What is the image of the point
(
0
,
4
)
(0,4) after a rotation of
18
0
∘
180
∘
counterclockwise about the origin?

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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A unit circle has  radius of 1 (r = 1).  For any point on the unit circle.

According to our question-

A unit circle has  radius of 1 (r = 1).  For any point on the unit circle, we have (by the Pythagorean Theorem):

x2 + y2 = 1

x2 + (-1/4)2 = 1

Hence, A unit circle has  radius of 1 (r = 1).  For any point on the unit circle

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Answer:  

= _51_x+ __1_y

    10          5

Step-by-step explanation:

The unit rate at which Caleb types is 20 words per minute.

The unit rate is the average speed at which an activity is done. The unit rate is the total words typed by Caleb per minute. It is calculated by dividing the total words typed by the total time.

Unit rate = total words / total time

100 / 5 = 20 words per minute

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The researcher in question has performed a meta-analysis. A meta-analysis is a statistical method used to synthesize the findings from multiple studies that have investigated a similar research question using the same variables and measurement strategies. In this case, the researcher is interested in examining the relationship between exercise and myasthenia gravis.

The process of conducting a meta-analysis involves several steps. First, the researcher identifies and selects relevant studies that meet specific criteria, such as using the same dependent and independent variables (in this case, exercise and myasthenia gravis). In this scenario, 28 studies were identified that meet these requirements.
Next, the researcher extracts the relevant data from each study, such as effect sizes, sample sizes, and other important information. This allows the researcher to compare and combine the results of the individual studies into a single, comprehensive statistical analysis.

In summary, the researcher has conducted a meta-analysis to synthesize the results from 28 studies examining the relationship between exercise and myasthenia gravis, allowing for a more comprehensive understanding of the topic.

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Step 1

State an expression for the probability of an event.

Number of required events = 4

Total number of events = 7

Step 2

Find the probabilities of defective batteries with replacement and without replacement

Step 3

Find the probabilities that both are defective.

Hence the probability that 2 batteries selected at random without replacement are both defective is 2/7

Answer:

12 + 15= 27/2 = 13.5 kg

Step-by-step explanation:

In the survey conducted in a city with a population of one million (10^6) people, a sample size of 1000 is collected. The sampling method used is random sampling with replacement and equal probabilities for everyone in the city.

Random sampling with replacement means that after selecting an individual for the sample, they are placed back into the population, and it is possible for them to be selected again for subsequent samples. This method allows each individual in the population to have an equal chance of being selected each time, as the selection process is independent for each sample.

By collecting a sample of size 1000 from a population of one million, the aim is to obtain a representative subset of the population that can provide insights and make inferences about the entire population. Random sampling helps ensure that the sample is unbiased and minimizes selection bias.

With the sample size of 1000, the survey can provide valuable information about the city's population, allowing for statistical analysis and generalizations to be made about the population as a whole. The sample size is large enough to provide a reasonable level of confidence in the survey results, assuming that the sample was selected randomly and with equal probabilities for everyone in the city.

By conducting a survey using random sampling with replacement and a sample size of 1000 in a city with a population of one million people, the researchers aim to gather representative data and make informed conclusions about the entire population based on the characteristics observed in the sample.

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The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.

This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

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The vertex of the quadratic function f(x) = 2x^2 + 4x - 3 is (-1, -5).To find the vertex of a quadratic function, calculate the x-coordinate using x = -b/2a and then substitute it back into the equation to find the y-coordinate. The resulting coordinates give you the vertex of the graph.

To determine the vertex of a quadratic function, we can use the formula x = -b/2a, where the quadratic function is in the form f(x) = ax^2 + bx + c.

The vertex of the quadratic function is the point (x, y) where the function reaches its minimum or maximum value, also known as the vertex.

In the equation f(x) = ax^2 + bx + c, we can see that a, b, and c are coefficients that determine the shape and position of the quadratic function.

