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2 years ago

I need help, fast! I'll give brainliest whoever answers

Mathematics

1 answer:

MrMuchimi2 years ago

5 0

Answer:

k = -2j+24

Step-by-step explanation:

We have 2 points on the trend line

(4,16) and (6,12)

We can find the slope

m = (y2-y1)/(x2-x1)

= (12-16)/(6-4)

= -4/2

= -2

The slope is -2

The y intercept is 24 (where it crosses the y axis)

Writing the equation in the form y= mx+b

k = -2j+24

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What’s the answer to this math question

Romashka [77]

Answer:

The answer would probably be c

Step-by-step explanation:

7 0

3 years ago

Solve the system of equations.<br> – 3y + 5x = 26<br> - 2 - 5x = -16

mylen [45]

Answer:

$y=-4,\:x=\frac{14}{5}$

Step-by-step explanation:

$\begin{bmatrix}-3y+5x=26\\ -2-5x=-16\end{bmatrix}$

Isolate x for -2-5x=-16:

$x=\frac{14}{5}$

$\mathrm{Substitute\:}x=\frac{14}{5}$

$\begin{bmatrix}-3y+5\cdot \frac{14}{5}=26\end{bmatrix}$

$Simplify$

$\begin{bmatrix}-3y+14=26\end{bmatrix}$

Isolate y for -3y+14=26:

$y=-4$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=-4,\:x=\frac{14}{5}$

7 0

2 years ago

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

Fofino [41]

Answer:

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:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

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

$18x = 3*31$

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

$x = 5.17$

So $\mu = 5.17$

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.

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

We want $P(X \geq 4)$

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

In which

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

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

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

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

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

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

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

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.

8 0

3 years ago

Use the augmented matrix to determine if the linear system is consistent. Is the linear system represented by the augmented matr

Crazy boy [7]

Answer:

The correct option is (A).

Step-by-step explanation:

If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.

$\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]$

Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:

$\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right]$

Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.

Thus, the correct option is (A).

8 0

3 years ago

The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. As a result, a rectan

Inga [223]

Answer:

The answer to your question is 10 dm

Step-by-step explanation:

Data

length of a rectangle = x + 4

height of a rectangle = x - 6

Area of the rectangle = 56 dm²

length of the square = x

Process

1.- Find x with the information given for the rectangle

Area = length x height

Substitution

56 = (x + 4)(x - 6)

Expand

56 = x² - 2x - 24

Equal to zero

x² - 2x - 24 - 56 = 0

Simplify

x² - 2x - 80 = 0

Factor

(x - 10)(x + 8) = 0

Equal to zero

x₁ -10 = 0 x₂ + 8 = 0

x₁ = 10 x₂ = -8

2.- Conclusion

The length of the square is 10 dm because there are no negative lengths.

5 0

3 years ago

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