Solve equation or formula for the variable specified
Xy-9z=4 for y

The translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5). (option b)

To translate the triangle two units to the left, we need to subtract 2 from the x-coordinates of each vertex, while leaving the y-coordinates unchanged. This is because moving the triangle left means we're decreasing its x-values.

So, let's apply this transformation to each point.

The first point, (-1, -1), becomes (-1 - 2, -1), which simplifies to (-3, -1).

The second point, (-1, -5), becomes (-1 - 2, -5), or (-3, -5).

The third point, (0.5, -5), becomes (0.5 - 2, -5), or (-1.5, -5).

These new coordinates give us the vertices of the triangle after it has been translated two units to the left.

Now that we have the new vertices, we can label them A', B', and C' to distinguish them from the original vertices. So, the translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5).

This is the second option in the answer choices given.

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An advance in technology in the production of good X causes:

c) a rightward shift in the supply curve for good X.

An advance in technology typically increases the efficiency of production and reduces the costs of production. This results in an increase in the quantity of goods that can be produced at a given price, causing the supply curve to shift to the right. The shift to the right reflects an increase in supply, meaning that at any given price, there is now a larger quantity of goods available for sale. This increase in supply tends to put downward pressure on the market price.

The determination of a rightward shift in the supply curve as a result of an advance in technology can be made through analyzing the relationship between price and quantity supplied using basic microeconomic principles.

The supply curve represents the relationship between the price of a good and the quantity of that good that producers are willing and able to supply to the market. An advance in technology that leads to an increase in production efficiency and a decrease in production costs can increase the quantity of goods that can be produced at any given price.

As a result, the supply curve will shift to the right, reflecting an increase in the quantity of goods supplied at each price point. This shift to the right indicates that there is now a larger quantity of goods available for sale at any given price, which can put downward pressure on the market price.

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The actual length of the living area is 134.4 feet if the length in the scale drawing is 16.8 in the scale.

To determine the actual length of the living space from a scale drawing, we need to use the scale factor, which is the ratio of the length in the drawing to the actual length. If the length in the scale drawing is 16.8 inches and the scale is given as a ratio of 1 inch in the drawing to 8 feet in actual size, we can set up a proportion:

1 inch (drawing) / 8 feet (actual)

= 16.8 inches (drawing) / x (actual)

We can cross-multiply and simplify to find x's value:

1 inch × x = 8 feet × 16.8 inches

x = (8 feet × 16.8 inches) / 1 inch

x = 134.4 feet.

Therefore, the actual length of the living space is 134.4 feet.

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Answer: <9

Step-by-step explanation:

Answer:

diagonal length = 12√2 inches

Step-by-step explanation:

If the perimeter of the square is 48 inches, the length of one side is one fourth of that, or 12 inches.  The diagonal creates a 45-45-90 triangle with two 12-in legs; we are to find the length of the diagonal.  Using the Pythagorean Theorem, we get

12² + 12² = (diagonal length)², or 2(12²) =  (diagonal length)²

Taking the square root of both sides, we get:

diagonal length = 12√2 inches

The volume, of the cement used to make the sidewalk is 8 ft³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, James is using cement to make a new sidewalk and new steps,

He will make a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick.

Volume = length x width x height

Volume = 8 x 4 x 0.25 = 8 ft³

Hence, the volume, of the cement used to make the sidewalk is 8 ft³

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Answer:

Physical means the actual wires.  Physical is concerned with how the wires are connected. Logical is concerned with how they transmit.

a. Logical

Step-by-step explanation:

...

The arrangement of network cabling between devices is a physical topology. which is the correct answer would be option (C).

The physical configuration of a network, such as the physical arrangement of wires, media (computers), or cables, is referred to as its topology. A link can connect two or more devices, and when the number of connections reaches two, they constitute a physical topology.

A physical network diagram depicts the connecting of devices via cables or wireless links. A logical network diagram, on the other hand, depicts data and signal transfer throughout a network.

Therefore, the arrangement of network cabling between devices is a physical topology.

Hence, the correct answer would be an option (C).

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The values areas are:

Figure 1 = 69.81 in²

Figure 2 = 192.50 ft²

Figure 3 = 153.50 yd²

Figure 4 = 296.00 in²

Figure 5 = 126.00 ft²

Figure 6 = 26.30 ft²

This exercise requires your knowledge about the area of compound shapes. For solving this, you should:

The steps and solutions for each given figure are presented below.

