In the given picture, find the measure of angle ADC.

The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].

Let's go step by step to find the LU factorization of matrix A.

Matrix A:

A =

[4, -8, 10]

[-8, 8, -7]

[6, -7, 3]

Step 1:

Initialize the L matrix as an identity matrix of the same size as A.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 2:

Perform Gaussian elimination to obtain U.

- Multiply the first row of A by (1/4) and replace the first row of A with the result.

A =

[1, -2, 2.5]

[-8, 8, -7]

[6, -7, 3]

- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[6, -7, 3]

- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Step 3:

Update the L matrix based on the operations performed during Gaussian elimination.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 4:

The resulting matrix A is the upper triangular matrix U.

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Therefore, the LU factorization of matrix A is:

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

learn more about LU factorization of matrix from this link.

https://brainly.com/question/33069156

#SPJ11

Answer:

To find 67% of an amount, we use the percentage multiplier of 0.67.

This is because 67% can be expressed as 67/100, and when we divide a number by 100, we are essentially moving the decimal point two places to the left. So, 67/100 can also be written as 0.67.

Therefore, the percentage multiplier to find 67% of an amount is 0.67.

a)The expected profit is $4,000. b)The standard deviation for the profit is approximately $4,898.98.

a) To calculate the expected profit, we multiply the profit by the probability of it happening:

Expected profit = Profit * Probability

Given:

Profit = $10,000

Probability = 40% = 0.4

Expected profit = $10,000 * 0.4 = $4,000

Therefore, the expected profit is $4,000.

b) To find the standard deviation for the profit, we need more information about the probability distribution of the profit. If we assume that the profit follows a Bernoulli distribution (with only two possible outcomes: getting the contract or not), we can calculate the standard deviation using the formula:

Standard deviation = √(Probability * (1 - Probability) * Profit^2)

Given:

Profit = $10,000

Probability = 40% = 0.4

Standard deviation = √\((0.4 * (1 - 0.4) * $10,000^2)\)

                = √(0.4 * 0.6 * $100,000,000)

                = √(24,000,000)

                ≈ $4,898.98

Therefore, the standard deviation for the profit is approximately $4,898.98.

Learn more about the standard deviation visit:

brainly.com/question/475676

#SPJ4

================================================

How to get that answer:

Plug h = 6 into each expression to find the number of each type sold

Then multiply each bagel count by the price of those bagels

The last step is to subtract the two revenues

118.50 - 57 = 61.50 dollars

Answer:

173

Step-by-step explanation:

6+4/8*2+(4+9)^2-3

6+4/8*2+13^2-3

6+4/8*2+169-3

6+1/2*2+169-3

6+1+169-3

173

3(x + 5)

The distributive property states that you are distributing whatever is outside the parenthesis to all terms within the parenthesis. For complex distributive questions, you will have to simplify the parenthesis first (if you can) before distributing.

In this case, the example given is 3(x + 5).

First, distribute 3 to all terms in the parenthesis by multiplication:

3(x + 5)

= (3 * x) + (3 * 5)

= 3x + 15

3x + 15 is your answer.

~

Another more complex distribute property can involve powers. Take for example:

(7x + 5)²

In this case, you will use the distributive method of FOIL, or (First, Outside, Inside, Last). Set the question:

(7x + 5)² = (7x + 5)(7x + 5)

First: 7x * 7x = 49x²

Outside: 7x * 5 = 35x

Inside: 5 * 7x = 35x

Last: 5 * 5 = 25

Next, combine like terms:

49x² + 35x + 35x + 25

49x² + (35x + 35x) + 25

49x² + (70x) + 25

49x² + 70x + 25 would be your answer.

~

Answer:

b, a, e, h, f

Step-by-step explanation:

just test each variable

you can skip the ones that seem obviously wrong, like c, when you figure out the pattern.

b. |-5|=|-5|

g. |-3|≠|6|

a. |3|=|3|

e. |6|=|6|

j. |2|≠|-3|

h. |6|=|-6|

f.|-3|=|-3|

The letters of the points that are on the graph of |x| = |y| are,

A(3, 3), E(6, 6), H(6, 6), F(2, 2), and B(5, 5).

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know | a | = a and | - a |  = a.

∴ The letters of the points that are on the graph of |x| = |y| is,

A(3, 3), E(6, 6), H(6, 6), F(2, 2), and B(5, 5).

learn more about modulus here :

https://brainly.com/question/14070556

#SPJ2

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

We have,

Carl Friedrich Gauss, known as the "Prince of Mathematicians," made significant contributions to number theory, geometry, physics, and statistics.

He formulated the fundamental theorem of arithmetic, developed concepts in differential geometry such as intrinsic curvature and Gaussian curvature, and formulated Gauss's law for electric fields.

Gauss's work laid the foundation for modern mathematics and his emphasis on rigor and precision influenced subsequent generations of mathematicians.

His legacy as one of the greatest mathematicians of all time is based on his profound theorems, laws, and concepts that continue to shape the field.

