A house has decreased in value by 35% since it was purchased. If the current value is 169,000 , what was the value when it was purchased?

Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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Answer:  See the image below.

You should integrate with respect to x

The calculated area of the region is 2.31

From the question, we have the following parameters that can be used in our computation:

y = eˣ

y = x² - 1

Make y the subject of the formula

y = eˣ

y = x² - 1

This means that by favoring convenience, you should integrate with respect to x

The area is calculated as

\(Area = \int\limits^a_b {e^x - x^2 - 2} \, dx\)

Integrate

\(Area = e^x - \frac{x^3}{3} - 2x|\limits^1_{-1}\)

Expand

Area = [e⁻¹ - (-1)³/3 - 2(-1)] - [e¹ - (1)³/3 - 2(1)]

Area = 2.31

Hence, the area is 2.31

The graph is attached

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Question

Sketch the region enclosed by the curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label the points of intercepts of the curves. then find the area of the region by integration.

y = eˣ

y = x² - 1

Answer:

Step-by-step explanation:

x^2= -25

x=5i and -5i

Answer:

The answer is 5

Step-by-step explanation:

x^2= -25

x=√-25

x=5

True. With similar triangles, the corresponding angles are equal. This property is one of the fundamental characteristics of similar triangles.

Similar triangles are triangles that have the same shape but possibly different sizes. They have corresponding angles that are equal, meaning that the angles in one triangle match the angles in the other triangle. This correspondence allows us to establish proportional relationships between the corresponding sides of the triangles.

The corresponding angles of similar triangles are equal because the angles are determined by the shape and orientation of the triangles, rather than their size. If two triangles have the same shape, their corresponding angles will be equal regardless of their size or position.

This property is the basis for many geometric proofs and calculations involving similar triangles. It allows us to solve problems involving proportions, ratios, and scaling.

By knowing that the corresponding angles of similar triangles are equal, we can confidently apply the principles of similarity to find missing side lengths, determine unknown angles, or establish relationships between different parts of the triangles.

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The double integral ∬R x^2+y^2/7x dA over the region R=[1,3]×[0,1] can be calculated as follows:

We have the double integral x^2+y^2/7x dA.Rewrite it in terms of polar coordinates as follows:x = rcosθ, y = rsinθ.

Therefore, the integral becomes r^2cos^2θ+ r^2sin^2θ/7rcosθ dA = ∬R (r^2/7) dA.Rewrite R in polar coordinates, R = {(r, θ): 1≤r≤3, 0≤θ≤π}.

Therefore, the integral becomes∫[0, π]∫[1, 3] r^2/7 r drdθ. Solving for the inner integral first, we have ∫[1, 3] r^2/7 r dr = [1/21 r^4] from 1 to 3 = 8/7.

The integral over θ is a simple one, and its solution is π. We can thus substitute the value of the integrals into the integral expression as follows: ∫[0, π]∫[1, 3] r^2/7 r drdθ = (8/7)(π) = 8π/7.

Therefore, the double integral ∬R x^2+y^2/7x dA over the region R=[1,3]×[0,1] is 8π/7.

Hence the answer is 8π/7.

Since the answer is required in 250 words,

this explains how the double integral has been calculated.

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If the two fractions are 1/4 and 1/6, then the two equivalent fractions are 2/8 and 2/12, respectively.

The numerator, which is found at the top of the fraction number, and the denominator, which is found at the bottom of the fraction number, are its two constituent parts.

The percentage is= 1/4

In both the denominator and the numerator, multiply it by two= 2/8

A fractional equivalent of 2/8 is 1/4.

Similarly,

For 1/6= 2/12

The fraction 2/12 is equivalent to 1/6.

Therefore, if the two fractions are 1/4 and 1/6, the two equivalent fractions are 2/8 and 2/12, respectively.

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Answer:

the slope is -1/4

Step-by-step explanation:

the change in y over the change in x from point (-2,-2) to (2,-3) is how to find the slope

y1-y2/x1-x2 = m

-2--3/-2-2 = -1/4

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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Answer:

Step-by-step explanation:volume of cylinder =π r²h

= 3.14 × 17×17×16

= 14519.31 inches square .

To paint the ceiling of a room that is 138 inches by 117 inches, you would need to purchase 3 pints of paint.

