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
if f(x)=-x+8 and f(-4), then the result is 12
True or False?
Answers
[tex] \sf \blue{True✅}[/tex]
Step-by-step explanation:Given,
[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]
Solution:
[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]
Hope it help youDrag each tile to the correct box. Not all tiles will be used.
Consider function f.
Place the steps for finding in the correct order.
Answers
If the function is f(x) = √(7x – 21). Then the inverse function of the function will be f⁻¹(x) = (1/7) x² + 3.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
f(x) = √(7x – 21)
Then the inverse function will be
x = √[7{f⁻¹(x)} – 21]
x² = 7f⁻¹(x) – 21
7f⁻¹(x) = x² + 21
f⁻¹(x) = (1/7) x² + 3
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Given the figure below solve for X
Answers
Answer:
x = 37
Step-by-step explanation:
Which function is shown in the graph below?
Answers
Answer: c
Step-by-step explanation:
It has been given that the point (3,1) is on the graph.
And in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option C
This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A B
C
D F
Frequency 5 10 15 3 2
Find the probability that a student earns a
Answers
Answer:
14.3%
Step-by-step explanation:
5 students got an A out of 35 total students. This means that the probability of students getting an A is 5/35 = 0.1428
A pound of chocolate costs 6 dollars. John buys p pounds. Write an equation to represent the total cost c that John pays.
0-0 2
Question 29
XS ?
Answers
Answer:
c=6p
Step-by-step explanation:
you multiply
6 dollars per pound by p pounds
pounds cancel out and you are left with dollars
that is the cost
You are asked to create a new computer password made up of 4 digits followed
by 3 letters.
Determine how many different computer passwords are possible if digits and
letters cannot be repeated.
Answers
Answer:if we start with 26 letters in the English/Latin alphabet: 26*25*24*23*
and modern Arabic numerals 0–9,
10*9 do the math by multiplying all
Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800. 2-digit numbers without repetitions:10*9=90. Number of passwords with 4 letters and 2-digit number without repetitions:
a) if the 2-digit numbers must be in one single position (examples:….XB73DY……..GZ57FE): 358800*90 = 32,292,000.
b) if the 2-digit numbers can be in each of the 5 possible positions (ex.:…73XBDY…X73BDY..XB73DY..XBD73Y..XBDY73…) 5*358800*90=161,460,000.
c) if both digits can be in (C6;2) = 6*5/2= 15 positions (ex.: 7XB3DY…X73BDY…..) 15*358800*90=484,380,000.26*25*24*23*10*9 = 32,292,000
Step-by-step explanation:
Table I contains outputs of the function f(x)=b^xf(x)=b
x
I need help
Answers
Answer: Table 1: Answer = 1. 404
Table 3 Answer = 1.66
Step-by-step explanation: i hope it's right if not, tell me
Answer the following questions
A. 10 -4 ×5=?
B. 3+8×4=?
C. (3+8)×4=?
Answers
Answer:
A=30
B=35
C=44
Step-by-step explanation:
A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?
Answers
Answer:8.8 pounds a day
Step-by-step explanation:
7 days in a week
28/7=4 kg a day
2.2*4=8.8
8.8 pounds
A gym has 65 members. If 35 are men and the
rest are women, what is the ratio of the female
members to the total members of the gym?
Answers
Answer:
Step-by-step explanation:
số nữ là 65- 35= 30
vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13
Which of the following values can be found by using the formula √1+tan^2 0?
Answers
cos and sec can be found
The requried simplified expression is 1 / cosØ, which is equivalent to secØ. The correct option is secØ.
Let's simplify the given expression and see which of the provided options match:
We are given the expression √(1 + tan²Ø).
Now, recall the trigonometric identity: tan²Ø = sin²Ø / cos²Ø.
Substitute this identity into the expression:
√(1 + sin²Ø / cos²Ø)
Next, find a common denominator for the fraction inside the square root:
√((cos²Ø + sin²Ø) / cos²Ø)
Since cos²Ø + sin²Ø = 1 (as per the Pythagorean trigonometric identity), the expression becomes:
√(1 / cos²Ø)
Now, we can take the square root of 1 and cos²Ø separately:
√1 / √cos²Ø
Simplify:
1 / cosØ
The simplified expression is 1 / cosØ, which is equivalent to secØ.
Therefore, the correct option is: secØ.
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The price of a coat is $65. In sale, the price is reduced by 15%. What is the price of the coat in sale?
