Let B1={u1,...,un} and B2=v1,...,vn be the ordinate basis of the vector space V. Let T:V→V be the linear operator defined by T U1=V1,T U2=V2, ...,T Un=Vn.
Prove that [T]B1B1= [I]B2B1. Hint: Compare the arrays column by column.

Answers

Answer 1

To prove that [T]B1B1 = [I]B2B1, we need to compare the arrays column by column.

Let's denote the vectors in B1 as u1, u2, ..., un and the vectors in B2 as v1, v2, ..., vn.

We know that T(u1) = v1, T(u2) = v2, ..., T(un) = vn. This means that the column vectors of the matrix [T]B1B1 are precisely the vectors v1, v2, ..., vn.

On the other hand, the identity operator I maps any vector u in V to itself, i.e., I(u) = u. Since B2 is an ordered basis for V, we can express any vector u in V as a linear combination of the vectors in B2:

u = a1v1 + a2v2 + ... + anvn,

where a1, a2, ..., an are scalars. Now, if we apply the identity operator I to this vector u, we get:

I(u) = u = a1v1 + a2v2 + ... + anvn.

This means that the column vectors of the matrix [I]B2B1 are precisely the vectors a1, a2, ..., an.

Now, let's compare the arrays column by column:

The first column of [T]B1B1 represents the vector T(u1) = v1, which is also the first column of [I]B2B1.

The second column of [T]B1B1 represents the vector T(u2) = v2, which is also the second column of [I]B2B1.

Continuing this comparison, we see that each column of [T]B1B1 matches the corresponding column of [I]B2B1.

Since the arrays match column by column, we can conclude that [T]B1B1 = [I]B2B1.

Therefore, the matrix representation of the linear operator T with respect to the bases B1 and B1 is equal to the matrix representation of the identity operator with respect to the bases B2 and B1.

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Related Questions

CAN SOMEONE HELP ME OUT PLEASE AND THANK YOU

CAN SOMEONE HELP ME OUT PLEASE AND THANK YOU

Answers

The answer is A,hope this helps

Answer:

second option

Step-by-step explanation:

The area (A) of a rectangle is length × width , thus

A = (4x + 8)(2x + 3) ← expand factors using FOIL

   = 8x² + 12x + 16x + 24 ← collect like terms

   = 8x² + 28x + 24

Solve for the indicated unknown part of each triangle

Solve for the indicated unknown part of each triangle

Answers

Answer and Explanation:

1) We can solve for the measure of \(\theta\) in this triangle by using the trigonometric ratio tangent.

\(\tan(\theta) = \dfrac{\text{opposite}}{\text{adjacent}}\)

↓ plugging in the given side values

\(\tan(\theta) = \dfrac{8}{13}\)

↓ taking the inverse tangent of both sides

\(\boxed{\theta = \tan^{-1}\left(\dfrac{8}{13}\right)}\)

2) We can solve for the measure of \(\theta\) in this triangle by (once again) using the trigonometric ratio tangent.

\(\tan(\theta) = \dfrac{\text{opposite}}{\text{adjacent}}\)

↓ plugging in the given side values

\(\tan(\theta) = \dfrac{7}{10}\)

↓ taking the inverse tangent of both sides

\(\theta = \tan^{-1}\left(\dfrac{7}{10}\right)\)

3) We can solve for the length of side x by using the ratio of the sides of a 45-45-90 triangle, which is:

1 : 1 : \(\sqrt2\)

So, to solve for x, we just have to divide the length of the hypotenuse by \(\sqrt2\):

\(\boxed{x = \dfrac{10}{\sqrt{2}}}\)

Note that this can be rationalized by multiplying the fraction by \(\frac{\sqrt2}{\sqrt{2}}\):

\(x = \dfrac{10}{\sqrt{2}} \cdot \dfrac{\sqrt2}{\sqrt2} = \dfrac{10\sqrt2}{2} = \boxed{5\sqrt2}\)

pls help if you can asap!!!!

pls help if you can asap!!!!

Answers

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

which of rthe following goups of scores would hav ethe smallest standard deviation 20, 40, 60, 80, 100

Answers

In dataset 60 is the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation.

n dataset C, the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation

Standard deviation is 60

What do you mean by standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.

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You want to buy a new coat. The coat cost $97. They mark it up by 63%. You have a coupon for 26% off and there is a sales tax of 3%. How much will the coat cost you?