To find out how many pints of paint are needed to paint the room's ceiling, we must first convert its dimensions from inches to feet:138 inches is equivalent to 11.5 feet (138 ÷ 12 = 11.5)117 inches is equivalent to 9.75 feet (117 ÷ 12 = 9.75)To determine the total square footage of the room, multiply the room's length and width:11.5 feet × 9.75 feet = 112.125 square feet

To calculate the amount of paint needed, divide the total square footage by the number of square feet that one pint of paint will cover:112.125 square feet ÷ 50 square feet per pint = 2.24 pints

Therefore, you would need to purchase approximately 2.24 pints of paint to paint the ceiling of a room that is 138 inches by 117 inches. However, since paint is often sold in whole pints, you would need to purchase 3 pints of paint.

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Answer:

A rational expression is a ratio of two polynomials. The domain of a rational expression is all real numbers except those that make the denominator equal to zero.

Step-by-step explanation:

The value of y is y ≥ 1/6.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

3y + 1/4 ≥ 3/4

Solve for y.

3y + 1/4 ≥ 3/4

3y ≥ 3/4 - 1/4

3y ≥ 2/4

3y ≥ 1/2

y ≥ 1/6

Thus,

y ≥ 1/6 is the value of y.

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Answer

259000000

Step-by-step explanation:

The volume of the shape when the length is changed by a scale factor of 3 is 105h/l ft³. Note that we don't have enough information to determine new volume without knowing the original height of the prism.

A scale factor is a number by which a shape is multiplied or divided to create an identical shape that is larger or smaller than the original shape. The scale factor can be expressed as a ratio or as a decimal.

If the length of the rectangular prism is changed by a scale factor of 3, then its new length will be 3 times the original length. Let's say the original length, width, and height of the prism are l, w, and h, respectively. Then we have:

Original volume = lwh = 35 ft^3

New length = 3l

New volume = (3l)wh

We want to find the new volume, so we need to express it in terms of the original volume. We can do this by substituting w = 35/(lh) into the expression for the new volume:

New volume = (3l)wh = (3l)(35/(lh))h = 105h/l

The new volume is 105h/l ft³. Note that we don't have enough information to determine the new volume without knowing the original height of the prism.

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The shape has a capacity of \(105h/l\ ft^3\) when the length is increased by a scale factor of 3. Note that without knowing the prism's initial height, we lack sufficient information to calculate the new volume.

A shape is multiplied or divided by a scale factor to produce an identical form that is larger or smaller than the initial shape. Both a ratio and a decimal can be used to describe the scale factor.

The rectangle prism's new length will be three times as long as its old length if its length is increased by a scale factor of 3. Let's assume that the prism's initial dimensions were l, w, and h, correspondingly. Next, we have:

Original volume = lwh

                           \(=35\ ft^3\)

New length = 3l

New volume = (3l)wh

We must express the new volume in terms of the old volume if we are to locate it. To accomplish this, we can change the formula for the new

volume as follows:

New volume = (3l)wh = (3l)(35/(lh))h = 105h/l

It is now \(105h/l\ ft^3\) in capacity. Note that without knowing the prism's initial height, we lack sufficient information to calculate the new volume.

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a) Mode = 34 (

b) Variance  ≈ 451.917 ; Standard Deviation ≈ 21.250

c) with a standard deviation of approximately 21.250, we can expect that the commuting times from home to work are somewhat spread out from the mean.

d) the approximate value of the 73rd percentile is 9.49.

e) the percentile rank would be 0%.

To calculate the statistics for the given data, we need to organize the data in ascending order first:

12, 13, 19, 24, 26, 28, 33, 34, 34, 56, 62, 73

(a) Mean:

The mean is calculated by summing all the values and dividing by the total number of values.

Mean = (12 + 13 + 19 + 24 + 26 + 28 + 33 + 34 + 34 + 56 + 62 + 73) / 12

    = 414 / 12

    ≈ 34.5 (rounded to one decimal place)

Median:

The median is the middle value when the data is arranged in ascending order.

Median = 28

Mode:

The mode is the value that appears most frequently in the data.

Mode = 34 (since it appears twice, which is more than any other value)

(b) Range:

The range is the difference between the largest and smallest values in the data.

Range = 73 - 12

     = 61

Variance:

The variance measures the average squared deviation from the mean.

Variance = Σ((X - Mean)^2) / n

        = ((12 - 34.5)^2 + (13 - 34.5)^2 + (19 - 34.5)^2 + ... + (73 - 34.5)^2) / 12

        ≈ 451.917 (rounded to three decimal places)

Standard Deviation:

The standard deviation is the square root of the variance.

