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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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Help please with this question.
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Yuliya22 [10]

Answer: 0.9104

Step-by-step explanation:

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Mean : \mu=12\text { cm}

Standard deviation : \sigma= 0.2\text{ cm}

Sample size : n=10

Since, they will declare the shipment defective and return it to the manufacturer if the average length of the 100 bolts is less than 11.97 cm or greater than 12.04 cm.

So for the shipment to be satisfactory, the length of the bolts must be between 11.97 cm and 12.04 cm.

We assume that the length of the bolts are normally distributed.

Let X be the random variable that represents the length of randomly picked bolt .

For Z score : z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

For x = 11.97

z=\dfrac{11.97-12}{\dfrac{0.2}{\sqrt{100}}}=-1.5

For x = 12.04

z=\dfrac{12.04-12}{\dfrac{0.2}{\sqrt{100}}}=2

By using the standard normal distribution table ,  the probability that the shipment is found satisfactory will be :-

P(511.97

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3 years ago
The faces of a tetrahedron die are numbered 1 to 4. If each of the 4 sides is equally likely to land down, what is the probabili
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Hello!

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Hugs!
8 0
3 years ago
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