I'll give brainliest

The regular price of the suit is $250.

What is the discounts ?

A discount is a reduction in the price of a product or service. It is often used as an incentive to encourage customers to buy a product or service, especially when the original price is considered too high.

Let's assume the regular price of the suit to be x.

According to the problem, the sale price of the suit after a 25% discount is $187.5.

This can be written as:

x - 0.25x = 187.5

Simplifying the equation:

0.75x = 187.5

Dividing both sides by 0.75:

x = 250

Hence, the regular price of the suit is $250.

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The vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).

What is the quadratic function?

A quadratic function is a function of the form [tex]f(x) = ax^2 + bx + c,[/tex] where a, b, and c are constants, and a is not equal to 0. It is a type of polynomial function that can be graphed as a parabola, which is a symmetric curve that opens either upwards or downwards.

Given the table of points for the continuous quadratic function h(x), we can find the vertex and range of the function. Since the function is quadratic and continuous, it can be represented in the standard form [tex]f(x) = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola.

To find the vertex, we can use the fact that the x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively. In this case, a = 1 (since the function is continuous and quadratic), and b can be found using any two points on the parabola:

[tex]b = (h(x2) - h(x1))/(x2 - x1) = (4 - 7)/(-2 + 1) = 3[/tex]

Therefore, the x-coordinate of the vertex is x = -b/2a = -3/2. To find the y-coordinate of the vertex, we can evaluate the function at this value of x:

[tex]h(-3/2) = (1)(-3/2 - h)^2 + k[/tex]

To solve for k, we can use one of the points on the parabola, say (-6, 12):

[tex]12 = (1)(-6 - h)^2 + k[/tex]

Expanding and simplifying, we get:

[tex]12 = (h - 6)^2 + k[/tex]

Substituting -3/2 for h, we get:

[tex]12 = (-(3/2) - 6)^2 + k\\\\12 = 81/4 + k\\\\k = -21/4[/tex]

Therefore, the vertex of the parabola is at the point (-3/2, -21/4).

To find the range of the function, we can look at the shape of the parabola. Since the coefficient of the quadratic term is positive, the parabola opens upwards, and the vertex is the lowest point on the graph. Therefore, the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -21/4. In interval notation, we can write the range as (-21/4, infinity).

Hence, the vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).

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A variable in mathematics is a number that can change depending on the issue. Several mathematical statements and equations use the generic letters x, y, and z. In other words, a variable is a symbol that stands for an unknowable numeric value. Say that x Plus 5 equals 10. The "x" variable is used here.

The variable "model of car driven" is qualitative because it is an attribute characteristic. Qualitative variables are those that are not numerical in nature but rather represent characteristics or categories that can be observed or measured through attributes. In this case, the model of the car driven is a type of attribute that describes the make and model of the car, such as Honda Civic, Toyota Corolla, etc.

Therefore, option B is the correct answer.

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Optiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

A qualitative variable is a type οf variable in statistics that describes a characteristic οr quality οf an οbject οr phenοmenοn. It is alsο called a categοrical variable, and it can be nοminal οr οrdinal. Nοminal variables have categοries that have nο inherent οrder, while οrdinal variables have categοries with a natural οrder οr ranking.

The variable "Mοdel οf car driven" is qualitative because it is an attribute characteristic. Qualitative variables are variables that are nοt numerical in nature but are based οn attributes οr characteristics. In this case, the mοdel οf the car driven is a categοrical variable that describes a particular characteristic οf the car, such as its make οr mοdel. This variable cannοt be measured quantitatively οr numerically, but rather it can be categοrized based οn specific attributes οr features.

Therefοre, οptiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

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The solution is, B , is the correct answer is 10.0923.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

the equation is, 2.02 + 8.102 - 0.0297

now, we have to solve it, by addition & subtraction.

we know,

First

2.02+8.102=10.122

Then 10.122-0.0297=10.0923

i.e. we get,

2.02 + 8.102 - 0.0297

=10.122-0.0297

=10.0923.

Hence, The solution is, B , is the correct answer is 10.0923.

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The exponential function that best matches the graph is given as follows:

E. y = 4^(x + 1).

An exponential function, with horizontal asymptote at y = 0, is defined as follows:

y = ab^x.

In which:

From the graph, when x = 0, y = 4, hence the parameter a is given as follows:

a = 4.

When x = -1, y = 1, meaning that when x increases by one, y is multiplied by 4, hence the parameter b is given as follows:

b = 4.