Thus,

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

Learn more about mathematicians here:

https://brainly.com/question/30613629

#SPJ12

Suppose a person lost 10 pounds in a month. This z-score tells you that x = 10 is 2.5  standard deviations to the right of the mean 5 pounds.

To verify that the z-score when x = 10 pounds is z = 2.5, we can use the formula:

z = (x - μ) / σ

where x is the value of the random variable, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we have:

z = (10 - 5) / 2 = 2.5

This confirms that the z-score when x = 10 pounds is z = 2.5.

To determine what the z-score tells us about the location of x = 10 pounds relative to the mean, we can use the definition of a z-score:

z = (x - μ) / σ

Rearranging the formula, we have:

x = μ + zσ

So, when z = 2.5 and σ = 2, we have:

x = μ + 2.5(2) = μ + 5

This tells us that x = 10 pounds is 5 pounds above the mean. Since the z-score is positive, x = 10 pounds is to the right of the mean.

Therefore, the z-score tells us that x = 10 is 2.5 standard deviations to the right of the mean of 5 pounds.

To know more about z-score refer here:

https://brainly.com/question/31613365#

#SPJ11

The probability that a test taker chosen at random takes 9 minutes or more to read the article is 0.38. Rounded to four decimal places, this is 0.3800.

To find the probability that a test taker chosen at random takes 9 minutes or more to read the article, we need to calculate the integral of the probability density function f(t) from 9 to 10 (since t is between 0 and 10).
∫(9 to 10) 0.012t^2 − 0.0012t^3 dt
Using the power rule of integration, we get:
[0.004t^3 - 0.0003t^4] from 9 to 10
Substituting the limits, we get:
[0.004(10)^3 - 0.0003(10)^4] - [0.004(9)^3 - 0.0003(9)^4]
Simplifying, we get:
0.38

Learn more about integration in probability: https://brainly.com/question/30570293

#SPJ11

Answer:

20$

Step-by-step explanation:

50% of 40= 20

Answer:

7x+20

Step-by-step explanation:

multiply (5+3x) by 2 and combine like terms

Answer:

B.

Step-by-step explanation:

The vertical line test is what I used to test this.

Sin(117°) can be expressed as a function of sin(58.5°) using the half-angle formula.

The half-angle formula for sine states that for an angle θ/2, the sine can be expressed as:

sin(θ/2) = ±√[(1 - cosθ)/2]

To find sin(117°), we can use the half-angle formula with θ = 234° (twice the angle we want to find).

sin(117°) = sin(234°/2) = sin(117°) = ±√[(1 - cos234°)/2]

To determine the sign of sin(117°), we need to consider the quadrant of the angle. Since 117° lies in the second quadrant, sin(117°) will be positive.

Now we calculate cos234° using the cosine function or trigonometric tables. Assuming cos234° is equal to b, we have:

sin(117°) = √[(1 - b)/2]

Therefore, sin(117°) can be expressed as a function of sin(58.5°) using the half-angle formula.

Learn more about half-angle formula here:

https://brainly.com/question/30400810

#SPJ11

Answer:

-26

Step-by-step explanation:

1. Replace the x with 6

2. Multiply -4 by 6 to get -24

3. Subtract 2 from -24 to get -26

-26 is the answer.

Answer:

\(\sqrt[5]{b}^{2}\)

Step-by-step explanation:

The number in which the value of 3 is 3-1/100 is 345. The correct option is a.

The given number is 43,781.

The value of the 3 in 43,781 is 3,000.

The value of 3-1/100 is 2.99.

We are supposed to find out in which number 2.99 is the value of the 3 in 43,781.

Given options are:

a. 345

b. 237,895

c. 5,732

We'll calculate the values of 3-1/100 in each option.

a. The value of 3-1/100 in 345 is 2.99.

So, the correct option is a.

To know more about value refer here:

https://brainly.com/question/9796766

#SPJ11

Answer:

12x +53,150 = 24.5x (production cost = revenue )

53,150 = 12.5x (subtract 12x from both sides and then divide 53,150 by 12.5)

x= 4,252 books

Step-by-step explanation:

The equation of the plane is: 3x + 24y - 2z + 31 = 0

To find an equation of a plane containing three points:

We can use the fact that the normal vector to the plane is perpendicular to any vector lying in the plane. We can find the normal vector by taking the cross product of two vectors lying in the plane, and then use the equation of a plane in point-normal form.

