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The volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

Given:

DC = 7

DA = 6

DE = 6

AB = 14

Height of the trapezoid:

ED = (DC/AB) * EA = (7/14) * EA = 0.5 * EA

Height = EA - ED = EA - 0.5 * EA = 0.5 * EA

Circumference of the cylindrical shell:

Circumference = 2 * π * AB = 2 * π * 14

Thickness of the cylindrical shell:

Since the trapezoid is being rotated about side DA, the thickness (Δx) will vary along DA. We'll integrate with respect to x from 0 to 6 (the length of DA).

Volume of the solid generated:

Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * EA * Δx]

Substituting EA = DE + DA = 6 + 6 = 12Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * 12 * Δx]

Integrating:

Volume = 2 * π * 14 * 0.5 * 12 * [x] from 0 to 6

Volume = 2 * π * 14 * 0.5 * 12 * (6 - 0)

Volume = 504 * π

Approximating to the nearest tenth:

Volume ≈ 504 * 3.14 ≈ 1586.6 cubic units (rounded to the nearest tenth)

Therefore, the volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).

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The prοbability οf drawing twο A cards is [tex]$1/8$[/tex] .

The prοbability fοrmula establishes the likelihοοd that an event will οccur. It is the prοpοrtiοn οf favοurite websites tο all favοurite websites. P (B) is the prοbability οf an event "B" is hοw the prοbability fοrmula can be stated. The number "n" (B) represents the favοurite mοments οf an event "B."

There are three cards, each labelled with the letter A οr D. Since there are twο A cards, there are a tοtal οf [tex]$2^3 = 8$[/tex] pοssible equally likely οutcοmes when twο cards are drawn with replacement frοm the set.

The pοssible οutcοmes are: AA, AD, DA, DD, AA, AD, DA, DD.

Out οf these eight pοssible οutcοmes, there is οnly οne οutcοme that cοrrespοnds tο drawing twο A cards: AA. Therefοre, the prοbability οf drawing twο A cards is  [tex]$1/8$[/tex] .

In οther wοrds,

[tex]$P(A,A) = \boxed{\frac{1}{8}}$[/tex].

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According to the evidence from graph a and graph b, graph a indicates that the model for the data was a good fit because it is a random.

Hence, the correct option is B.

Based on graph a, the residual plot shows a random scattering of points around the horizontal line at y=0. This indicates that the residuals (the differences between the observed and predicted values) are distributed randomly and do not show any clear pattern. This suggests that the data points are evenly distributed around the regression line, indicating a good fit for a linear regression model.

On the other hand, graph b shows a residual plot with a clear pattern or trend. The residuals are not randomly scattered, but instead show a curved pattern or a fan-like shape. This indicates that the model used to fit the data may not be appropriate, as it is not capturing the underlying relationship between the variables accurately.

Hence, the correct option is B.

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-- The given question is incomplete, the complete question is

"The residual plots from two different sets of bivariate data are graphed below. Explain, using evidence from graph a and graph b which graph indicates that the model for the data was a good fit and what is the reason?

A. Graph A because it is symmetrical

B. Graph A because it is random

C. Graph B because there is a pattern

D. Graph B because it is symmetrical" --

Step-by-step explanation:

you have to subtract them which would be -1.05

Answer:

(2, 3)

Step-by-step explanation:

     9x - 7y = -3                

+   -9x + 15y = 27

             8y = 24           (Divide by 8 on both sides)

             8   =  8

y = 3

Substitute y = 3 in any of the two equations.

9x - 7(3) = -3

9x - 21 = -3

     +21 = +21         (Add 21 on both sides)

 9x     =  18               (Divide by 9 on both sides)

  9      =   9

x = 2

Answer:

Therefore, there are approximately 102 kilocalories in the snack bar.

Step-by-step explanation:

One gram of fat provides 9 kilocalories (kcal), while one gram of carbohydrate and protein provide 4 kcal each. So, to find the total number of kilocalories in the snack bar, we can use the following formula:

Total kcal = (grams of fat * 9) + (grams of carbohydrate * 4) + (grams of protein * 4)

Plugging in the values, we get:

Total kcal = (6 * 9) + (10 * 4) + (2 * 4)

Total kcal = 54 + 40 + 8

Total kcal = 102

Therefore, there are approximately 102 kilocalories in the snack bar.

