Cullumber company had $170,000 of net income in 2021 when the selling price per unit was $152, the variable costs per unit were $96, and the fixed costs were $574,800. management expects per unit data and total fixed costs to remain the same in 2022. the president of cullumber company is under pressure from stockholders to increase net income by $106,400 in 2022.
Answers
The number of units sold in 2021 = 13,300 units.
The number of units that would have to be sold in 2022 to reach the stockholder's desired profit level = 15,200 units.
Assuming that Cullumber company sells the same number of units in 2022 as it did in 2021, the selling price in order to reach the stockholder's desired profit level = $160.
The net income of a company is its profit function, derived by the formula:
Profit = Sales - Cost.
Sales are the product of the number of units sold and per unit selling price.
Cost is the sum of fixed costs and the product of the number of units produced to the variable cost per unit.
Assuming the number of units sold in 2021 to be x,
we can say sales = $152x, and
cost = ${574800 + 96x}.
Therefore, profit = sales - cost,
or, 170000 = 152x - {574800 + 96x},
or, 170000 = 56x - 574800
or, 56x = 574800 + 170000 = 744800,
or, x = 744800/56 = 13300.
Therefore, the number of units sold in 2021 was 13,300.
In 2022, the desired profit = $170,000 + $106,400 = $276,400.
Assuming the number of units sold in 2022 to be n, at the same unit data and fixed cost, we can say that:
Sales = $152n, and
Cost = ${574800 + 96n}.
Therefore, profit sales - cost,
or, 276400 = 152n - {574800 + 96n},
or, 276400 = 56n - 574800,
or, 56n = 574800 + 276400 = 851200,
or, n = 851200/56 = 15200.
Therefore, the number of units sold in 2022 should be 15,200 to reach the desired profit of the stakeholders.
When the number of units sold in 2022 is the same as in 2021, that is, the number of units = 13,300, we assume the per unit selling price to be $P.
Now we can say that,
Sales = $13300P.
Costs = ${574800 + 96*13300} = ${574800 + 1276800} = $1851600.
Therefore, profit = sales - cost,
or, 276400 = 13300P - 1851600,
or, 13300P = 1851600 + 276400 = 2128000,
or, P = 2128000/13300 = 160.
Therefore, the new selling price per unit to reach stockholders' desired profit, assuming the number of units sold in 2022 to be the same as in 2021 is $160.
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Related Questions
Question 4 (Essay Worth 10 points)
(05.06; 05.07 MC)
A prism and two nets are shown below:
Image of a right triangular prism and 2 nets. The triangle bases have base 4, height 3, and diagonal side 5. The length of the prism from the bases is 8.6. Net A has 3 rectangles in a row. The middle one has sides AC and CD. This middle one has triangle ABC on top and identical triangle below. Net B is the same except that the triangle base ABC is on top of the last rectangle which has sides AC and CD. Units are in inches.
Part A: Which is the correct net for the prism? Explain your answer. (2 points)
Part B: Write the measurements of Sides AB, BC, and CD of the correct net. (4 points)
Part C: What is the surface area of the prism? Show your work. (4 points)
Answers
Answer:
115.2 in^2
Step-by-step explanation:
total surface area Stot = 113.2 in2
lateral surface area Slat = 103.2 in2
top surface area Stop = 6 in2
bottom surface area Sbot = 6 in2
explain please thanks :)
Answers
Answer:
24
Step-by-step explanation:
The question is saying, how many three digit numbers can be made from the digits 3, 4, 6, and 7 but there can't be two of the same digit in them. For example 346 fits the requirements, but 776 doesn't, because it has two 7s.
Okay, on to the problem:
We can do one digit at a time.
First digit:
There are 4 digits that we can choose from. (3, 4, 6, and 7)
Second digit:
No matter which digit we chose for the first digit, there is only going to be 3 of them left, because we already chose one, and you can't repeat that same digit. So there are 3 options.
Third digit:
Using the same logic, there are only 2 options left.