Answers

Answer:

$120.51

Step-by-step explanation:

$97 * 1.63 = $158.11

$158.11 * (1-.26) = $117.00

$117.00 * 1.03 = $120.51

Encuentra el perímetro de la circunferencia cuyo diámetro es de 6 cm

Answers

Answer:

Circumference = 2*pi*r

Diameter = 6 cm

Radius = 3 cm

Circumference = 2*22/7*3

= 18.85 cm.....

Step-by-step explanation:

Hope this helps you....

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a line is drawn thru (1,2) forming a right triangle with the positive x and y axies. what is the slope of line forming the smallest triangle (smallest area)

Answers

The slope of the line forming the smallest right triangle, when a line is drawn through the point (1, 2), is 2.

The slope of the line forming the smallest right triangle with the positive x and y axes, when a line is drawn through the point (1, 2), can be determined as follows.

First, let's consider the two axes as the legs of the right triangle, and the line drawn through (1, 2) as the hypotenuse. The slope of the hypotenuse can be calculated by finding the difference in y-coordinates divided by the difference in x-coordinates between the two endpoints.

Since the x-coordinate of the point where the line intersects the x-axis is 0 (positive x-axis), and the y-coordinate of the point where the line intersects the y-axis is 0 (positive y-axis), the difference in y-coordinates is 0 - 2 = -2, and the difference in x-coordinates is 0 - 1 = -1.

Therefore, the slope of the line forming the smallest right triangle is -2/-1 = 2.

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Help!!!!!! ASAP help

Help!!!!!! ASAP help

Answers

Answer:

A

Step-by-step explanation:

Notice that its y-intercept is (0,-5), so it crosses the y-axis at (0,-5)

Then, we notice that it is going doing from [-10,-2] and remains the same from[-2, 10]. Thus, the best choice is A

the most obvious answer for this would most likely be A . it’s the most reasonable

Drag each number to the correct location on the image. Each number can be used more than once, but not all numbers will be used.

Drag each number to the correct location on the image. Each number can be used more than once, but not

Answers

Answer:

5     3

6     4

4     2

Step-by-step explanation:

Find the product.


-0.3(4.1) =

Answers

Answer:

-1.23

Step-by-step explanation:

-0.3 x 4.1 = -1.23.

A negative number times a positive number equals a negative number.

-0.3(4.1) the answer is -1.23

During 2021, its first year of operations, Pave Construction provides services on account of $160,000. By the end of 2021, cash collections on these accounts total $110,000. Pave estimates that 25% of the uncollected accounts will be uncollectible. In 2022, the company writes off uncollectible accounts of $10,000.
1. Record the adjusting entry for uncollectible accounts on December 31, 2021.
2-a. Record the write-off of accounts receivable in 2022.
2-b. Calculate the balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022).
3-a. Assume the same facts as above but assume actual write-offs in 2022 were $15,000. Record the write-off of accounts receivable in 2022.
3-b. Assume the same facts as above but assume actual write-offs in 2022 were $15,000. Calculate the balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022).

Answers

Pave Construction provides services on account for bad dept of $40,000. Write-off of accounts receivable in 2022 is Allowance for Uncollectible Accounts (balance sheet) = $10,000. The balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) will be  $30,000.The balance of Allowance for Uncollectible Accounts at the end of 2022 will be $25,000 (assuming actual write-offs of $15,000).

Adjusting entry for uncollectible accounts on December 31, 2021:

Bad Debt Expense (income statement) = $40,000 ([$160,000 - $110,000] * 0.25)

Allowance for Uncollectible Accounts (balance sheet) = $40,000

Write-off of accounts receivable in 2022:

Allowance for Uncollectible Accounts (balance sheet) = $10,000

Accounts Receivable (balance sheet) = $10,000

Balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022):

The balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) will be $40,000 - $10,000 = $30,000.

Write-off of accounts receivable in 2022 (assuming actual write-offs of $15,000):

Allowance for Uncollectible Accounts (balance sheet) = $15,000

Accounts Receivable (balance sheet) = $15,000

Balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) (assuming actual write-offs of $15,000):

The balance of Allowance for Uncollectible Accounts at the end of 2022 (before adjustment in 2022) will be $40,000 - $15,000 = $25,000.

