=cost
profit-8000
then
another cost is 15rand per mug
but profit of 35 rand
35-15=20
profit of 20rand per mug

profit=R20m-8000
where m=number of mugs sold
(R20 means 20 rand)

f(m)=R20m-8000

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The width of a rectangle is 61 centimeters more than the length. The perimeter is 406 centimeters. Find the length and the width.

Answers

$Step \; 1: \; Assign \; Variables \; for \; the \; unknown \; that \; we \; need \; to \; find$

$Let \; x \; be \; length \; of \; the \; rectangle$

$Step \; 2: \; Set \; up \; equation \; based \; on \; information \;\n given \; about \; the \; rectangle$

$Statement \; 1: Width \; of \; a \; rectangle \; \nis \; 61cm \; more \; than \; the \; length\n\nWidth \; = \; 61+x\n\nStatement \; 2: \; The \; perimeter \; is \; 406cm\n\nPerimeter=2(Length+Width)\nPerimeter =2(x+61+x)\n\nSo \; the \; mathematical \; equation \; would \; be \n 2(x+61+x)=406$

$Step \; 3: \; Solve \; the \; equation \; by \n undoing \; whatever \; is \; done \; x.\n\n2(x+61+x)=406\nGroup \; and \; Combine \; like \; terms \; inside \; the \; parenthesis\n\n2(2x+61)=406\nDistribute \; 2 \; in \; the \; left \; side \; of \; the \; equation\n\n4x+122=406\nSubtract \; 122 \; on \; both \; sides\n\n4x+122-122=406-122\nSimplify \; on \; both \; sides\n\n4x=284\nDivide \; on \; both \; sides\n\n(4x)/(4)=(284)/(4)\nSimplify \; fractions \; on \; both \; sides\n\nx=71$

$Conclusion:\nLength=x=71cm\nSubstituting \; 71 \; for \; x \; and \; find \; Width \; value.\nWidth=61+x=71+61=132cm\n\nLength \; is \; 71 cm \; and \; Width \; is 132cm$

Final answer:

The length of the rectangle is 71 centimeters and the width is 132 centimeters.

Explanation:

To find the length and width of the rectangle, we can set up a system of equations. Let's denote the length of the rectangle as L and the width as W. We know that W = L + 61. The formula for the perimeter of a rectangle is P = 2L + 2W. Plugging in the given values, we have 406 = 2L + 2(L + 61). Simplifying this equation, we get 406 = 4L + 122. Subtracting 122 from both sides, we obtain 284 = 4L. Dividing both sides by 4, we get L = 71. Finally, substituting the value of L into the equation W = L + 61, we find W = 71 + 61 = 132. Therefore, the length of the rectangle measures 71 centimeters and the width measures 132 centimeters.

Learn more about Rectangle dimensions here:

brainly.com/question/31677552

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Which equation matches the function shown in the graph?A. Y= sin(x-pi)+3
B. Y= 3cos(x+pi)
C. Y= 3sin(x-pi)
D. Y= 3cos(x-pi)

Answers

Option C is correct. The equation that matches the function shown in the graph is expressed as y = 3sin(x-π)

The general formula for a sine function is expressed as;

y = Asin(x+Ф)

A is the amplitude i.e the maximum point on the curve. From the diagram, we can see that the maximum point is at 3 (factor 3 elongates the curve).

A = 3

Also, since the graph translates to the right by π, hence Ф = -π

Substituting the resulting values into the formula, we will have;

y =3sin(x+ (-π))

y = 3sin(x-π)

Hence the equation that matches the function shown in the graph is expressed as y = 3sin(x-π)

Learn more about since graph here: brainly.com/question/16262155

Answer:

its c ! just took the test :)

If the x- intercept is 2 and the y- intercept is -5 and the slope is 1/3. Write in equation in slope intercept form and standard form.

Answers

Answer:

The equation in slope-intercept form is

$y=(5)/(2)x-5$

The equation in the standard form will be:

$(5)/(2)x-y=5$

Step-by-step explanation:

The x-intercept is obtained when we set the value y=0

As the x-intercept is 2, therefore the point representing

the x-intercept will be: (2, 0)

The y-intercept is obtained when we set the value x=0

As the y-intercept is -5, therefore the point representing

the y-intercept will be: (0, -5)

So we get the two points

(2, 0)

(0, -5)

Finding the slope between (2, 0) and (0, -5)

$\left(x_1,\:y_1\right)=\left(2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)$

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)$

$m=(-5-0)/(0-2)$

$m=(5)/(2)$

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

Here m is the slope

substituting the values m = 5/2 and the point (2, 0)

$y-0=(5)/(2)\left(x-2\right)$

so writing the equation in slope-intercept form

As we know that the slope-intercept form is

$y=mx+b$

here

m = gradient or slop

b = y-intercept

$y=(5)/(2)\left(x-2\right)$

$y=(5)/(2)x-5$

Hence, the equation in slope-intercept form is

$y=(5)/(2)x-5$

Writing the equation in the standard form form

As we know that the equation in the standard form is

$Ax+By=C$

where x and y are variables and A, B and C are constants

As we already know the equation in slope-intercept form

$y=(5)/(2)x-5$

so the equation in the standard form will be:

$(5)/(2)x-y=5$

A set of equations is given below:Equation E: c = 2d + 1
Equation F: c = 3d + 7

Which statement describes a step that can be used to find the solution to the set of equations?

Equation F can be written as c = 3(c − 1) + 7.
Equation F can be written as c = 2(c − 7) + 1.
Equation F can be written as d + 1 = 3d + 7.
Equation F can be written as 2d + 1 = 3d + 7.

Answers

The correct answer is 'Equation F can be written as 2d + 1 = 3d + 7'. In order to find the answer to a system of equations, the two equations must be set equal to each other. For instance, if we had the equations x = y + 1 and x = 3y - 1, we would set the two equations equal to one another to find the answer.

x = y + 1
x = 3y - 1
y + 1 = 3y - 1
1 = 2y - 1
2 = 2y
1 = y

x = y + 1
x = 1 + 1
x = 2

We can use this to solve the set of equations above.

2d + 1 = 3d + 7
1 = d + 7
-6 = d

c = 2d + 1
c = 2(-6) + 1
c = -12 + 1
c = -11

Hope this helps!

Answer:

Its the last choice.

Step-by-step explanation:

I took the test

A measurement can be precise without being accurate.
a. True
b. False

Answers

The answer is B. false. Being precise in a measurement needs to be accurate and exact in details. without one factor of its doesn't prove that it would be relevant in information because the measurement is not exact and accurate

lois wants to send a box of oranges to a friend by mail. The box of oranges cannot excede a mass of 10 kg. If each orange has a mass of 200g, what is the maximum number she can send?

Answers

Answer:

Maximum number of oranges Lois can send is:

Step-by-step explanation:

Lois wants to send a box of oranges to a friend by mail.

The box of oranges cannot exceed a mass of 10 kg.

1 kg=1000 g

10 kg=10000 g

i.e. Mass of box cannot exceed 10000 g

Each orange has a mass of 200 g.

Mass of 50 oranges=50×200 g

=10000 g

Hence, maximum number of oranges Lois can send is:

easy first cover kilograms into grams 1kg=1000g. resulting in 10,000g dividing that by the weight of the oranges getting 10,000/200=50 so the answer is 50 oranges. (assuming they all weigh the same)

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