Let's first find two vectors lying in the plane by taking the differences between the three given points:

v1 = <(-2) - (-4), 5 - 1, 1 - (-4)> = <2, 4, 5>

v2 = <(-2) - (-4), 6 - 1, 3 - (-4)> = <2, 5, 7>

Now we can take the cross product of v1 and v2 to find a normal vector to the plane:

n = v1 x v2 = <(4)(7) - (5)(5), -(2)(7) + (5)(2), (2)(5) - (4)(2)> = <-3, -24, 2>

We want the coefficient of x in the equation of the plane to be 3, so we need to scale the normal vector by a factor of -1/3:

n' = (1/3)<3, 24, -2> = <1, 8, -2/3>

Now we can use any of the three given points to write the equation of the plane in point-normal form. Let's use the first point (-4, 1, -4):

(x - (-4), y - 1, z - (-4)) · <1, 8, -2/3> = 0

Simplifying and multiplying through by 3 to eliminate the fraction, we get:

3x + 24y - 2z + 31 = 0

So an equation of the plane containing the three points (-4, 1, -4), (-2, 5, 1), (-2, 6, 3) in which the coefficient of x is 3 is 3x + 24y - 2z + 31 = 0.

For more similar questions on plane:

https://brainly.com/question/24048256

#SPJ11

Answer:

P.=2(2x+5)+2(x-10)=80cm

6x-10=80

x=90/6=15cm

Area= L*W= 35*5=175 squared cm= 0.0175 squared m

Cost= 0.24 * 0.0175 = GHc 0.0042

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.  The cost of weeding the rectangular plot is 0.0042 GHc.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

A.) The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Therefore, we can write,

Perimeter of the rectangel = 2(L+W)

80 = 2[(2x+5)+(x-10)]

80/2 = 2x+5+x-10

40 = 3x -5

40+5 = 3x

x = 15

Hence, the value of x is 15.

B.) The length of the rectangle = (2x+5) = 2(15)+5 = 35 cm = 0.35 m

The width of the rectangle = (x-10) = 15-10 = 5 cm = 0.05 m

Now, the area of the rectangle = L×B = 0.35m × 0.05m  = 0.0175m²

C.) Given the cost of weeding 1m² is 0.24, therefore, the cost of weeding the rectangular plot is

Cost = 0.0175 × 0.24 = 0.0042 GHc

Hence, the cost of weeding the rectangular plot is 0.0042 GHc.

Learn more about Rectangle:

https://brainly.com/question/15019502

#SPJ2

Answer:

168

Step-by-step explanation:

21*8=168

Answer:

168 ft ^2

Step-by-step explanation:

Tofind the Area of a rectangle you multiply the Length by the width. By doing this we get the equation Area = 21 * 8. By doing multiplication we get area to be 168.

The graph of the function f(x) = x² + 3 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = x² + 3

The above function is a quadratic function that has been transformed as follows

Shifted up by 3 units

Next, we plot the graph using a graphing tool by taking note of the above transformation rule

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ4

Answer:

9

Step-by-step explanation:

if you think bout it 24/6 is 4 and 36/9 is 4

Answer:

562496

Step-by-step explanation:

I think

Answer: see explanation

Step-by-step explanation:

1 is a function

2 is not a function

The corresponding percentage error in the calculation of the volume of the box is 44%.

a) Percentage error in the calculation of the surface area of the box:

Using the formula for the differential of S, we have:

dS = ∂S/∂x * dx + ∂S/∂y * dy∂S/∂x =

4x∂S/∂y = 4x

From this, the percentage error in S is given by:

(dS/S) * 100 = [(∂S/∂x * dx)/S + (∂S/∂y * dy)/S] * 100

= [(4x * 0.02)/S + (4x * 0.03)/S] * 100

= (0.02 + 0.03) * 100

= 5%

Hence, the corresponding percentage error in the calculation of the surface of the box is 5%.

b) Percentage error in the calculation of the volume of the box:

Using the formula for the differential of V, we have:

dV = ∂V/∂x * dx + ∂V/∂y * dy∂V/∂x

= 2xy∂V/∂y

= x^2

From this, the percentage error in V is given by:

(dV/V) * 100 = [(∂V/∂x * dx)/V + (∂V/∂y * dy)/V] * 100

= [(2xy * 0.02)/V + (x^2 * 0.03)/V] * 100

= (0.04y/x + 0.03x/y) * 100

= (0.04/0.03)(y/x)(0.03x/y + 0.04y/x)

= (4/3)(0.03 + 0.08)

= 0.44 or 44/100

Hence, the corresponding percentage error in the calculation of the volume of the box is 44%.

Know more about volume here:

https://brainly.com/question/14197390

#SPJ11

The vector space that has exactly one basis is the trivial vector space, which is the vector space containing only the zero vector.

A basis for a vector space is a set of linearly independent vectors that span the entire space. In a non-trivial vector space (a space that contains more than just the zero vector), there are infinitely many possible bases. This is because any set of linearly independent vectors that span the space can be used as a basis.

However, in the trivial vector space, there is only one vector (the zero vector), and it is linearly independent of itself. Therefore, the trivial vector space has exactly one basis, which is the set containing only the zero vector. Any other set of vectors in the trivial vector space is linearly dependent, and therefore cannot be used as a basis.

Find out more about trivial vector space,

brainly.com/question/14375935

#SPJ4

Find out more about vector spaces

brainly.com/question/14375935

#SPJ4

the farmer plants 7 525 acres

The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1