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melisa1 [442]
2 years ago
13

An article reports Sales have grown by 30% this year to $200 million, what were sales before the growth?

Mathematics
1 answer:
Varvara68 [4.7K]2 years ago
8 0

Answer:

Price before growth = $ 153.85 million

Step-by-step explanation:

Given:

Percentage = 30%

Rate after Increase =new value= $200 million

To Find:

Sales before growth =old value= ?

Solution:

We Know the formula for Percentage growth which is given by the formula

Percentage growth= \frac{Difference value}{old value}*100%

Now let old value = x

So

Difference = New Value - x

                  = 2000 - x

We have formula

Percentage growth= \frac{Difference value}{old value}*100%

Putting in values

30 %= \frac{Difference value}{old value}*100%

30 = \frac{Difference value}{old value}*100

Putting in values

30 = \frac{200-x}{x}*100

multiplying both sides by x

it becomes

30 x = (200-x)*100

Multiplying inside

30 x = 20000 - 100 x

Adding 100 x on both sides

30 x + 100 x = 20000 - 100 x + 100 x

it becomes

130 x = 20000

Dividing both sides by 130

\frac{130*x}{130}=\frac{20000}{130}

itgives us

x = $ 153.85 million

Price before growth = $ 153.85 million

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Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 10x2+4xâ1, 3xâ4x2+3, and
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I suppose

H=\mathrm{span}\{10x^2+4x-1,3x-4x^2+3,5x^2+x-1\}

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  • Independence:

Compute the Wronskian determinant:

\begin{vmatrix}10x^2+4x-1&3x-4x^2+3&5x^2+x-1\\20x+4&3-8x&10x+1\\20&-8&10\end{vmatrix}=-6\neq0

The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of H is 3.

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so the vectors do span P_2.

The vectors comprising H form a basis for it because they are linearly independent.

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Answer:

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