answer options:

x= 3, -4

x= 5, -1

x= 0, 5

x= 1, 5

There are several transformations that can be applied to a pentagon in order to map it onto itself. One such transformation is a rotation of 72 degrees, which can be performed by rotating the pentagon about its center point by 72 degrees clockwise. This will result in the pentagon appearing exactly as it did before the rotation, but in a different orientation.

Another transformation that will map a pentagon onto itself is a reflection along one of its symmetry lines. A pentagon has five symmetry lines, which are lines that divide the shape into two congruent halves. Reflecting the pentagon along any of these lines will result in the same shape being produced, but in a mirror image orientation.

Finally, a translation can also be used to map a pentagon onto itself. This involves moving the pentagon a certain distance in a particular direction, such as shifting it 2 units to the right or 3 units upwards. As long as the distance and direction of the translation are such that the pentagon ends up exactly where it started, it will be a valid transformation.

Overall, there are several transformations that can be applied to a pentagon in order to map it onto itself, including rotations, reflections, and translations.

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Felipe needs a total of 6 liters of lemonade for all 12 glasses. Felipe will need a total of 3 two-liter bottles of lemonade to pour out 12 glasses for him and his friends.

Determining the total amount of lemonade needed:

12 glasses x 500 milliliters per glass = 6,000 milliliters.

Converting the total amount of lemonade needed to liters:

6,000 milliliters / 1,000 milliliters per liter = 6 liters.
Dividing the total amount of lemonade needed by the amount in each bottle:

6 liters / 2 liters per bottle = 3 bottles.

Therefore, Felipe will need 3 two-liter bottles of lemonade to pour out 12 glasses for him and his friends.

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Therefore, a person starts with a hand of cards without any Wild (Wild or Wild draw four) is 0.5741

and a number of outcomes of event 'B' is 16007560800.

total number of cards = N = 108

wild cards = 4

wild draw four = 4

we have 4 different colors and each color has 25 cards with break down as

zero numbered card = 1

numbered from 1 to 9 = 2 each (total 18)

skip = 2

draw two = 2

reverse = 2

skip, draw two and reverse are action cards

therefore, in a deck of UNO we have 3*2*4 = 24 action cards

a seven-card hand is dealt to each player from a well shuffled pack of card.

therefore, as each card is equally likely, we have total possible outcomes as 108C7

Ω is a event of every possible outcome and it has 108C7 = 27883218168 elements

an equally likely model is a model where equal weights are attached to every outcome and thus the probability of each outcomes become equal.

1) let 'A' be the event a whole hand is of action cards.

we have a total of 24 action cards in a UNO deck of 108 cards.and we have to draw a hand of 7 cards

total number of outcomes for event 'A' is 24C7

therefore, the probability that a player starting with a whole hand of action cards is

= [tex]24C7\n108C7\n[/tex]

= 0.0000124

therefore, a person starts with a whole hand of action card is 0.0000124

and the number of outcomes of event 'A' is 346104

2) let 'B' be the event that a hand of card is without any wild card

therefore we have a total of 100 cards that do not have any wild ( wild or wild draw four) cards

therefore a hand of 7 out of 100 cards for event 'B' can be drawn in 100C7 total ways

therefore, the probability that a player starts with a hand of cards without any Wild (Wild or Wild draw four) cards is

= [tex]100C7\n108C7\n[/tex]

= 0.5741

therefore, a person starts with a hand of cards without any Wild (Wild or Wild draw four) is 0.5741

and the number of outcomes of event 'B' is 16007560800.

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The median weight of the black bass caught by the fisherman is 10.5 pounds.

To find the median, we need to arrange the weights in order from smallest to largest: {6, 7, 8, 12, 13, 14}. Since there are an even number of weights, the median is the average of the two middle values, which are 8 and 12. Therefore, the median weight is (8+12)/2 = 10.5 pounds.

The median is a measure of central tendency that represents the middle value in a dataset. It is less sensitive to extreme values than the mean and is useful for describing the typical value in a skewed distribution.

In this case, the median weight of 10.5 pounds indicates that half of the black bass caught by the fisherman weighed less than 10.5 pounds, and half weighed more than 10.5 pounds.

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Answer:

Step-by-step explanation:

It's given that, The height of three basketball players is 210 cm, 220 cm and 191 cm.

h₁ = 210 cm

h₂ = 220 cm

h₃ = 191 cm

Total number of observations = 3.

Average = Sum of all observations/Total number of observations.

↠ Average = h₁ + h₂ + h₃/3

↠ Average = 210 +220 + 191 /3

↠ Average = 430 + 191/3

↠ Average = 621/3

↠ Average = 207

Therefore, The required average height is 207 cm.