The figure 1 is composed by a rectangle and a semicircle. Therefore, you should sum the area of these geometric figures.

Area of rectangle  - \(A_{rectangle}=l.w\), where:

l= length (12 in)and w=width (5 in).

\(A_{rectangle}=l.w=12*5=60 in^{2}\)

Area of semicircle- \(A_{semicircle}=\frac{Area circle}{2}=\frac{\pi*r^{2} }{2}\), where:

r= radius ( \(\frac{w}{2} =\frac{5}{2} =2.5\)) and π = 3.14

\(A_{semicircle}=\frac{Area circle}{2}=\frac{\pi*2.5^{2} }{2}=9.81 in^{2}\)

Therefore, \(A_{fig1}= 60 + 9.81=69.81 in^{2}\).

The figure 2 is composed by a parallelogram and a trapezoid. Therefore, you should sum the area of these geometric figures.

Area of parallelogram - \(A_{parallelogram}=b.h\), where:

b= length of the base (11 ft)and h=height (7 ft).

\(A_{parallelogram}=b.h=11*7=77ft^{2}\)

Area of trapezoid - \(A_{trapezoid}=\frac{(a+b)*h}{2}\), where:

a= long base (20-7=13 ft ), b = short base (8 ft) and height (11 ft)

\(A_{trapezoid}=\frac{(a+b)*h}{2}=\frac{(13+8)*11}{2}=\frac{21*11}{2}=\frac{231}{2}=115.50\)

Therefore, \(A_{fig2}= 77+ 115.5=192.50 ft^{2}\).

The figure 3 is composed by a triangle and a trapezoid. Therefore, you should sum the area of these geometric figures.

Area of triangle - \(A_{triangle}=\frac{b*h}{2}\), where:

b= length of the base (19 yd) and h=height (7 yd).

\(A_{triangle}=\frac{b*h}{2} =\frac{19*7}{2} =\frac{133}{2}= 66.5 yd^{2}\)

Area of trapezoid - \(A_{trapezoid}=\frac{(a+b)*h}{2}\), where:

a= long base (19 yd ), b = short base (10 yd) and height (13-7=6 yd)

\(A_{trapezoid}=\frac{(a+b)*h}{2}=\frac{(19+10)*6}{2}=\frac{29*6}{2}=29*3=87 yd^2\)

Therefore, \(A_{fig3}= 66.5+ 87=153.50 yd^{2}\).

The figure 4 is composed by two rectangles. Therefore, you should sum the area of these geometric figures.

Area of rectangle 1  - \(A_{rectangle}=l.w\), where:

l= length (16+5=21 in)and w=width (8 in).

\(A_{rectangle}=l.w=21 *8=168 in^{2}\)

Area of rectangle 2  - \(A_{rectangle}=l.w\), where:

l= length (16 in)and w=width (5 in).

\(A_{rectangle}=l.w=16*8=128 in^{2}\)

Therefore, \(A_{fig4}= 168+ 128=296.00 in^{2}\).

The figure 5 is composed by a square and a parallelogram. Therefore, you should sum the area of these geometric figures.

Area of square - \(A_{square}=l^2\), where:

l= length (9 ft).

\(A_{square}=l^{2}=9^2=81 ft^{2}\)

Area of parallelogram - \(A_{parallelogram}=b.h\), where:

b= length of the base (9 ft)and h=height (14-9=5 ft).

\(A_{parallelogram}=b.h=9*5=45ft^{2}\)

Therefore, \(A_{fig5}= 81+ 45=126.00 ft^{2}\)

The figure 5 is composed by a triangle and a semicircle. Therefore, you should sum the area of these geometric figures.

Area of triangle - \(A_{triangle}=\frac{b*h}{2}\), where:

b= length of the base (6 yd) and h=height (4 yd).

\(A_{triangle}=\frac{b*h}{2} =\frac{6*4}{2} =\frac{24}{2}= 12 yd^{2}\)

Area of semicircle- \(A_{semicircle}=\frac{Area circle}{2}=\frac{\pi*r^{2} }{2}\), where:

r= radius ( \(\frac{6}{2} =3\)) and π = 3.14

\(A_{semicircle}=\frac{Area circle}{2}=\frac{\pi*3^{2} }{2}=14.3 yd^{2}\)

Therefore, \(A_{fig6}= 12+ 14.3=26.3 yd^{2}\)

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True, the joint probability of Y1 and Y2 taking on the value 1 simultaneously is 1/3.

