BRAINLIEST!!! MATH HELP ME ASAP PLS!!!

BRAINLIEST!!! MATH HELP ME ASAP PLS!!!

Answers

Answer 1

Answer:

  -0.0062 and 27.5

Step-by-step explanation:

You can write the equation of the line using the 2-point form:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

The given values of the variables are ...

  (h, T) = (10000, -34.5) and (15000, -65.5)

Putting these into the formula, we have ...

  T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)

  T = -31/5000(h -10000) -34.5

  T = -0.0062h +62 -34.5

  T = -0.0062h +27.5

The appropriate choice is ...

  -0.0062 and 27.5

BRAINLIEST!!! MATH HELP ME ASAP PLS!!!

Related Questions

The perimeter of a rectangle is 61 centimeters. The length is 4.1 centimeters longer than the width, w. Which equation can be used to find the width of this rectangle?

Answers

Answer:

P=2(length+width)

the length is 4.1 cm more than the width: l=4.1+w

61=(2(4.1+w+w))

61=8.2+2w+2w

61-8.2=4w

4w=52.8

w=13.2

Answer:

14 46\14

Step-by-step explanation:

p=L+W

p=61

L=4.1

W=?

61=4.1+W

61=4.1W

61\4.1=4.1\4.1

=14 46\14

A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 96 feet per second. The quadratic function h(t)=96t−16t2 gives the height h (in feet) of the debris at time t (in seconds) after the explosion. How many seconds will it take before the debris falls back to the ground?

Answers

Answer:

6 seconds

Step-by-step explanation:

We have to find the t-intercepts of the function. To do so, let's set h(t) = 0.

0 = 96t - 16t²

0 = 16t(6 - t)  -- Factor 96t - 16t²

16t = 0 or 6 - t = 0  -- Use Zero Product Property

t = 0 or t = 6 -- Solve for t

We're not looking for the solution t = 0 because that represents when the debris was launched. Therefore, the answer is 6 seconds.

Answer: 6 seconds

Step-by-step explanation: factor

Solve x2 + 4x − 4 = 0
Answer Choices:
x = -2 ± √16 all over 2
x = -4 ± √2
x = -2 ± 2 √2
x = 4 ± √18 all over 2

Answers

Answer:

third option

Step-by-step explanation:

Given

x² + 4x - 4 = 0 ( add 4 to both sides )

x² + 4x = 4

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 4 + 4, that is

(x + 2)² = 8 ( take the square root of both sides )

x + 2 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( subtract 2 from both sides )

x = - 2 ± 2[tex]\sqrt{2}[/tex]

The answer is the third choice

The quadratic equation 4x2 + 45x + 24 = 0 was solved using the Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a. One solution is −10.69. What is the other solution? Round to the hundredths place.

Answers

Answer:

The other solution is 0.56

Step-by-step explanation:

The quadratic equation is;

4x^2 + 45x + 24

a is the coefficient of x^2 which is 4

b is the coefficient of x which is 45

c is the third number which is 24

Using the quadratic formula, we have

x = {-b ± √(b^2-4ac)}/2a

So inputing the values we have highlighted above, we have

x = {-45 ± √(45^2-4(4)(24)}/2(4)

x = {-45 ± √(2025-4(4)(24)}/2(4)

x = {-45 ± √1641}/2(4)

x = {-45 ± 40.51}/2(4)

x = (-45+40.51)/8 or (-45-40.51)/8

x = 0.56 or -10.69

Answer:

-0.56

Step-by-step explanation:

The guy above was nearly correct, not correct. He said it was positive when it is actually negative.

Hope this helps!

If sin θ=4/5 and 90°<θ<180°, what is cos θ?

Answers

Answer:

Cos ∅ = 3/5

BUT COSINE IS NEGATIVE IN THE SECOND QUADRANT.

Thus cos∅= -3/5

An umbrella has 8 ribs which are equally spaced (see fig.). Assuming umbrellato
be a flat circle of radius 45 cm, find the area between the two consecutive ribs of
the umbrella.​

Answers

Answer:

Yes.