Hence the function is defined as follows:

y = 4(4)^x

y = 4^(x + 1).

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Answer:

B. 10 yd., 14 yd., 17 yd.

Step-by-step explanation:

In a right triangle, the squares of the sums of the two shorter sides must equal the square of the longer side(which is the hypotenuse)

From the combinations given only the set 10 yd, 14 yd. and 17 yd does not obey this rule

10² + 14² = 296
17² = 298
So this does not match

Answer:

A ∩ B = {6, 12}

Step-by-step explanation:

A ∩ B means only the terms A and B have in common.

Therefore, A ∩ B = {6, 12}

Answer:

Step-by-step explanation:

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. Therefore, the diagonal of the square is twice the radius of the circle, or 10 mm.

To find the area of the square, we can use the formula A = s^2, where s is the side length of the square. The diagonal of the square is √2 times the side length, so we have:

10 mm = √2 x s

s = 10 mm / √2

The area of the square is:

A = s^2 = (10 mm / √2)^2 = 100 mm^2 / 2 = 50 mm^2

To find the area of the circle, we can use the formula A = πr^2, where r is the radius of the circle. We are given that the radius is 5 mm, so:

A = π(5 mm)^2 = 25π mm^2

To find the shaded section, we need to subtract the area of the circle from the area of the square. The shaded section is the remaining area of the square after the circle has been inscribed. Therefore, the shaded section is:

Shaded Section = Square Area - Circle Area

Shaded Section = 50 mm^2 - 25π mm^2

Shaded Section ≈ 10.79 mm^2 (rounded to two decimal places)

Answer: x^2 + (y – 3)^2 = 36

Step-by-step explanation:

The standard equation of a circle with center at (h, k) and radius r is

(x - h)^2 + (y - k)^2 = r^2.

If the center lies on the y-axis, then h = 0:  (x - 0)^2 + (y - k)^2 = r^2

If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36

So, among the given equations, your

x^2 + (y – 3)^2 = 36 is correct

The values of the missing entries are given below:

x  2  1  3  5  0

y  0  1  1   9  4

Given:

y= x^2 - 4x + 4

= (x-2)^2

Thus, when y= 0, (x-2)^2 =0

x =2 (substitute y=0 into the equation)

When x= 1,  y = (1-2)^2 = 1

When y =1, (x-2)^2 =1, x-2 ± 1

x= 3, or x=1 (choose 3)

when x= 5, y= (5-2)^2 = 3^2 =9

when x = 0,  y= (0-2)^2 = 2^2 = 4

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As n increases, the area of the regular polygon approaches the area of the circle.

The correct option is (b)

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle.

The polygon area can be expressed in terms of the area of a triangle.

Let s denote the side length of triangle.

r hypotenuse of right triangle.

h height of the triangle.

let n be the number of sides of the regular polygon.

The area of polygon is given by:

polygon area = n(12sh)

The correct statement is:

As n increases, the area of the regular polygon approaches the area of the circle.

As n increases , the triangle will be smaller and smaller. h approaches r so that rh approaches [tex]r^2[/tex]

" Since, as the number of sides of the polygon increases the polygon start approaching to the circumference of circle and as n tends to infinity the polygon will tend to take the shape of the circle "

Therefore, The correct option is (b)

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The given question is incomplete, complete question is:

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle.

Let s be the side length of the polygon,

let r be the hypotenuse of the right triangle,

let h be the height of the triangle, and

let n be the number of sides of the regular polygon.

polygon area = n(12sh)

Which statement is true?

a. As r increases, the area of the regular polygon approaches the area of the circle.

b. As n increases, the area of the regular polygon approaches the area of the circle.

c. As s increases, the area of the regular polygon approaches the area of the circle.

d. As h increases, the area of the regular polygon approaches the area of the circle.

Answer:

Step-by-step explanation:

225 miles because you have to divide 100 by 4 that would give me 25 MPG and be asked, how many miles can the car travel using? Nine gallons of gasoline? So that would be right here, And that's at 225 Miles that it can travel with nine gallons of gasoline.

Therefore , the solution of the given problem of equation comes out to be (1, -4) is a solution to the equation 4x - 2y = 12.

The equivalent sign (=) is used in arithmetic equations to signify the equality of two propositions. It is shown that it is possible to compare various numerical factors by using mathematical techniques, which have served as manifestations of reality. For instance, the equal sign divides the number 12 even the solution y + 6 = 12 in two distinct portions. How many characters also are present from either end of such a character can be calculated. Conflicting symbol readings are prevalent.

