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, Calvinâ€™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:

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Answers

Because M is the midpoint of segment AT
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Answers

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

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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:

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How many solutions does the system of equations below have?
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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.

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
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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
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Step-4 : Add up the first 2 terms, pulling out like factors :
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Add up the last 2 terms, pulling out common factors :
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Step-5 : Add up the four terms of step 4 :
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Equation at the end of step
1
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(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

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2.3 Solve : q-6 = 0

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q = 6

Supplement : Solving Quadratic Equation Directly

Solving q2-4q-12 = 0 directly
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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.

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Root plot for : y = q2-4q-12
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Answers

Answer:

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

Step-by-step explanation:

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Answer:

Step-by-step explanation:

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

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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.

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You can do
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Answer:

The distance travelled by Rubina is 600 m.

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Doubt clarification - use comment section.

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