To find the vertex, we need to determine the x-coordinate using the formula x = -b/2a. The x-coordinate gives us the location along the x-axis where the vertex is located.

Once we have the x-coordinate, we can substitute it back into the equation f(x) to find the corresponding y-coordinate.

Let's consider an example. Suppose we have the quadratic function f(x) = 2x^2 + 4x - 3.

Using the formula x = -b/2a, we can find the x-coordinate:

x = -(4) / 2(2)

x = -4 / 4

x = -1

Now, we substitute x = -1 back into the equation f(x) to find the y-coordinate:

f(-1) = 2(-1)^2 + 4(-1) - 3

f(-1) = 2(1) - 4 - 3

f(-1) = 2 - 4 - 3

f(-1) = -5

Therefore, the vertex of the quadratic function f(x) = 2x^2 + 4x - 3 is (-1, -5).

In general, to find the vertex of a quadratic function, calculate the x-coordinate using x = -b/2a and then substitute it back into the equation to find the y-coordinate. The resulting coordinates give you the vertex of the graph.

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The eccentricity of the ellipse whose coordinates of vertex are (±10, 0) and foci coordinates are (±1, 0) is 0.1

Given,

Foci (± 1,0) and vertices (± 10,0) .

Here,

Eccentricity : Measure of how nearly circular it is. Eccentricity is defined as c/a, where c is the distance from the center to a focus and a is the distance from the center to a vertex.

Thus to measure the eccentricity firstly measure c and a.

a = distance from center to vertex

a = 10

c = distance from center to focus .

c = 1

Now ,

e = c/a

e = 1/10

e = 0.1

Thus eccentricity is 0.1 .

Eccentricity of ellipse is always in the range 0 < e < 1 .

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The length s of the arc that subtends a central angle of measure 6 rad in a circle of radius 4 cm is 24.00 cm.

Length s of the arc- The formula to find the length s of the arc that subtends a central angle θ in a circle of radius r is given by:

s = rθ

Where s = length of the arc (in meters or centimeters)

r = radius of the circle (in meters or centimeters)

θ = central angle (in radians)

Given, r = 4 cm θ = 6 rad

Substituting these values in the above formula, we get

s = rθ

= 4 cm × 6 rad

= 24 cm

Therefore, the length s of the arc is 24.00 cm (rounded to two decimal places).

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Answer:

Answer for this is 62 * 2 = 126

Step-by-step explanation:

Answer:

14×9=126

Step-by-step explanation:

how do you explain it lol

The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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Audience reach is a metric that is used to measure of the total audience size for a specific provide platform.

Audience reach answers the question of how many people have had the opportunity to consume (i.e. read, watch, and/or hear) news coverage of whatever you're watching. This metric is based on known circulation, viewership, audience size and followers of media outlets or social media users who publish the content in question. For the audience size of the publication/social media user providing the content is identified and then this number is added to the audience size of all other outlets publishing the content to give the total audience reach.

Hence, required answer is audiance reach.

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The function f(x) = x(x-3) is a polynomial, which is continuous everywhere. Therefore, the function is continuous for all values of x. Thus, the answer is Ol: The function f is continuous for all values of x.

The function f(x) = x(x-3) is a polynomial function, which means it is continuous everywhere. Therefore, the function has no points of discontinuity or intervals of discontinuity.

To find the limit of the function as x approaches a particular value, we can simply substitute the value of a into the function and evaluate the expression. The function f(x) = x(x-3) is continuous everywhere so , f is continuous at all values of x.

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Answer:

20 units

Step-by-step explanation:

Let the length be x. According to the question,

➝ Width = 15% of the length

➝ Width = 15/100x

➝ Width = 3/20x

We have the perimeter of the rectangle that is 46 units.