Here,

To find the values of missing entries, we can pick any arbitrary value of x and solve for y. Let's take x=1.

4(1) - 2y = 12

Simplifying the equation, we get:

-2y = 8

Dividing both sides by -2, we get:

y = -4

So, when x=1, y=-4. Therefore, the missing entries in the table are (1, -4).

Using this value, we can also check that the equation 4x - 2y = 12 is satisfied:

4(1) - 2(-4) = 4 + 8 = 12

So, (1, -4) is a solution to the equation 4x - 2y = 12.

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The solution to the inequality is x ≤ 1.

Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.

To solve this inequality, we must first perform the operations on the left side of the equation to get an expression equal to 4. We can start by simplifying the fraction on the left side of the equation. We can multiply both the numerator and denominator by x, which will give us 5x - 3 = x + 2x. We can then add 3 to both sides to get 5x = 3 + 2x, which can then be simplified to 3x = 3. Finally, we can divide both sides by 3 to get x = 1. Therefore, the solution to the inequality is x ≤ 1.

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Answer:

[tex]A. \;x^2 -7x + 1[/tex]

[tex]B.\;5x^2 + 2x[/tex]

Step-by-step explanation:

Standard Form of Polynomial
Standard form of a polynomial is written in the descending order of the power of the variable.

The standard form of polynomial is given by

[tex]f(x) = a_nx^n + a_{n-1}x^{n-1}+....... + a_1x + a_0[/tex]
where [tex]x[/tex] is the variable and [tex]a_i,\; i = 0...n[/tex] are coefficients.

The only two expressions in standard form are
[tex]A. \;x^2 -7x + 1[/tex]

and
[tex]B.\;5x^2 + 2x[/tex] (here the constant a₀ is 0)

1.) Skewed left

2.) a. z-score = 0.54
    b. z-score = 0.77

    c. z-score = -0.77
3.) a. z-score = 1.24

    b. Large Chain

    c. Local Brewery

4.) a. The middle 95% of six-packs at the local brewery will have an average fill between 327.50 ml and 329.70 ml.

     b. The middle 95% of six-packs at the large chain will have an average fill between 327.75 ml and 328.25 ml.

What is the z-score?

In statistics, the z-score, also known as the standard score, is a measure of how many standard deviations an observation or data point is above or below the mean of the data set.

1.)

Skewed Left, since the possible values are clustered towards the upper limit of 330 ml, and it is impossible to fill the bottle with more than 330 ml.

2.)

a. z-score = (328.6 - 328.3) / 0.9 * √6 = 0.54

b. z-score = (328.6 - 328.3) / 0.9 * √12 = 0.77

c. z-score = (327.9 - 328.3) / 0.9 * √1 = -0.77

3.)

a. z-score = (328.6 - 328) / 0.7 * √6 = 1.24

b. Large Chain, since the z-score for the large chain is higher, indicating a larger average fill for the bottles in the six-pack.

c. Local Brewery, since the z-score for the local brewery is lower, indicating a smaller average fill for the bottles in the twelve-pack.

4.)

a. The middle 95% of six-packs at the local brewery will have an average fill between 327.50 ml and 329.70 ml.

b. The middle 95% of six-packs at the large chain will have an average fill between 327.75 ml and 328.25 ml.

Hence,

1.) Skewed left

2.) a. z-score = 0.54
    b. z-score = 0.77

    c. z-score = -0.77
3.) a. z-score = 1.24

    b. Large Chain

    c. Local Brewery

4.) a. The middle 95% of six-packs at the local brewery will have an average fill between 327.50 ml and 329.70 ml.

     b. The middle 95% of six-packs at the large chain will have an average fill between 327.75 ml and 328.25 ml.

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The coordinates of the image point would be U'(5,2).

Coordinate is a pair of numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.


To translate a point R(x, y) using T h,k, you take the x-coordinate of R, subtract h, and add k to the y-coordinate of R. Therefore, the coordinates of the point L' after translating L(2, -5) using T-3, -4 would be L'(-1, -9).

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The surface area of the rectangular prism, found by summing the surface areas of the six rectangular faces is about 2,600 square inches

A rectangular prism is a three dimensional solid with six rectangular faces, such that faces of the prism that face each other are parallel and congruent.