The amount of money Makayla spent on the movies during the year she joined the club will be represented by (m) = 6x + 25.

We have to represent the given situation with a function. The club charges a registration fee of 55 dollars and the discount value for the club members is 6 dollars per ticket. Here, we will use x to represent the number of movie tickets.

The domain is represented by m and so it should be a whole number. It cannot be an integer as integers include negative numbers too. It cannot be a rational number because it cannot include decimals and as we know we can't buy part of a ticket. It can also not be a real number because it can't include irrational numbers.

So, our function will be (m) = 6x + 25.

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The percentage by which the median earnings of college degree exceed that of high school degreed for 1973 for men is 17.9%

College: Women= 4400

H.School: Women = 3300

Solving we have

The base number is the high  school women.

The difference is 4400 - 3300 = 1100

So the % = (1100/3300) * 100% = 33.3%

1973

The base number is again high school 5600

Difference: 6600 - 5600 = 1000

% = (1000/5600) * 100% = 17.9

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See the aattached image.

The ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

An alternate exterior angle is an angle formed by a pair of lines and a transversal, such that the angle is located on the outside of the two lines, and on the opposite side of the transversal. More specifically, if line AB is intersected by transversal CD at point E, and angles 1 and 2 are formed as shown in the diagram below, then angle 1 and angle 2 are alternate exterior angles:

Alternate exterior angles are congruent if the two intersected lines are parallel. This means that the measure of angle 1 is equal to the measure of angle 2.

So, ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

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The approximate distance between Padma and the bear is 21.2 ft, which corresponds to option A.

The approximate distance between Padma and the bear, we can use trigonometry. Since James and Padma are on opposite sides of the 100-ft-wide canyon,

we can form two right triangles with the bear's position as one of the vertices.

Step 1: Determine the horizontal distance from James to the bear.

Since the angle of depression from James to the bear is 45 degrees, the horizontal distance (x) and vertical distance (y) are equal due to the properties of a 45-45-90 right triangle. Therefore, x = y. Since the canyon is 100 ft wide, x + y = 100 ft. We can solve for x:

x + x = 100

2x = 100

x = 50 ft

Step 2: Determine the vertical distance from James to the bear.
Since x = y in the 45-45-90 right triangle, the vertical distance from James to the bear is also 50 ft.

Step 3: Determine the horizontal distance from Padma to the bear.
We can now use Padma's angle of depression, 65 degrees, to find the horizontal distance (p) from Padma to the bear. Using the tangent function:

tan(65) = vertical distance / horizontal distance

tan(65) = 50 ft / p

Solving for p:

p = 50 ft / tan(65) ≈ 21.2 ft

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The opening of the pail has a diameter of approximately 55.4 inches (since it's twice the diameter of the base).

Based on the information you provided, it sounds like you have some great supplies for making sand castles at the beach with your friends.

Firstly, let's take a look at the pail. You mentioned that it has a base with a circumference of 87 inches, which means that the diameter of the base is approximately 27.7 inches (since circumference = pi x diameter). The pail is also 12 inches tall and has an opening on top that is twice the diameter of the base. Therefore, the opening has a diameter of approximately 55.4 inches (since it's twice the diameter of the base). With these measurements, you can use the pail to make some pretty big sand castles!

Next, you mentioned a plastic pyramid mold that has a square base with an edge that measures 6 inches and is 7 inches tall. This mold should be perfect for making pyramid-shaped sand castles. Just fill it with sand, pack it down, and carefully remove the mold to reveal your pyramid!

Finally, you mentioned an empty soup can with a diameter of 5.25 inches and is 6.5 inches tall. This can could be used to make cylindrical shapes in your sand castles. Simply pack sand around the can, press down firmly, and carefully remove the can to reveal your cylinder.

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The predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00.

You are asked to find the predicted total sales (s) for the ice-cream parlor when the average temperature (t) is 72°F, using the trend line equation s = 12.75t + 32.

Step 1: Plug the given temperature (72°F) into the trend line equation:
s = 12.75(72) + 32

Step 2: Calculate the value of 12.75(72):
12.75 * 72 = 918

Step 3: Add 32 to the result from Step 2:
918 + 32 = 950

So, the predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00. Therefore, the correct answer is (a) $950.00.