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6. Which expression is equivalent to the
algebraic expression below?
3(2x - 1)
A. + 2
B. X-1
C. -6x .- 3
D. -6x - 1
Course 3/4 Benchmark Test - End of Year​

Answers

Answer:

C. -6x . -3

Step-by-step explanation:

3 x 2x = 6x

3 x -1 = -3

i hurry i need help asap

i hurry i need help asap

Answers

It is the first chart

Find the value of a' and 'b' if 2/ 7+3√5 =a-b√5​

Answers

Step-by-step explanation:

Grazie don't forget to follow narin po

Find the value of a' and 'b' if 2/ 7+35 =a-b5
Find the value of a' and 'b' if 2/ 7+35 =a-b5
Find the value of a' and 'b' if 2/ 7+35 =a-b5

Answer:

\(a=\frac{7}{2} \ \ ,\ \ \ b=\frac{3}{2}\)

Step-by-step explanation:

\(\frac{2}{7+3\sqrt{5} } =\frac{2\times \left( 7-3\sqrt{5} \right) }{\left( 7+3\sqrt{5} \right) \left( 7-3\sqrt{5} \right) }\)

         \(=\frac{2\times \left( 7-3\sqrt{5} \right) }{7^{2}-\left( 3\sqrt{5} \right)^2 }\)

         \(=\frac{2\times \left( 7-3\sqrt{5} \right) }{49-45 }\)

         \(=\frac{2\times \left( 7-3\sqrt{5} \right) }{4 }\)

         \(=\frac{7-3\sqrt{5} }{2 }\)

         \(=\frac{7}{2} -\frac{3}{2} \sqrt{5}\)

Then

a = 7/2

b = 3/2

Find the slope of the line passing through the points (-9,4) (8,4)

Answers

Answer:

slope = 0  

Step-by-step explanation:

1) Use the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\), to solve for the slope. Use the x and y values of the given points, substitute them into the formula, and solve like so:

\(m = \frac{(4)-(4)}{(8)-(-9)} \\m = \frac{4-4}{8+9} \\m = \frac{0}{17} \\m = 0\)

Thus, the slope is 0.

200 = 1000 - n/4. What is the value of n? Show working out, please.

Answers

Answer:

n = 3200

Step-by-step explanation:

200 = 1000 - \(\frac{n}{4}\) ( subtract 1000 from both sides )

- 800 = - \(\frac{n}{4}\) ( multiply both sides by 4 to clear the fraction )

- 3200 = - n ( multiply both sides by - 1 )

n = 3200

the following are scores made on a science test.80,90,90,85,60,70,75,85,90,60,80,what is the median of these scores​

Answers

Answer:

80

Step-by-step explanation:

Put them in order from least to greatest and find the middle number

what is the domain of the function shown in the graph below?

what is the domain of the function shown in the graph below?

Answers

The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.

What is a domain?

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using set builder notation, the domain of this function shown in the graph above can be written as follows;

Domain = {-4, ∞}

Domain = {x|x ≥ -4}

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John has been in the hospital for three days. He is stable but not showing any significant improvement. John’s mom receives a call from her brother, who has a farm a little over 200 miles from them, where he raises pasture-reared pigs. He tells his sister that brucellosis has been diagnosed at his farm, and brucellosis can infect people. He reminds her that over the Thanksgiving holidays when they visited that John helped to pull some stillborn piglets from the birth canal of a sow experiencing a difficult labor (dystocia). Could John have brucellosis? She thanks her brother and immediately goes to find someone to give them this information.
The doctors request that the standard tube agglutination (STA) test for Brucella spp. is run on John’s previously collected and banked serum and CSF samples. The STA is a quick screening test. Currently, there is no growth on any culture plates streaked with CSF from John, but Brucella spp. are slow-growers and it is too early to expect any growth.
The request also alerts the diagnostic laboratory that samples from John may be infected with Brucella spp. and additional precautions should be observed to prevent laboratory personnel from inadvertently becoming infected.
Based on the additional history and clinical presentation, a probably diagnosis of brucellosis is made, and John begins treatment with a combination of three antibiotics demonstrated to be efficacious against Brucella spp.
:: we don't know the antibiotic. most probably common ones
Multiple interactions are occurring in a very short

Answers

In this scenario, multiple interactions are occurring within a very short period, each with unique dynamics and ramifications for the individuals involved.

The interactions are as follows: John's uncle called his mother to inform her of an outbreak of brucellosis at his farm, which John may have contracted while helping with a difficult labor case of a sow experiencing dystocia. His mother then contacts the hospital's doctor with this information, requesting that they screen John for brucellosis using a quick screening test called the standard tube agglutination (STA) test.

After the doctor receives the request, additional precautions are taken to prevent the spread of Brucella spp. to the lab staff. The STA test is run on John's previously collected and banked serum and CSF samples. Based on the additional history and clinical presentation, a probable diagnosis of brucellosis is made, and John begins treatment with a combination of three antibiotics that are effective against Brucella spp.

