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4 years ago

What is greater 95 percent or 0.9

2 answers:

7 0

Percent means out of one hundred so 95 percent equals:

$\frac{95}{100} = 0.95$

From this, we can see that 0.95 is bigger than 0.9 so we can conclude:

$95\% > 0.9$
95 percent is greater than 0.9.

nikklg [1K]4 years ago

3 0

95% is larger because 0.9 is like 90% and 95% is more than 90%

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[10 points] Given matrix A =  2 2 3, −6 −7 8 (a) (5 points). Show that A has no LU decomposition. (b) (5 points). Find the dec

ch4aika [34]

Answer:

Both the answers are as in the solution.

Step-by-step explanation:

As the given matrix is not in the readable form, a similar question is found online and the solution of which is attached herewith.

Part a:

Given matrix is : A = $\left[\begin{array}{ccc}0&3&4\\1&2&3\\-3&-7&8\end{array}\right]$

Here,

$det(A) =\left|\begin{array}{ccc}0&3&4\\1&2&3\\-3&-7&8\end{array}\right| = -55 \neq 0.$

Then, A is non-singular matrix.

Here, A₁₁= 0.

If we write A as LU with L lower triangular matrix and U upper triangular matrix, then A₁₁=L₁₁U₁₁.

So, As

A₁₁ = 0 gives L₁₁U₁₁= 0 ,

This indicates that either L₁₁= 0 or U₁₁ = 0.

If L₁₁= 0 or U₁₁ = 0, this would made the corresponding matrix singular, which contradicts the condition as A is non-singular.

Therefore, A has no LU decomposition.

Part b:

By the implementation of the various row operations

interchange R1 and R2

$\left[\begin{array}{ccc}1&2&3\\0&3&4\\-3&-7&8\end{array}\right]$

R3+3R1=R3

$\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&-1&17\end{array}\right]$

R3+(1/3)R2 = R3

$\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&0&55/3\end{array}\right]$

Therefore, U = $\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&0&55/3\end{array}\right]$ .

Here, LP = E₁₂=E₃₁=-3 &E₃₂=-1/3

$LP=\left[\begin{array}{ccc}0&1&0\\1&0&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&0&0\\0&1&0\\-3&0&1\end{array}\right]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&-1/3&1\end{array}\right]$

$LP=\left[\begin{array}{ccc}0&1&0\\1&0&0\\-3&-1/3&1\end{array}\right]$

$LP=\left[\begin{array}{ccc}1&0&0\\0&1&0\\-1/3&-3&1\end{array}\right]\left[\begin{array}{ccc}0&1&0\\1&0&0\\0&0&1\end{array}\right]$

So now U is given as

$U=\left[\begin{array}{ccc}1&2&3\\0&3&4\\0&0&55/3\end{array}\right]\\L=\left[\begin{array}{ccc}1&0&0\\0&1&0\\-1/3&-3&1\end{array}\right]\\P=\left[\begin{array}{ccc}0&1&0\\1&0&0\\0&0&1\end{array}\right]\\$

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3 years ago

Write an equation of the line that passes through point (5,6) and has a slope of 2.

qwelly [4]

y = - \frac{2}{5} x - 2

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 2x + 5y = 10 into this form

subtract 2x from both sides

5y = - 2x + 10 ( divide all terms by 5 )

y = - \frac{2}{5} x + 2 ← point- slope form with slope m = - \frac{2}{5}

Parallel lines have equal slopes hence

y = - \frac{2}{5} x + c is the partial equation of the parallel line

to find c, substitute ( 5, - 4 ) into the partial equation

- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2

y = - \frac{2}{5} x - 2 ← equation of parallel line

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4 years ago

Bella has 6.3 kilograms of berries.she packs 0.35 kilogram of berries into each container.she then sells each container for 2.99

yKpoI14uk [10]

6.3 / 0.35 = 18
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3 years ago

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Which property would be useful in proving that the product of two rational numbers is ALWAYS rational?

aleksandrvk [35]

C. A rational number is a number that can be expressed as the ratio of two whole numbers. The product of the rational numbers a/b and c/d are also equal to a rational number ac/bd.

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3 years ago

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What value in place of the question mark makes the polynomial below a

mel-nik [20]

Answer:

Step-by-step explanation:

Given

x² + 12x

To make the polynomial a perfect square

add ( half the coefficient of the x- term)²

= x² + 12x + 6²

= x² + 12x + 36

= (x + 6)² ← a perfect square

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3 years ago