Step-by-step explanation:

You are correct except to the nearest hundredth it is 795.54 cm^2.

greater than (−8) but less than (−2)

Answers

Answer:

-8 < x < -2

start number line at -10 and end it at 0

draw an open circle* over the dash indicating -8 and -2

connect the open circles

*open circle because it is less than and greater than, not less than or equal to and greater than or equal to

Answer:

-8<x<-2

Step-by-step explanation:

yw luv :D

Plz Help, and solve. Show your work. I will give Brainliest. A - 7 = -13 solve and show your work 10X - 8 = 9X + 8 Can a right triangle have sides that measure 12, 16, and 20? Show your work and answer.

Answers

Answer:

A - 7 = -13

Add 7

A = -6

10X - 8 = 9X + 8

Add 8

10X = 9X + 16

Subtract 9X

X = 16

In a right triangle, where a and b are the shorter sides, and c is the longer side a^2+b^2=c^2

Thus, plug in the values.

12^2+16^2=20^2

144+256=400

400=400.

Because the equation is true, 12, 16, and 20 can be a right triangle

Hope it helps <3

Answer:

For the first question/equation, A=-6. You can just add seven on both sides.

A-7+7=-13+7          A=-6

For the second question, X=16. You can minus 9x on both sides, then plus 8 on both sides. 10X-9X-8+8=9X-9X+8+8=X=16

For the last one, yes, it can because of 12^2+16^2=20^2. Which simplified is . 144+256= 400. So, yeah. It can be a right triangle.

can anyone help me please ​

Answers

Answer:

It is -1

Step-by-step explanation:

You have to use pemdas, so 5 squared is 25. Than 25 times 4 is 100. Than 2-100 is -98. Than -98/7 is -14. Than you have to add 12 and 1 so the answer is -1.

the answer of mine is also 5

Which of the following is a point-slope equation for a line with the point
(-2, 4) and a slope of 3?
O A. y-2-3(x-4)
B. y-4-3(x-2)
O C. y +2 = 3(x-4)
O D. y - 4 - 3(x+2)

Answers

Hi there! :)

Answer:

Choice D. (y - 4) = 3(x + 2)

Step-by-step explanation:

An equation in point-slope form is:

(y - y1) = m(x - x1)

Where:

y1 = y-coordinate of a point

m = slope

x1 = x-coordinate of a point

In this instance, the point given is (-2, 4) with a slope of 3. Therefore, the equation in point-slope form would be Choice D. (y - 4) = 3(x + 2)

Answer:

Step-by-step explanation:

answer is C

Because formula of equation of slop is

Y-y1=m(x-x1)

Is 3/4 = 9/12 greater or less than 1/2

Answers

Answer:

greater than

Step-by-step explanation:

To compare 3/4 to 1/2, let's convert 1/2 so that it has a denominator of 4. This would then be 2/4. Because 3 > 2, 3/4 > 2/4 which means 3/4 > 1/2.

Answer:

Greater

Step-by-step explanation:

It is greater than 1/2 because when you divide the fractions you get- 1/2 = 0.5, 3/4 = 0.75 And this makes it greater.

For which of the following compound inequalities is there no solution?

Answers

Answer:

D

Step-by-step explanation:

|6y-3|+8=35

|6y-3|=35-8

|6y-3|=27

[|x-a|=b⇒x-a=± b]

6y-3=±27

1. case 1

6y-3=27

6y=27+3

6y=30

y=30/6=5

case 2.

6y-3=-27

6y=-27+3

6y=-24

y=-24/6=-4

so D

6m≤36

m≤36/6

or m≤6

and m+24≥20

m≥20-24

m≥-4

no solution as m≤-6 and m≥-4

Identify the image of ∆XYZ for a composition of a 50° rotation and a 40° rotation, both about point Y. Plz give an explanation will give brainiest.

