<span>She has fixed costs of $250.
Her variable costs are $1,000 for the first thousand posters,
Her variable costs are $800 for the second thousand
Her variable costs are $750 for each additional thousand posters.
To calculate Average fixed cost that is AFC per poster we need two factors: Total fixed cost = 250 and Number of poster = 1000
So now AFC will be (250/1000) that is 0.25.</span>
Answer: Volkswagen Emission scandal
Explanation: The Supervisory Board should be “responsible for monitoring the Management and approving important corporate decisions , however “investors and governance experts say the emissions scandal shows that it lacks the independence and authority to do this” .
1nternal Controls
Many officials at Volkswagen were unaware of any wrongdoing, although this suggests the company can be salvaged and there are people at the top that can help turn this back around. It does also highlight the need for serious improvement in terms of the firm's internal controls. For issues on a scale as large as this, there should be a sound whistle blowing system in place to alert the correct people of such instances, so action can be taken before any issue further escalates
Answer:
C) $13,167
Explanation:
Since the sales was made FOB destination, the freight charges were included in the invoice, so the total purchase was $13,300.
Horton uses the net method of accounting for purchase discounts, so it will always record the inventory purchases with the applicable discount whether they received them or not.
$13,300 x 99% = $13,167
Since Horton was unable to pay in time, the $133 discount is recorded as a discount lost (expense account).
Answer:
The vectors does not span R3 and only span a subspace of R3 which satisfies x+13y-3z=0
Explanation:
The vectors are given as
![v_1=\left[\begin{array}{c}-4&1&3\end{array}\right] \\v_2=\left[\begin{array}{c}-5&1&6\end{array}\right] \\v_3=\left[\begin{array}{c}6&0&2\end{array}\right]](https://tex.z-dn.net/?f=v_1%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%261%263%5Cend%7Barray%7D%5Cright%5D%20%5C%5Cv_2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-5%261%266%5Cend%7Barray%7D%5Cright%5D%20%5C%5Cv_3%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%260%262%5Cend%7Barray%7D%5Cright%5D)
Now if the vectors would span the
, the rank of the consolidated matrix will be 3 if it is not 3 this indicates that the vectors does not span the
.
So the matrix is given as
![M=\left[\begin{array}{ccc}v_1&v_2&v_3\end{array}\right] \\M=\left[\begin{array}{ccc}-4&5&6\\1&1&0\\3&6&2\end{array}\right]\\](https://tex.z-dn.net/?f=M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dv_1%26v_2%26v_3%5Cend%7Barray%7D%5Cright%5D%20%5C%5CM%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C1%261%260%5C%5C3%266%262%5Cend%7Barray%7D%5Cright%5D%5C%5C)
In order to calculate the rank, the matrix is reduced to the Row Echelon form as
![\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{9}{4}&\frac{3}{2}\\ 3&6&2\end{array}\right] R_2 \rightarrow R_2+\frac{R_1}{4}](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%5C%5C%203%266%262%5Cend%7Barray%7D%5Cright%5D%20R_2%20%5Crightarrow%20R_2%2B%5Cfrac%7BR_1%7D%7B4%7D)
![\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{9}{4}&\frac{3}{2}\\ 0&\frac{39}{4}&\frac{13}{2}\end{array}\right] R_3 \rightarrow R_3+\frac{3R_1}{4}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3%2B%5Cfrac%7B3R_1%7D%7B4%7D%5C%5C)
![\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{39}{4}&\frac{13}{2\\ 0&\frac{9}{4}&\frac{3}{2}}\end{array}\right] R_2\:\leftrightarrow \:R_3](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%7D%5Cend%7Barray%7D%5Cright%5D%20R_2%5C%3A%5Cleftrightarrow%20%5C%3AR_3)
![\approx \left[\begin{array}{ccc}-4&5&6\\ 0&\frac{39}{4}&\frac{13}{2}\\ 0&0&0\end{array}\right] R_3 \rightarrow R_3-\frac{3R_2}{13}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%265%266%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%5C%5C%200%260%260%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3-%5Cfrac%7B3R_2%7D%7B13%7D%5C%5C)
As the Rank is given as number of non-zero rows in the Row echelon form which are 2 so the rank is 2.
Thus this indicates that the vectors does not span 
<em>Now for any vector the corresponding equation is formulated by using the combined matrix which is given as for any arbitrary vector and the coordinate as </em>
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Now converting the combined matrix as
![\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{9}{4}&\frac{3}{2}&|&\frac{4y+x}{4}\\ 3&6&2&|&z\end{array}\right] R_2 \rightarrow R_2+\frac{R_1}{4}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%26%7C%26%5Cfrac%7B4y%2Bx%7D%7B4%7D%5C%5C%203%266%262%26%7C%26z%5Cend%7Barray%7D%5Cright%5D%20R_2%20%5Crightarrow%20R_2%2B%5Cfrac%7BR_1%7D%7B4%7D%5C%5C)
![\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{9}{4}&\frac{3}{2}&|&\frac{4y+x}{4}\\ 0&\frac{39}{4}&\frac{13}{2}&|&\frac{4z+3x}{4}\end{array}\right] R_3 \rightarrow R_3+\frac{3R_1}{4}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%26%7C%26%5Cfrac%7B4y%2Bx%7D%7B4%7D%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%26%7C%26%5Cfrac%7B4z%2B3x%7D%7B4%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3%2B%5Cfrac%7B3R_1%7D%7B4%7D%5C%5C)
![\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{39}{4}&\frac{13}{2}&|&\frac{4z+3x}{4}\\ 0&\frac{9}{4}&\frac{3}{2}&|&\frac{4y+x}{4}\end{array}\right] R_3 \leftrightarrow R_2\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%26%7C%26%5Cfrac%7B4z%2B3x%7D%7B4%7D%5C%5C%200%26%5Cfrac%7B9%7D%7B4%7D%26%5Cfrac%7B3%7D%7B2%7D%26%7C%26%5Cfrac%7B4y%2Bx%7D%7B4%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Cleftrightarrow%20R_2%5C%5C)
![\approx \left[\begin{array}{ccccc}-4&5&6&|&x\\ 0&\frac{39}{4}&\frac{13}{2}&|&\frac{4z+3x}{4}\\ 0&0&0&|&\frac{13y+x-3z}{13}\end{array}\right] R_3 \rightarrow R_3-\frac{3R_2}{13}\\](https://tex.z-dn.net/?f=%5Capprox%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D-4%265%266%26%7C%26x%5C%5C%200%26%5Cfrac%7B39%7D%7B4%7D%26%5Cfrac%7B13%7D%7B2%7D%26%7C%26%5Cfrac%7B4z%2B3x%7D%7B4%7D%5C%5C%200%260%260%26%7C%26%5Cfrac%7B13y%2Bx-3z%7D%7B13%7D%5Cend%7Barray%7D%5Cright%5D%20R_3%20%5Crightarrow%20R_3-%5Cfrac%7B3R_2%7D%7B13%7D%5C%5C)
From this it is seen that whatever the values of the coordinates does not effect the value of the plane with equation as

So it is verified that the subspace of R3 such that it satisfies x+13y-3z=0 consists of all vectors.
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Answer:
$2,445
Explanation:.
Calculation for the approximate market value of the firm
First step is to calculate the FCFE
FCFE = 205 - 22(1 - .35) + 25
FCFE=205-22(.65) + 25
FCFE=205-14.3+ 25
FCFE = 215.70
Second Step is to calculate the Market Value
Market Value = (215.70×1.02)/(.11 - .02)
Market Value=220.014/0.09
Market Value= $2,445
Therefore the approximate market value of the firm will be $2,445