Crossfire Company segments its business into two regions—East and West. The company prepared a contribution format segmented income statement as shown below:



Total Company East West
Sales $ 1,120,000 $ 770,000 $ 350,000
Variable expenses 840,000 616,000 224,000
Contribution margin 280,000 154,000 126,000
Traceable fixed expenses 155,000 65,000 90,000
Segment margin 125,000 $ 89,000 $ 36,000
Common fixed expenses 70,000
Net operating income $ 55,000


Required:

1. Compute the companywide break-even point in dollar sales.

2. Compute the break-even point in dollar sales for the East region.

3. Compute the break-even point in dollar sales for the West region.

4. Prepare a new segmented income statement based on the break-even dollar sales that you computed in requirements 2 and 3. What is Crossfire’s net operating income (loss) in your new segmented income statement?

5. Do you think that Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region?

If a standard deviation for binomial distribution n = 48 p = 3/5 . The standard deviation is 3.39.

Using this formula to determine or find the  standard deviation for the binomial distribution

σ =√np(1−p)

Where:

n = 48

p = 3 / 5 or 0.6

σ  = ?

Let plug in the formula so as to determine the standard deviation

σ =√ (48) (0.6) ( 1 - 0.6)

σ =√ (48) (0.6)  (0.4)

σ =√ 11.52

σ = 3.39

Therefore we can conclude that  3.39 is the standard deviation.

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9 + 3x ≥ -6​

9 is adding on the left, then it will subtract on the right

3x ≥ -6​ - 9

3x ≥ -15

3 is multiplying on the left, then it will divide on the right

x ≥ -15/3

x ≥ -5

The conditional statement for "The vertices of a triangle are not collinear" is "if the points are not collinear then they are vertices of triangle."

Conditionals are commands used in programming languages to handle choices. Particularly, conditionals carry out various calculations or actions based on whether a boolean condition defined by the programmer evaluates to true or false.

The hypothesis is a prediction of what will transpire in your experiment. The words "IF" and "THEN" are frequently used when writing the hypothesis. For instance, "I will fail the test if I don't study." Your independent and dependent variables are reflected in the "if" and "then" statements.

"The vertices of a triangle are not collinear" has a conditional statement that reads, "If the points are not collinear, then they are vertices of the triangle."

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Given the rectangle ABCD, you can identify that it is divided into two Right Triangles:

• You can find the length of the rectangle by applying the following Trigonometric Function:

In this case, you can set up that:

Then, substituting values and solving for "l", you get:

• In order to find the width of the rectangle, you can use this Trigonometric Function:

In this case, you can say that:

Therefore, substituting values and solving for "w", you get:

• Now you need to use the following formula for calculating the area of a rectangle:

Where "l" is the length and "w" is the width.

Substituting the length and the width of the given rectangle into the formula and evaluating, you get:

Hence, the answer is: Option C.

Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.

There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.

We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.

Matt has the following transformational abilities:

Reflection (Flip)

A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.

Rotations as a Congruence Transformation

Rotations as a Congruence Transformation

A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. A rotation must include indicate the clockwise or counterclockwise direction. This information can be used to calculate the degree, quantity, and direction of a revolution.

Translational congruence transformation

We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.

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The derivative of y =  [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is

y' =  [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2  [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]

The derivative of a function f(x) represents its rate of change.

We have,

y = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex]

Putting log on both sides.
[ log a² = 2 log a ]

log y = 1/2 log [tex]\frac{x(x+4)}{(5x+1)(3x+7)}[/tex]

log y = 1/2 [ log x(x+4) - log (5x +1)(3x + 7) ]

log y = 1/2 [ log x(x+4) - log(5x + 1) - log (3x + 7) ]

Derivation on both sides.

[ d(logx)/dx = 1/x ]

d (log y) / dx = d [ {1/2 log x(x+4) - log(5x + 1) - log (3x + 7)} ] / dx

1/y y' = 1/2[ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]

y' = y/2 [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]

y' =  [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2  [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]

Thus,

The derivative of y =  [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is

y' =  [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2  [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]

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Answer:

Yes, it is a linear function.  For every input there is only 1 output.

Step-by-step explanation:

The after tax cost of debt for the bond is 2.73%

Given,

The face value of the bond, FV = $1000

Present value of the bond, PV = $995.28

Maturity period = 19 years

Coupon rate = 3.5%

Total tax rate = 22%

We have to find the after tax cost of debt for the bond.

The bond pays interest semiannually ;

so coupon rate = 3.5/2 = 1.75

Coupon payment , pmt= 0.0175 x 1000 = $17.5

Maturity, nper = 19 years x 2 = 38

Compute yield rate using spreadsheet = Rate(nper,pmt,-PV, FV)

Then,

= RATE(38, 17.5, -995.28, 1000)

Rate or yield is computed as 3.5%

The present value is negative as it is a cash outflow.