\(\longrightarrow \sf {Perimeter_{(Rec.)} = 2(L + W) } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{20x + 3x}{20} \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{23x}{20} \Bigg \rgroup } \\ \)

\(\longrightarrow \sf {\dfrac{46}{2}= \dfrac{23x}{20}} \\ \)

\(\longrightarrow \sf {23= \dfrac{23x}{20}} \\ \)

\(\longrightarrow \sf {23 \times 20 = 23x} \\ \)

\(\longrightarrow \sf {460= 23x} \\ \)

\(\longrightarrow \sf {\cancel{\dfrac{460}{23}} = x} \\ \)

\(\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\ \)

Therefore, length of the rectangle is 20 units.

Answer:

what.....................

Answer:

muchas gracias por los puntos

que tengas un buen dia

Answer:65 + 0.20(65) = 65 + 13 = 78..they would have to sell 78 to get the bonus(65 - 60) / 65 = 5/65 = 0.0769 x 100 = 7.69 rounds to 7.7 % decrease compared to the 65 pizza's sold yesterday

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

angles E and G are congruent to each other because they are vertical angles.

Answer:7

Step-by-step explanation:

6p-4+7p+3=90

13p-1=90

13p=91

p=7

Answer:

\(y=10x-3\)

Step-by-step explanation:

Slope-intercept equations are in the form \(y=mx+b\), where m is the slope of the line and b is the y-intercept of the line. We are given 10 as our slope, and -3 as our y-intercept. Therefore, the equation is \(y=10x-3\)

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Answer:

\(\huge\boxed{\sf{y=10x-3}}\)

Step-by-step explanation:

Hello.

Since we are given the slope and the y-intercept of the line (the point where the graph touches the y-axis), we can easily identify the equation of the line and write it in slope-intercept form, which looks like so:

y=mx+b, where m stands for the slope of the line and b stands for the y-intercept of the line.

All we have to do is plug in the values:

y=mx+b

m = 10

y=10x+b

Easy-peasy, right? ;)

b = -3

y=10x+(-3)

y=10x-3

And we're done!

I hope it helps & have an outstanding day!

\(\boxed{imperturbability}\)

Answer 10x8=80+3

Step-by-step explanation:

i.d.k 83?????

The positive number but a negative result would be :

C. Irene is scuba diving at –30 feet. She swims 10 feet toward the surface to watch a school of fish.

The positive value is she swam 10 feet up to the surface, but she is still below the surface, which would be a negative result.

The situation that would involve a change that is from a positive number but ended in a negative number is option C.

This option tells us that at the negative number she was 30 feet below the surface of the water, while at positive number she was 10 feet up the water surface.

This is a number that is greater than 0.

This is a number that is less than 0.

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The point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Let’s plot the given points E, F and G on the graph and try to find the missing point H:

Now, the length of the side EF will be:

EF = √((3-1)² + (5-5)²)EF = 2 units

The length of the side FG will be:

FG = √((6-3)² + (1-5)²)FG = √10 units

The length of the side EG will be:

EG = √((6-1)² + (1-5)²)EG = √26 units

Therefore, the total length of the three sides of the fence will be:2 + √10 + √26 units

Now, the perimeter of the fenced area with 4 sides EFGH is:16 = 2 + √10 + √26 + EHThe length of EH will be:

EH = 16 - 2 - √10 - √26EH = 11.60 units

We need to plot the missing point H which is at a distance of 11.60 units from point E along the line passing through points E and F.

Using the slope formula we find that the slope of the line passing through points E and F is: m = (y2 - y1)/(x2 - x1) = (5 - 5)/(3 - 1) = 0Therefore the line passing through E and F is a horizontal line as it has zero slope.

The distance between points E and H is 11.60 units and point H will be on the same horizontal line passing through E and F.Therefore, the x-coordinate of point H will be:

EH = √((x2-x1)² + (y2-y1)²)11.60 = √((x-1)² + (5-5)²)

Solving the above equation:

(x-1)² = 134.56(x-1)

= ±√134.56x

= 1 + √134.56 or x = 1 - √134.56

Therefore, the point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

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Note that the above problems are solved using the knowledge of the sum of angles in a triangle.