We have 4 choices for the first digit, 3 choices for the second, and 2 for the third.
Hence, this is 4 * 3 * 2 = 24 three-digit numbers that can be made.
Which number has a repeating decimal form?
O A.
[tex] \sqrt{15} [/tex]
OB.
[tex] \frac{11}{25} [/tex]
O C.
[tex] \frac{3}{20} [/tex]
O D.
[tex] \frac{2}{6} [/tex]
Answers
Answer:
D. [tex] \frac{2}{6} [/tex]
Step-by-step explanation:
2÷ 6 = 0.33333
As you can see 3 is repeating.
Therefore [tex] \frac{2}{6} [/tex] as repeating decimal form.
please help, performance task: trigonometric identities
Answers
The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
How to solve the trigonometric equations?Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)
The equation can be split as follows:
y = 1 - cos(x)
y = 2 - 2sin²(x)
Next, we plot the graph of the above equations (see graph 1)
Under the domain interval (-π, π), the curves of the equations intersect at:
(-π/3, 0.5) and (π/3, 0.5)
Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)
The equation can be split as follows:
y = 4cos⁴(x) - 5cos²(x) + 1
y = o
Next, we plot the graph of the above equations (see graph 2)
Under the domain interval [0, 2π), the curves of the equations intersect at:
(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
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If you receive a 25% DISCOUNT off an item costing $22.00, how much money do you save?
Answers
Answer:
The amount of money you saved by receiving a discount of 25% is $5.5
Step-by-step explanation:
Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. Selling price is the actual price at which an article is sold after any reduction or discounts in the cost price.
discount is always calculated on the cost price of the article
formula to calculate the discount and discount %
Discount = List Price - Selling Price
Discount (%) = (Discount/cost price) × 100
here, in the question discount % is given = 25%
cost price of the item = $22
therefore using the above mentioned discount percentage formula:
25 = (Discount/22)×100
25/100 = Discount/ 22
0.25 × 22 = Discount
$5.5 = Discount
thus ,
the amount of many you saved by receiving a discount of 25% is $5.5
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complete the square to rewrite y=x^2+8x+3 in vertex form and then identify the minimum y-value of the function
Answers
The vertex-form of the quadratic equation is given by y = (x + 4)² - 13, and the minimum value of y is of -13.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, k is the minimum value of y, and if a < 0, it is the maximum value.
In this problem, the equation is:
y = x² + 8x + 3.
Completing the squares, the function is:
y = (x + 4)² - 13
13 is subtracted as (x + 4)² = x² + 8x + 16, hence for the equations to be equal 13 has to be subtracted. k = -13 is also the minimum value of y.
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The minimum y-value of the function for the parabolic equation is -13.
What is the vertex of a parabolic equation in quadratic form?The vertex for an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v= -\dfrac{b}{2a}}[/tex]
From the given equation:
y = x² + 8x + 3
The parameters for the parabola are:
a = 1, b = 8, c = 3
[tex]\mathbf{x_v= -\dfrac{8}{2\times 1}}[/tex]
[tex]\mathbf{x_v= -4}[/tex]
If we replace the value of [tex]\mathbf{x_v= -4}[/tex] to find the minimum value of [tex]\mathbf{y_v}[/tex] value, we have:
[tex]\mathbf{y_v = -13}[/tex]
Thus, the parabola vertex is (-4,-13). If a< 0, the vertex is a maximum value and If a>0, the vertex is a minimum value.
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A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A. 5/18
B. 4/9
C. 1/2
D. 5/9
Answers
The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.The total sample will have 9 numbers
S = { 1,2,3,4,5,6,7,8,9} = 9
Even Number = { 2,4,6,8} = 4
Odd Number = { 1,3,5,7,9} = 5
P ( A ) = ( 4 / 9 )
P ( B ) = ( 5 / 9 )
The probability will be calculated as:-
P( A:B ) = [tex]\dfrac{P(A)\times P(B)}{P(B)}[/tex]
P( A:B ) =[tex]\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }[/tex]
P( A:B ) = 4 / 9
Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).