The answer is  approximately 120 kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein.

What are kilocalories? Kilocalories, also known as calories, are a unit of energy used to calculate the amount of energy in food. The number of kilocalories in food is calculated based on the number of grams of protein, carbohydrate, and fat it contains. Kilocalories are used by the body to fuel its processes and maintain its vital functions. The energy in food is released when it is digested, absorbed, and transported to the cells where it is used to produce ATP, the body's primary source of energy. ATP is used to power cellular processes such as metabolism, respiration, and movement. How many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein? To calculate the number of kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein, we need to know the number of kilocalories per gram of each macronutrient. Protein and carbohydrates each contain 4 kilocalories per gram, while fat contains 9 kilocalories per gram. To calculate the number of kilocalories in the snack bar, we multiply the number of grams of each macronutrient by the number of kilocalories per gram and then add them together. Here is the calculation:6 grams of fat x 9 kilocalories per gram of fat = 54 kilocalories10 grams of carbohydrate x 4 kilocalories per gram of carbohydrate = 40 kilocalories2 grams of protein x 4 kilocalories per gram of protein = 8 kilocalories. Total kilocalories = 54 + 40 + 8 = 102Therefore, a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories.
A snack bar with 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories. This is calculated as follows: (6 grams fat x 9 kcal/g) + (10 grams carbohydrate x 4 kcal/g) + (2 grams protein x 4 kcal/g).

Therefore, answer is 120 kilocalories.

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The distance between the centers of the two wheels is approximately 11.86 feet.

The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.

Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula

C = πd

Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:

C = πd = π(0.5) = 1.57 feet (approx.)

The length of the conveyor belt is given as 15 feet. So we can write

2C + d = 15

Substituting the value of C, we get

2(1.57) + d = 15

3.14 + d = 15

d = 11.86 feet

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A) Quartile 1 (Q1): 2, Quartile 2 (Q2): 6, Quartile 3 (Q3): 7, Decile 1 (D1): 1, Decile 2 (D2): 2, Decile 3 (D3): 3, Decile 4 (D4): 7

B) Quartile 1 (Q1): 11, Quartile 2 (Q2): 14, Quartile 3 (Q3): 16, Decile 1 (D1): 11, Decile 2 (D2): 12, Decile 3 (D3): 14, Decile 4 (D4): 17

C) Quartile 1 (Q1): 77, Quartile 2 (Q2): 85, Quartile 3 (Q3): 94, Decile 1 (D1): 71, Decile 2 (D2): 81, Decile 3 (D3): 87, Decile 4 (D4): 98

D) Quartile 1 (Q1): 42, Quartile 2 (Q2): 66, Quartile 3 (Q3): 86, Decile 1 (D1): 28, Decile 2 (D2): 42, Decile 3 (D3): 57, Decile 4 (D4): 98

E) Quartile 1 (Q1): 100, Quartile 2 (Q2): 117, Quartile 3 (Q3): 133, Decile 1 (D1): 33, Decile 2 (D2): 100, Decile 3 (D3): 111, Decile 4 (D4): 147

F) Quartile 1 (Q1): 113, Quartile 2 (Q2): 126, Quartile 3 (Q3): 146, Decile 1 (D1): 110, Decile 2 (D2): 113, Decile 3 (D3): 121, Decile 4 (D4): 848

Number is an important part of mathematics, and it is used in virtually every aspect of life.

A) First, we need to arrange the data in order:

[1,1,2,2,2,2,2,3,3,3,3,4,5,6,6,7,7,7,7,9,9]

The median is the middle value of the data set. Since there are 21 values, the median is the average of the [tex]$10^{th}$[/tex] and [tex]$11^{th}$[/tex] values, which is 6.

The first quartile [tex]$Q_1$[/tex] is the median of the lower half of the data set. The lower half of the data set is [1,1,2,2,2,2,2,3,3,3], which has 10 values. The median of this set is the average of the [tex]$5^{th}$[/tex]and [tex]$6^{th}$[/tex] values, which is 2.

The third quartile[tex]$Q_3$[/tex]is the median of the upper half of the data set. The upper half of the data set is [4,5,6,6,7,7,7,7,9,9], which also has 10 values. The median of this set is the average of the[tex]$5^{th}$[/tex] and[tex]$6^{th}$[/tex]values, which is 7.

