Units Sold to Break Even, Unit Variable Cost, Unit Manufacturing Cost, Units to Earn Target Income

Werner Company produces and sells disposable foil baking pans to retailers for $2.25 per pan. The variable cost per pan is as follows:
Direct materials $0.24
Direct labor 0.60
Variable factory overhead 0.73
Variable selling expense 0.17

Fixed manufacturing cost totals $115,117 per year. Administrative cost (all fixed) totals $15,698.

1. Compute the number of pans that must be sold for Werner to break even.
________ pans

2. Conceptual Connection: What is the unit variable cost? What is the unit variable manufacturing cost? Round your answers to the nearest cent.
Unit variable cost $ ______
Unit variable manufacturing cost $______

3. How many pans must be sold for Werner to earn operating income of $5,049?
______ pans

4. How much sales revenue must Werner have to earn operating income of $5,049?
$______

Answers

Answer 1

If Werner Company produces and sells disposable foil baking pans to retailers for $2.25 per pan, and the variable cost per pan are [Direct materials $0.24, Direct labor 0.60, Variable factory overhead 0.73, Variable selling expense 0.17] while, fixed manufacturing cost totals $115,117 per year and Administrative cost (all fixed) totals $15,698, then:

1. 256,000 Pans must be sold for Werner to break even.

2. The unit variable cost is $1.74, and the unit variable manufacturing cost is $1.57.

3. 266400 pans must be sold for Werner to earn an operating income of $5,049.

4. A sales revenue of $599,400 must Werner have to earn operating income of $5,049.

First, we have to calculate the number of pans that must be sold for Werner to break even.

Given, Fixed manufacturing costs $115,117

And, Fixed administrative costs $15698

Therefore, Total fixed costs $[tex](115,117+15,698)=130,815[/tex]

Also given, Selling price per unit $2.25

And, total Variable costs per unit $[tex](0.24+0.60+0.73+0.17)=1.74[/tex]

Contribution margin per unit = $[tex](2.25-1.74)=0.51[/tex]

[Since, contribution margin is the difference of the selling price and the variable costs]

Now, formula to calculate Break-even units goes as

(Total fixed costs / unit contribution margin).

Therefore, Break-even units in our case = [tex]\frac{130,815}{0.51}=256,000[/tex] units.

Secondly, we are required to calculate the unit variable cost and the unit variable manufacturing cost.

The unit variable cost is already calculated to be $1.74.

And, the unit variable manufacturing cost is the sum of all the variable costs excluding the variable selling expense, i.e., [tex](1.74-0.17)=1.57[/tex].

Thirdly, we will have to calculate the number of pans must be sold for Werner to earn an operating income of $5,049.

Already calculated, Total fixed costs are $130,815 and Contribution margin per unit $0.51.

Given, target operating income is $5049.

Now, formula to calculate Desired Units to earn profit goes as

(Total fixed cost + Target operating income)/(Contribution margin),

i.e., in our case, [tex]\frac{130815+5049}{0.51} = \frac{135864}{0.51}=266400[/tex] unit pans must be sold for Werner to earn an operating income of $5,049.

Lastly, We need to calculate the sales revenue must Werner have to earn operating income of $5,049.

Since, [Sales revenue = (Desired units * selling price)]

And desired units = 266400, while Selling price per unit, given as $2.25.

Therefore, Sales revenue = [tex](266,400*2.25)=599,400[/tex].

That is, a sales revenue of $599,400 must Werner have to earn operating income of $5,049.

Variable Cost: These are costs that change proportionally to the quantity of the goods or service that a business produces, changes.

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Related Questions

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]​

Answers

(A) (m,n) = g(n,m) for all positive integers m,n,

(B) (m,n + 1) = g(m + 1,n) for all positive integers m,n,

(D) (2m,2n) = (g(m,n))2 for all positive integers m,n

Explanation

[tex] \rm f(m,n,p) = \sum \limits_{i = 0}^{p} {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]

[tex]\rm {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]

[tex]\rm {}^{m} C_{i} \dfrac{(n + i)!}{p!(n - p + i)!} \times \dfrac{(n + p)!}{(p - i)!(n + i)!} [/tex]

[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]

[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]

[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!n!} \times \dfrac{n!}{(n -p + i)!(p - i)!} [/tex]

