Mathematics High School

Calvin works at a facility which processes apples. It costs the facility $0. 68 to make either a jar of applesauce or a bottle of apple juice. Due to the nature of the process and contractual agreements, Calvin’s facility must make and sell three jars of applesauce for every two bottles of apple juice. A jar of applesauce sells for $2. 20, and a bottle of apple juice sells for $3. 15. If the facility has annual overhead costs of $368,500, not including production costs, how many bottles of apple juice will the facility have sold when it breaks even every year? Round to the nearest whole bottle, if necessary. A. 38,789 b. 77,579 c. 116,368 d. 167,500.

Answers

Answer 1

The number of bottles the facility requires to sell when it breaks is given by

a system of two simultaneous equations.

When the facility breaks even, it would have sold 77,579 bottles of apples juice.

Reasons:

The cost to make a jar of applesauce or a bottle of apple juice = $0.68

Number of jars of applesauce to be sold foe every 2 bottles of apple juice = 3 jars

The selling price for a jar of applesauce = $2.20

Selling price for a bottle of apple juice = $3.15

Annual overhead cost excluding production cost = $368,500

Required: Number of bottles of apple juice sold by the facility when it breaks even annually.

Solution:

Let J represent the number of bottles of apple juice sold, and let S represent the number of jars of apple sauce, by excluding the production cost, we have;

(3.15 - 0.68)·J + (2.2 - 0.68)·S = 368,500

S : J = 3 : 2

Which gives;

[tex]\displaystyle \frac{S}{J} = \mathbf{ \frac{3}{2}}[/tex]

[tex]\displaystyle S= \frac{3}{2} \cdot J[/tex]

Therefore;

[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot S = (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{368,500}[/tex]

Which gives;

[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{ \frac{19 \cdot J }{4} } = 368,500[/tex]

[tex]\displaystyle J = \frac{368,500 \times 4}{19} = \frac{1474000}{19}=77578\frac{18}{19} \approx 77,579[/tex]

The number of bottles of apple juice sold, J ≈ 77,579 bottles

Learn more about simultaneous equations here:

https://brainly.com/question/10724274

Related Questions

Write the slope-intercept form of the equation of the line. ​

Answers

The slope- intercept of the line is y= x + 2. This is because for every time you go up or “rise” 1 unit you move to the right or “run” 1 unit. Therefore, 1/1 is just 1 so we can just leave this as x, however 1x would still work. Also, the line first touches the y-axis when x is 0 and y is 2. Therefore, the slope intercept is 2. So the slope intercept form of this line is still y = x + 2.

Plz HELP...(MATH)........

Answers

Answer:

36 times

Step-by-step explanation:

Because half the marbles are blue, you can predict that about half of the 72 times you will choose the blue marble, or 36 times.

I was so late when I got to this question I could of helped earlier:/

How many solutions does the system of equations below have?
4x + 10y = –7
–3x + 9y = –14
No solution
One solution
Infinitely solutions

Answers

Answer:

There is one solution to this system of equations

Step-by-step explanation:

When solving, there is a specific point of intersection which is (7/6,-7/6), making the answer one solution.

Which of the functions below could have created this graph? O A. F(x) = - x ^ 0 + x ^ 3 - x ^ 2 O B. F(x) = - x ^ 2 + 4x ^ 3 - 2x ^ 2 C. F(x) = x ^ 9 + 12x ^ 8 + x ^ 7 D. F(x) = x ^ 2 + 4x ^ 4 + 20x ^ 2

Answers

Answer:

B

Step-by-step explanation:

even roots bounce at (0,0)

negative leading coefficient: initial graph descending to right, curve up

4 local extremes means remaining 5 degree of the function

The function F(x) = - x⁷ + 4x³ - 2x² could have created the given graph. which is the correct answer would be an option (B).

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To create a graph of the function F(x) = - x⁷ + 4x³ - 2x², you can follow these steps:

Choose a range of x-values to use for the graph. For example, you might choose x = -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2.

Substitute each x-value into the function to find the corresponding y-value. For example, if x = -1, then y = F(-1) = - (-1)⁷ + 4(-1)³ - 2(-1)² = -1 + 4 + 2 = 5.

Plot the points (x, y) on a coordinate plane. For example, you would plot the point (-1, 5) on the coordinate plane.

Connect the points with a smooth curve to create the graph of the function.

