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Therefore, both functions have the same axis of symmetry equation, which is x = -3.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are one of the central objects of study in mathematics and have many applications in various fields such as physics, economics, engineering, and computer science. A function is typically represented using a mathematical expression or equation, and it can be analyzed and manipulated using a variety of mathematical techniques.

Here,

Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.

For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.

For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.

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If the house value of $89,548 and two points, attorney's fees $324, title fees $105, then closing cost is option (b) $2,219.96

Closing costs are fees associated with the purchase or refinance of a property that are paid at the closing of the transaction.

To calculate the closing cost, we need to add up all the fees associated with the purchase of the house.

First, we need to calculate the cost of the points. Two points on a house value of $89,548 would be

2 x $89,548 x 0.01 = $1,790.96

Next, we need to add the attorney's fees and title fees

$1,790.96 + $324 + $105 = $2,219.96

Therefore, the correct option is (b) $2,219.96

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Answer:

14

Step-by-step explanation:

c = 2[tex]\pi r[/tex]

c = 2[tex]\pi[/tex]7

x = 14[tex]\pi[/tex]

Helping in the name of Jesus.

The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].

Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).

Given:

[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]

Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.

We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:

The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50

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The diameter of the semicircle for the given area of the semicircle 1. 2717 square meters is equal to 1.8 meters.

Area of a semicircle = 1. 2717 square meters

The area of a semicircle is given by the formula,

A = πr^2 / 2

where A is the area

And r is the radius of the semicircle.

Rearrange the formula to solve for r,

r = √(2A/π)

Substituting the given value of A = 1.2717 square meters into this formula, we get,

⇒ r = √(2 × 1.2717 / π)

⇒ r = 0.9 meters

Since the diameter of a semicircle is twice the radius,

The diameter of this semicircle is equal to,

d = 2r

  = 2 × 0.9

   = 1.8 meters

Therefore, the diameter of the semicircle is equal to 1.8meters.

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The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of the denominators.

To solve the equation (4)/(x) + (1)/(2) = (5)/(x):

Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 2x.

Multiply the left side of the equation by 2/2 to get:

(8)/(2x) + (1)/(2) = (5)/(x)

Combine the two fractions on the left side of the equation:

(8+1)/(2x) = (9)/(2x)

Set the left side of the equation equal to the right side:

(9)/(2x) = (5)/(x)

Cross-multiply:

9x = 10x

Simplify:

x = 0

Therefore, the solution to the equation is x = 0.

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Answer:  (x + 3) (x - 3) (x^2 + 9) (x^2 - 9)

Step-by-step explanation: We can use the difference of squares formula to factor x^4 - 81 as (x^2 + 9)(x^2 - 9).

Then, we can use the difference of squares formula again to factor x^2 - 9 as (x + 3)(x - 3).

Therefore, the complete factorization of x^4 - 81 is (x + 3)(x - 3)(x^2 + 9)(x^2 - 9).

The total cups of milk orange juice Enrique has in refrigerator is equal to  18 cups.

Gallons of milk Enrique has in his refrigerator = 1 gallon

Pint of orange juice Enrique has in his refrigerator = 1 pint

Convert gallons to cups and pint to cups .

There are ,

16 cups = 1 gallon of milk

And 2 cups = 1 pint of orange juice

Enrique has 16 cups of milk

and 2 cups of orange juice.

Total cups of milk and orange juice in refrigerator

=16 cups of milk + 2 cups of orange juice

= 18 cups of milk and orange juice

Therefore, in total Enrique has  18 cups of liquid in his refrigerator.

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The probability of accepting the whole shipment is 0.384, or about 38.4%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

This is a binomial probability problem, where the probability of a defect (or non-conformance) is p=0.11 and the sample size is n=27. We want to find the probability of having at most one defect in a sample of 27 tablets.

Let X be the number of defects in the sample. Then X follows a binomial distribution with parameters n=27 and p=0.11. We want to find P(X ≤ 1), which is the probability of having 0 or 1 defects in the sample.

Using the binomial distribution formula, we have:

P(X ≤ 1) = P(X = 0) + P(X = 1)

= (27 choose 0) * [tex](0.11)^{0}[/tex] * [tex](0.89)^{27}[/tex] + (27 choose 1) * [tex](0.11)^{1}[/tex] * [tex](0.89)^{26}[/tex]

= (1) * (1) * [tex](0.89)^{27}[/tex] + (27) * (0.11) * [tex](0.89)^{26}[/tex]

= 0.384

Therefore, the probability of accepting the whole shipment is 0.384, or about 38.4%.

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The ratio of LM to FG is 3:4, so correct option is A.

A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.

The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.

Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.

Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.

If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).