[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]

[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]

[tex] \rm f(m,n,p) = {}^{n + p} C_{p}{}^{m + n} C_{p}[/tex]

[tex] \rm \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} = {}^{m + n} C_{p}[/tex]

Now,

[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} [/tex]

[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} {}^{m + n} C_{p}[/tex]

[tex] \rm g (m,n) = {2}^{m + n} [/tex]

[tex] \rm(A) \: g(m,n) = q(n,m)[/tex]

[tex] \rm(B) \: g(m,n + 1) = {2}^{m + n + 1} [/tex]

[tex] \rm g(m + n,n ) = {2}^{m + 1 + n} [/tex]

[tex] \rm(D) \: g(2m,2n) = {2}^{2m + 2n} [/tex]

[tex] = \rm( {2}^{m + n} {)}^{2} [/tex]

[tex] = \rm(g(m,n)) {}^{2} [/tex]

Suppose the line tangent to the graph of fat x=3 is y= 4x+2 and suppose y=6x-1 is the line tangent to the graph of g at x = 3. Find the line tangent to the following curves at x = 3.
a. y = f(x)g(x)
b.y = f(x)/g(x)

Answers

The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point

a)y=24x²+8x-2 at x=3.

b) y=(4x+2)/(6x-1) at x=3.

What is tangent?

The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point

Given

f at x=3 is y= 4x+2

g at x=3 is y=6x-1

f(3)= 4x+2  and g(3)=6x-1

y=f(x)g(x)

at x=3,

Solution for a:

y=f(3)g(3)

=(4x+2)(6x-1)

=24x²-4x+12x-2

=24x²+8x-2

So y=24x²+8x-2 at x=3.

Solution for b:

y=f(3)/g(3)

=(4x+2)/(6x-1)

So y=(4x+2)/(6x-1) at x=3.

Therefore y=24x²+8x-2 at x=3 for y = f(x)g(x) and  y=(4x+2)/(6x-1) at x=3 for y = f(x)/g(x).

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Multiple Choice
11) The intersection of 2 line segments can be
I.
a point
II. a line segment
a ray
IV.
a line
III.
A. I only
C. I and IV
12) The intersection of 2 distinct rays can be
I. a point
II. a line segment
III. a ray
IV. a line
A. I only
C. I, II and III
B. I and II
D. all of the above
I. a point
III. a ray
13) The intersection of 2 distinct lines can be
II. a line segment
IV. a line
A. I only
C. I, III and IV
B. IV only
D. all of the above
B. IV only
D. all of the above

Answers

Step-by-step explanation:

[tex](3 \sqrt{3 - 2 \sqrt{2)(3 \sqrt{3 - 2 \sqrt{2)} } } } [/tex]

Question
Graph the line passing through (3, 4) whose slope is m = -1.

Answers

Answer: See attached

Step-by-step explanation:

See attached

Determine whether the relation is a function. Explain. { ( 2 , 5 ) , ( 4 , − 2 ) , ( 3 , 3 ) , ( 5 , 4 ) , ( − 2 , 5 ) } Multiple choice question. cross out A) Yes; for each element of the domain, there is only one element of the range. cross out B) Yes; for each element of the range, there is only one element of the domain. cross out C) No; the elements –2, 3, 4, and 5 are in both the domain and the range. cross out D) No; the element 5 occurs twice in the range.

Answers

Yes; for each element of the domain, there is only one element of the range.

Function and relations

For a relation in coordinate form to be a function, there is must nor be repetition in the value of its coordinate.

Given the following relation as shown  { ( 2 , 5 ) , ( 4 , − 2 ) , ( 3 , 3 ) , ( 5 , 4 ) , ( − 2 , 5 ) }, since there is no repetition in its domain values, hence the relation is a function.

We can conclude therefore that Yes; for each element of the domain, there is only one element of the range.

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Points S, T, and P lie on a number line. Their coordinates
are 0, 1, and x, respectively. Given SP = PT, what is the value of x?

Answers

The value of x associated with the point P on a number line is 0.5.

