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likoan [24]
2 years ago
5

If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form

: A= {A C} {B D}, find the value of a-b +c+d. 2x+8y=7 4x-2y=9 Please help, i dont know which number would be which letters
Mathematics
2 answers:
IrinaVladis [17]2 years ago
8 0

Answer: a-b+c+d =4


Step-by-step explanation:

The given system of equation is

2x+8y=7\\4x-2y=9

from this we have the following matrices

A_1 =\begin{bmatrix}\\2 &8 \\ \\4&2 \\\end{bmatrix}\ ,X=\begin{bmatrix}\\x\\ \\y\\\end{bmatrix}\text{and}\ C=\begin{bmatrix}\\7\\ \\9\\\end{bmatrix}

the given matrix A =\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}

On comparing Matrix  A_1 with Matrix A

\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}=\begin{bmatrix}\\2&8 \\ \\4 &-2 \\\end{bmatrix}

we have the following values

a=2 ,b=4,c=8,d=-2

Thus a-b+c+d =2-4+8+(-2)=4

iren [92.7K]2 years ago
7 0
Matrix A ={ 2 8}{4 -2}, so a-b+c+d = 2-4+8+(-2) = 4


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A certain kind of sheet metal has, on average, 3 defects per 18 square feet. Assuming a Poisson distribution, find the probabili
Fofino [41]

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75.8% probability that a 31 square foot metal sheet has at least 4 defects.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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In which

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e = 2.71828 is the Euler number

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In this problem, we have that:

3 defects per 18 square feet.

So for 31 square feet, we have to solve a rule of three

3 defects - 18 square feet

x defects - 31 square feet

18x = 3*31

x = \frac{31*3}{18}

x = 5.17

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Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.

Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.

So

P(X \leq 3) + P(X \geq 4) = 1

We want P(X \geq 4)

So

P(X \geq 4) = 1 - P(X \leq 3)

In which

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-5.17}*(5.17)^{0}}{(0)!} = 0.0057

P(X = 1) = \frac{e^{-5.17}*(5.17)^{1}}{(1)!} = 0.0294

P(X = 2) = \frac{e^{-5.17}*(5.17)^{2}}{(2)!} = 0.0760

P(X = 3) = \frac{e^{-5.17}*(5.17)^{3}}{(3)!} = 0.1309

So

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0057 + 0.0294 + 0.0760 + 0.1309 = 0.242

Finally

P(X \geq 4) = 1 - P(X \leq 3) = 1 - 0.242 = 0.758

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

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