Answers

Answer:

Answer D

Step-by-step explanation:

Triangle XYZ  is rotated by a composition of 50°+40°=90° counter-clockwise. When a geometrical figure is rotated by any degree, then its shape or size does not change. A 90 degree rotation is a rotation by one quadrant, if you think of it on a coordinate plane. This inference should show you that choice D is the correct answer.

Kermit's favorite iced tea is made with 15 1515 tea bags in every 2 22 liters of water. Peggy made a 12 1212-liter batch of iced tea with 90 9090 tea bags. What will Kermit think of Peggy's iced tea?

Answers

Correct question is;

Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12-liter batch of iced tea with 90 tea bags. What will Kermit think of Peggy's iced tea? Choose 1 answer: (Choice A) A It is too strong.

(Choice B) B It is too weak.

(Choice C, Checked) C It is just right.

Answer:

C - It is just right

Step-by-step explanation:

We are given that;

The Number of tea bags needed to make every 2 liters of water = 15 tea bags.

Thus,

For each liter of water, the number of tea bags needed = 15/2 = 7.5 tea bags.

Now, kermit needs to make 12 liters of iced tea.

Therefore, total number of tea bags required for 12 liters of iced tea = 12 × 7.5 = 90 tea bags.

Now, Peggy also took 90 tea bags to make a 12-liter batch of iced tea.

Therefore, kermit would think that the mixture of Peggy's tea is just right.

Correct option is C

Jeffrey is 5 years older than his brother. If j represents Jeffrey's age, the expression j−5 can be used to find his brother's age. If Jeffrey is 23, how old is his brother

Answers

Answer:

18

Step-by-step explanation:

j represents Jeffrey's age

j - 5 represents brother

Jeffrey is 23 so j = 23

j-5 = 23-5 =18 = brother

Answer:

J=23

Then J-5= his brother

substitute and u will find j-5=23-5

=18 so his brother age is 18 years old

Step-by-step explanation:

Kendra rides a bicycle on a path that is 84 miles her average speed is 7 miles per hour to find about how long the trip takes solve the distance formula d = rt for t then substitute to find the time the trip takes

Answers

Answer:

Hello There!

~~~~~~~~~~~~~~~~~~

Kendra is planning to ride her bike that is 84 miles long. She plans to average 7 miles per hour. How long will the trip take?

-----

time = distance/rate

-----

t = 84 miles/7 m/hr = (84/7)hrs = 12 hrs.

Cheers,

Stan H.

------

So the answer is 12 hours.

------

Hope this helped you. Brainliest would be nice!

The two triangular prisms shown are similar. The
dimensions of the larger prism were multiplied by a
scale factor of to create the smaller prism.
When the large prism was reduced, the surface area
changed by a factor of
125
10
8
25
8
10
о
who arlin aloo
8
10
10
8​

Answers

Answer:  The surface area is reduced by a factor of 16/25

Step-by-step explanation:  The area is the square measurements. So squaring the factor of the linear measurement change is the quick way is to determine the factor for the area.

The longer way-- if you had to prove your conclusion:

Compute the area of each side, add all the five sides of the prisms and find the ratio.

The area of the large prism is 500 square units.

The area of the smaller prism is 320 square units

320/500 = 32/50,  reduce again  16/25

Answer:

B. 16/25

Step-by-step explanation:

Just took the Pre-Test on Edg (2020-2021)!

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)

Answers

Answer: I hope it helps :)

x=6 , y=6√3x =23√3 , y=23u =12 , v= 6a =18√2 , b =18x = 13 , y= 13

Step-by-step explanation:

1.

[tex]Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}[/tex]

2.

[tex]Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23[/tex]

3.

[tex]Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6[/tex]

4.

[tex]Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}[/tex]

5.

[tex]Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y[/tex]

Yo can someone please help me ​

Answers

Answer:

Addition Property of Equality

Step-by-step explanation:

When doing algebra, you need to reverse operations. When you reverse an operation, you use one of the properties. For example, if you add 3x to undo subtracting 3x, you are using the addition property of equality, because the equation still equal.

I'm always happy to help :)

If there we're 25 people in class voting,how many votes does it take to win a majority? ​

Answers

Answer:

it takes 13 votes to win a majority

Step-by-step explanation:

half+1 in the case of 25

it takes 13 votes to win a majority ( because there is nothing called half vote)

Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D'E'F’G’H’I’

Which rule represents the translation of hexagon DEFGHI to hexagon D’E’F’G’H’I’?

(x,y)—> (x-8,y-7)

(x,y) —> (x-7,x-8)

(x,y) —> ( x-4,x-5)

(x,y) —> ( x-5,y-4)

Answers

Answer:

The answer is "[tex]\bold{(x,y)\longrightarrow (x-8, y-7)}[/tex]".

Step-by-step explanation:

In the given question some data is missing. so, the correct answer to this can be explained in the following example:

In the given example, point D  is also known as the coordinates in the (2, 5), and in the coordination of the D prime (D') and after translation its co-ordinates value is (-6, -2). Since the very first choice is only accurate as:

⇒2-8 = -6

⇒ 5-7 = -2

It can try certain things too and see why this alone is the correct translation.  

The gray figure has been transformed in different ways.

Tell whether each statement is True or False.

Answers

Answer:

False ,false,true, true and true

Step-by-step explanation:

A shipping container is in the shape of a cube and has a side length of 6ft. It can hold 4 smaller boxes of flour.
If the dimensions of the shipping container are tripled, what is the max number of smaller boxes of flour that the shipping box can hold

Answers

Answer:

c. 108

Step-by-step explanation:

Given

Shape of container: Cube

Initial dimension of the container = 6ft by 6ft by 6ft

Initial Number of boxes = 4

Required

Calculate the number of boxes when the dimension is tripled

The first step is to calculate the initial volume of the box;

[tex]Volume = Length * Length * Length[/tex]

[tex]Volume = 6ft * 6ft * 6ft[/tex]

[tex]Volume = 216ft^3[/tex]

This implies that the container can contain 4 small boxes when its volume is 216;

Represent this as a ratio;

[tex]4 : 216[/tex]

The next step is to calculate the volume when the dimension is tripled;

[tex]New\ Length = Old\ Length * 3[/tex]

[tex]New\ Length = 6ft* 3[/tex]

[tex]New\ Length = 18ft[/tex]

Hence;

[tex]Volume = 18ft * 18ft * 18ft[/tex]

[tex]Volume = 5832ft^3[/tex]

Let the number of boxes it can contain be represented with x

Similarly, represent this as a ratio

[tex]x : 5832[/tex]

Equate both ratios;

[tex]4 : 216 = x : 5832[/tex]