How to find the locations of a point on a number line

In accordance with the statement, the condition SP = PT means that the locations of points S, T and P on the number line are 0, 1, x, so that S < P < T and that point P is equidistant of points S and T. Then, the location of the missing point is determined by the midpoint formula:

P = 0.5 · S + 0.5 · T

P = 0.5 · 0 + 0.5 · 1

P = x = 0.5

The value of x associated with the point P on a number line is 0.5.

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A shredding machine can shred 20 sheets of paper in 14 seconds. The bin has room
for 1000 sheets of shredded paper.
How long will it take to fill the bin if the machine has to stop for 3 minutes after every
200 sheets to prevent overheating?

Answers

Answer:

See below

Step-by-step explanation:

Rate = 20 sheets  / 14 seconds =   10/7  sheet / sec

every 200 sheets is 4 rest periods =  12 minutes

1000 sheets / (10/7 sheet/ sec)  +       12 min

  700 seconds + 12 minutes

   = 700 seconds + 720 seconds = 1420 seconds = 23 min 40 sec

the ice rink sold 95 tickets for a total of 828.00. general admission tickets are $10.00 each and youth tickets are $8.00 each. how many of each did they sell

Answers

Answer:

GA =34

Y = 61

Step-by-step explanation:

GA= GENERAL ADMISSION =$10

Y= YOUTH =$8

GA+Y= 95

GA=95-Y

10GA+8Y=828

10(95-Y)+8Y=828

950-10Y+8Y=828

-2Y= 122 MULTIPLY BY (-1)

2Y= 122

Y= 61

GA= 34

There were 61 youth tickets sold and 34 general admission tickets

Electric utility poles in the form of right cylinders are made out of wood that costs $13.72 per cubic foot. Calculate the cost of a utility pole with a radius of 0.75 ft and a height of 40 ft. Round your answer to the nearest cent.

Answers

Answer:

So what you have to do is go back to you lesson and read till you find an answer just like this one and read how to do it when u do that go back and to the quick check and find an answer that is similar. the reason why I'm telling you this is cause I cant calculate it right. or what you can do is calculate it right on here.

Step-by-step explanation:

https://www.inchcalculator.com/cubic-footage-calculator/

PLEASE HELP SIMPLIFY 4(m + ( -2) + 15

Answers

Answer:

[tex] \sf \large \: 4m+52[/tex]

Step-by-step explanation:

4(m−2+15)

=(4)(m+−2+15)

=(4)(m)+(4)(−2)+(4)(15)

=4m−8+60

=4m+52

Answer:

4m+52

Step-by-step explanation:

A sequence starting with 0 but each number is two times three less than the previous number

Answers

The sequence starting with 0 but each number is two times three less than the previous number is as follows:

0, -6, -12, -18, -22

How to find sequence?

A sequence is defined as an arrangement of numbers in a particular order.

The most common sequence are the arithmetic and the geometric sequence.

The sequence starts with 0 but each number is two times three less than the previous number.

This means the first term of the sequence is 3.

Hence,

2 times 3 less than the previous number means:

Aₙ = Aₙ₋₁ - 2(3)

where,

n = number of terms

Let's use the formula to find the other numbers in the sequence,

A₂ = A₂₋₁ - 2(3) = 0 - 6 = -6

A₃ = A₃₋₁ - 2(3) = -6 - 6 = -12

A₄ = A₄₋₁ - 2(3) = -12 - 6 = - 18

A₅ = A₅₋₁ - 2(3) = -18 - 6 = - 22

Therefore, the sequence starting with 0 but each number is two times three less than the previous number is as follows:

0, -6, -12, -18, -22

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3
Un camión está cargado con 10 pies cúbicos de pajote. El chofer entrega 25
C
3
pies cúbicos de pajote en la primera parada y 3 pies cúbicos de pajote en la
segunda parada. En la tercera parada recoge 11½ pies cúbicos de pajote que no
quiere el cliente. ¿Cuánto pajote queda en el camión después de la tercera
parada?

Answers

Answer is 140

According to the question,

Given that,

111 + 10 + 25 - 2 × 3

calculate the term

121 + 25 - 6

121 + 19

140

Una solicitud de licencia de manejar comercial

(DL 44C). Al firmar este formulario significa

que usted se compromete a hacerse un análisis

químico para determinar el contenido de alcohol

o drogas en su sangre. Si se niega a firmarlo, el

Departmento de Vehículos Motorizados (DMV)

no expedirá o renovará su licencia de manejar.