The first dummy random variable is defined as follows:

Let X be the random variable representing the number on the first dice. Then, the dummy random variable Y1 is defined as:

Y1 = 1 if X is either 1, 2, or 3

Y1 = 0 otherwise

Similarly, the second dummy random variable is defined as:

Let Z be the random variable representing the number on the second dice. Then, the dummy random variable Y2 is defined as:

Y2 = 1 if Z is either 3, 4, 5, or 6

Y2 = 0 otherwise

Since Y1 and Y2 are independent, their joint probability distribution can be computed by multiplying their marginal probabilities.

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1)

To compute P(Y1=1), we need to find the probability that X is either 1, 2, or 3. Since each face of a fair dice has an equal probability of appearing, we have:

P(X=1) = P(X=2) = P(X=3) = 1/6

Therefore,

P(Y1=1) = P(X=1 or X=2 or X=3) = P(X=1) + P(X=2) + P(X=3) = 3/6 = 1/2

Similarly, to compute P(Y2=1), we need to find the probability that Z is either 3, 4, 5, or 6. Again, since each face of a fair dice has an equal probability of appearing, we have:

P(Z=3) = P(Z=4) = P(Z=5) = P(Z=6) = 1/6

Therefore,

P(Y2=1) = P(Z=3 or Z=4 or Z=5 or Z=6) = P(Z=3) + P(Z=4) + P(Z=5) + P(Z=6) = 4/6 = 2/3

Thus,

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1) = (1/2) * (2/3) = 1/3

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Answer:

The half-life of carbon-14 is 5,730 years. This means that every 5,730 years, half of the carbon-14 in a sample will decay. So, if a sample contains 32% of its original amount of carbon-14, it is about 2 * 5,730 = 11,460 years old.

However, it is essential to note that radiocarbon dating is not an exact science. There is a margin of error of about 20 years. So, the skull's actual age could be between 11,260 and 11,660 years old.

Here is a formula that can be used to calculate the age of a sample using radiocarbon dating:

```

Age = (5,730 * ln(A/Ao)) / ln(2)

```

Where:

* Age is the age of the sample in years

* A is the amount of carbon-14 in the sample

* Ao is the original amount of carbon-14 in the sample

* ln is the natural logarithm function

In this case, A = 0.32 and Ao = 1.0. So, the age of the skull is:

```

Age = (5,730 * ln(0.32) / ln(2)) = 11,460 years

```

Step-by-step explanation:

Answer:

4535 years.

Step-by-step explanation:

The formula used to calculate the age of a sample by carbon-14 dating is3:

t=−0.693ln(N0​Nf​​)​×t1/2​

where:

t is the age of the sample

Nf is the number of carbon-14 atoms in the sample after time t

N0 is the number of carbon-14 atoms in the original sample

t1/2 is the half-life of carbon-14 (5730 years)

In your case, the skull contains 32% of its original amount of carbon-14, which means that Nf/N0 = 0.32. You can plug in this value and the half-life into the formula and get:

t=−0.693ln(10.32​)​×5730

Using a calculator, you can simplify this expression and get:

t=−1.139×−0.693×5730

t=4534.7

Answer: 70.9 miles per hour

Step-by-step explanation:

The total distance traveled is 1188 miles (66313- 65125).

Since this was over 16.75, you'll want to divide 1188 by 16.75.

1188/16.75 = 70.9253731

And then round that off to 70.9

Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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28 is your answer.

Explanation:

DO THE MATH

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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The percentage of data between 13.8 and 30.2 in a normally distributed data set with a mean of 22 and a standard deviation of 4.1 is approximately 94.19%.

To solve this problem, we can first standardize the values of interest using the standard normal distribution formula, z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation.

For the lower value of 13.8, we have z = (13.8 - 22) / 4.1 = -1.95. For the upper value of 30.2, we have z = (30.2 - 22) / 4.1 = 2.05.

Next, we can use a calculator to find the area between these two z-scores. Alternatively, we can use the complement rule to find the area to the left of -1.95 and the area to the right of 2.05, and subtract their sum from 1.

Using a calculator, we find that the area between -1.95 and 2.05 is approximately 0.9419 or 94.19%. Therefore, approximately 94.19% of the data falls between 13.8 and 30.2 in this normally distributed data set.