Therefore, we can conclude that function F(x) = - x⁷ + 4x³ - 2x² could have created the given graph.

Learn more about the graphs here:

brainly.com/question/16608196

#SPJ2

Which values from the set negative 6, negative 4, negative 3, negative 1, zero, 2, satisfy this inequality?





Negative one half x, plus 3, is greater than or equal to 5.

Answers

Answer:

- 6

Step-by-step explanation:

- [tex]\frac{1}{2}[/tex] x + 3 ≥ 5 ( subtract 3 from both sides )

- [tex]\frac{1}{2}[/tex] x ≥ 2 ( multiply both sides by  2 to clear the fraction )

- x ≥ 4

Multiply both sides by - 1, reversing the symbol as a result of multiplying by a negative quantity.

x ≤ - 4

The only value from the set which satisfies the inequality is

x = - 6

Please help :)
M is the midpoint of segment AT.
Solve for X and AM

Answers

Because M is the midpoint of segment AT
So AM = TM
<=> 5x = 3x + 4 <=> 5x - 3x = 4
<=> 2x = 4 <=> x = 2

The answer: x = 2
Ok done. Thank to me :>

Manolo and Annalisa make handbags. Manolo made 16 handbags the first day and 12 each day after
that. Annalisa made 8 the first day and 12 each day after that.

Answers

Based on the amount being made by Manolo and Annalisa every day, the amount both made on the various days were:

Annalisa made 8 bags on Day 1Manolo had made 40 bags by Day 3

Annalisa is said to have made 8 bags on the first day so this is the number of bags that should be put in the table for having been made in the first day.

Manolo made 16 bags on the first day and then 12 bags each day after that. The total number of bags made by the third day by Manolo would be:

= 16 + 12 + 12

= 40 bags

In conclusion, Annalisa made 8 bags on Day 1 and Manolo had made 40 bags on the 3rd day.

Find out more about this at https://brainly.com/question/11864663.

if p(q) = q^2 4q- 12 then what is p(-1)

Answers

the solution:

(1): "q2" was replaced by "q^2".

Step by step solution :

STEP
1
:
Trying to factor by splitting the middle term

1.1 Factoring q2-4q-12

The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .

-12 + 1 = -11
-6 + 2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
q2 - 6q + 2q - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
2 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q+2) • (q-6)
Which is the desired factorization

Equation at the end of step
1
:

(q + 2) • (q - 6) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : q+2 = 0

Subtract 2 from both sides of the equation :
q = -2

Solving a Single Variable Equation:

2.3 Solve : q-6 = 0

Add 6 to both sides of the equation :
q = 6

Supplement : Solving Quadratic Equation Directly

Solving q2-4q-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = q2-4q-12

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Aq2+Bq+C,the q -coordinate of the vertex is given by -B/(2A) . In our case the q coordinate is 2.0000

Plugging into the parabola formula 2.0000 for q we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 12.0
or y = -16.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = q2-4q-12
Axis of Symmetry (dashed) {q}={ 2.00}
Vertex at {q,y} = { 2.00,-16.00}
q -Intercepts (Roots) :
Root 1 at {q,y} = {-2.00, 0.00}
Root 2 at {q,y} = { 6.00, 0.00}

please help me quick

Answers

Answer:

D) The answer is AB and HG

Step-by-step explanation:

sides that are equal:

AD=EH

DC=EF

BC=FG

AB=HG

Which expression can be used to find the surface area of the following triangular prism?
5
5
2.
11
8.

Answers

Answer:

214.

Step-by-step explanation:

To get Surface area take

(cross section area) × 2 +(perimeter of crossection area × length)

the cross section area is a triangle

so area of a triangle =1/2 base times height

1/2×8×2=8

let's get perimeter of cross section

the cross section is still at triangle so let's find its perimeter.

5+5+8=18

18×length of which is 11

18×11=198

and 188 + 16=214. that's the answer

maybe you can get a expression from the work that I've just done cuz I can't see the answers clearly in the picture you have taken.if you don't mind just send the picture back then I'll get the answer.

What is the solution to this quadratic equation

Answers

The answer is: B, C, and E

(0,12)
(2,0)
(6,0)

plz help with my math hw

Answers

Answer:

cant see

Step-by-step explanation:

HELP ME WITH THIS PLEASEEE !

Answers

Answer:

34 i think i got it really wrong but...