Answers
Step-by-Step Explanation:
Price of the Coat = $65
Step 1 :- Find 15% of $65.
= 15/100 * 65
= 975/100
=> 9.75
15% of $65 = $9.75
Step. 2 :- Subtract $9.75 from $65.
= 65 - 9.75
=> 55.25
Price of the Coat in Sale = $55.25
I need help answering these questions for geometry :)
1. What happens to the measure of the interior angles as the number of sides of the polygon increases? Explain your answer.
2.What happens to the measure of the exterior angles as the number of sides of the polygon increases? Explain your answer.
4. Explain what happens to the total sum of interior angles as the number of sides in the polygon changes.
5. Explain what happens to the total sum of exterior angles as the number of sides in the polygon changes.
Answers
The answers to the question have been written below
The changes to a polygon1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.
2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0
Hence the value of the exterior would move towards 0 as its sides increases.
4. As the total sum of the of the polygon changes, it would tend towards infinity.
5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.
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What is the solution for x in the equation?
5
3x + 4 =
2
OA. * = -4
OB. * = 4
12
O C.
OD.
X
x =
-1/7/20
Answers
Equations are separated by an equal sign. The value of x is given as -6/5
Equations and valuesGiven the equations below;
5(3x + 4) = 2
Expand
5(3x) + 5(4) = 2
15x +20 = 2
Subtract 2 from both sides
15x = 2 - 20
15x = -18
x = -18/15
x = -6/5
Hence the value of x is given as -6/5
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What remainder is represented by the synthetic division below?
A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0.
Answers
The remainder represented by synthetic division is -5.
What is synthetic division?
Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.
Given
A vertical line and a horizontal line combine to make an L shape.
There are two rows of entries within the shape.
Row 1 has entries 2, 10, 1, 5.
Row 2 has entries blank, -10, 0, -5.
Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;
x + 5 = 0
x = -5
Hence, the divisor of the synthetic division is -5.
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Answer:
its a) -5
Step-by-step explanation:
When given
Slope= -6/5
Y-intercept= 2
What is this in Point-Slope form?
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]
Find: [tex]\textsf{The equation in point-slope form}[/tex]
Solution: We need to take the values that were given to us and plug them into the point-slope form. It doesn't seem like the problem is asking for anything more than that so we will leave it at that.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).
Answer:
[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
Step-by-step explanation:
[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]
We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).
Then, we substitute these values into the Point-Slope Form to find the equation.
Here are both forms for future reference:
⇒ Slope-Intercept Form: y = mx + b
[ Where: m is the slope, and b is the y-intercept (when x = 0). ]
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
[ Where: m is the slope, and (x₁, y₁) is a given point. ]
Substitute the values into the Point-Slope Form:
[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
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Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
Answers
The steps of student B are in the correct order but the steps of student A are in the incorrect order.
What is a perpendicular and parallel line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines and the lines that never intersect are known as parallel lines.
We have:
You are given AB and point C. Construct a line parallel to AB that passes through point C
The correct way to draw a parallel line to AB that passes through point C is:
1. Draw a line that intersects points B and C.2. Place the compass on point B, and swing an arc that crosses line AB and line BC. Label the points D and E.3. Keep the compass at the same width, and place it on point C.4. Swing an arc that crosses line BC, and label the point F.5. Open the compass to the width between points D and E.6. Keeping the compass at the same width, place it on point F.7. Swing an arc that intersects the arc created from line BC at point C.8. Mark the intersection of the two arcs as point G.9. Draw a line through point C and point G.The steps of student B are in the correct order but the steps of student A are in the incorrect order.
Thus, the steps of student B are in the correct order but the steps of student A are in the incorrect order.
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12. For which of the following quadratic equations are the roots 2 and 57
O A. x²-3x - 10=0
B. x² - 11x 10 = 0
c. x² - 7x + 10 = 0
D. x² + 7x-10=0
O
O
O
Answers
Answer: x²-59x+114=0
explanation:
If the roots are 2 and 57, then:-
sum of roots = 2+57 = 59
and, product of roots = 2×57 = 114
the quadratic equation is given by,
x²-(sum of roots)x+(product of roots)=0
so, x²-59x+114=0 will be the desired quadratic equation.
so, none of the options are correct.
the correct answer is x²-59x+114=0.
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What is 2*4*6.5*24.5
Answers
Answer:
1274
it is 1274
Step-by-step explanation:
mark as brainlest for the answer thankyou
I need help with this: -1/4 x (-7/9)
Answers
Multiply -1/4 by -7/9 ((To do this, multiply the numerator by the numerator and the denominator by the denominator.)