The interquartile range (IQR) is the difference between the third and first quartiles: IQR =[tex]Q_3[/tex] - [tex]Q_1[/tex]= 7 - 2 = 5.

To find the deciles, we need to divide the data into $10$ equal parts. Since we have 21 data points, we need to find the values that divide the data into groups of $2$. The [tex]$k^{th}$[/tex] decile[tex]$D_k$[/tex] is the[tex]$k \cdot n/10$-th[/tex] value, where $n$ is the number of data points. The deciles are:

$D_1 = 1, D_2 = 2, D_3 = 2, D_4 = 2, D_5 = 3,$

$D_6 = 6, D_7 = 7, D_8 = 7, D_9 = 9$

B) Again, we need to arrange the data in order:

$10,11,12,12,14,14,14,15,15,15,15,16,16,16,17,17,14,14$

The median is the average of the[tex]$9^{th}$[/tex] and[tex]$10^{th}$[/tex] values, which is $15$.

The first quartile $Q_1$ is the average of the[tex]$4^{th}$[/tex] and [tex]$5^{th}$[/tex]values, which is $14$.

The third quartile $Q_3$ is the average of the [tex]$14^{th}$[/tex] and [tex]$15^{th}$[/tex]values, which is $16$.

The interquartile range (IQR) is [[tex]Q_3[/tex] - [tex]Q_1[/tex]= 16 - 14 = 2].

To find the deciles, we need to divide the data into [10] equal parts. Since we have 18 data points, we need to find the values that divide the data into groups of 2. The deciles are:

[[tex]D_1[/tex]= 10, D_2 = 12, D_3 = 14, D_4 = 14, D_5 = 14,]

[[tex]D_6[/tex]= 15, D_7 = 15, D_8 = 16, D_9 = 17]

From the above calculation, it can be seen that the quartiles and deciles of each set of data differ.

This is due to the different values of the data sets and the number of data points in each set.

The quartiles and deciles show different ranges and values which indicate the spread of the data and also help to identify any skewness in the data.

Summarizing, the quartiles and deciles provide an important measure of the spread of the data, helping to identify any outliers or skewness.

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Step-by-step explanation:

with 2 cubes we have 12 faces to paint.

each face has 2 options (black or white).

so, we have a total of 2¹² possible outcomes.

a probability is always the ratio of

desired cases / totally possible cases

so, we need to find a way to express the desired cases of both cubes being painted the same way.

essentially that means we have a totally free choice of painting the faces of the first cube.

that is 2⁶ possible outcomes.

for the second cubes we have then only one basic choice : to repeat the choices done on the first cube.

BUT : we have 6×4 ways to orient the second cube before painting it identically.

6 ways to pick e.g. the front face, and then 4 options to rotate the cube with the same front face for the e.g. top face.

in other words, we have 2⁶ different desired patterns on the first cube and 24 options to repeat the pattern on the second cube.

that means the desired options are 2⁶×1×24

so, the probability for them to be identical is

24×2⁶ / 2¹² = 24/2⁶ = 3/2³ = 3/8 = 0.375

The probability that after they are painted, the cubes can be rotated to be identical in appearance is (a) 64/9

Probability is a branch of mathematics that deals with the study of random phenomena or events with uncertain outcomes.

Let's start by assuming that one of the cubes has the black face facing up. The other cube can be painted in any of the possible ways.

Let's list all the possible configurations for the second cube.

There are six faces, and each can be painted either black or white. Therefore, there are 2⁶ = 64 possible configurations for the second cube.

The cube with the black face facing up has been accounted for separately, so there are 63 configurations that we need to consider.

If the second cube is painted all black or all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the black or white face is facing up.

There are two such configurations. If the second cube has exactly one white face and five black faces, there are three ways to position it so that the cubes look identical. There are three such configurations

.If the second cube has two white faces and four black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.

If the second cube has three white faces and three black faces, there are eight ways to position it so that the cubes look identical. There are eight such configurations.

If the second cube has four white faces and two black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.

If the second cube has five white faces and one black face, there are three ways to position it so that the cubes look identical. There are three such configurations

.If the second cube is painted all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the white face is facing up. There are two such configurations.

