Mathematics College

If fixed costs are $561,000 and the unit contribution margin is $8.00, what is the break-even point in units if variable costs are decreased by $0.50 a unit?

Answers

Answer 1

Answer:

66,000 units

Step-by-step explanation:

Break-Even Sales (units) = Fixed Costs ÷ Unit Contribution Margin = $561,000 ÷ ($8 + $0.50) = 66,000 units

Answer 2

The break-even point in units after the decrease in variable costs is 66,000 units.

Given that the fixed costs are $561,000 and the original unit contribution margin is $8.00, we first calculate the original break-even point:

[tex]\[ \text{Original Break-even point in units} = \frac{561,000}{8} \][/tex]

[tex]\[ \text{Original Break-even point in units} = 70,125 \text{ units} \][/tex]

Now, since variable costs are decreased by $0.50 a unit, the new unit contribution margin becomes:

[tex]\[ \text{New Unit Contribution Margin} = 8 + 0.50 \][/tex]

[tex]\[ \text{New Unit Contribution Margin} = 8.50 \][/tex]

Using the new unit contribution margin, we calculate the new break-even point:

[tex]\[ \text{New Break-even point in units} = \frac{561,000}{8.50} \][/tex]

[tex]\[ \text{New Break-even point in units} = 66,000 \text{ units} \][/tex]

Therefore, the new break-even point in units, after the decrease in variable costs, is 66,000 units.

Related Questions

I need to simplify this equation and don't know how, please help!
[tex] \frac{ \frac{y}{x} - \frac{x}{y}}{ \frac{1}{y}-\frac{1}{x}} [/tex]

Answers

[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{\frac{y}{x}-\frac{x}{y}}{\frac{1}{y}-\frac{1}{x}}\implies \cfrac{\textit{LCD of \underline{xy}}}{\textit{LCD of \underline{xy} also}}\implies \cfrac{\frac{y^2-x^2}{xy}}{\frac{x-y}{xy}}\implies \cfrac{y^2-x^2}{\stackrel{ }{xy}}\cdot \cfrac{\stackrel{ }{xy}}{x-y} \\\\\\ \cfrac{y^2-x^2}{x-y}\implies \cfrac{(y-x)(y+x)}{x-y}\implies \cfrac{\stackrel{ }{(y-x)}(y+x)}{-\stackrel{ }{(y-x)}}\implies \cfrac{y+x}{-1} \\\\\\ -(y+x)\implies -y-x[/tex]

True or false The coefficient of (x^(k)) (y^(n-k)) in the expansion of (x+y)^n equals (n choose k)

Answers

This is under the binomial theorem. A binomial theorem is an equation that predicts the sequence when a binomial is raised to certain power. The general form of the equation is (a+b)^n. The equation for the binomial theorem would be

nCk a^(n-k) b^k, where k is the kth term of the expanded form, n is the nth power. The coefficient of the term in the binomial expansion is nCk or n!/k!(n-k)!.

What is the diameter of a circle with a circumference of 4pi?

Answers

C = πD [C=circumference, D=diameter]

4π = πD ⇒ D = 4π/π = 4 units

What is the diameter of a circle with a circumference of 4pi? = 2x radius = 8 Inches.

A number is K units to the left of 0 on the number line. Describe the location of its opposite

Answers

------------------------(- K)-------------0-------------(+K)-----------------

K unit to the left of 0, means K is negative.
The opposite of (-K) is (+K), both are symmetric vs. the origin "0", then its location will be +K

an architectural drawing lists the scale as 1/4"=1'. if a bedroom measures 2 1/2" by 3 3/4" on the drawing, how large is the bedroom?

Answers

One way to solve this type of problem is to use proportions.

1/4" equals 1 ft
2 1/4" corresponds to how many feet? Call this "x."

Then 1
--
4 1 ft
------------------ = -----------
9
--- x
4

Solve this for x. First, reduce the first set of fractions. That boils down to (1/9).

Equate (1/9) to 1/x. It's obvious that x = 9 (feet).

Use the same method to find the length of the bedroom.

Answer:

The answer is 10 ft by 15 ft

Step-by-step explanation:

2 1/2 is also 2 2/4

Since 1/4 = 1

2/4 = 2 feet

Plus the whole number being 2 from 2 2/4 equates to 8 feet

because 2 is the same as 8/4.

2 2/4 = 10 feet

Do the same with 3 3/4 and you get 15 feet total.

Resulting in 10 ft by 15ft

at the end of the month, a medical office has 86 envelopes remaining. if the office uses 7 envelopes per day, on which day will the office likely run out of envelopes?

Answers

86/7 = 12.28 days worth

so they will run out on the 13th day of the next month

What related number sentence shows the commutative property addition 3+9=12

Answers

The related number sentence that shows the commutative property addition for the equation 3+ 9 + 12 is 9 + 3 = 12

Please take note, the commutative property of addition is
a + b = c
b + a = c
a + b = b + a

Commutative originates from the word move around or commute, therefore, commutative property refers to the act of moving stuff around. In addition, the rule is a + b = b + a; wherein from the example above, means 9 + 3 = 3 + 9. They want to say that the computation uses the Commutative Property, if at any time, a computation depends on moving stuff around

A plane travel from California and back it took one hour long on the way out than it did on the way back the planes average speed was 300 miles an hour the average speed on the way back with 350 miles an hour how many hours did the trip take

Answers

recall your d = rt, distance = rate * time

the distance the plane travelled over and back was the same distance, say "d", since it simply went over to that city and then it came back from it.

if it took say "t" hours to come back, on the way over, it took then " t + 1 ", because it took longer on the way out by 1 hour.

and we know the speed rates.... ok

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{going out}&d&300&t+1\\ \textit{coming back}&d&350&t \end{array} \\\\\\ \begin{cases} \boxed{d}=300(t+1)\\ d=350t\\ ----------\\ \boxed{300(t+1)}=350t \end{cases}[/tex]

solve for "t" to see how many hours it took on the way back.

the whole trip took then (t + 1) + t

in a right triangle, what is the product of sin b and tan c and product of sin c and tan b

Answers

check the picture below.

Using the formula in model 1, choose the correct answers for the total amount and amount of interest earned in the following compound interest problem. $500 at 4% for 5 years, compounded annually. Total Amount = $ Interest Amount =$

Answers

The formula to find the total amount is
A=p (1+r)^t
A total amount?
P present value 500
R interest rate 0.04
T time 5years
A=500×(1+0.04)^(5)=608.33

To find the interest amount just subtract the amount of the present value from the total amount
interest amount
608.33−500=108.33

Answer:

608.33

108.33

Step-by-step explanation:

Found answer in above answer.

Prove the identity

cos(-x)/[1+sin(-x)]=secx+tanx

Answers

↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓

Two kinds of thread are being compared for strength. fifty pieces of each type of thread are tested under similar conditions. brand a has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand b has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. construct a 95% confidence interval for the difference of the population means.

Answers

let x = 78.3
y = 87.2
σₓ = 5.6 and σ₍y₎ = 6.3
number of pieces n = 50
z = z-score value =1.96 in this case

A 100(1-α)% confidence interval for the difference in large sample means is:

(x – y) ± z x √( σₓ² / n+ σ₍y₎²/n)

by putting the values,
=(78.3-87.2) ± 1.96 x √(5.6² /50 + 6.3² /50)

= -8.9 ± 2.34
= [-11.24, -6.56]

Final answer:

In this case, we have two different brands of thread and we have data about their tensile strength. We calculate the standard error of the difference between their means and use that to construct a 95% confidence interval. The result suggests the average tensile strength of Brand B is significantly higher than that of Brand A.

Explanation:

To construct a 95% confidence interval for the difference of the population means between the two types of threads, we first need to calculate the standard error of the difference which is the square root of the sum of the squares of the standard deviations divided by the respective sample sizes. In this case, the sample sizes for brands A and B are both 50.

The standard error of the difference = sqrt[(5.6^2/50) + (6.3^2/50)] = approximately 1.18

Since we are trying to build a 95% confidence interval, we have to look at the z-score corresponding to this confidence level. A 95% confidence interval corresponds to 1.96 standard deviations either side of the mean, thus the z-score is 1.96.

We can then calculate the confidence interval as:
Lower limit = (78.3 - 87.2) - 1.96 x 1.18 = -11.52
Upper limit = (78.3 - 87.2) + 1.96 x 1.18 = -7.08

So the 95% confidence interval for the difference between the mean tensile strengths of the two thread types is approximately (-11.52, -7.08) kilograms.

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A pallet stacked with bags of cement weighing a total of 5501 N must be pushed up a 2.30-m incline to a 75.0-cm high platform. What force, in Newtons, must be applied to get the job done?

Answers

Assume that the incline is frictionless.
Refer to the diagram shown below.

Note that 75 cm = 0.75 m.
Therefore the angle of the incline is given by
sin(x) = 0.75/2.3 = 0.3261.

The weight pushed up the incline is W = 5501 N.
The component of the weight acting down the incline is
W*sin(x) = 5501*0.3261 = 1793.9 N

The force, F, should overcome this weight acting along the incline, therefore
F = 1794 N (nearest integer)

Answer: 1794 N

under which of the following operations are the polynomials 3x+2 and 4y-11 not closed

Answers

Lets check all the choices:

A. subtraction:

(3x+2)-(4y-11)=3x+2-4y+11=3x-4y+13

similarly, (4y-11)-(3x+2)=-3x+4y-13

both are polynomials (of 2 variables)

B. (3x+2)(4y-11)=12xy-33x+8y-22, which is a polynomial

C. (3x+2)+(4y-11)=3x+2+4y-11=3x+4y-9, which is a polynomial

D.
both [tex] \frac{3x+2}{4y-11} [/tex] and [tex] \frac{4y-1}{3x+2} [/tex] are rational expressions in 2 variables, not polynomials

Answer: D

How to simplify?
2a - 4b - 16 + (3a + 7 ) - 8

Answers

2a + 3a -4b -16+7-8 group terms
= 5a -4b -17

Rachel pays $15.20 for a pack of 8 towels. Find the unit price in dollars per towel .

Answers

15.20 / 8 = 1.90 per towel <==

Final answer:

The unit price of a towel is calculated by dividing the total cost of the pack ($15.20) by the number of towels in the pack (8), which equals $1.90 per towel.

Explanation:

In order to find the unit price in dollars per towel, we simply divide the total cost of the pack by the number of towels in the pack. So for Rachel who paid $15.20 for a pack of 8 towels, to find the cost per towel, you'd divide $15.20 by 8.

To calculate:

Divide the total cost by the number of items: $15.20 / 8

This equals $1.90. So, the cost per towel, or unit price, is $1.90.

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Translate the sentence into an equation. Nine more than the quotient of a number and 7 is equal to 3 . Use the variable y for the unknown number.

Answers

Hi!

Nine more = 9 +
Quotient of a number and 7 = y/7
Equal to three = = 3

Put it together:

9 + y/7 = 3
^ the answer

Bonus points if you can tell me what y equals ;)

Hope this helps! :)

The equation is 9+ y/7 = 3

What is equation?

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S

Given statement:

Nine more than the quotient of a number and 7 is equal to 3.

let the number be y

The 9+ y/7 = 3

quotient of a number and 7 is y/7

and, nine more than= 9+ y/7

So, 9+ y/7 = 3

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Find an implicit and an explicit solution of the given initial-value problem. (use x for x(t).) dx dt = 2(x2 + 1), x(π/4) = 1

Answers

[tex]\displaystyle \dfrac{dx}{dt}=2(x^2+1)\\\\ \int_{t_0}^t dt=\int_{x_0}^x\dfrac{dx}{2(x^2+1)}\\\\ t-t_0=\dfrac{1}{2}\int_{x_0}^x\dfrac{dx}{(x^2+1)}\\\\ t-t_0=\dfrac{1}{2}\left[\arctan(x)\right]_{x_0}^x\\\\ t-t_0=\dfrac{1}{2}\left[\arctan(x)-\arctan(x_0)\right][/tex]

We'll use [tex]x(\pi/4)=1[/tex], considering that [tex]x_0=1, t_0=\dfrac{\pi}{4}[/tex]:

[tex]t-t_0=\dfrac{1}{2}\left[\arctan(x)-\arctan(x_0)\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\left[\arctan(x)-\arctan(1)\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\left[\arctan(x)-\dfrac{\pi}{4}\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\arctan(x)-\dfrac{\pi}{8}\\\\ t-\dfrac{\pi}{8}=\dfrac{1}{2}\arctan(x)\\\\ \boxed{\arctan(x)=2t-\dfrac{\pi}{4}}[/tex]

Applying tan in the both sides:

[tex]\arctan(x)=2t-\dfrac{\pi}{4}\\\\ \tan(\arctan(x))=\tan\left(2t-\dfrac{\pi}{4}\right)\\\\ \boxed{x(t)=\tan\left(2t-\dfrac{\pi}{4}\right)}[/tex]

if I'm going to the lake that is 60 miles away and I'm driving 40 miles per hour how long would it take for me to get there

Answers

About 1.5 hours since you would do distance divided by the rate to get the time.

Ed ate 3/8 of the pizza and jen ate 1/4 of the pizza. How much of the pizza is left

Answers

one third is left, i think. Sorry, I might be off.

First of all, Ed ate 3/8 of the pizza and jen ate 1/4 of the pizza which means that they are total 3/8+1/4=3/8+2/8=5/8 of the pizzas. Also, we know the pizza has portion of 1 or 8/8 in this case, so 8/8-5/8=3/8 represent the portion of pizza is left. As a result, the pizza is 3/8 left. Hope it help!

A local grocer wants to find out whether how many mixed flower bouquets in his inventory everyday. To that end, kept records of the daily bouquet sales for the last 27 days. The average number of bouquets sold every day was 11.8 and the sample standard deviation is 2.3. Construct a 99% confidence interval for the number of bouquets sold on a given day..

Answers

Given:
n = 27, sample size
df = n-1 = 26, degrees of freedom
xb = 11.8, sample mean
s = 2.3, sample standard deviation.

Because population statistics are not known, we should use the Student's t-distribution.
At 99% confidence interval, the t-value = 2.779 (from tables).
The confidence interval is
11.8 +/- 2.779*(2.3/√(27)) = 11.8 +/- 1.23 = (10.57, 13.03)

Answer: (10.6, 13.0) to the nearest tenth

I thought of a number, doubled it, then decreased by 17. Then I divided the result by 3. I got 15. What was my number?

Answers

is your answer 31 .. i might be wrong but i tried

The number person thinking about is 14.

Given that, I thought of a number, doubled it, and then decreased it by 17. Then I divided the result by 3. I got 15.

What is the equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number be x.

Double it=2x

Decreased it by 17=2x+17

Divided the result by 3=(2x+17)/3

The result is equal to 15.

(2x+17)/3=15

⇒2x+17=45

⇒2x=28

⇒x=14

Therefore, the number person thinking about is 14.

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Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.

Answers

he delivers 224 papers every day

Answer:

Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.

Step-by-step explanation:

From 512 to 68, there are a total of 444 houses, of which 222 are pairs, which is half, if it is even with the previous two, would be 224, otherwise, 222, if one yes and the other does not, 223.

Anya graphed the line (y – 2) = 3(x – 1) on the coordinate grid. The slope of her line is .

Answers

ur equation is in this form : y - y1 = m(x - x1)....in this form , point slope form, the slope can be found in the m position.

y - 2 = 3(x - 1)
y - y1 = m(x - x1)

so u see, the slope (the number in the m position) = 3

Answer:

Step-by-step explanation:

took quiz on edge

E=mc2 is one of the most recognizable equations in the world. In this task, you’ll attempt to understand it better. Let’s start with what the letters mean. The letter E stands for energy, the letter m stands for mass, and the letter c stands for the speed of light. The meaning of this equation is that you can completely convert mass into energy. a. Rewrite the equation to solve for the speed of light, c. Use rational exponents instead of roots.