Standard Deviation = sqrt(Variance)

                 ≈ sqrt(451.917)

                 ≈ 21.250 (rounded to three decimal places)

(c) The value of the standard deviation tells us about the spread or variability of the data. In this case, with a standard deviation of approximately 21.250, we can expect that the commuting times from home to work are somewhat spread out from the mean. There is a variation of about 21.250 minutes around the average commuting time.

(d) To find the approximate value of the 73rd percentile, we can use the formula:

Percentile = (p/100) * (N + 1)

where p is the desired percentile (73) and N is the total number of data points (12).

Percentile = (73/100) * (12 + 1)

          = 0.73 * 13

          ≈ 9.49

Therefore, the approximate value of the 73rd percentile is 9.49.

(e) To find the percentile rank of 44, we need to determine the percentage of data points that are less than or equal to 44. We can use the formula:

Percentile Rank = (Number of data points ≤ 44 / Total number of data points) * 100

Since there are no data points less than or equal to 44, the percentile rank would be 0%.

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Answer:

Barbados won the Bronze.

Step-by-step explanation:

The information indicates that Jamaica finished before Barbados, but behind Trinidad which means that Trinidad was the first one, then Jamaica and the third one was Barbados:

1. Trinidad

2. Jamaica

3. Barbados

Then, it indicates that Haiti finished before Guyana, but behind Barbados which indicates that Haiti was in 4th place after Barbados and  the last one was Guyana:

1. Trinidad

2. Jamaica

3. Barbados

4. Haiti

5.Guyana

According to this, the answer is that Barbados won the Bronze.

Answer: 4/5

Step-by-step explanation: Just divide 132/165 and get 0.8 which we know is equal to 4/5.

Simplemente divida 132/165 y obtenga 0.8, que sabemos que es igual a 4/5.

Answer:

4/5

Step-by-step explanation:

132/165

11*3*4/11*3*5

4/5

Answer:

124.72

Step-by-step explanation:

Answer:

Step-by-step explanation:

4% of 128.72 = 0.04 * 128.72

                    = 5.1488

The percent of increase in motorcycle production is approximately 9.75%, and the percent of decrease in Sarah Walker's long-distance phone bills is approximately 42.07%.

To find the percent increase in motorcycle production, we use the formula:

Percent Increase = (New Value - Old Value)/Old Value x 100%

Plugging in the given values, we get:

Percent Increase = (318000 - 291500)/291500 x 100% = 9.75%

Therefore, the percent of increase in motorcycle production is approximately 9.75%.

To find the percent decrease in Sarah Walker's phone bills, we use the formula:

Percent Decrease = (Old Value - New Value)/Old Value x 100%

Plugging in the given values, we get:

Percent Decrease = (40.10 - 22.90)/40.10 x 100% = 42.07%

Therefore, the percent of decrease in Sarah Walker's long-distance phone bills is approximately 42.07%.

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Answer:

  108°

Step-by-step explanation:

The two given angle are vertical angles, which means they are congruent.

  (x +81)° = 4x°

  81 = 3x . . . . . . . subtract x, divide by °

  27 = x . . . . . . . . divide by 3

  (27 +81)° = 108° . . . . find the angle measure

The two marked angles have measures of 108°.

Answer:

\( \sqrt{ 384} \)

Step-by-step explanation:

Well I commented this already but I'm not sure if you saw it. If you're trying to convert it all to a radical form then you square the 8 and multiply it by the 6.

\(8 \sqrt{6} \)

8² = 64

64 • 6 = 384

\( \sqrt{ 384} \)

Answer:

The slope othe line is - 1

Answer:

-1/4

Step-by-step explanation:

If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

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Answer:

3) 3k+20

4) 4+2d

Step-by-step explanation:

You first have to distribute by multiplying the number next to the expression in the parenthesis. Then you combine like terms.

3) 5(k+4)-2k

  Step 1: (5×k= 5k) (5×4=20) equation is now 5k+20-2k

  Step 2: 5k-2k=3k since they both have the same variable you combine like terms. Equation is now 3k+20 (Final answer)

4) 2(3+d-1)

  Step 1: (2×3=6) (2×d=2d) (2×[-1]=2) Equation is now 6+2d-1.

  Step 2: (6-2=4) Since both 6 and 1 don't have any variable their like terms and you combine them. Equation is now 4+2d (Final answer)