Probability Math Question

For the system of equations that follows, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in

Rainbow [258]

Answer:

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Step-by-step explanation:

From the question we are told that

System of equations given as

x₁ + 3x₂ + x₃ + x₄ = 3;

2x₁ - 2x₂ + x₃ + 2x₄ = 8;

x₁ - 5x₂ + x₄ = 5

Matrix form

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$ $\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}$

Generally the echelon reduction is mathematically applied as

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -2 times the 1st row to the 2nd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}$

Multiply the 2nd row by -1/8

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -1 times the 2nd row to the 3rd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}$

Multiply the 3rd row by -8/41

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -1/8 times the 3rd row to the 2nd row

Add -1 times the 3rd row to the 1st row

$\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -3 times the 2nd row to the 1st row

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

3 0

2 years ago

Write the expression as a single logarithm<br> 2 ln 7 + ln(x+5) - ln(x-3)

yulyashka [42]

Answer:

ln ((49(x+5))/x-3)

7 0

2 years ago

Irene's mean score on 5 tests is 88%. What is

Anestetic [448]

Answer: The least score she can get on her next test is 455 points.

Step-by-step explanation: From the available information, her current mean score is 88%, and that was achieved from a total of 5 tests. Hence, her mean score was computed as follows;

Mean = (Summation of data)/observed data

Where the observed data is 5 and the mean is 88. Therefore the mean can now be expressed as,

88 = Summation of data/5

By cross multiplication we now have

88 x 5 = Summation of data

440 = Summation of data.

So, if she wants to raise her mean score on her next test to 91%, her least possible score would be derived as

91 = (Summation of data)/5

By cross multiplication we now have

91 x5 = Summation of data

455 = Summation of data

Therefore, on her next test, she must score at least 455 points.

4 0

2 years ago

Please help! (Find the area of the shaded region)

jeyben [28]

Answer:

9.43 ft

Step-by-step explanation:

First, we need to find the area of the entire circle(shaded & unshaded), which is 12.57, with a radius of 2 ft. Next, we find the area of the white area, and NOT the shaded area, which is 3.14, with a radius of 1 ft. Now, we need to subtract the white area(3.14) from the total area(12.57), which is 9.43.

Hope this helps!

8 0

3 years ago

A 3 cm x 3 cm rectangle sits inside a circle with radius of 4 cm.

Vitek1552 [10]

Given:

Rectangle inside a circle.

To find:

The area of the shaded region.

Solution:

Length of a rectangle = 3 cm

Width of a rectangle = 3 cm

Area of a rectangle = length × width

= 3 × 3

Area of a rectangle = 9 cm²

Radius of a circle = 4 cm

Area of a circle = πr²

= 3.15 × 4²

Area of a circle = 50.24 cm²

Area of shaded region = Area of circle - Area of rectangle

= 50.24 - 9

= 41.24 cm²

The area of the shaded region is 41.24 cm².

5 0

3 years ago

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