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if 13n-6 = 98 what is the value of n
Answers
Answer:
n = 8
Step-by-step explanation:
13n-6 = 98
Solution:
13n = 98+613n = 104n = 104/13n = 8Hence the value of n is 8.
13n - 6 = 98
13n = 98 + 6
13n = 104
n = 104/13
n = 8
f(x) = 3x + 2
g(x) = x^2 + 1
find gf(x) in the form ax^2 + bx + c
please add an explanation because i’ve seen it being solved i just do not understand some steps
like, where does 12x come from
Answers
Answer:
g(f(x)) = 9x² + 12x + 5
Step-by-step explanation:
g(f(x))
= g(3x + 2) ← substitute x = 3x + 2 into g(x)
= (3x + 2)² + 1
to expand (3x + 2)² = (3x + 2)(3x + 2)
each term in the second factor is multiplied by each term in the first factor
3x(3x + 2) + 2(3x + 2) ← distribute both parenthesis
= 9x² + 6x + 6x + 4 ← collect like terms
= 9x² + 12x + 4
then
g(f(x)) = (3x + 2)² + 1 = 9x² + 12x + 4 + 1 = 9x² + 12x + 5
One lucky day, you meet a leprechaun who promises to give you fantastic wealth, but hands you only a penny before disappearing. You head home and place the
penny under your pillow. The next morning, to your surprise, you find two pennies under your pillow. The following morning, you find four pennies, and the morning after
that, eight pennies.
Suppose that you could keep making a single stack of the pennies. After how many days would the stack be long enough to reach a star that is about 3x10¹3 km
away? (Assume that 1 penny = 1.5 mm)
Answers
The number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
How to find the number of days the penny would stack?Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with
first term a = L and common ratio , r = 2.Since the number of pennies after n days equals N = 2ⁿ
Let
L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSo, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L
Number of days pennies would stack to reach starMaking n subject of the formula, we have
n = ㏒(D/L)/㏒2
Since D = the distance of the star = 3 × 10¹³ km = 3 × 10¹⁶ m, and L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSubstituting the values of the variables into the equation, we have
n = ㏒(D/L)/㏒2
n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2
n = ㏒(3/1.5 × 10¹⁹)/㏒2
n = ㏒(2 × 10¹⁹)/㏒2
n = ㏒2 + ㏒10¹⁹/㏒2
n = (19㏒10 + ㏒2)/㏒2
n = (19 + 0.3010)/0.3010
n = 19.3010/0.3010
n = 64.1
n ≅ 64 days
So, the number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
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An equilateral triangle has the height BO= 80 cm. Considering, height BO splits the base (segment) AC into two equal segments of size x/2, find X.
Answers
Answer:
Given - an equilateral triangle
An equilateral triangle means all sides equal and all angle equal to 60°
In triangle BOA
sin 60° = OB/ AB
√3/2. = 80/AB
AB = 160√3/3
X = 160√3/3
The graph of the function f(x) = (x-3)(x + 1) is shown.
-10-8-6
q
10-
Which describes all of the values for which the graph is
positive and decreasing?
all real values of x where x < -1
all real values of x where x < 1
all real values of x where 1
O all real values of x where x > 3
Answers
Answer:
x < -1
Step-by-step explanation:
Draw a parabola (the graph) passing trough two x-intercepts -1 and 3 and open up.
The table gives the average monthly precipitation, in inches, in Seattle, Washington, from January through July, where January is month 1 and July is month 7. How would you describe the relationship between the variables in the data? Select all that apply.
There is a linear association between the month and average monthly precipitation.
There is a nonlinear association between the month and average monthly precipitation.
As the number of months increases, the average monthly precipitation, in inches, increases.
As the number of months increases, the average monthly precipitation, in inches, decreases.
Answers
The relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases. Then the correct option is D.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The table gives the average monthly precipitation, in inches, in Seattle, Washington, from January through July, where January is month 1 and July is month 7.
