In the diagram, m_ECA = 120.
m.BCD =

We are given a set of vectors S and we need to determine whether each given vector can be written as a linear combination of the vectors in S.

(a) For vector (2, -1, -2), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (2, -1, -2). By solving the system of equations, we find that k₁ = -1 and k₂ = 0, so the vector can be written as a linear combination of the vectors in S.

(b) For vector (8, -14, 27/4), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (8, -14, 27/4). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

(c) For vector (1, -8, 12), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, -8, 12). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

(d) For vector (1, 1, -1), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, 1, -1). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

Learn more about vectors here: brainly.com/question/29740341

#SPJ11

When an organization with a functional structure diversifies into related product-markets, it generally maintains its functional structure.

In a functional structure, the organization is organized based on specialized functions such as marketing, finance, operations, and human resources. Each function operates independently, and decisions are made within each functional unit. When diversifying into related product-markets, the organization can leverage its existing functional expertise to support the new product lines or markets.

Maintaining the functional structure allows the organization to retain the benefits of specialization and efficiency within each function. It also enables the organization to capitalize on the existing knowledge, skills, and resources of each functional area, ensuring a smoother transition into new product-markets.

This approach minimizes disruption and allows the organization to effectively manage the integration of new product lines while maintaining focus on core competencies. By leveraging the existing functional structure, the organization can adapt and respond to the specific requirements of each product-market while maximizing operational efficiency.

Learn more about leverage here:

https://brainly.com/question/30469369

#SPJ11

Answer:

the first point is (-3,0) the second is (0,-1)

Step-by-step explanation:

Step 1

Given:

Required: To say what the graph tells us of the value of k

Step 2

Since k, represents the horizontal shift, and the horizontal shift is 5 units to the right.

K is therefore negative

Hence k is less than zero.

Answer = option

Answer:

sorry i coldent find the anser

Step-by-step explanation:

ello

+v+

Answer:

The slope indicates that the soup kitchen uses 63 cans per day. The y-intercept shows that there were initially 825 cans at the soup kitchen.

Step-by-step explanation:

The number of observations strictly less than 24 is 7.

The five-number summary consists of the minimum value (13), the first quartile (Q1) or 25th percentile (24), the median or second quartile (Q2) or 50th percentile (38), the third quartile (Q3) or 75th percentile (51), and the maximum value (69).

Since Q1 represents the value below which 25% of the observations lie, and the five-number summary indicates that Q1 is 24, it means that 25% of the observations are less than or equal to 24.

Therefore, the number of observations strictly less than 24 is 25% of 33, which equals 7.

For more questions like Number click the link below:

https://brainly.com/question/17429689

#SPJ11

To find the point P on the line y=3x that is closest to the point (50,0), we need to use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

Where A, B, and C are the coefficients of the equation of the line in the form Ax + By + C = 0.

In this case, the equation of the line y=3x can be written as -3x + y = 0. So we have:

A = -3, B = 1, C = 0

Now we can plug in the values of (50,0) and solve for x and y to find the point P that is closest to it:

distance = |-3x + y| / sqrt((-3)^2 + 1^2)
distance = |-3x| / sqrt(10)

To minimize the distance, we need to minimize |-3x|. This occurs when x = 0. So the point P that is closest to (50,0) is the point (0,0).
To find the point P on the line y = 3x that is closest to the point (50, 0), we need to minimize the distance between P and (50, 0).

Let P(x, y) be a point on the line y = 3x. The distance between P and (50, 0) is given by the distance formula:

D = sqrt((x - 50)^2 + (y - 0)^2)

Since y = 3x, we can rewrite the distance formula as:

D = sqrt((x - 50)^2 + (3x)^2)

To minimize the distance, we can minimize the square of the distance (D^2), as it avoids dealing with the square root:

D^2 = (x - 50)^2 + (3x)^2

Now, we can find the derivative of D^2 with respect to x and set it to 0 to find the critical points:

d(D^2)/dx = 2(x - 50) + 2(3x)^2 * 6x = 0

Solve this equation to find the x-coordinate of the point P. Then, use y = 3x to find the corresponding y-coordinate. Finally, you'll have the coordinates of the point P that is closest to (50, 0).

Visit here to learn more about  derivative : https://brainly.com/question/25324584
#SPJ11

Answer:

Approximately 8.234 inches.

Step-by-step explanation:

The area for a sphere is 4πr²

=> r² = 213 : 4 : π = approx. 16.95
=> r = sqrt (16.95) = approx. 4.117

=> d = 4.117 x 2 = approx. 8.234 inches

hope this helps :o

In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

To know more about Equation related question visit:

https://brainly.com/question/29657983

#SPJ1

correct answer is estimated useful life of the machine is 7 years.