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Answer:

6cm

Step-by-step explanation:

all the sides of a square are identical so we can assume the missing side as x

since all four sides are the same and the perimeter is the sum of all sides, we can write

x+x+x+x=24cm

4x=24cm

x=24/4

x=6cm

Here is a two-way table that summarizes the information:

The marginal frequencies (totals) are shown in the last row and last column. The dealership has a total of 98 cars on its lot, which is the sum of the new and used cars. There are 55 new cars and 15 used cars, which is the sum of the domestic and foreign cars in each category.

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it is crucial to ensure that data collection methods and instruments meet the required accuracy standards.

Digitization positional errors can still prevent accurate analysis or decision making even if they are less than the required positional accuracy of the data. This is because the accuracy of the output or results depends on the accuracy of the input data.

For example, suppose a GPS receiver is used to collect data on the location of a pipeline, and the positional accuracy requirement is 5 meters. However, due to various factors such as signal interference or poor satellite coverage, the receiver only achieves an accuracy of 2 meters. Even though the positional error is less than the required accuracy, the resulting data may still be insufficient for the intended purpose, such as accurately identifying potential hazards or planning maintenance activities.

Inaccurate data can lead to wrong decisions, increased risks, and financial losses. Therefore, it is crucial to ensure that data collection methods and instruments meet the required accuracy standards.

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Digitization positional errors may be less (say 2 meters) than the required positional accuracy of the data (say 5 meters) yet still prevent achieving the desired level of accuracy for the intended use of the data.

The correct answer is "No, P(A) ≠ P(A|B)".

If the occurrence of one event has no bearing on the likelihood that the other will also occur, then the two events are independent.

The likelihood that both occurrences A and B will occur is defined mathematically as being equal to the product of the probabilities of A and B (i.e., P) (A and B).

Let event A = heavy traffic and event B = bad weather.

P(A)=  25/30 and P(B)=25/30

Two events are independent if the occurrence of one does not change the probability of the occurrence of the other.

This means P(A) = P(A|B) or P(B) = P(B|A).

For event A (heavy traffic), P(A) = 80/100 = 0.8.

For event B (bad weather), P(A|B) = 25/30 = 0.833.

Since P(A) ≠ P(A|B), events A and B are not independent.

So, the correct answer is "No, P(A) ≠ P(A|B)".

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Based on the graph, it appears that F(x) is a downward-facing parabola that has been shifted horizontally and vertically.

The vertex of the parabola is located at the point (3,-3), so the equation must include (x - 3) and (y + 3). Additionally, since the graph is narrower than the graph of G(x) = x^2, there must be a coefficient that is greater than 1 in front of the squared term.

Looking at the answer choices, we can eliminate options B and D because they have positive coefficients in front of the squared term, which would result in an upward-facing parabola. Option C has a negative coefficient in front of the squared term, which would result in a wider parabola than the graph shown.

Therefore, the correct answer is A, F(x) = 3(x-3)^2 - 3.

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The best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Mrs. Brown's yard has three ant hills, each with a different number of ants. To estimate the total number of ants in the yard, we simply add up the number of ants in each hill.

The first hill has 4,867,190 ants, the second has 6,256,304, and the third has 3,993,102. When we add these numbers together, we get a total of 15,116,596 ants in Mrs. Brown's yard. Of course, this is just an estimate, as there may be other ant hills or individual ants scattered around the yard.

However, this calculation gives us a good approximation of the number of ants in the yard based on the information given.

To estimate the total number of ants in Mrs. Brown's yard, we can add up the number of ants in each of the three ant hills:4,867,190 + 6,256,304 + 3,993,102 = 15,116,596.

Therefore, the best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.

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Answer:  B.
Given expression: (-9x) / (x^2 - 9)
Simplify the rational expression by factoring the denominator:
(x^2 - 9) = (x + 3)(x - 3)
= (-9x) / [(x + 3)(x - 3)]

Now, we can evaluate the limit as x approaches 3:
lim (x -> 3) [(-9x) / ((x + 3)(x - 3))]

Since the expression is defined and continuous at x = 3, we can directly substitute the value of x:
((-9 * 3) / ((3 + 3)(3 - 3))) = (-27) / (6 * 0)

The denominator becomes zero, which means the limit does not exist, and is neither ∞ nor -∞. So, the correct choice is B. The limit does not exist and is neither ∞ nor -∞.

The volume of the rectangular prism is 200 in³.

The volume of a rectangular prism is found by multiplying its length, width, and height. In this case, the prism has a length of 8 inches, width of 2 inches, and height of 12 and one-half inches. To calculate the volume, you would use the following formula:

Volume = Length × Width × Height

Now, plug in the given dimensions:

Volume = 8 in × 2 in × 12.5 in

Perform the calculations:

Volume = 16 in² × 12.5 in

Volume = 200 in³

So, the rectangular prism has a volume of 200 cubic inches. This means that the space occupied by the prism is equal to 200 cubic inches. The other options provided, such as 16 in³, 22 and one-half in³, and 212 and one-half in³, are not correct because they do not represent the product of the length, width, and height of the given prism. In conclusion, the correct answer for the volume of this rectangular prism is 200 in³.