Month 1 2 3 4 5 6 7
Average monthly precipitation 5.2 3.9 3.3 2.0 1.6 1.4 0.6
Then the relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases.
Then the correct option is D.
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Z varies directly as x and y, z=6 when x=2 and y=6 find the value of z when x=3 and y=8
Answers
Answer:
12
Step-by-step explanation:
Direct Variation. I think it's gonna be like this.
SInce Z is not inversely to y , its varies directly to both.
Then it's,
Z=kxy, where k is constant.
subst. Z=6,x=2 and y=6.
6=k×2×6
6=k×12=12k
6=12k=½
the formula connecting them is
Z=½xy
Z=½×3×8
Z= 1×3×8÷2
Z=24÷2
Z=12.
That's my solution.
(5x-1) -(2-8x) for x = 0.75
Answers
Which of the following is an example of a quadratic equation?
A. y = 216+6
B. x²-64 = 0
C. y = 4x+6
D. x+10 = 33
Answers
Answer: B
Step-by-step explanation:
A quadratic equation has degree 2.
What is the range of the given data set?
Answers
Answer:
6
Step-by-step explanation:
21 - 15 = 6
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2). How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2. The area of parallelogram 1 is equal to the area of parallelogram 2. The area of parallelogram 1 is 2 square units less than the area of parallelogram 2
Answers
The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2
How to compare the areas?The coordinates are given as:
Parallelogram 1: (0, 2), (2, 6), (6, 4), and (4, 0).
Parallelogram 2: (2, 0), (4, -6), (2, -8), and (0, -2)
Next, calculate the base and the height
For parallelogram 1, we have:
Base = (0, 2) and (2, 6)
Height = (6, 4), and (4, 0).
So, we have:
[tex]Base = \sqrt{(0 - 2)^2 + (2 -6)^2} = \sqrt{20}[/tex]
[tex]Height = \sqrt{(6 - 4)^2 + (4 -0)^2} = \sqrt{20}[/tex]
The area is:
Area = Base * Height
Area = √20 * √20
Area = 20
For parallelogram 2, we have:
Base = (0, -2) and (4, -6)
Height = (4, -6) and (2, -8)
So, we have:
[tex]Base = \sqrt{(0 -4)^2 + (-2 +6)^2} = \sqrt{32}[/tex]
[tex]Height = \sqrt{(4 - 2)^2 + (-6 +8)^2} = \sqrt{8}[/tex]
The area is:
Area = Base * Height
Area = √32 * √8
Area = 16
By comparing both areas, we have:
20 is greater than 16 by 4
This means that the area of parallelogram 1 is greater by 4 units
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PLEASE HELP ME WITH THIS
Answers
Answer:
Vertex
Vertex are the end points of parabola where it opens up
locus are the group of points
latus rectum is the line parallel to it .
What number were both the numerator and denominator multiplied by to arrive at the equivalent fraction? What number were both the numerator and denominator multiplied by to arrive at the equivalent fraction ?
Answers
Answer:
Both the numerator and denominator should be multiplied by the same number to arrive at the equivalent fraction.
Step-by-step explanation:
Equivalent fractions = two or more than two fractions are said to be equal if both results the same fraction after simplification.
For example, consider the fraction 1/3
Multiplying numerator and denominator with 2, we get 1/3 × 2/2 = 2/6
Multiplying numerator and denominator with 3, we get 1/3 × 3/3 = 3/9
Multiplying numerator and denominator with 4, we get 1/3 × 4/4 = 4/12
Therefore, we can conclude that,
1/3 = 2/6 = 3/9 = 4/12 these are equivalent fractions.
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Answer: 2 and 6/8
Step-by-step explanation:
I'm gonna need so help
Answers
Answer:
-4 and -6 are the answers
simplify the equation ( 3(3) × 3 (4) ) ÷ 3 (2)
Answers
Answer:
(3(3) × 3(4) ) ÷ 3(2)
(9 × 12) ÷ 6
108 ÷ 6
18
Step-by-Step Solution:
= (3(3) * 3(4)) / 3(2)
= (9 * 3(4)) / 3(2)
= (9 * 12) / 3(2)
= (108) / 3(2)
= 108/6
=> 18
Find the length of diagonal BC of ABCD to the nearest hundredth.