The surface area of the rectangular prism is the sum of the surface areas of the six rectangular faces of the prism

The area of the rectangles that make up the surface are;

A₁ = 8 inches × 36 inches = 288 square inches

A₂ = 23 inches × 8 inches = 184 square inches

A₃ = 23 inches × 36 inches = 828 square inches

A₄ = 23 inches × 8 inches = 184 square inches

A₅ = 8 inches × 36 inches = 288 square inches

A₆ = 23 inches × 36 inches = 828 square inches

The surface area of the rectangular prism, A, is therefore;

A = A₁ + A₂ + A₃ + A₄ + A₅ + A₆

Therefore;

A = 288 + 184 + 828 + 184 + 288 + 828 = 2600

The surface area of the rectangular prism is 2,600 square inches

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Answer:

2.42

Step-by-step explanation:

To find the diameter divide by 3.14 or pi. That equals 2.42038216561 but 2.42 is the rounded answer (if you are rounding to the hundredths place)

The exact perimeter of the triangle is 2√5 + √34 + 5√2.

To find the perimeter of the triangle, we need to find the distances between its vertices and add them up. Let's use the distance formula to find the three distances:

Distance between (2, -2) and (-2, 0):
d1 = √[(2 - (-2))^2 + (-2 - 0)^2]

= √[(4)^2 + (-2)^2]

= √(16 + 4)

= √20

= 2√5

Distance between (2, -2) and (-1, -7):

d2 = √[(2 - (-1))^2 + (-2 - (-7))^2]

= √[(3)^2 + (5)^2]

= √(9 + 25)

= √34

Distance between (-2, 0) and (-1, -7):

d3 = √[(-2 - (-1))^2 + (0 - (-7))^2]

= √[(-1)^2 + (7)^2]

= √(1 + 49)

= √50

= 5√2

Now, we can add up the distances to find the perimeter:

perimeter = d1 + d2 + d3

= 2√5 + √34 + 5√2

Therefore, the exact perimeter of the triangle is 2√5 + √34 + 5√2.

The perimeter of a triangle is the total length of its three sides. To find the perimeter, you simply add the lengths of the three sides together.

For example, if a triangle has side lengths of 5 cm, 6 cm, and 7 cm, its perimeter would be:

Perimeter = 5 cm + 6 cm + 7 cm

Perimeter = 18 cm

So the perimeter of the triangle is 18 cm.

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There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.

To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:

C(26, 4) = 26! / (4! * 22!) = 14,950

Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:

Therefore, the total number of such words is:

4 * 3 * 1 = 12

Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:

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Answer:

[tex]4\sqrt2[/tex]

Step-by-step explanation:

1) a=4 and b=8

2) Let geometric mean is g. [tex]g=\sqrt ab[/tex] or you can do [tex]g=\sqrt 4 times8[/tex]

3) g=[tex]4\sqrt2[/tex]

Given the Figure shown below is, ΔABC~ΔAXY if so, 1.67 is the scale factor between the two triangles.

The ratio between the scale of an original thing and a new object that is a representation of it but has a different size is known as a scale factor (bigger or smaller).

Consider two comparable squares as an illustration. One has a side length of 2 inches, while the other has a side length of 4 inches. This results in a scale factor of 1: 2 from the small square to the huge square. The scale factor between these two comparable squares is 1: 2, or tiny square to huge square.

Given that,

12 / 20 = 17 / x

or, 12 x = 340

or, x = 28.33

on the other hand,

25 / 15 = 1.66

20 / 12 = 1.66

28.33 / 17 = 1.66

now, scale factor = 1.67

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For the given insertion sort program the answer is (E) I, II, and III.

What is insertion sort?

Insertion sort is a simple sorting algorithm that works by repeatedly iterating through the elements of an array, or a list, and inserting each element into its proper position within the sorted portion of the array. The algorithm maintains a sorted sublist of elements, which starts as the first element of the array, and then iterates through the remaining unsorted elements one-by-one, comparing each element with the elements in the sorted sublist and moving them to the right until the correct position is found. In other words, insertion sort iteratively expands the sorted sublist by inserting each new element into its correct position, until the entire array is sorted. The time complexity of the insertion sort algorithm is O(n^2) in the worst-case scenario, where n is the number of elements in the array, but it can perform much better on small datasets or partially sorted arrays.

According to given conditions:

For the first question:

After the first pass of the outer loop, the array will be [2, 5, 4, 1, 3, 6]. After the second pass, the array will be [2, 4, 5, 1, 3, 6]. After the third pass, the array will be [1, 2, 4, 5, 3, 6]. Therefore, the answer is (C) [1, 2, 4, 5, 3, 6].