• Su nombre verdadero y completo.

• Un reporte de examen médico aprobado Medical Examination Report (MER). El formulario

federal válido (orginal o copia) del reporte del

examen médico Medical Examination Report

(MER) (MCSA-5875) y el formulario del certificado del examinador médico Medical Examiner’s Certificate Form (MEC) MCSA-5876

al solicitar la licencia de manejar o el permiso;

tal reporte debe ser expedido por un doctor en

los Estados Unidos que esté licenciado en medicina (M.D.), un doctor licenciado en osteopatía

(D.O.), un médico asistente con licencia (P.A.),

un enfermero practicante avanzado y registrado

(APN) o un doctor quiropráctico autorizado. Los

conductores que tengan certificados para manejar autobuses escolares, autobuses de actividades

estudiantiles School Pupil Activity Bus Certificate (SPAB), autobuses de jóvenes, vehículos

paratránsito para el público en general General

Public Paratransit Vehicle (GPPV) o co certificados para manejar vehículos de labores agrícolas

deben tener un examen médico expedido por

un doctor en medicina, un médico asistente con

licencia, un enfermero practicante avanzado y

registrado o un quiropráctico que esté autorizado en el registro nacional de examinadores médicos certificados National Registry of Certified

Medical Examiners (§12517.2 del CVC).

Se requiere un reporte médico fechado en los 2

últimos años para cualquier tipo de solicitud de

licencia CDL y luego cada 2 años.

Nota: No envíe por correo su reporte médico

a la patrulla de caminos California Highway

Patrol (CHP). El formulario MER y el formulario

del certificado MEC pueden presentarse en una

oficina del DMV o ser enviados por correo directamente al DMV para actualizarlos. Envíe por

correo sus formularios MER y MEC a la siguientedirección por lo menos 4 semanas antes que se

venza su reporte médico anterior o su privilegio

para manejar vehículos CMV puede invalidarse.

Envíe el reporte médico a:

Department of Motor Vehicles

CDL/PDPS Unit, MS G204

PO Box 942890

Sacramento, CA 94290-0001

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What inequality represents all the values of x for y <

-5(x - 8) - 2 when y = 7?

Answers

Answer:

(−∞, 31/5) or x <31/5 (the graph will start a little bit past 6 and will be a open circle and head to the left)

Answer:

x< 6[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

7<-5(x -8) - 2  Distribute the 5

7<-5x + 40 - 2

7<-5x +38  Subtract 38 from both sides

-31<-5x  Divide both sides by -5

[tex]\frac{31}{5}[/tex] >x  When you divide both sides by a negative number, you must flip the sign.

or

x < 6 [tex]\frac{1}{5}[/tex]

Please help! Thank you

Answers

2/11 sq ft. Hope this helps
A might be the answer.

6c3c² +d³ for c = 5 and d = 3

Answers

Answer:

6(5)3(5)² + (3)³

Step-by-step explanation:

Put this into your calculator just like this

what is the sum of the number k and the number before it and the number after it?

Answers

Answer:

3k

Step-by-step explanation:

k+(k-1)+(k+1)=3k

The numbers of students in the 8 schools in a district are given below.
(Note that these are already ordered from least to greatest.)
185, 235, 255, 266, 269, 303, 370, 381
Send data to calculator
Suppose that the number 381 from this list changes to 237. Answer the following.
(a) What happens to the median?
(b) What happens to the mean?
O It decreases by 0
O It increases by 0
O It stays the same.
O It decreases by 0
O It increases by 0
O It stays the same.

Answers

Part (a)

The middle values were nitially 266 and 269, but now they are 255 and 266. Thus, the median changes from 267.5 to 260.5, meaning it decreases by 7.

Part (b)

The sum before the change is 2264, but after, it is 2120. This means the sum decreased by 144, and thus the mean decreased by 16.

Question 5 of 10
This circle is centered at the origin, and the length of its radius is 10. What is
the circle's equation?
5+ 10.
O A ²+²=10
OB. +²2=100
O c. x10+10=100
O D. x+y=10

Answers

The equation of circle is [tex]x^2+y^2=100[/tex]

The standard equation of a circle with center (h, k) and radius r is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex] ........(1)

This is the equation needed for the circle with a center at A(h, k) and a radius equal to r since it describes the relationship between the coordinates of any point on the circumference.

Now according to the question, it is given that the circle has the center at origin and length of its radius is 10.

Center = (h, k)=(0, 0)

Radius(r) = 10 units

Now, substituting the given values in (1) we get;

⇒[tex]x^2+y^2=100[/tex]

Therefore, the equation of circle centered at origin with radius 10 is [tex]x^2+y^2=100[/tex]

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solve the following: The quotient of c and −19 is 38.

Answers

Answer:

your quotient should be 57

so you would start with 38 and you gotta think hmm

C+(-19)=38

okay so you would change -19 to positive 19

and then add that to 38

and then you would get 57

so therefore C=57

so

57+(-19)=38

Answer:

57

Step-by-step explanation:

Write and solve an equation to answer the question.

How many people must attend the third show so that the average attendance per show is 3000?

Write an equation.
Write an equation
write one
Equation:_ =3000

Answers

An equation to answer the question of how many people must attend the third show to have an average attendance of 3,000 when the other show attendance numbers are 2580, and 2920 is 9,000 = 2,580 + 2,920 + x.

What is an equation?

An equation is a mathematical expression or statement that shows that two values are equal.

An equation uses the equation mark (=).

Data and Calculation:

To have an average attendance per show of 3,000 for three shows, a total of 9,000 people must attend the three shows (3,000 x 3).

Attendance for the first show = 2,580

Attendance for the second show = 2,920

Total attendance for the two shows = 5,500

Required attendance for the third show, x = 9,000 = 2,580 + 2,920 + x

x = 9,000 - 5,500

x - 3,500

Thus, the equation for the third show attendance is 9,000 = 2,580 + 2,920 + x where x = 3,500.

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Question Completion:

And the other show attendance numbers are 2580 and 2920.

Evaluate |r| when r=−29.

Answers

Answer:  29

Reason: The absolute value erases the negative sign.

Saying |-29| = 29 means that the number -29 is 29 units from 0 on the number line.

Answer: 29

Step-by-step explanation: The absolute value of -29 is 29. An absolute value is a number's distance from 0. -29 + 29 = 0, therefore the absolute value is 29.

what are all values of x such that 1-2/3x<=-3 is satisfied

Answers

The possible values of x will belong to the set A = [9, ∞).

We have the following inequality -

1 - 2x/3 ≤ -3

We have to determine all values of x.

What is Inequality ?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

According to the question, we have the following inequality -

1 - 2x/3 ≤ -3

Subtract 1 from both sides -

-2x/3 ≤ -4

Multiply by -1 on both sides -

2x/3 ≥ 4

Multiply by 3/2 on both sides -

x ≥ 9

Hence, the possible values of x will belong to the set A = [9, ∞).

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Let f(x) = x3 + 10, g(x) = x2 - 8, and h(x) = 5x + 4. Find the rule for the function.

Answers

The rule f ( x ) - g ( x ) is given as x^3 - x^2 + 18

Given data

f(x) = x3 + 10, g(x) = x2 - 8, and h(x) = 5x + 4

How to find f(x) - g(x)

f(x) - g(x) = ( x3 + 10 ) - ( x2 - 8 )

= ( x3 + 10 ) - ( x2 - 8 )

opening the parenthesis gives

= x3 + 10 - x2 + 8

collecting like terms gives

= x3 - x2 + 18

Hence we can say that f(x) - g(x) = x3 - x2 + 18

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complete question

The complete question is attached

Which number sentence is not true?
A.|-20|<20
B.|9|=9
C.|-20|>|9|
D.|9|<|20|​

Answers

Answer:

A

Step-by-step explanation:

that should be an equal sign

4m - t=m, for m
Solving for M

Answers

The solution of the given equation 4m - m - t = 0  for m is t/3.

According to the given question.

We have a linear equation in two variables i.e. 4m - t = m.

As we know that, an equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Since, we have to solve the given equation 4m - t = m for m. So, the solution of the equation 4m - t = m for m is given by

4m - t = m

⇒ 4m - m - t = 0   (subtracting m both the sides)

⇒ 3m - t = 0

⇒  3m = t   (adding t both the sides)

⇒ m = t/3.