The dynamics of these interactions are centered on the shared concern for John's health and safety, and the potential for Brucella spp. to infect other hospital staff, diagnostic lab personnel, and even family members who came into contact with him.

The ramifications for the participants are numerous, from the need for additional laboratory safety precautions to the psychological effects of being diagnosed with a rare disease. Additionally, John's family will need to be informed of the diagnosis and potential risks, and his uncle's farm may face financial losses and reputational damage due to the outbreak of brucellosis.

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Complete Question:  

John has been in the hospital for three days. He is stable but not showing any significant improvement. John’s mom receives a call from her brother, who has a farm a little over 200 miles from them, where he raises pasture-reared pigs. He tells his sister that brucellosis has been diagnosed at his farm, and brucellosis can infect people. He reminds her that over the Thanksgiving holidays when they visited that John helped to pull some stillborn piglets from the birth canal of a sow experiencing a difficult labor (dystocia). Could John have brucellosis? She thanks her brother and immediately goes to find someone to give them this information.

The doctors request that the standard tube agglutination (STA) test for Brucella spp. is run on John’s previously collected and banked serum and CSF samples. The STA is a quick screening test. Currently, there is no growth on any culture plates streaked with CSF from John, but Brucella spp. are slow-growers and it is too early to expect any growth.

The request also alerts the diagnostic laboratory that samples from John may be infected with Brucella spp. and additional precautions should be observed to prevent laboratory personnel from inadvertently becoming infected.

Based on the additional history and clinical presentation, a probably diagnosis of brucellosis is made, and John begins treatment with a combination of three antibiotics demonstrated to be efficacious against Brucella spp.

:: we don't know the antibiotic. most probably common ones

Multiple interactions are occurring in a very short time frame. Discuss the dynamics of these interactions and the ramifications for the participants.

Find the perimeter of the shape below:

A four sided figure EFGH is shown. E is located at negative 1, 6. F is located at 2, 4. G is located at negative 1, 3. H is located at -3, 3
options:
1)
12.4 units
2)
13.4 units
3)
15.1 units
4)
16.8 units

Answers

Answer:

12.4

Step-by-step explanation:

i took the test!!

Answer:12.4

i took the test........

Find the perimeter of the shape below:A four sided figure EFGH is shown. E is located at negative 1,

The coordinates of then vertical of parallelograms WXYZ are W(-2,3) , X(-1,0) , Y(5,2) and Z (4,5) the slope of
I’ll give brainliest

The coordinates of then vertical of parallelograms WXYZ are W(-2,3) , X(-1,0) , Y(5,2) and Z (4,5) the

Answers

Answer:

The slope of WX and WY

Step-by-step explanation:

For us to have a rectangle, the angles at the edges equal 90

What this mean is that the width and the length are at 90 degrees

Hence, we can say that they are perpendicular to one another

Thus, we can calculate the slopes of both to drive home our point

Hence, by calculating the slopes of WX and WY, We can proof that we have a rectangle

PLEASE ANSWER THIS QUESTION 50 POINTS RIGHT ANSWERS ONLY

PLEASE ANSWER THIS QUESTION 50 POINTS RIGHT ANSWERS ONLY

Answers

Answer:

The period of this graph is 7.

Select all expressions that have a value greater than √3.15.

pi/3

5 - sqrt(3)

1 1/2 - sqrt(2)

6.2 - sqrt(2/2)

Answers

After considering all the given options we conclude that all the options have a greater value than √3.15 except for π/3, then the greatest value from the lot is Option D, which is  6.2 - √(2/2)

In order to evaluate the greatest expression from the lot that has a higher value than √3.15, we have to apply simplification for every option.

Therefore,

π /3) = 1.04

5 - √(3) = 2.2679

1 1/2 - √(2) = 0.0857

6.2 - √(2/2) = 5.2

Therefore, the expression that is  greater than rest of the option and higher in value in comparison to √3.15 is 6.2 - √(2/2)

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I really need help. The four tables represent functions.
Which table represents a non-linear function?

I really need help. The four tables represent functions.Which table represents a non-linear function?

Answers

Answer:

C

Step-by-step explanation:

Look at your Y-values. If you look at the constant difference for A. You will get a constant difference of 4 meaning its linear. B will give you a constant difference of 9 which also means that it is linear. D has a Constant difference of 1. However, C has no constant difference as the difference between each value changes, therefore meaning that it is not linear

3x - 5 = -3 is the answer positive or negative

Answers

Answer:

x = 2/3

0r 0.6(6)

both are positive

Step-by-step explanation:

3x - 5 = -3 is the answer positive or negative?