So we have:

LMN / FGH = 18 / 32

(x²) = 18 / 32

x² = 9 / 16

x = (3 / 4)

Therefore, the ratio of LM to FG is 3:4, which is option A.

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The answer to the question is C

Answer:

Let x be width and y = length of barn wall y + 2x =20Area = xy= x(20 - 2x)=20x -2x^2dA/dx = 20 - 4xmax at dA/dx =0 so 20 - 4x = 0x=5 y=10 max area is 50 sq ft

Answer:

parallelogram kite kite trapazoid

Therefore, the dimensions of the crate that minimize the cost of materials are approximately:

l = 1.587 ft
w = 2.519 ft
h = 3.159 ft

To minimize the cost of materials, we need to find the dimensions of the crate that will minimize the surface area of the crate. Let's call the height, width, and length of the crate "h", "w", and "l", respectively.

We know that the volume of the crate is 16 ft3, so we can write:

lwh = 16

We want to minimize the cost of materials, which is determined by the surface area of the crate. The surface area consists of the top, bottom, front, back, left, and right sides of the crate. The cost of the materials for the base is twice the cost of the materials for the sides, and the cost of the materials for the top is half the cost of the materials for the sides. Let's call the cost of the materials for the sides "c".

The surface area of the crate can be written as:

2lw + 2lh + 2wh

We can use the volume equation to solve for one of the variables, say "h":

[tex]h = \frac{16}{(lw)}[/tex]

Now we can substitute this expression for "h" into the surface area equation:

[tex]2lw + 2l(\frac{16}{(lw))} + 2wh[/tex]

Simplifying this expression gives:

[tex]2lw + 32/l + 2wh[/tex]
To find the dimensions that minimize this expression, we need to take the partial derivatives with respect to "l" and "w" and set them equal to zero:
[tex]\frac{d}{dl} (2lw + 32/l + 2wh) = 2w - \frac{32}{l^2} = 0\\[/tex]

[tex]\frac{d}{dw} (2lw + 32/l + 2wh) = 2l + 2h = 2l + 2(16/(lw)) = 2l + 32/(lw) = 0[/tex]
Solving these equations for "l" and "w" gives:

[tex]l = 2^{(1/3)}\\w = 2^{(2/3)}[/tex]

Substituting these values into the equation for "h" gives:

[tex]h = 8/(2^{(2/3)})[/tex]

Therefore, the dimensions of the crate that minimize the cost of materials are approximately:

l = 1.587 ft
w = 2.519 ft
h = 3.159 ft

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The dimensions of the box that minimize the cost of materials are approximate:

x ≈ 2.52 ft

y ≈ 3.55 ft

z ≈ 2.52 ft

Let's denote the length, width, and height of the box as x, y, and z,

respectively. We are given the volume of the box is [tex]16 ft^3[/tex], so we

have:

x × y × z = 16

We are also given that the material used to make the base costs twice as

much (per square foot) as the material in the sides.

Let's denote the cost of the material for the sides as c, so the cost of the

material for the base is 2c.

The area of the base is xy, so the cost of the material for the base is

2cxy.

Similarly, the material used to make the top costs half as much (per

square foot) as the material in the sides.

Let's denote the cost of the material for the top as 0.5c.

The area of the top is also xy, so the cost of the material for the top is 0.5cxy.

The cost of the material for the four sides is simply 4cz.

Therefore, the total cost of materials is:

C(x, y, z) = 2cxy + 4cz + 0.5cxy

Simplifying, we have:

C(x, y, z) = (2.5c)xy + 4cz

We want to minimize this function subject to the constraint that the volume of the box is [tex]16 ft^3[/tex]:

x × y × z = 16

We can use the method of Lagrange multipliers to solve this constrained optimization problem:

L(x, y, z, λ) = (2.5c)xy + 4cz - λ(xyz - 16)

Taking partial derivatives with respect to x, y, z, and λ, we get:

dL/dx = 2.5cy - λyz = 0

dL/dy = 2.5cx - λxz = 0

dL/dz = 4c - λxy = 0

dL/dλ = xyz - 16 = 0

From the first two equations, we can solve for λ:

λ = 2.5cy/yz = 2.5cx/xz

Setting these two expressions equal to each other and simplifying, we get:

y/x = z/y

This implies that x:y:z = 1:√2:1, since we know that the dimensions of the box must be in proportion to each other.

Substituting this into the constraint x × y × z = 16, we get:

x = 2∛2

y = 2∛4

z = 2∛2

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The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.

No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.

The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.

The p value for this test is 0.788, which is greater than the alpha level of 0.01.

The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.

This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.

The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.

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Answer:

Step-by-step explanation:

To convert a fraction to a decimal, you divide the numerator by the denominator. The line in the middle of a fraction is essentially a large division sign.