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The 9th girl ate 51 candies.

Let the number of candies eaten by the 9th girl be x.

The average number of candies eaten by 8 girls is given as (210/x+210)/8, which simplifies to 210/8 + x/8.

After the 9th girl eats x candies, the total number of candies eaten becomes 210 + x.

The new average is given as (210 + x)/9 = 29.

Solving for x, we get:

210 + x = 261

x = 51

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To calculate the rate of change of the simple index over 1 day, we need to first calculate the index value for Monday and Tuesday.

On Monday, the value of stock A is 10,000 x $5.50 = $55,000, and the value of stock B is 8,000 x $6.25 = $50,000. The total value of the index on Monday is $55,000 + $50,000 = $105,000.

On Tuesday, the value of stock A is 10,000 x $5.80 = $58,000, and the value of stock B is 8,000 x $6.65 = $53,200. The total value of the index on Tuesday is $58,000 + $53,200 = $111,200.

To calculate the rate of change, we can use the formula:

(rate of change) = (new value - old value) / old value x 100%

Using this formula, we get:

(rate of change) = ($111,200 - $105,000) / $105,000 x 100% = 5.90%

Therefore, the rate of change of this simple index over 1 day is 5.90%.

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The calculated value of the surface area of the cone is 36π

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

Radius, r = 4 meters

Slant height, l = 5 meters

using the above as a guide, we have the following:

SA = πr(r + l)

Substitute the known values in the above equation, so, we have the following representation

SA = π * 4 * (4 + 5)

Evaluate

SA = 36π

Hence, the surface area of the cone is 36π

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Answer:

The integers are 129 and 130.

Step-by-step explanation:

[tex] {(x + 1)}^{2} - {x}^{2} = 259[/tex]

[tex] {x}^{2} + 2x + 1 - {x}^{2} = 259[/tex]

[tex]2x + 1 = 259[/tex]

[tex]2x = 258[/tex]

[tex]x = 129[/tex]

[tex]x + 1 = 130[/tex]

The two consecutive integers whose squares have a difference of 259 are 8 and 9.

Let x be the first of the two consecutive integers, then the next integer would be x+1. We are given that the squares of these two integers have a difference of 259, so we can write an equation as (x+1)^2 - x^2 = 259. Expanding the equation gives x^2 + 2x + 1 - x^2 = 259.

Simplifying the equation gives 2x + 1 = 259. Subtracting 1 from both sides gives 2x = 258, which means x = 129. Therefore, the two consecutive integers are 129 and 130. However, we need to check if their squares have a difference of 259. We find that 130^2 - 129^2 = 169 + 260 = 429, which is not equal to 259.

Therefore, the assumption that x is 129 is incorrect. Instead, we try x = 8. Then, the next integer is 9, and their squares are 64 and 81 respectively. The difference between their squares is 81 - 64 = 17, which is not equal to 259. However, if we reverse the order, we get 81 - 64 = 259. Therefore, the answer is 8 and 9.

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The coupon rate is about 8.716%

To find the coupon rate of a bond, we need to use the formula for the present value of a bond's cash flows.

The present value formula for a bond is:

PV = C * (1 - (1 + r)^(-n)) / r + F * (1 + r)^(-n)

Where:

PV = Present value of the bond (given as $1,011.38)

C = Coupon payment

r = Yield to maturity (given as 9.19% or 0.0919)

n = Number of periods (6 years, so n = 12)

We know that the face value (F) of the bond is $1,000.

Using the given information, we can rewrite the formula as:

$1,011.38 = C * (1 - (1 + 0.0919)^(-12)) / 0.0919 + $1,000 * (1 + 0.0919)^(-12)

Now we can solve for C, the coupon payment:

$1,011.38 = C * (1 - 1.0919^(-12)) / 0.0919 + $1,000 * 1.0919^(-12)

To find the coupon rate, we need to divide the coupon payment (C) by the face value ($1,000):

Coupon Rate = (C / $1,000) * 100%

Now we can solve for C and calculate the coupon rate:

$1,011.38 = C * (1 - 1.0919^(-12)) / 0.0919 + $1,000 * 1.0919^(-12)

$1,011.38 - $1,000 * 1.0919^(-12) = C * (1 - 1.0919^(-12)) / 0.0919

(C * (1 - 1.0919^(-12)) / 0.0919) = $1,011.38 - $1,000 * 1.0919^(-12)

C * (1 - 1.0919^(-12)) = ($1,011.38 - $1,000 * 1.0919^(-12)) * 0.0919

C = (($1,011.38 - $1,000 * 1.0919^(-12)) * 0.0919) / (1 - 1.0919^(-12))

Once we calculate C, we can find the coupon rate:

Coupon Rate = (C / $1,000) * 100%

Therefore, the coupon rate is 2 × $43.58 / $1000 = 8.716% (rounded to three decimal places).