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Answer:

C

Step-by-step explanation:

4(5)+10-12=18

Answer:

3,333.33

Step-by-step explanation:

Let Sharon's wage be represented with x

Sharon's wage under scheme a = 0.06x + x

Sharon's wage under scheme b = 0.045x + x + 50

If her wage is equal under both schemes, the two schemes are equal in value and can be equated to find her wage

0.045x + x + 50 =  0.06x + x

1.06x = 1.045x + 50

Collect like terms

1.06x - 1.045x = 50

0.015x = 50

x = $3,333.33

The expression in the format "5(blank space 1) + (blank space 3)(blank space 4) + 8(blank space 7)" represents a mathematical expression with three terms. To create the expression with the given conditions, we can use the following format:

5(blank space 1) + (blank space 3)(blank space 4) + 8(blank space 7)

Here are four options for each blank space:

Option 1:

Blank space 1: x

Blank space 3: 2

Blank space 4: y

Blank space 7: z

So the expression would be:

5x + 2y + 8z

Option 2:

Blank space 1: a

Blank space 3: 3

Blank space 4: b

Blank space 7: c

So the expression would be:

5a + 3b + 8c

Option 3:

Blank space 1: m

Blank space 3: 4

Blank space 4: n

Blank space 7: p

So the expression would be:

5m + 4n + 8p

Option 4:

Blank space 1: r

Blank space 3: 1

Blank space 4: s

Blank space 7: t

So the expression would be:

5r + s + 8t

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Answer:

Step-by-step explanation:

The statement "x = y² - 9" is not a function because for some values of y, there are multiple corresponding values of x.

A relation between a set of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Now in the given question ,

In particular, when y = 3, there are two possible values of x (x = 0 and x = 6), so (3, 0) and (3, 6) are two points on the graph of this equation. This violates the definition of a function, which states that for each input (in this case, y), there can only be one output (x). The other statements are not relevant to determining whether the equation is a function.

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Based on the data information of a Privett Company related to all amount payable, liabilities, etc. The amount of quick assets is equals to the $116,938. So, option(d) is correct choice for answer here.

We have a data of Privett Company, it consists amount'data in different fields regarding company like account payable, receivable, cash , etc. We have to determine the value of the amount of quick assets.

Quick assets include cash, accounts receivable, and marketable securities, which are equities and debt securities that can be converted into cash within one year. Formula to calculate the quick assets of a company is Quick assets = Accounts receivable + Cash + Marketable securities.

So, needed all these three amounts for it.

Amount of company related to Accounts receivable = $60,450

Cash amount of company = $17,192

Amount of company related to Marketable securities = $39,296

Substitute all known values in above formula,

=> Quick assets = $60,450 + $17,192 + $39,296

= $116,938

Hence, required value is $116,938.

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Answer:

The outer term gets multiplied by each term inside the parenthesis

-(a³b²c²) - (a²b³c²) + (a²b²c³)

3, 2, 2     2, 3, 2      2, 2, 3

-a²b²c²(a+b-c)

= -a³b²c² - a²b³c² + a²b²c³

\((\frac{3}{8} )^{-2}\)

\((\frac{8}{3})^{2}\)

\((\frac{8}{3} )\times(\frac{8}{3} )\)

\(\frac{8\times8}{3\times3}\)

\(\frac{64}{9}\) or \(7.1111111\)

Kim travelled 35 km on a paved surface and 6 km off-road which took 1.4 hours and 0.6 hours respectively

Speed of Kim when cycling on paved surfaces: 25 km/hr

Speed of Kim when cycling off-road = 10 km/hr

Distance covered by Kim = 41 km

Time is taken by Kim = 2 hours

Let x be the time Kim travels on a paved surface, and y represents the time off-road

Using the formula:

Speed = Distance/Time

Distance travelled by Kim on paved surface = 25*x

Distance travelled by Kim off-road = 10*y

x + y = 2-------(1)

25x + 10y = 41-------(2)

Multiplying equation (1) with 25 and equating with (2) we get:

25x + 25y = 50

25x + 10y = 41

15y = 9

y = 0.6 hours

x = 1.4 hours

Distance travelled on paved surface = 25*1.4 = 35 km

Distance travelled off-road = 10*0.6 = 6km

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Answer:

.2%

.6%

40.25%

Step-by-step explanation:

There are 100 blocks in a grid so a complete grid is 100 %

a 2/10 out of 1 block is shaded

2/10  out of 100

.2 out of 100

out of 100 means percent

.2 %

b 3/5 out of 1 block is shaded

6/10 out of 100

.6 out of 100

out of 100 means percent

.6%

c 40 /100 + 1/4  out of 1 block

40% + .25 %

40.25%

The length of the tree's shadow will be 35.59 ft.