Let's check Jackie's work

1/200 = 0.005

3/10 = 0.3

7/8 = 0.875

4/5 = 0.8

Jackie listed 7/8 as 0.625, which is incorrect. 7/8 is 0.875

So, 0.625 is your answer.

The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

What is equations?

Equivalent equations are algebraic equations that are having identical roots or solutions.

The soccer ball specifications require a diameter of 8.65 inches, with an allowable margin of error of 0.05 inch.

This means that the actual diameter of any new soccer ball should be within the range of 8.60 inches to 8.70 inches. The equation that can be used to find the diameter of a new soccer ball is d = 8.65 ± 0.05, where d represents the diameter. The symbol "±" indicates that the diameter can be either 0.05 inches larger or smaller than the specified diameter of 8.65 inches.

It is important to ensure that the diameter of a soccer ball falls within this allowable range to comply with the specifications and ensure fair play.

Therefore, The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

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The guy wire must be about 55 feet long and the slope of the guy wire, expressed as a fraction is 25/11.

We can use the Pythagorean Theorem to find the length of the guy wire. Let's call the length of the guy wire "g".

g^2 = 50^2 + 22^2

g^2 = 2500 + 484

g^2 = 2984

g ≈ 54.65

So the guy wire must be about 55 feet long.

The slope of the guy wire is the ratio of the vertical distance it covers to the horizontal distance it covers. In this case, the vertical distance is 50 feet (the height of the pole) and the horizontal distance is 22 feet. So the slope is

50/22 = 25/11

Therefore, the slope of the guy wire is 25/11.

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The length of the rectangular prism given the volume, width and height is 19 yd.

Volume of a rectangular prism = length × width × height

Volume of the prism = 2,280 yd³

Width of the prism = 20 yd

Height of the prism = 6 yd

Length of the prism = x

So,

Volume of a rectangular prism = length × width × height

2,280 = x × 20 × 6

2,280 = 120x

divide both sides by 120

x = 2,280 / 120

x = 19 yd

Therefore, the length is 19 yd

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Answer:

Step-by-step explanation:(3)(6)+(4) = 18+4= 22

To determine if the sample fairly represents the population, we need to consider whether the sample is representative and whether there is any bias present in the sampling process.

If the principal surveyed fifty 8th graders in a way that ensures that each 8th grader in the population has an equal chance of being selected, then the sample can be considered representative. This means that the sample accurately reflects the characteristics of the population, and any conclusions drawn from the sample can be applied to the population.

However, if the sampling process was biased in some way, the sample may not be representative of the population. For example, if the principal only surveyed 8th graders in one class or in one particular group, the sample may not be representative of the entire 8th-grade population at Harding Middle School. In this case, any conclusions drawn from the sample may not accurately reflect the entire population.

Therefore, the key factor in determining whether the sample fairly represents the population is the sampling method used. If the sampling method is random and unbiased, then the sample can be considered representative of the population.

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1.) parallelogram

2.) trapezoid

3.) kite

4.) parallelogram

The parallelogram is a type of quadrilateral that has the following unique properties such as:

The kite is also a type of quadrilateral that has two pairs of adjacent equal sides with a pair of opposite angles that are equal.

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A The histogram is the best graph showing the average scores of 5 UCI volleyball teams in UCI history. Because it allows us to divide the data into as many or as few groups as we want and clarify the comparison between them.

We would like to view the average points data of the top 5 UCI basketball players in UCI history. There are two types of charts used to present data. The first is a histogram and the second is a scatterplot. We have to decide which picture is the best. Now, as we know, scatter charts are used to plot observations based on points to show the relationship between two data sets. A histogram is a type of bar chart in which all values are divided. Divides the range of results in the data into classes or groups. It can help identify outliers or gaps in the data. After discussing the features of the two graphs, shows the average score of 5 UCI basketball players in UCI history, the histogram is the best choice here because it allows us to divide and share the difference between clearly.

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complete question:

The above figure complete the question..

you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?

The expanded form of the given expression (h² − h) + (5h + 6)-(3h² +4h - 9) is -2h² + 15.

Given the expression in the question;

(h² − h) + (5h + 6) - (3h² + 4h - 9)

Expanding an algebraic expression means to remove any parentheses and simplify the expression as much as possible.

In the given expression, we have three sets of parentheses:

(h² − h)

(5h + 6)

(3h² +4h - 9)

To expand the expression, we will remove the parentheses and simplify the resulting terms.

(h² − h) becomes h² - h

(5h + 6) remains the same

(3h² +4h - 9) becomes 3h² + 4h - 9

Putting all the terms together, we get:

h² - h + 5h + 6 - (3h² + 4h - 9)

Now, we will distribute the negative sign to all the terms inside the parentheses:

h² - h + 5h + 6 - 3h² - 4h + 9

Simplifying further by combining like terms, we get:

h² - 3h² - h + 5h - 4h + 6  + 9

-2h² + 15

Therefore, the expanded form is -2h² + 15.