Answers

[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ E=mc^2\implies \cfrac{E}{m}=c^2\implies \sqrt{\cfrac{E}{m}}=c\implies \left( \frac{E}{m} \right)^{\frac{1}{2}}=c[/tex]

If 2(x -1) = 14, then x =

Answers

remember you can do anything to an equestion as long as you do it to both sides

2(x-1)=14
divide both sides by 2
x-1=7
add 1 to both sides
x=8

If the given equation is represented as "2(x - 1) = 14", then the value of the variable "x" is 8.

To solve the equation 2(x - 1) = 14 for x, we use algebraic techniques to separate x.

First, we distribute the 2 to both terms inside the brackets;

2x - 2 = 14,

Next, we separate the variable x by adding 2 to both sides of the equation:

2x - 2 + 2 = 14 + 2,

Simplifying the equation:

2x = 16,

At last , to solve for x, we divide both sides of the equation by 2:

We get,

(2x) / 2 = 16 / 2,

x = 8,

Therefore, the solution to the equation 2(x - 1) = 14 is x = 8.

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The equation of a given circle in general form is x2+ y2 − 8x + 12y + 27 = 0. Write the equation in standard form, (x − h)2 + (y - k)2 = r2, by completing the squares in the equation. Show your work in a table.

Answers

The equation of the circle is [tex] x^{2} + y^{2} +8x+12y+27=0[/tex]

we take x-es and y-s 'close' to each other, and complete the square:

[tex]x^{2}+8x + y^{2} +12y+27=0[/tex]

write the coefficients of the linear terms (the x and y with degree 1) as 2*'something', to see how to complete the square:

[tex]x^{2}+2*4*x + y^{2} +2*6*y+27=0[/tex]

which means that [tex]x^{2}+2*4*x[/tex] needs [tex] 4^{2} [/tex]

and [tex]y^{2} +2*6*y[/tex] needs [tex] 6^{2} [/tex] to become perfect square trinomials:

[tex](x^{2}+2*4*x + 4^{2})-4^{2} + (y^{2} +2*6*y+ 6^{2})-6^{2} +27=0[/tex]

[tex] (x+4)^{2}+ (y+6)^{2}=16+36-27 [/tex]
[tex] (x+4)^{2}+ (y+6)^{2}=25 [/tex]

[tex](x-(-4))^{2}+ (y-(-6))^{2}= 5^{2} [/tex]

Answer: [tex](x-(-4))^{2}+ (y-(-6))^{2}= 5^{2} [/tex]

Answer:

Step Reason

x2 + y2 - 8x + 12y + 27 = 0 given

x2 - 8x + y2 + 12y = -27 Isolate the constant term

x2 - 8x + 16 + y2 + 12y + 36 = -27 + 16 + 36 Complete the square by adding . 16 and 36 to both sides.

(x2 - 2∙4∙x + 42) + y2 + 12y + 36 = 25 Group and rearrange terms in x.

(x - 4)2 + y2 + 12y + 36 = 25 (a - b)2 = a2 - 2ab + b2

(x - 4)2 + (y2 + 2∙6∙y + 62) = 25 Group and rearrange terms in y.

(x - 4)2 + (y + 6)2 = 25 (a + b)2 = a2 + 2ab + b2

(x - 4)2 + (y + 6)2 = 52 Take the square root to find r = 5.

Step-by-step explanation:

this is the exact answer from plato

hope this helps a little bit :))

The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs is allowed for team who will play, which of the following function notation matches the situation?

Answers

For problems involving algebra, you have to formulate algebraic equations to be able to solve the problem. Algebraic equations are mathematical terms which include variables to denote the unknown numbers.

For this problem, you are to find the total cost which consists of cost for the gun rent and cost for the paintballs. Hence, your equationmust consist of two terms. The equation must be:

Total cost = 100x + 1000

The term x denotes the number of guns. Hence, it must be multiplied with 100 to determine the cost. On the otherhand, the constant 1000 is for the paintballs. Since it was given that each team must have 2000 paintballs, then it follows that they must pay 1000 Php.

What are the next two numbers in the pattern 3.1, 3.11, 3.11, 33.11

Answers

33.11, 311 im pretty sure this is right, if it is not can you please correct me?

What is the place value for 5 in the number 12354897

Answers

It would be in the ten thousands place.

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