To determine the estimated useful life of the machine, we will use the given information and apply the straight-line depreciation formula:

Depreciation Expense = (Cost - Residual Value) / Useful Life

We know the following:

Cost = $17,500
Depreciation Expense = $2,000 per year
Residual Value = 20% of Cost = 0.20 x $17,500 = $3,500

Now, we will plug these values into the formula and solve for Useful Life:

$2,000 = ($17,500 - $3,500) / Useful Life

Simplifying the equation:

$2,000 = $14,000 / Useful Life

Now, divide both sides by $14,000:

Useful Life = $14,000 / $2,000

Useful Life = 7 years

So, the estimated useful life of the machine is 7 years.

Learn more about estimated useful life click here

https://brainly.com/question/30328867

#SPJ11

Answer:  see screenshot

Step-by-step explanation:

took test

Answer:

no

Step-by-step explanation:

Answer:

Increase by 3.

Step-by-step explanation:

4 x 21 = 84

84 x 2 = 168

Begin to try numbers.

5 x 22 = 110

6 x 23 = 138

7 x 24 = 168

7 - 4 = 3

24 - 21 = 3

Increase each side by 3 ft. for a total dimension of 7 ft. x 24 ft.

Answer:

its a. rhejhdhrhrjdhr

The standard form of the equation of this ellipse is \(\frac{(x\;+\;5)^2}{5^2} +\frac{(y\;-\;6)^2}{8^2}=1\)

In Mathematics, the standard form of the equation of an ellipse can be represented by the following mathematical equation:

\(\frac{(x\;-\;h)^2}{a^2} +\frac{(y\;-\;k)^2}{b^2}=1\)

Where;

From the information provided above, we have the following parameters about the equation of this ellipse:

Vertices = (-5, -2) and (-5, 14)

Point = (0, 6)

Since the vertices are located at (-5, -2) and (-5, 14), we would determine the coordinates of the center (h, k) by using the midpoint formula as follows:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(-5 - 5)/2, (-2 + 14)/2]

Midpoint or center (h, k) = (-5, 6).

Since the point (0, 6) lies on the ellipse, we would determine the value of a and b as follows:

\(\frac{(0\;-\;h)^2}{a^2} +\frac{(6\;-\;k)^2}{b^2}=1\)

b² = (k - 14)²             b² = (k + 2)²

b² = (6 - 14)²             b² = (6 + 2)²

b² = (-8)²                   b² = 8²

b = √64 = 8.             b = √64 = 8.

a = x - h

a = 0 - (-5)

a = 5

Therefore, the required equation of this ellipse is given by;

\(\frac{(x\;-\;h)^2}{a^2} +\frac{(y\;-\;k)^2}{b^2}=1\\\\\frac{(x\;+\;5)^2}{5^2} +\frac{(y\;-\;6)^2}{8^2}=1\)

Read more on ellipse here: https://brainly.com/question/29657760

#SPJ1

The generalization of exercise 13 states that for a fixed non-negative integer r and any integer n greater than or equal to r, the summation of i from r to n is equal to (n+1) times the summation of i from r to r+1. This can be proved using mathematical induction.

To prove this generalization, we will use mathematical induction. First, we will verify that the statement holds for the base case where n = r. In this case, the left-hand side of the equation becomes r, and the right-hand side becomes (r+1)r, which is also equal to r. Thus, the statement holds for the base case. Next, we assume that the statement holds for some arbitrary integer k greater than or equal to r. That is, we assume that the summation of i from r to k is equal to (k+1) times the summation of i from r to r+1.

Now, we need to prove that the statement also holds for k+1. We can do this by adding (k+1) to both sides of the equation for k:

(r+(k+1))∑(i)=((k+1)+1)|i=r(r)(r+1)+(k+1)

Expanding the right-hand side gives:

(r+(k+1))∑(i)=((k+1)+1)|i=r(r)(r+1)+(k+1)

= (r+(k+1))(r+1) + (k+1)

= (k+2)(r+1)

And this is equal to the right-hand side of the equation for k+1. Thus, we have shown that if the statement holds for k, then it also holds for k+1. By mathematical induction, the statement holds for all integers n greater than or equal to r.

Learn more about mathematical induction here: https://brainly.com/question/29503103

#SPJ11

The probability of Jack picking a yellow or white sock is 0.6 (60%).

The probability of Jack picking a blue sock is 4/14 (28.6%)

The probability of Jack picking a red sock is 3/14 (21.4%)

The probability of Jack picking a white sock is 2/14 (14.3%)

The probability of Jack picking a yellow sock is 1/14 (7.1%)

Therefore, the probability of Jack picking a yellow or white sock is 0.6 (60%)

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

The area of the traingle AOB is 30 (Rounded up result)

Step-by-step explanation:

7.8 cm and 10 cm.