Step-by-step explanation:

Find ℎ(x) = f(x) − g(x)

Answers

I need to know what f(x) and g(x) is first

Answer:

h(x) = 7x - 3

Step-by-step explanation:

f(x) = 4x − 1 and g(x) = −3x + 2

h(x) = f(x) - g(x)

h(x) = 4x - 1 - (-3x + 2)

h(x) = 4x - 1 + 3x - 2

h(x) = 7x - 3

Help me find three different ratios that are equivalent to 3:11!! I need a explanation too!

Answers

You can do
3 * 2 and 11 * 2 which would be 6:22 and is still equal to the ratio 3:11. Your explanation can be the when divided by 2 or the number you multiplied by, you would get the original ratio
Examples:
6:22
9:33
12:44

No files or links please!

graph y= -4/3 x+2 using the slope and y-intercept


slope: 3


y-intercept: (0,-2)

Answers

this is the line as it passes through (-2) and 3

HELP!!!

42 is the product of 6 and y

Answers

Answer:

7

Step-by-step explanation:

Divide the 42 by 6 to get your answer. 42/6=7

This also works in reverse. 6*7=42

The answer: 42 is the product of 6 and y=7

Ok done. Thank to me :>

Find the distance travelled by Rubina if she takes 4 rounds of rectangular park whose length and breadth is 45m and 30m

please give me a valid answer with a step by step explanation and i will mark you as brainliest

Answers

Length (l) = 45 mBreadth (b) = 30 mWe know, perimeter of a rectangle = 2(length + breadth)Therefore, perimeter of the rectangle = 2(I + b) = 2(45 + 30) m = 2 × 75 m = 150 mSo, the distance travelled by Rubina = 4 × 150 m= 600 m

Answer:

The distance travelled by Rubina is 600 m.

Hope you could get an idea from here.

Doubt clarification - use comment section.

lesson 5 practice problems

Answers

Answer:

Step-by-step explanation:

ok ill help but can soke one help me too

If f(x) = 2x - 1 and g(x) = x^2 - 3x - 2, find (f + g)(x).​

Answers

Answer:

SEE attched pic

Step-by-step explanation:

Download symbolab

2+2=4 but you plus me = forever



i got smooth with it​

Answers

dam bro

thats pretty smooth

An equation of a line is y = 3x -7. What would the SLOPE of a line parallel to this equation be?

Answers

Answer:

3

Step-by-step explanation:

If two lines are parallel then their slope is the same

y=mx+b

m= slope

b= y-intercept

your answer would be 3 :) have a good day


Will mark brainliest

Answers

Answer:

Point  H is in the first Quadrant (5,4)

Step-by-step explanation:

Answer:

quadrant 1

Step-by-step explanation:

yw:)

Un terreno Forma rectangular mide X +4 de alto y de base X +10 indica la expresión algebraica que expresa el área del terreno

Answers

Answer:

X^2+14x +40

Step-by-step explanation:

La base es x+4 y la altura es x+10 multiplicas la base por la altura


It takes 5 minutes to fill an empty aquarium to a depth of
5/8
meters. What is the unit rate in minutes per meter?

Answers

Answer:

1/8 meters per minute

Step-by-step explanation:

5/8 ÷ 5

I hope this helps!!

solve the following methods

Answers

don't know when you find out tell me


Please helpppppppppppp

Answers

Answer:

5/4

Step-by-step explanation:

35/4 ÷ 14 = 5/4

That means 14 was multiplied by 5/4 to get 35/2

URGENT!!! THANK YOU!!!!!

Answers

Answer:

101,100

280

Here's your answer

Will give brainliest

Answers

Slope equals rise over run

The distance of the points is 4 units down and 2 units right

-4/2 = -2

Slope = -2

​George has $3 in his savings account. He then adds $4 per day to the account. Let y represent the total amount in the account after x days.

Which equation represents this situation in the form of y=mx+b ?

Question 9 options:

y = 4x + 3


y = 3x + 4


y = 3/4x - 3


y = 4/3x - 4

Answers

Answer:

The answer is the 1st option, y = 4x + 3

Step-by-step explanation:

x is the amount of days that the 4 dollars will be multiplied by

( 4 * x )

The + 3 is the money that George already had in his savings account, so that money will be added to the total amount in his savings account.

( 4x + 3 )

Lastly, the y stands for the total amount of money in his savings account so the answer is the 1st option.

y = 4x + 3

Hope this helps! :)

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