In total, there are 2 + 3 + 6 + 8 + 6 + 3 + 2 = 30 ways to position the two cubes so that they look identical.

There are 63 × 64 possible configurations for the two cubes, so the probability of the cubes being able to be rotated to be identical in appearance is given by:

30/ (63×64) = 64/9

Therefore, the correct answer is (a) 64/9.

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Answer:

Function decreasing: where x is (-4; 0) and (2; 4)

Function increasing: where x is (0; 2)

Step-by-step explanation:

Decreasing is the part in graph where function goes down. Increasing is the part where function goes up.

The function to model the value of p of the car after t years can be expressed as:

p(t) = 28,175 * (1 - 0.085)^t

where 0.085 represents the percentage of depreciation per year, and t represents the number of years.

To find the value of the car after 6 years, we substitute t = 6 into the function:

p(6) = 28,175 * (1 - 0.085)^6

p(6) = 28,175 * 0.5386

p(6) ≈ 15,199.35

Therefore, the value of Jeff's car after 6 years will be approximately $15,199.35.

Answer: D.) 2x + 22 = 50

Step-by-step explanation:

P=2(l+w)

2x+22=50 is correct because

2 times x is 2 times the unknown length

11 times 2 is 22 so, you add that to the 2x

50 is the perimeter

For the logarithm to be positive, the argument of the logarithm (i.e., 2x+c) must be greater than zero.

Solve the inequality 2x+c > 0 for x:

2x > -c

x > -c/2

Therefore, for x > -c/2, the logarithm Y=log(2x+c) will be positive.

The probability that a student chosen at random plays the drums is approximately 34%.

What is probability?

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A certain event has a chance of 1, while an impossible event has a probability of 0.

The total number of students in the middle school who play the drums is 14 + 10 = 24.

The total number of students in the middle school is:

5 + 12 + 14 + 4 + 12 + 5 + 10 + 8 = 70

The probability of selecting a student who plays the drums at random is:

24/70 = 0.34285714285714286

To express this probability as a percentage, we multiply by 100 and round to the nearest whole number:

0.34285714285714286 * 100 ≈ 34

Therefore, the probability that a student chosen at random plays the drums is approximately 34%.

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Answer:

To find the values of a and b, we need to substitute the coordinates of the given point (11,3) into both equations and solve for a and b.

Substituting (11,3) into the first equation ax-2y=5:

a(11)-2(3)=5

11a-6=5

11a=11

a=1

Substituting (11,3) into the second equation 2x-by =8:

2(11)-b(3)=8

22-3b=8

-3b=-14

b=14/3

Therefore, a=1 and b=14/3.

Answer:

a = 1

b = 4.67 OR 14/3

Step-by-step explanation:

ax - 2y = 5

a(11) - 2(3) = 5

11a - 6 = 5

11a = 11

a = 1

2x - by = 8

2(11) - b(3) = 8

22 - 3b = 8

3b = 14

b = 4.67 OR 14/3

Answer:

dont no ok i dont konow ask an easy one

#

If it rained on Monday, Tuesday, Thursday and Friday Last week then probability of rain would be 4/7 as there are 7 days in a week.

Total days in week = total outcome = 7days
Possible outcome = 4
P(rain) = 4/7

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The length AC of the triangle is 4.47 units.

The diagram on the graph is a triangle. The question wants us to find the length AC of the triangle.

To find the length AC in the triangle, we have to use distance formula as follows:

Therefore,

A = (1, 1)

C = (3, 5)

AC = √(y₂ - y₁)² + (x₂ - x₁)²

AC = √(5 - 1)² + (3 - 1)²

AC = √4² + 2²

AC = √16 + 4

AC = √20

Hence,

AC = 4.472135955

AC = 4.47 units

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263 more story artists are there than ​interns.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number

In actual values

Number of story artists = 1620 x 20% = 1620 x 20/100 = 324

Number of interns = 1620 x 5% = 1620 x 5/100 = 81

Difference = 324 - 81 = 263

Hence, 263 more story artists are there than ​interns.

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Complete question:

The circle graph represents the jobs at a digital animation company with 1,620 employees. How many more story artists are there than interns​?

See the image attached.

The two missing points on the line are:

(0, -1)

(-5, 0)

And the slope, using these points, is a = -1/5

Remember that a general linear equation is:

y = ax + b

Where a is the slope and b is the y-intercept.