[tex]\bf{\dfrac{-1(-7)}{4\times9)} \ \ \to \ \ \ Multiply }[/tex]
Do the multiplications in the fraction -1(-7) / 4 x 9.
[tex]\bf{\dfrac{7}{36} \ \ \Rightarrow \ \ \ Answer }[/tex]
{ Pisces04 }What function is shown in the graph above?
Answers
By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.
What kind of function represents the graph?
Graphically speaking, linear functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). Linear functions are characterized by slope and intercept:
y = m · x + b (1)
Slope
m = (7 - 0)/[9 - (- 6)]
m = 7/15
Intercept
b = 4
By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.
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What is the y-intercept of the function f(x) = 2.3*?
A. (0,6)
B. (2,0)
C. (0,2)
OD. (0,3)
Answers
What is the solution to this system of equations? x + y = 2 and y - z = -3 and x + y - z = 0
Answers
Answer:
x = 3
y = -1
z = 2
Step-by-step explanation:
if x+y = 2, and x+y-z = 0, then we can substitute 2 for x+y. this means 2-z=0, meaning z=2. if y-z=-3, then y-2=-3, and y=-1. x+y=2 which means x-1=2 so x=3. plug in the values to check your answer.
A cyclist is stationary when a second cyclist passes travelling at a constant speed of 8 m s−1. The first cyclist then accelerates for 5 s at a constant rate of 2 m s−1 before continuing at constant speed until overtaking the second cyclist. By sketching both graphs, find the equations of the two straight line sections of the graphs and hence find how long it is before the first cyclist overtakes the second.
Answers
Answer:
im not too sure about that sorry!
Step-by-step explanation:
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It takes 15 seconds for the first cyclist to overtake the second cyclist.
How can you find how long it took before the first cyclist overtakes the second?First, identify the two phases of the first cyclist's motion.
Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.
Phase 2: The cyclist travels at a constant speed of 8 m/s.
Find the equations of the two straight-line sections of the graph.
The equations of the two straight-line sections of the graph are as follows:
Phase 1:
s = [tex]2t^2[/tex]
Phase 2:
s = 8t
where s is the distance traveled by the cyclist and t is the time
Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist
The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.
Let t be the time it takes the first cyclist to overtake the second cyclist.
The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).
Setting these two expressions equal to each other, we get:
8t = 8(t - 5)
Solving for t, we get:
t = 15
Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist
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What are the more appropriate measures of center and spread for this data
set?
35 40 45
55
90
hi
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
select two choices: one for the center and one for the spread.
a. better measure of spread: the standard deviation
select two choices: one for the center and one for the spread
Answers
The more appropriate measure of center is mean.
The more appropriate measure of spread is standard deviation.
What is mean and standard deviation?Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.
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Which is the best estimate to the nearest one percent of startfraction 7 over 15 endfraction?
Answers
The best estimate to the nearest one percent of the fraction; 7/15 is; 47%.
What is the best estimate of the fraction to the nearest percent?From the task content, it follows that the fraction given whose estimate is to be determined is; 7/15.
The fraction expressed as a percentage is;
(7/15) × 100 %
= 46.667%.
Hence, when rounded to the nearest one percent; = 47%.
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A, B, C, D got stuck with this problem
Answers
9x-7=-52
Show all work and justify each step
Answers
Answer:
x = -5
Step-by-step explanation:
9x - 7 = -52
we want to single out x,
add 7 to both sides to be one step closer to getting x alone
9x - 7 + 7 = -52 + 7
9x = -45
divided both sides by 9 to get x alone
9x / 9 = -45 / 9
x = -5
Let me know if you need any clarification!
[tex] 9x - 7 = - 52[/tex]
Firstly rearrange the variable on the left side of the equation...
[tex]9x = - 52 + 7[/tex]
Calculate the sum or differences
[tex]9x = - 45[/tex]
[tex]x = - \frac{45}{9} \\ [/tex]
[tex]x = - 5[/tex]
:)
..
sara scores -4 marks if she got 3 correct answers how many were incorrect
Answers
The number of answers that were incorrect will be 7.
How to depict the information?From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:
3 - x = -4
where x = incorrect answer
3 - x = -4
-x - 4 - 3
-x = -7
x = 7
In conclusion, the number of answers that were incorrect will be 7.
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