Answers
The length of BC as shown in the diagram is 6.32units
Calculating distance between two pointsThe formula for calculating the distance between two points is expressed as:
D = √(x2-x1)²+(y2-y1)²
Given the following coordinate points (3, 6) and (5, 0)
Substitute
BC = √(0-6)²+(5-3)²
BC = √(36+4)
BC = √40
BC = 6.32 units
Hence the length of BC as shown in the diagram is 6.32units
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Solve for X
picture below
Answers
Explanation u make it equivalent to 4^3x=4^4(x+1) then u solve it to 3x=4(x+1) which equals x=-4
how many spherical balls of diameter 15cm can be covered by 40 square metres of material
Answers
Answer:
It's very simple: divide the 40 m² area by area of 1 one sphere
[tex] \frac{40 \: m {}^{2} }{3.41 \times 15m {}^{2} } = 565[/tex]
The probability distribution for a
random variable x is given in the table.
-10
-5
15
20
Probability
.20
15
.05
.15
Find the probability that x ≥ 5
Answers
Answer:
Step-by-step explanation:
Comment
There is only 1 number under probability that is greater than or equal to 5. That number is 15
There are 4 possible answers. Only 1 is successful.
Answer: P(y≥5) = 1/4 or 0.25
HELP! WILL GIVE BRAINLIEST AND 100 POINTS!
A study showed that low-intensity vibration therapy reduces pain levels in patients with fibromyalgia. During each session in the study, vibration pads were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether low-intensity vibration therapy also reduces pain in patients suffering from ruptured disks in the lumbar region of the back. Three hundred male patients are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (4 points)
Part B: If the study consisted of 150 male and 150 female patients instead of 300 male patients, would you change the study design? If so, how would you modify your design ? If not, why not? (4 points)
Part C: Could your design be double-blind? Explain. (2 points)
Answers
Answer:
Part A: The appropriate design for the study includes;
Treatment used; Chamomile oil treatment
Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves
Treatment assignment; Treatment should be assigned to patients with pinched nerves
Variables that should be measured; Reduction or relief of pain as reported by the patients
Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female
Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.
Step-by-step explanation:
Please help asap
What is the domain and range of T
Answers
Answer:
Domain = {-3, -2}Range = {-4, -3, 4}Step-by-step explanation:
The domain is the set of x-values, and the range is the set of y-values.
In a market survey, 100 traders sell fruits, 40 sell apples, 46 oranges, 50 mangoes. 14 apples and oranges. 15 apples and mangoes, and 10 sell the three fruits. Each of the 100 traders sells at least one of the three fruits. Find the number that sell oranges and mangoes only.
Answers
The number of traders that sell oranges and mangoes only are 17.
How to determine the common differenceSince there are three sets, use the formula
n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)
A represents apple traders = 40
O represents orange traders = 46
M represents mangoes traders = 50
A∪O∪M = total traders = 100
A∩O = 14
O∩M = ?
A∩M = 15
A∩O∩M = 10
Substitute values into the formula
100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10
100 = 146 - 29 - O∩M
100 = 117 - O∩M
Make O∩M subject of formula
- O∩M = 100 -117
O∩M = 17 traders
Therefore, the number of traders that sell oranges and mangoes only are 17.
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One third of a number less than nine equal to seven
Answers
Step-by-step explanation:
Let the number be denoted by x.
Now, we are given a word phrase as follows one-third of a number less than nine is equal to seven.
Now this word phrase could be mathematically expressed as a equation by: one third of x is 1/3 x
And this number less than 9 is given by :
9- 1/3x
Now, this number is equal to 7.
I.e. we finally have:
9- 1/3x = 7
The person who answered is correct