If that line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can look at line e and find the two missing y-values, for the first point we have:

(0, -1)

For the second point we have:

(-5, 0)

Using these two, we will get the slope:

a = (0 + 1)/(-5 - 0) = -1/5

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Step-by-step explanation:

To find Sara's semi-monthly salary, we need to divide her annual salary by the number of semi-monthly periods in a year.

Since there are 24 semi-monthly periods in a year (twice a month), we can divide her annual salary by 24 to get her semi-monthly salary:

$37,560 ÷ 24 = $1,565.00

Therefore, Sara's semi-monthly salary to the nearest cent is option C) $1,565.00.

Answer:

660cm^2

Step-by-step explanation:

area of 2 triangle= 10×12

= 120cm^2

area of 3 rectangles= (13×15×2)+(10×15)

= 390+150

= 540cm^2

surface area of triangular prism

= 540+120

= 660cm^2

There are 13,800 different ways to have the first, second, and third place winners without any ties.

In a rubber duck regatta with 25 people competing and each person having only one entry, we can determine the number of ways to have the first, second, and third place winners by using permutations.
Step 1: Calculate the number of options for the first place winner.

There are 25 contestants, so there are 25 options for the first place.
Step 2: Calculate the number of options for the second place winner.

Since the first place winner has been determined, there are 24 remaining contestants to choose from for the second place.
Step 3: Calculate the number of options for the third place winner.

After determining the first and second place winners, there are 23 remaining contestants to choose from for the third place.
Step 4: Multiply the number of options for each place to get the total number of possible outcomes.
25 options (first place) × 24 options (second place) × 23 options (third place) = 13,800 possible outcomes.

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Answer:

92 hours

Step-by-step explanation:

7 * 12 + 8 = 92

Answer: C. The median of 20 is the most accurate to use, since the data is skewed.

The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.

In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.

Step-by-step explanation:

The total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1 is 21 liters.

When a ratio of 20:1 is given for milk and water, it means that for every 20 parts of milk, there is 1 part of water. Therefore, the total number of parts in the mixture is 20 + 1 = 21.

We know that Rico mixed 20 liters of milk, which represents 20 parts of the mixture. To find the corresponding volume of water, we can use the ratio given.

The ratio of milk to water is 20:1, which means that for every 20 parts of milk, there is 1 part of water. Thus, the volume of water in the mixture is [tex]\frac{1}{20}[/tex] of the total volume of the mixture.

Volume of water = [tex]\frac{1}{20}[/tex] x Total volume of the mixture

Since we know that the volume of milk is 20 liters, we can substitute that value in the equation to solve for the total volume of the mixture:

20 = ([tex]\frac{20}{21}[/tex]) x Total volume of the mixture

Total volume of the mixture = (20 × 21) ÷ 20

= 420 ÷ 20

= 21 liters

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The complete question is:

What is the total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1?

The percent increase in her pay is by 26.06% if she takes the new job.

A quantity's percentage increase is a way to represent how much it has grown in comparison to its starting point. The formula is as follows: take the new value, remove the original value, divide the outcome by the original value, and then multiply by 100%. When comparing two quantities, such as incomes, prices, or test scores, it is common to use the percentage increase to gauge how much has changed. A value rise is indicated by a positive percent increase, whilst a value loss is shown by a negative percent increase.

Given that, the pat increases from $8.25 an hour to $8.25 an hour.

percent increase = [(new value - old value) / old value] x 100%

Substituting the values we have:

percent increase = [(10.40 - 8.25) / 8.25] x 100%

percent increase = 26.06%

Therefore, Lily's pay would increase by 26.06% if she takes the new job.

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Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.

To convert 42 feet to yards and feet, we need to know that there are 3 feet in 1 yard. We can divide the total number of feet (42) by 3 to get the number of yards, and then take the remainder to get the remaining feet.

So, 42 feet divided by 3 feet/yard equals 14 yards. This means that Greg's backyard is 14 yards wide.

To find the remaining feet, we can multiply the decimal part of the result by 3. So, 0.333 x 3 = 0.999. Since we cannot have a fraction of a foot, we round up to the nearest whole foot, which gives us 1 foot.

Therefore, Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.

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