10) when computed, x = 13°
11) when computed m∠S = 158°

12) when computed, ∠P = 115.625°; ∠Q = 21.125°; ∠R = 43.25°

13) when computed, angles L, J, K is 52°, 45°, 83° respectively.
14) When computed,

∠b = 108°

∠c = 36°

∠d = 36°

Note that the Triangles Theorem posits that the sum of Angles in a Triangle = 180°

10) To solve for x, we know that:

Given the above, we can state:

8x-44 = 180/3
8x-44 = 60

8x = 60 +44

x = 104/8

x = 13°

Thus x = 13°

11) For this problem, the key to solving for x is to note that the triangle is isosceles.

This means that,

15x - 31 = 9x + 11

Thus, collecting like terms, we have:

15x-9x = 11+ 31

24x = 42

x = 42/24

Thus,

x = 1.75

Since we are looking for m∠S, we can arrive at this by removing (15x - 31 ) + (9x + 11) from 180° based on the rule of the Sum of Angles in a triangle.
That is:

180 -  (15x - 31 ) + (9x + 11) = m∠S

To do this, we must impute the value of x in to the above equation:
⇒ m∠S = 180 -  ((15 * 1.75) - 31 ) + ((9 * 1.75) + 11)
⇒ m∠S = 180 -  (-4.75) + 26.75
m∠S = 180 -  22; thus

m∠S = 158°

12) <M, <P, <R, recall that the sum of the interior angles of triangle MPR will add up to 180 degrees

so <M + <P + <R = 180

We have ∠P is 14 less than five times x = 5x-15

∠Q is five less than x = x - 5

∠R is nine less than twice x =2x - 9

Recall the angle sum property of the triangle: The sum of all angles of a triangle is 180°

So, 5x -15 + x - 5 + 2x - 9 = 180°

Collect like terms to get

8x - 29 = 180

8x = 180+29

Thus,

x= 26.125

So,∠P  = 5x-15

=5 (26.125) -15

∠P = 115.625°

∠Q =x-5

=26.125 - 5

∠ Q =21.125°

∠R = 2x - 9

=2(26.125)-9

Thus

∠R = 43.25°

To confirm, if the above ∠ sum up to 180°, we say

Check 43.25+21.125+115.625

⇒ 43.25+21.125+115.625 = 180° is TRUE.

13) To solve for ∠J, ∠K  and ∠ L, recall that

The sum of the interior angles of triangle JKL will add up to 180 degrees

so <J + <K + <L = 180

L = measure of angle L

J = measure of angle J = L - 7

K = measure of angle K = 2L - 21

Thus, L + L-7 + 2L - 21 = 180; Collect like terms and we have

4L - 28 = 180

4L = 208

L = 52°,

If L is 52 then

J = L - 7 = 52 - 7

= 45°

K = 2L - 21 = 2(52) - 21

= 83

To check that they all sum up to 180° we say:

52+ 45+83

= 180°


14)

The sum of angle in a triangle is 180 degrees

Hence <b + <c + <d = 180

13x-35 + 5x - 19 + 2x + 14 = 180

13x+5x+2x-35-19+14 = 180

20x-40 = 180

20x = 180 + 40

20 x = 220

x = 220/20

x = 11

Get <b

<b = 13x-35

<b = 13(11) - 35

<b = 143-35

<b = 108 degrees

Get <c

c =5x-19

<c = 5(11)-19

<c = 55-19

<c = 36degrees

Get <d

<d = 2x+14

<d = 2(11) + 14

<d = 22+14

<d = 36 degrees

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Full Question for Number 14:
In ΔBCD if bc =bd angle b = 13x-35 angle c =5x-19 and angled d = 2x+14 find x and the measure of each angle

Answer:

I filled it in for you. Hope it helps xx

Answer:

-8.7 degrees

Step-by-step explanation:

22.2-30.9=-8.7

Answer:

its 0.59

Step-by-step explanation:

Because if you divide 7.08 and 12 then you get the answer.