Tangent function is one of the six trigonometric functions in mathematics. In heights and distances, tangent of the angle of elevation or depression can be used to calculate the distance or height of an object as -

tanФ = [P]/[B]

The domain and range of the tangent function is -

Domain - R - {(2k+1)π/2}     [where k is an integer]

Range - R  [where R is the set of real numbers]  

Given is angle of elevation of the sun during a certain time of day as 42.4°. At this specific time day a 32.5 foot tree casts a shadow on the ground.

Assume that angle of elevation is equal to Ф

Now, using the tangent function, we can write -

tanФ = [tree height] / [tree shadow]

tan(42.4) = 32.5 / [tree shadow]

tree shadow = (32.5/tan(42.4))

tree shadow = 32.5/0.913 = 35.59 ft

Therefore, the length of the tree's shadow will be 35.59 ft.

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Answer:

100ml bottle is cheapest per ml

Step-by-step explanation:

The 80 ml bottle sells for 55 so that makes 80 ml for 5500 p which calculates to 68.75p per ml.

the 2 50 ml bottles will cost 45+22.50  = 67.50 which makes 100 ml for 6750p

this makes it 67.5p per ml which is cheaper than the 80 ml bottle

The area under the normal curve up to z = 0.36 is P(Z ≤ 0.36) and is equal to 0.64. To find the value of P(Z ≤ 0.36), the standard normal distribution table is used. We can find the value by looking up the closest z-value on the standard normal distribution table.

The value of 0.36 is not exactly found in the table, however, the closest value to it is 0.35. Using the standard normal distribution table, the area to the left of z = 0.35 is 0.6368. Since we need to find P(Z ≤ 0.36), this area needs to be added to the area from 0.36 to 0.35, which is 0.0032. Adding the two values will give us the answer: 0.6368 + 0.0032 = 0.64.Therefore, the area under the normal curve up to z = 0.36 is P(Z ≤ 0.36) and is equal to 0.64. In order to find the area under the normal curve up to z = 0.36, we need to find the value of P(Z ≤ 0.36), which is the probability of a standard normal variable taking a value less than or equal to 0.36. To find this probability, we use the standard normal distribution table, which provides the area to the left of a given z-value.The standard normal distribution table is usually presented in the form of a table that gives the area to the left of a given z-value. For example, if we want to find the area to the left of z = 1.96, we look up the value 1.9 in the first column and the value 0.06 in the second column. We then add these two values to get the area to the left of z = 1.96, which is 0.9750. Similarly, we can find the area to the left of any other z-value by using the standard normal distribution table.To find the area under the normal curve up to z = 0.36, we first need to find the closest value to 0.36 in the standard normal distribution table. In this case, the closest value is 0.35. We then look up the area to the left of z = 0.35 in the standard normal distribution table, which is 0.6368. Since we need to find the area to the left of z = 0.36, we need to add the area from 0.35 to 0.36, which is 0.0032. Adding these two values gives us the area under the normal curve up to z = 0.36, which is 0.6368 + 0.0032 = 0.64.

The area under the normal curve up to z = 0.36 is P(Z ≤ 0.36) and is equal to 0.64. This means that the probability of a standard normal variable taking a value less than or equal to 0.36 is 0.64. To find this probability, we used the standard normal distribution table, which provides the area to the left of a given z-value. We found the area to the left of z = 0.35, which is the closest value to 0.36 in the standard normal distribution table. We then added the area from 0.35 to 0.36 to get the area under the normal curve up to z = 0.36, which is 0.64.

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The difference between an actual score and a predicted score is called a residual.

In various fields such as statistics, econometrics, and data analysis, the term "residual" refers to the difference between the observed or actual value of a variable and the value predicted by a model or estimation method. It represents the unexplained or leftover variation in the data after considering the model's predictions.

In the context of regression analysis, the predicted score is obtained by fitting a regression model to the data and using it to estimate the expected value of the dependent variable. The difference between the actual value and the predicted value for a specific observation is the residual for that observation.

Residuals play a crucial role in assessing the goodness of fit of a regression model. By examining the pattern and properties of residuals, such as their mean, variance, and distribution, analysts can evaluate how well the model captures the underlying relationships in the data and identify any systematic deviations or outliers.

Overall, residuals provide valuable information for understanding the accuracy and precision of predictions made by a model and can be used to refine and improve the model's performance.

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Answer:

D and E

C

Step-by-step explanation: