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Schach [20]
2 years ago
7

Please help me with this.

Mathematics
1 answer:
OLga [1]2 years ago
8 0

Swapping rows alters the sign of the determinant:

\begin{vmatrix} x & y & z \\ -8 & 2 & -12 \\ u & v & w \end{vmatrix} = - \begin{vmatrix} x & y & z \\ u & v & w \\ -8 & 2 & -12 \end{vmatrix}

Multiplying a single row by a scalar scales the determinant by the same amount:

\begin{vmatrix} x & y & z \\ u & v & w \\ -8 & 2 & -12 \end{vmatrix} = -2 \begin{vmatrix} x & y & z \\ u & v & w \\ 4 & -1 & 6 \end{vmatrix}

Then

\begin{vmatrix} x & y & z \\ -8 & 2 & -12 \\ u & v & w \end{vmatrix} = -(-2) \begin{vmatrix} x & y & z \\ u & v & w \\ 4 & -1 & 6 \end{vmatrix} = 2\times(-6) = \boxed{-12}

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David inherited some money from his uncle. He invested half of the money with Bernie
ValentinkaMS [17]
Given:
Let x be the whole amount inherited.
1/2 * x - invested with Bernie Madoff
1/3 * x - lost due to identity theft
1/8 * x - lost in casino
40,000 - remainder

x - x/2 - x/3 - x/8 = 40,000

LCM: 
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24, 

   x * 24/24 = 24x / 24
x/2 * 12/12 = 12x / 24
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x/8 *   3/3   = 3x / 24
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24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 * x/24 = 24 * 960,000/24
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x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
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960k - 480k - 320k - 120k = 40k
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3 years ago
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scoray [572]
To solve this we can make it into an equation, which looks like this

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y = x + 10 (for Alice)

The we subtract one equation from the other to solve

0 = x - 10
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x = 10

Now we replace x in whichever equation and we get 20

So, each girl will read 20 books for them to be at the same book.

Hope this helps, remember that Jesus loves you
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oksian1 [2.3K]
According to the Central Limit Theorem, the distribution of the sample means is approximately normal, with the mean equal to the population mean (1.4 flaws per square yard) and standard deviation given by:
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