Hence, the solution of the given equation 4m - m - t = 0  for m is t/3.

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The length of a rectangle is two more than triple the width. If the perimeter is 84 inches, find the
dimensions.
The width is
The length is
Submit Question
inches.
inches.

Answers

The length and width is 32 inches and 10 inches.

Let us assume the width of rectangle be w. So, length of rectangle = 3w + 2. As per the known fact, the length and width of rectangle for perimeter is related as - Perimeter = 2 (length + width)

Keep the values in formula to find the value of width

84 = 2 (3w + 2 + w)

Performing addition in bracket

84 = 2 (4w + 2)

Performing multiplication

84 = 8w + 4

8w = 84 - 4

Performing subtraction

8w = 80

w = 80 ÷ 8

Performing division

w = 10 inches

Finding length now -

Length = 3×10 + 2

Length = 30 + 2

Length = 32 inches

Hence, the length and width is 32 inches and 10 inches.

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Write 0.45 kg in g, mg and ng

Answers

Answer:

450g

450,000mg

450,000,000,000ng

Explaination:

Kg to g (x1,000)

Kg to mg (x1,000,000)

kg to ng (x1,000,000,000,000)

In G is
450 g
I think that in mg it’s the same

To make a sand sculpture Arthur used 2 cm³ of red sand with a density of 4 g/cm³ 7 cm³ of yellow sand with a density of 5 g centimeter and 5 cm³ of brown sand with a density of 6 g cubiccm³ what is the average density of the sculpture in grams per cubic centimeter express your answer as decimal to the nearest 10th.

Answers

Answer:

  5.2 g/cm³

Step-by-step explanation:

Given a sculpture consisting of 2 cm³ at 4 g/cm³, 7 cm³ at 5 g/cm³, and 5 cm³ at 6 g/cm³, you want its average density.

Mass

The total mass of the sculpture is the sum of the masses of the components. Each of those is the product of its volume and density.

  red sand: (2 cm³)(4 g/cm³) = 8 g

  yellow sand: (7 cm³)(5 g/cm³) = 35 g

  brown sand: (5 cm³)(6 g/cm³) = 30 g

The total mass of the sculpture is ...

  total mass = 8 g + 35 g + 30 g = 73 g

Volume

The total volume of the sculpture is the sum of the volumes of its parts:

  total volume = 2 cm³ +7 cm³ +5 cm³ = 14 cm³

Average density

The density is the ratio of mass to volume:

  ρ = (total mass)/(total volume) = (73 g)/(14 cm³) = 73/14 g/cm³

  = 5 3/14 g/cm³ ≈ 5.2 g/cm³

The average density of the sculpture is about 5.2 g/cm³.

Find the slope-intercept form of the line through (−1,3) and (7,−8)

Answers

Answer:

[tex]\sf y =\dfrac{-11}{8}x +\dfrac{13}{8}[/tex]

Step-by-step explanation:

Slope-intercept form:  y = mx + b

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

( -1, 3) ;  x₁ = -1  & y₁ = 3

(7, -8) ; x₂ = 7 & y₂ = -8

Slope can be obtained by the formula:

    [tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                [tex]\sf =\dfrac{-8-3}{7-[-1]}\\\\\\=\dfrac{-8-3}{7+1}\\\\\\=\dfrac{-11}{8}[/tex]

Now, we can find the y-intercept,

[tex]\sf y = \dfrac{-11}{8}x + b\\\\Substitute \ any \ one \ of \ the \ point \ in \ the \ above \ equation.\\\\\text{Here, we are substituting (-1 ,3)}\\\\3 = \dfrac{-11}{8}*(-1) + b\\\\3 = \dfrac{11}{8}+b\\\\b = 3 - \dfrac{11}{8}\\\\b = \dfrac{3*8}{1*8}-\dfrac{11}{8}\\\\b= \dfrac{24-11}{8}\\\\b= \dfrac{13}{8}[/tex]

Slope-intercept form:

          [tex]\sf y =\dfrac{-11}{8}x +\dfrac{13}{8}[/tex]

                   

     

What is the opposite of the number located at point d.

Answers

Answer:

-7

Step-by-step explanation:

The number located at point D is 7, And the opposite of 7 is -7.

The opposite of point d on the number line would be -7
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