For the second question:

Statement 1 will execute 6 times because there are 6 elements in the array. Statement 2 will also execute 6 times because each element in the array will be moved to its correct position during the insertion sort. Therefore, the answer is (E) 6, 6.

For the third question:

To correctly separate the words in listofWords with commas and enclose them in braces, we need to iterate through the list and add each word to the result string followed by a comma (except for the last word) and a space. Then we need to remove the last comma and space and add the opening and closing braces. This can be achieved with the following expression and condition:

Expression: listofWords.get(k) + ", "

Condition: k != listofWords.size() - 1

Therefore, the answer is (A) expression: listofWords.get(k) + ", ", condition: k != listofWords.size() - 1.

For the fourth question:

To sort the integers in elements in descending order, we need to make two changes to the sort method:

I. Replace line 9 with: if (elements[k] > elements[index])

II. Replace lines 15-17 with:

Line 15: int temp = elements[index];

Line 16: elements[index] = elements[j];

Line 17: elements[j] = temp;

III. Replace line 3 with: for (int j = elements.length - 1; j > 0; j--) and replace line 7 with: for (int k = 0; k < j; k++)

Therefore, for the given insertion sort program the answer is (E) I, II, and III.

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The value of x from the adjoining figure​ given as pentagon is 85°.

An angle is a geometric figure formed by two rays, or lines, that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees, radians, or other units of angular measurement, and it represents the amount of rotation between the two rays. Angles are often used in geometry, trigonometry, physics, and other fields to describe the orientation of objects and the relationships between them. Some common types of angles include acute angles (less than 90°), obtuse angles (greater than 90°), and right angles (exactly 90°).

Here,

This is a pentagon with sum of angle as 540 degrees.

50+x=180

x=130°

x+80+120+125+130=540

x=540-455

x=85°

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The mean number of employees who work on a given day is less than the median number of employees who work on a given day and option C is correct.

In statistics, we frequently choose a representative value that roughly describes the full collection to represent a set of data. The label "measure of central tendency" denotes that this representative value is one around which the data is centred. The mean, median, and mode are these central tendencies.

Mean = sum of all values/frequency

Mean = (20(0.01) + (21(0.1)) + (22(0.1)) + (23(0.4)) + (24(0.3))

mean is 22.7.

The median id the value of X for which P(X<x) is greater than or equal to 0.5 and P(X>x) is greater than or equal to 0.5. Therefore, median is 23.

Mode is the value of X having maximum probability. Therefore, mode is 23.

Hence, the mean number of employees who work on a given day is less than the median number of employees who work on a given day and option C is correct.

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The solution of the given problem of area comes out to be the regular decagon is approximately 324.16 cm².

Its surface area is a reliable indicator of its overall size. When figuring out the right triangle squared, the environment is taken into account. The surface area of everything determines its overall size. The total of the volumes from each of the twelve vertical sides makes up the water volume inside a cuboid. Utilize the following formula to get the box's dimensions: The region is represented by 2lh, 2lw, & 2hW. (SA). The area is represented by the flexible shape's entire surface area.

Here,

The area of ​​a regular decagon can be calculated using the formula:

Area = (perimeter x apothem) / 2

For a regular decagon with a side of 6.8 cm and an apothem of 9.52 cm, the perimeter can be calculated as 10 times the length of the side, that is:

Perimeter = 10 x 6.8 cm = 68 cm

Therefore, the area of ​​the decagon is:

Area = (68 cm x 9.52 cm) / 2 = 324.16 cm²

So, the area of ​​the regular decagon is approximately 324.16 cm².

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The completed balance sheet is given below:

A balance sheet is a financial statement that shows the financial position of a company at a specific point in time. It provides information about a company's assets, liabilities, and equity, and helps to illustrate the overall financial health of the company.

The Balance Sheet

Sheffield company

balance sheet (partial)

December 31, 2023

Plant Assets

Land $3,926,000

Building $28,650,000

Less: Accumulated Depreciation (14,396,250)

Net Building $14,253,750

Equipment $49,569,000

Less: Accumulated Depreciation (4,127,795)

Net Equipment $45,441,205

Total Plant Assets $63,620,955

Note that the buildings and equipment are shown at their net book value, which is the original cost less the accumulated depreciation.

The accumulated depreciation represents the portion of the cost that has been expensed over time due to wear and tear, obsolescence, or other factors.

The land is not depreciated, so its original cost is shown.

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