10/2= 5 cm

Then Reversed Pitagora's Formula:

Square root of the calc "(7.8^2)-(5^2)" = 60,84 - 25 = 35,84

Then Square root of 35, 84 is 5,98.

5.98 is the height of the triangle AOB

With the height we can calculate the area

We use the formula (B*H)/2

So is (10*5,98)/2, that makes 29,9

Just round up to 30 and that's the area.

The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;

Part A:

Part B:

Part C:

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the x and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.

Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10

Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50

Therefore;

Part B:

Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the x and y-values is a linear function, which can be found as follows;

Slope of the equation, m = ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

Part C:

The slope of the function is the coefficient of the variable x in the equation, y = m•x + c

The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c

Learn more about finding relationship between variables here:

https://brainly.com/question/4219149

#SPJ1

Answer:

23.9% = 47400

divide both sides by 23.9 to find 1%

1% = 1983.26359

now multiply by 100 to find total number of doctors

1983.26359 X 100

100% = 198326

Answer:

She will need to fill her spoon twice, once adding in the full amount, and the second adding half the amount.

3/4  ÷ 4/8

=3/4 * 2/1

=6/4

=1.5

So, that much amount would be needed o be added to the recipe during the two times

Jaden may have had a ["smaller", "larger"] sample size. The correct choice is: "larger."

Jaden may have had ["more", "less"] variability (a ["larger", "smaller"] standard deviation) in his survey responses.
Your answer: more (a larger standard deviation)

In statistics, the sample size is the measure of the number of individual samples used in an experiment. For example, if we are testing 50 samples of people who watch TV in a city, then the sample size is 50. We can also term it Sample Statistics.

Sample size refers to the number of participants or observations included in a study. This number is usually represented by n.

The size of a sample influences two statistical properties:

1) the precision of our estimates and

2) the power of the study to draw conclusions.

To learn more about “standard deviation” refer to the https://brainly.com/question/475676

#SPJ11

Answer

Law of Sines

Step-by-step explanation:

If you have all three side lengths, you can use law of sines.

side length a/sin of angle a=side length b/sin of angle b=side length c/sin of angle c

not sure if that makes sense but look up the law of sines!

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

for such more question on Hexadecimal numbers

https://brainly.com/question/28280312

#SPJ8

Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

Know more about the fraction

brainly.com/question/78672

#SPJ1

A basis for the subspace is given by the three vectors consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2]:

[1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

To find a basis for the given subspace, we need to determine the linearly independent vectors that span the subspace.

Let's rewrite the given vector as a linear combination of the standard basis vectors in R4:

[x1, -2x1+x2, -9x1+4x2, -5x1-7x2] = x1[1, 0, 0, -5] + x2[0, 1, 4, -7] + 0[0, 0, 0, 1]

Thus, the subspace is spanned by the vectors [1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

To check for linear independence, we can set up the following augmented matrix and row reduction:

[ 1 0 0 | 0 ]

[ 0 1 4 | 0 ]

[ 0 -2 -9 | 0 ]

[-5 -7 0 | 0 ]

Using row operations, we can reduce this to:

[ 1 0 0 | 0 ]

[ 0 1 0 | 0 ]

[ 0 0 1 | 0 ]

[ 0 0 0 | 0 ]

Since the only solution is the trivial solution, the vectors are linearly independent.

Therefore, a basis for the subspace is given by the three vectors:

[1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

To read more about  linearly independent vectors:

https://brainly.com/question/30576106

#SPJ4

To answer the question of how many DVDs Movie Meet shipped to the nearest ten, we need to round the number \(264,398\)to the nearest ten. On rounding off, we get \(264,400\)

To find the nearest ten for the number of DVDs Movie Meet shipped last year, we'll follow these steps:

1. Look at the number given: \(264,398\) DVDs.

2. Identify the digit in the tens place. In this case, it's \(9\) (from \(90\) in \(398\)).

3. Check the digit to its right (in the one's place). If it's \(5\) or greater, round up. If it's \(4\) less, round down. In this case, it's \(8\), so we'll round up.

4. Add \(1\) to the digit in the tens place (\(9 + 1 = 10\)) and replace the digits to the right with zeros. Following these steps, we find that to the nearest ten, Movie Meet shipped approximately \(264,400\) DVDs to its customers last year.

Learn more about rounding off:

https://brainly.com/question/30453145

#SPJ11

Answer:

-4721613632.87 or -4721613632.9 or -4721613633

Step-by-step explanation:

10x9.2^-13 = 10x-472161363.287 = -4721613632.87 or you can round -4721613632.9 or -4721613633

Answer:

40

_________________

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

Learn more about  uniform distribution here:

https://brainly.com/question/32291215

#SPJ11