3x - 5 = -3

3x = -3 + 5

3x = 2

x = 2/3

0r 0.6(6)

What time is it in new orleans louisiana right now.

Answers

New Orleans, Louisiana is in the Central Time Zone. Currently, March, 3rd, 2022, it is 10:25 am.

. which of the two series i ""c & h or one oh per c seems to have a greater imfs. how did you reach this conclusion?

Answers

Based on the given information, it is not clear what the series "i ""c & h" or "one oh per c" refers to, and therefore it is not possible to determine which series has a greater imfs (incomplete metamorphic foliation). Further clarification or context is needed to reach a conclusion.

Without specific details or context about the series "i ""c & h" and "one oh per c," it is difficult to determine which one has a greater imfs. The concept of imfs typically pertains to geological structures and metamorphic foliation, where certain rock formations exhibit incomplete or partial foliation due to various geological processes. It is unclear how the terms "i ""c & h" and "one oh per c" relate to geological features or imfs.

To evaluate the relative imfs of the two series, one would need information about the intensity, extent, and characteristics of the metamorphic foliation observed in each series. This could include factors such as the degree of folding, preferred mineral alignment, grain size, and the presence of deformation features. Without such details, it is not possible to determine which series has a greater imfs.

To reach a conclusion, further information or clarification is needed regarding the nature of the series "i ""c & h" and "one oh per c" and how they relate to the concept of imfs.

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a bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles. you randomly select one marble from the bag. what is the probability that you select a gold marble? write your answer as a reduced fraction. p (gold marble)

Answers

After solving, the probability that we select a gold marble is 2/31.

In the given question,

A bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles.

So, Total marbles = 2+8+21

Total marbles = 31

As we know that, probability refers to the likelihood that an event will occur. If we don't know how such an event will end out, we can analyze the probability or likelihood of various outcomes. Statistic is the analysis of events that follow a probability distribution.

We have to randomly select one marble from the bag then we have to find the probability that we select a gold marble is

P(G) = Total number of gold marble/Total marbles

P(G) = 2/31

Hence, the probability that we select a gold marble is 2/31.

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If the odds against debroah's winning first prize are 3 to 5, what is the probability that she will win 1st prize?

Answers

Answer:

See below

Step-by-step explanation:

Odds AGAINST are 3 to5        then odds FOR are  2 to 5

    2/5   = .4 = 40%   chance of winning

Rewrite the fraction 2/7 as a division expression with the same numbers.

Answers

Answer:

EZ. Btw you kinda already did it. 2/7 is a division problem. Another way is 2 divided by 7

Step-by-step explanation:

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Will this produce a horizontal, vertical, or diagnol line?(10 Points)- Horizontal- Vertical- O Diagonal HELPPPP PLEASE I ONLY HAVE 6 MINUTES LEFT HELP ME Read this short passage and answer the question below:Excerpt from The Little MermaidBy Hans Christian Andersen"Come, little sister," said the other princesses; then they entwined their arms and rose up in a long row to the surface of the water, close by the spot where they knew the prince's palace stood. It was built of bright yellow shining stone, with long flights of marble steps, one of which reached quite down to the sea. Splendid gilded cupolas rose over the roof, and between the pillars that surrounded the whole building stood life-like statues of marble. Through the clear crystal of the lofty windows could be seennoble rooms, with costly silk curtains and hangings of tapestry; while the walls were covered with beautiful paintings which were a pleasure to look at. In the center of the largest saloon a fountain threw its sparkling jets high up into the glass cupola of the ceiling, through which the sun shone down upon the water and upon the beautiful plants growing round the basin of the fountain. Now that she knew where he lived, she spent many an evening and many a night on the water near the palace. She would swim much nearer the shore than any of the others ventured to do; indeed once she went quite up the narrow channel under the marble balcony, which threw a broad shadow on the water. Here she would sit and watch the young prince, who thought himself quite alone in the bright moonlight. She saw him many times of an evening sailing in a pleasant boat, with music playing and flags waving. She peeped out from among the green rushes, and if the wind caught her long silvery-white veil, those who saw it believed it to be a swan, spreading out its wings.Based on details in the story, the reader can conclude that the little mermaid A) cares more about humans than her sisters do B) loves the beauty of the princes palace more than her home C) is unhappy with her life below the sea D) is too shy to try and talk to the prince Can someone plz help due in a couple minutes only 3 question I will mark braniliest ! Four students have rewritten the expression with rational exponent xi in radical form as shown.JodieMarkPaulSallyWho has rewritten this expression correctly?A. JodieB. MarkC. PaulD. Sally