The cost of debt is 3.5%

The tax rate is 22%

After tax cost of debt = 3.5 (1 - 0.22)  = 2.73%

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Answer:

0.053

Step-by-step explanation:

the probability of taking a Boston creme first is 6/19 (19 is the total doughnuts in the box), then the probability of taking a chocolate glazed second would be 3/18 (bc there would be 18 left after taking one first). then multiply these fractions together. as a decimal you get 0.053 to 3 decimal places

Based on the given figure, you can conclude:

x-intercepts:

x = 0

x = number in between 100 and 125, approximately 105

x = number greater than 175, approximately 180

y-intercepts:

y = 0

For the second and third x-intercepts there is no possible to specifiy the exact numbers due to the scale units of the graph.

5 to the 6th power is:

This, written in expanded form, is:

The total cost of transporting 12 tons is $8000 and number of tons the company transporting is 23.

The total cost of transporting 12 tons can be calculated by keeping the value of number of tons in the formula.

Total cost = 6500 + 125×12

Performing multiplication on the Right Hand Side of the equation

Total cost = 6500 + 1500

Performing addition on the Right Hand Side of the equation

Total cost = 8000

The number of tons can be calculated by keeping the total cost in the formula.

9375 = 6500 + 125n

125n = 9375 - 6500

Performing subtraction on Right Hand Side of the equation

125n = 2875

n = 2875 ÷ 125

Performing division

n = 23

So, the total cost is $8000 and number of tons is 23.

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Answer:

C

Step-by-step explanation:

[tex]x^2 - 2x - 1 = 0\\x^2 = 2x + 1\\x^4 = 4x^2 + 4x + 1\\x^4 = 4(2x + 1) + 4x + 1\\x^4 = 8x + 4 + 4x + 1\\x^4 = 12x + 5[/tex]

Explanation

Step 1

eliminate the parenthesis applyng distributive property

I hope this helps you

We will have the following:

So, the simplification is equal to 1.1.

***Explanation***

First, we multiply all the values that are asked to be multiplied, and we also operate all the exponents. [We recall that a value at the power of a number is the number of times the value is multiplied by itself], then we get that:

Finally we operate the simpler and lower in the hierarchy of operations expressions:

Check the picture below.

Explanation:

If we have a function g(x) = -f(x), then g(x) will be f(x) reflected across the x-axis.

If g(x) = f(x) - c, g(x) will be f(x) shifted c units down

If g(x) = f(x + c), g(x) will be f(x) shifted c units to the left.

In this case, the initial function is f(x) = |x| and g(x) = -|x + 3| - 2, then

g(x) = -f(x + 3) - 2

Therefore, g(x) will be the initial function reflected across the x-axis, shifted 3 units to the left and 2 units down.

Answer:

So, the graph for y = -|x + 3| - 2 will be:

Answer:

48 gallons of paint are needed.

Step-by-step explanation:

Set up a proportion.

Like this: x is for the unknown number of gallons.

[tex]\frac{3}{75} = \frac{x}{1200}\\ 75(x)= 3(1200)\\ 75x=3600\\x= 3600/75\\x= 48 Answer[/tex]

Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.

The Chebyshev's Theorem calculates the minimal percentage of observations that are within a certain range of standard deviations from the mean. A wide variety of probability distributions can be used with this theorem. Another name for Chebyshev's Theorem is Chebyshev's Inequality.

Given Mean (X) = 3.86, Standard deviation (SD) = 3.36

According to Chebyshev’s Theorem,

1-1/k^2  proportion of values lies between Mean ± (k × SD )

Given k = 2.

k = x - mean /SD

1-1/k^2 =1-1/2^2

⇒1-1/4=1-0.25

⇒0.75

Therefore Proportion Value = 75%

If k= 2

75% Chebyshev’s intervals are

Lower Limit = Mean - (k × SD )

⇒3.86 - (3.36×2)

⇒3.86 - 6.72 = - 2.86

Upper Limit = Mean + (k × SD )

⇒3.86 + (3.36 × 2)

⇒3.86+6.72 = 10.58

Hence the Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.

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Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. The tax rate t that maximizes revenue for the government is 66.992%.

Revenue can be defined as the amount or the income a person or an organization generated from the sales of goods and services.