Convert ratios to fractions

[tex]\frac{4}{216} = \frac{x}{5832}[/tex]

Multiply both sides by 5832

[tex]5832 * \frac{4}{216} = \frac{x}{5832} * 5832[/tex]

[tex]5832 * \frac{4}{216} = x[/tex]

[tex]\frac{5832 *4}{216} = x[/tex]

[tex]\frac{23328}{216} = x[/tex]

[tex]108 = x[/tex]

[tex]x = 108[/tex]

Hence, the maximum number of boxes it can contain is 108

find the value of x. 43°

Answers

Answer: x = 137°

Step-by-step explanation:

When a quadrilateral is inscribed in a circle, the opposite angles are supplementary.

x + 43° = 180°

      x   =  137°

The value of x is 137°.

What is inscribed quadrilateral?

The quadrilateral whose all 4 vertices lie on the circumference of the circle is called an inscribed quadrilateral.

In inscribed quadrilateral opposite angles are supplementary i.e. sum of those opposite angles is 180°.

Here given in the picture that the measurements of the two opposite angles in the inscribed quadrilateral in the circle are 43° and x°.

So as we know in the inscribed quadrilateral opposite angles are supplementary.

So sum of those opposite angles in the quadrilateral is 180°.

so we can write x+43°= 180°

⇒ x = 180°- 43°

⇒ x = 137°

Therefore the value of x is 137°.

Learn more about inscribed quadrilateral

here: https://brainly.com/question/26690979

#SPJ2

An employee is paid a salary of \$73,840 per year, plus benefits and overtime (time and a half) on hours worked over 40 per week, working as a civil servant. What is the regular time hourly rate of pay for this employee, and what is her total income in a month where she works 40 hours, 44 hours, 43.5 hours, and 40 hours, weekly, in the month?
A.$37.00/hr and \$6,336.25 in total income
B. $35.50/hr and \$6,079.38 in total income
C.$37.50/hr and \$6,421.88 in total income
D.$36.00/hr and \$6,165.00 in total income

Answers

Answer:

B. $35.50/hr and \$6,079.38 in total income

Step-by-step explanation:

Given the following :

Total regular pay earning for the year = $73,840

Let basic salary = b

Overtime = 1.5b

Regular earning per week :

Regular year earning / number of weeks per year

$73840 / 52 = $1420

Regular hours = 40

Regular earning per week = $1420

Regular earning per hour = $1420 / 40

Regular earning per hour = $35.50

Number of overtime hours :

4 hours + 3.5hours = 7.5hours

Overtime pay per hour = 1.5 * regular earning

Overtime pay per hour = 1.5 * 35.5 = $53.25

Total overtime pay = Overtime pay per hour * Number of overtime hours

Total overtime pay = $53.25 * 7.5

Total overtime pay = 399.375

Total pay for the month :

160 regular hours + 7.5 overtime hours

(160 * 35.5) + $399.375

$5,680 + 399.375 = $6,079.375

= $6,079.38

URGENT...Please help me with this question!!!!!!

Answers

Answer:

option 2

Step-by-step explanation:

The problem can be solved using Pythagoras' identity for a right triangle.

The angle between due East and due North is 90°

The solution here involves using the Cosine rule.

let x be the direct distance between house and office, then

x² = 17² + 21² - 2(17)(21)cos90° → option 2

Note that since cos90° = 0 the equation reduces to

x² = 17² + 21² ← Pythagoras' identity

The text classifies information systems as either operations or management support information systems. Which one of the following would not be classified as an operations support system?
A. Transaction processing systems
B. Process control systems
C. Enterprise collaboration systems
D. Decision support systems

Answers

Answer:

D. Decision support systems

Step-by-step explanation:

Operation Support System, sometimes referred to a group of computer programs that is used by the communications service provider for carrying out various operations or functions, such as monitoring, controlling, analyzing and managing a telephone or computer network.

It is often used by professionals such as Network planners, service designers, operations, architects and engineering teams in the service provider.

There are however, types of Operation Support System which are being used for different and specific purpose. They are classified into the following categories:

1. Transaction Processing Systems

2. Process control system

3. Enterprise collaboration system

4. Enterprise Resource

Hence, from the question above, the DECISION SUPPORT SYSTEM is not classified as Operation Support System.

A ball is dropped from a window 24 m high. How long will it take to reach the ground? Acceleration is 9.8 m/s^2 because of gravity. PLS SHOW WORK

Answers

Answer:

0.638 seconds

Step-by-step explanation:

Since the ball is being dropped from a height of 24 meters, the equation will look like this:

24=9.8/s^2.

This is asking for how much seconds it will take for the ball to fall 24 meters to the ground.

Solve the equation:

24(s^2)=9.8

(s^2)=0.408

s^2=0.408

root the number:

0.638

you can round it to the nearest whatever it's asking you to round it to

Im not an expert, so please excuse me if it's not done correctly

Which property was used to write the equation in step 2? Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.

Answers

Answer:

Distributive Property

Step-by-step explanation:

If we have an equation where we multiply something in parentheses by a certain term, then we can apply the distributive property to simplify it.

In this case: [tex]5(x-7)=55[/tex]

We can multiply [tex]x-7[/tex] by 5 to simplify this equation - this is the distributive property.

[tex]5x - 35 = 55[/tex]

So the property used to write the equation in Step 2 was the distributive property.

Hope this helped!

Answer:

the answer is didrtbutive

Step-by-step explanation:

hope it helps.

have a good day:)

A high school wants to sell postage stamps with the school logo on them. The fundraising group have purchased 500 sheets of stamps at $16/sheet plus $50 to create the image. They plan to sell each sheet for $20. a) Write an equation that represents the cost of obtaining the stamps. b) Write an equation that represents the income from sales. c) For each equation, set up a table of values. d) Graph each equation on the same set of coordinate axis. e) What is the minimum number of sheets the group must sell so they don't lose any money? f) How much profit will they make if they sell 500 sheets?

Answers

Answer:

a) Cost

[tex]C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050[/tex]

b) Sales income

[tex]S(q)=20q\\\\S(500)=20\cdot 500 = 10,000[/tex]

c) Table of values

[tex]\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right][/tex]

d) Attached

e) Breakeven point = 12.5 sheets

f) Profit at 550 sheets = $1,950

Step-by-step explanation:

a) We have a fixed cost for the image, at $50.

We also have a variable cost of $16 a sheet.

The purchased quantity is 500 sheets.

Then, the cost function is:

[tex]C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050[/tex]

b) The price for each sheet is $20, so the income from sales are:

[tex]S(q)=20q\\\\S(500)=20\cdot 500 = 10,000[/tex]

c) Table of values

[tex]\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right][/tex]

d) Attached

e) The minimum number of sheets the group must sell so they don't lose any money is the breakeven point (BEP) and can be calculated making the income sales equal to the cost:

[tex]S(q)=C(q)\\\\20q=50+16q\\\\(20-16)q=50\\\\4q=50\\\\q=50/4=12.5[/tex]

f) This profit can be calculated as the difference between the sales income and the cost:

[tex]P(500)=S(500)-C(500)\\\\P(500)=20\cdot 500-(50+16\cdot 500)=10,000-8,050=1,950[/tex]

The given number of 500 sheets of stamps purchased at $16/sheet with

a plan to sell each sheet for $20 gives the following values;

(a) Cost, C = 50 + 16·q

(b) Income, R = 20·q

(c) Please find the included table of values and the attached graph

(e) Approximately 403 sheets

(f) $1,950

Which method can be used to derive the equations?

(a) The cost per sheet of stamp = $16/sheet

The cost to create the image = $50

Amount at which they plan to sell each sheet, P = $20

Therefore

Cost of obtaining the stamps, C = 50 + 16·q

(b) The income from sale, R = Number of units sold × P

Which gives;

R = 20·q

(c) The table of values are therefore;

C = 50 + 16·q

[tex]\begin{array}{|c|c|c|}q&C=50+16 \times q\\0&50\\1&66\\2&82\\3&98\\4&114\\5&130\\6&146\\7&162\\8&178\\9&194\\10&210\\11&226\\12&242\\13&258\\14&274\end{array}\right][/tex]

R = 20·q

[tex]\begin{array}{|c|c|c|}q&R = 20 \times q\\0&0\\1&20\\2&40\\3&60\\4&80\\5&100\\6&120\\7&140\\8&160\\9&180\\10&200\\11&220\\12&240\\13&260\\14&280\end{array}\right][/tex]

Please find attached the required graph created with MS Excel

e) The minimum number of sheets the group must sell is given as follows;

The cost of the sheets purchased = 50 + 16 × 500

Which gives;

At point of profitability; Income = Cost

50 + 16 × 500 = 20·[tex]q_{min}[/tex]

[tex]q_{min} = \dfrac{50 + 16 \times 500}{20} =402.5 \approx \mathbf{403}[/tex]

The minimum number the sheets they must sell, [tex]q_{min}[/tex] ≈ 403 sheets

(f) The profit made by selling 500 sheets is; 20·q - (50 + 16·q)

Where;

q = 500

Which gives;

20 × 500 - (50 + 16 × 500) = 1,950

The profit made from selling 500 sheet = $1,950

Learn more about graphs of functions here:

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