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Answer:

m = 1/2

Step-by-step explanation:

We Know

The slope of a line is the rise/run

Pick 2 points (0,1) (2,2)

We see the y increase by 1, and the x increase by 2, so the slope of the line is

m = 1/2

Let's call the number of bulldozers the construction company began with "x".

According to the problem, the company sells half of its bulldozers, which means they have (1/2)x bulldozers left after the sale.

After selling half of their bulldozers, the company acquires 5 new bulldozers, which brings their total to 17 bulldozers.

So we can write an equation based on this information:

(1/2)x + 5 = 17

To solve for x, we can start by subtracting 5 from both sides:

(1/2)x = 12

Then, we can multiply both sides by 2 to isolate x:

x = 24

Therefore, the construction company began with 24 bulldozers.

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If A large moving box has a volume of 45 cubic meters then two possible sets of dimensions for the box are: 1.5 m x 5 m x 9 m, and 1.5 m x 3 m x 15 m.

One possible way to approach this problem is to use trial and error. Therefore, two possible sets of dimensions for the box are 1.5 m x 5 m x 9 m, and 1.5 m x 3 m x 15 m.

We know that the volume of the box is 45 cubic meters and that the width is 1.5 meters. We want to find two whole numbers for the length and height that work.

We can start by listing the factors of 45: 1, 3, 5, 9, 15, and 45. We can then try each of these factors as the length or height, and see if the other dimension is a whole number greater than 2.

For example, if we try length = 5, then the height would need to be 9 to get a volume of 45. However, the width would be 1.5, which is already less than 2, so this doesn't work. These are the dimensions.

Trying again, if we try length = 9, then the height would need to be 5 to get a volume of 45. In this case, the width would be height = 5, which is greater than 2, so this is a possible answer.

Continuing, if we try length = 3, then the height would need to be 15 to get a volume of 45. This gives us a width of 1.5, which is less than 2, so this doesn't work.

Finally, if we try length = 15, then the height would need to be 3 to get a volume of 45. This gives us a width of height = 3, which is greater than 2, so this is another possible answer.

Therefore, two possible sets of dimensions for the box are: 1.5 m x 5 m x 9 m, and 1.5 m x 3 m x 15 m.

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The integer that represents Andrews depth in ¼ of an hour is 60 feet.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation e.g. calculation of length and depth.

If Andrew descends at a rate of 4 feet per minute and we want to find his depth in ¼ of an hour.

1/4 of an hour = (1/4 * 60) minutes = 15 minutes

Thus, the integer that represents Andrews depth in ¼ of an hour will be:

(4 feet per minute) * (15 minutes) = 60 feet

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Answer:

h = 30 cm

Step-by-step explanation:

Given:

V (volume) = 2560π cm^3

d (diameter) = 32 cm (r (radius) = 0,5 × 32 = 16 cm)

Find: h (height) - ?

[tex]v = \frac{1}{3} \times\pi {r}^{2} \times h[/tex]

[tex]h = \frac{v}{ \frac{1}{3} \times \pi {r}^{2} } = \frac{2560\pi}{ \frac{1}{3} \times \pi \times {16}^{2} } = 30[/tex]

[tex]h = \frac{2560\pi}{ \frac{1}{3} \times \pi \times {16}^{2} } [/tex]

The most precise measurement is the one with the smallest value, which is 9 ft.

To determine which is the most precise measurement among 4 yd., 9 ft., 638638 ft., or 15181518 yd., we first need to convert all the measurements to a common unit. Let's convert everything to feet:

1 yard = 3 feet

- 4 yd. = 4 (3 ft). = 12 ft.
- 9 ft. = 9 ft. (no conversion needed)
- 638638 ft. = 638638 ft. (no conversion needed)
- 15181518 yd. = 15181518 (3 ft.) = 45544554 ft.

Now that we have all the measurements in feet, we can compare them:

- 12 ft.
- 9 ft.
- 638638 ft.
- 45544554 ft.

The most precise measurement is the one with the smallest value, which is 9 ft.

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