Given function :

Total sale  = S(t) = 7−6∛t

Hence,

Expression for Revenue rate = r(t) = tS(t)

Now let substitute and solve  expression

r(t) = t (7−6∛t)

= 7t−6(t)^4/3

Differentiate the expression

d[r(t)] dt = r′(t)

r′(t) = 7− (4/ 3) 6(t)^1/3

=7−8(t) ^1/3 ........ expression (1)

Maximum revenue

r′(t) = 0

Substitute and solve expression (1)

0 =7−8(t)^1/3

(t) = (7/8)^3

= 0.66992 × 100

= 66.992%

Therefore we can conclude that the tax rate t that maximizes revenue is 66.992%.

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The complete question is :

Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)

S(t)=7−6∛t

There is a 0.6915 = 69.15% probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented below:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the albumin levels are given as follows:

[tex]\mu = 35, \sigma = 5[/tex]

The probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l is one subtracted by the p-value of Z when X = 32.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (32.5 - 35)/5

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% probability.

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Answer:

1 == B No Solutions

2 == A One Solution

3 == C Infinitely Many Solutions

Explanation:

We first find go through each system and see which has one solution, no solutions, and infinitely many solutions.

1.

x

length:15 cm

width: 14 cm

Explanation

Step 1

Let

w represents the width of the rectangle

l represents the length of the rectangle

a)The width of a rectangle is 4 less than the length,hence

write this in math terms, replace

b)the area of the rectangle is 165 square cm

the area of a rectangle is given by

Step 2

now, solve the equations

a) replace the w from equation (1) into equation(2)

b) now, we have a quadratic equation in the form

hence, we can use the quadratic formula to solve

let

a=1

b=-4

c=-165

replace

therefore

as we are searchinf for a distance, the only valid answer is 15

so, the answer is length= 15 cm

c) finally, replace the l value into equation (1) to find the width

therefore, the width is 11 centimeters

I hope this helps you

The graph of function d is a reflection across the y-axis of the graph of function t.

In Geometry, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function t(x) = -4x + 72 would be transformed to function d:

d(x) = -(-4x) + 72.

d(x) = 4x + 72.

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Complete Question:

The temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x) = -4x + 72. The temperature x hours after 10 a.m. is represented by d(x) = 4x + 72. Describe the transformation from the graph of t to the graph of d.

-7a - 2y + 7 + 2y + 5a

Reordering:

(-7a + 5a) + (-2y + 2y) + 7 =

= -2a + 7 =

= 7 - 2a

In population 1:

Pattern is changing by 13.5 to 11.5 to 8.3

Which is 2 then 3.2.

In population 2:

Population is decreasing by 2.

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

Given.

Pattern in which population is changing are:

In population 1:

It is changing by 13.5 to 11.5 to 8.3

Which is 2 then 3.2.

In population 2:

Population is decreasing by 2.

Completing the table:

Population 1            Population 2

      42.8                             29

      38.6                              27

     33.4                              25

      27.2                              23

Graph is mentioned below.

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After all the transaction, money left in the bank account is $15.8872.

Given that, you open your bank account on April 16 with a tax refund check of $145.00. You pay Sell Phone $65.34 on April 18.

A tax refund is a reimbursement to a taxpayer for any excess amount paid to the federal government or a state government.

On  April 16th balance in the account = $145.00 cost of phone = $65.34 on April 18.

Balance on April 18 = 145.00-65.34

= $79.66

Deposited check $9.76 on 23rd April for 35 hours

Balance on 23rd April = 79.66+9.76

=$89.42

Since, the check deposited only for 35 hours, again balance on 24th April will be $79.66

On 24th April you brought clothes from BargainsRUs for

61.32+4% of 61.32

= 61.32+2.4528

= $63.7728

So, the remaining balance in the account = 79.66-63.7728

=$15.8872

Therefore, after all the transaction, money left in the bank account is $15.8872.

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The proof that Q R S T is a parallelogram is given and enumerated in the following paragraph.

A mathematical proof is a deductive argument for a mathematical declaration that demonstrates that the provided assumptions logically ensure the conclusion.

The proof that the above-named geometrical shape is a parallelogram goes thus:

Statements                                            Reasons

1. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex]                                 Given

2. [tex]\overline{RS}[/tex] ≅ [tex]\overline{QT}[/tex]                                 Given

3. [tex]\overline{RT}[/tex] ≅ [tex]\overline{TR}[/tex]                                 Reflexive Property

4. [tex]\Delta QRS[/tex]  ≅ [tex]\Delta STQ[/tex]                  SSS Congruence Theorem

5. A 1  ≅  A 4                   CPCTC Property

6. A 2  ≅  A3            CPCTC Property

7. QR | ST                    Alternate Interior Angles Converse

8. QT | RS                    Alternate Interior Angles Converse

9. Q R S T is a parallelogram         Definition of parallelogram      

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