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A. The correct option for similarity is option D -  Both estimate proportions of the data contained within k standard deviations of the mean.

Both the Empirical Rule and Chebyshev's Theorem are used to estimate the proportion of data contained within a certain number of standard deviations from the mean.

Therefore, option 'D' is the correct answer: Both estimate proportions of the data contained within k standard deviations of the mean.

B. The correct option for difference is option A - The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

The Empirical Rule assumes that the distribution is approximately symmetric and bell-shaped, while Chebyshev's Theorem makes no assumptions about the shape of the distribution.

Another difference is that the Empirical Rule is only applicable for normal distributions, while Chebyshev's Theorem can be applied to any distribution.

Therefore, option 'A' is the correct answer: The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

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The probability that the flight will leave on time when it is not raining is approximately 0.83.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).

According to the given information:

To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).

Let:

P(rain) = 0.07 (probability of rain)

P(delayed) = 0.17 (probability of delay)

P(rain and delayed) = 0.02 (probability of rain and delay)

We can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case, we want to find P(on time | not raining), which can be expressed as:

P(on time | not raining) = P(on time and not raining) / P(not raining)

Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:

P(on time | not raining) = P(on time) / (1 - P(rain))

We can now substitute the given probabilities to calculate the required probability:

P(on time | not raining) = P(on time) / (1 - P(rain))

P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))

P(on time | not raining) = (1 - 0.17) / (1 - 0.07)

P(on time | not raining) = 0.83

So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).

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The total area of two triangle tablecloths for one table = 8ft²,

height =  6mm,

The total area of the den = 430ft²,

height of the rhombus =  12ft,

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

Triangles:

a) Area of triangle = 1/2 * base * height = 1/2 * 4in * 5in = 10in²

b) Area of triangle = 1/2 * base * height = 1/2 * 6ft * 10ft = 30ft²

c) Area of triangle = 1/2 * base * height = 1/2 * 12m * 15m = 90m²

Total area of two triangle tablecloths for one table = 2 * 1/2 * 2ft * 4ft = 8ft²

Parallelogram:

a) Area of parallelogram = base * height = 6in * 9in = 54in²

b) Area of parallelogram = base * height = 2ft * 5ft = 10ft²

c) Area of parallelogram = base * height = 3yds * 7yds = 21yds²

height = Area/base = 78mm²/13mm = 6mm

Rectangle:

a) Area of rectangle = length * width = 8ft * 6ft = 48ft²

b) Area of rectangle = length * width = 13ft * 5ft = 65ft²

Total area of the den = (2 * 9ft * 15ft) + (2 * 8ft * 10ft) = 270ft²+ 160ft² = 430ft². Charles has enough paint because one gallon of paint will cover 440 square feet of wall space.

Rhombus:

a) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 12yds * 12yds = 72yds²

b) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 10ft * 25ft = 125ft²

c) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 16in * 22in = 176in²

height of the rhombus = 2(area/diagonal1) = 2(72ft²/12ft) = 12ft

Trapezoid:

a) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (6ft + 7ft) * 10ft = 65ft²

b) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (5yds + 8yds) * 4yds = 26yds²

c) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (9in + 11in) * 13in = 130.5in²

d) Height of trapezoid = 2(area/(base1 + base2)) = 2(32km²/16km) = 4km

Hence, the total area of two triangle tablecloths for one table = 8ft²,

height =  6mm,

The total area of the den = 430ft²,

height of the rhombus =  12ft,

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Thus, the area of the actual bridge deck is found as 1750 square feet.

A scale factor refers to the amount by which an object is multiplied to produce a second object of different size but with the same appearance. Just a larger or smaller version of the original is created, not an exact copy.

Given dimension-

Length l = 24 inches

width w = 4 1/5 = 21/5 inches

Convert inches to feet:

1 foot = 12 inches.

Scaled length = 24 inches ÷ 12 inches/foot = 2 feet

Scaled width =21/5 inches ÷ 12 inches/foot = 21 / 5*12 = 0.35 feet

Now, scale factor = 50.: 1

Actual length = Scaled length × Scale factor

Actual length = 2 feet × 50 = 100 feet

Actual width = Scaled width × Scale factor

Actual width = 0.35 feet × 50 = 17.5 feet

Area of actual bridge deck:

Area = Actual length × Actual width

Area = 100 feet × 17.5 feet

Area = 1750 square feet

Thus, the area of the actual bridge deck is found as 1750 square feet.

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Answer: 4 milimeters

Step-by-step explanation:

1 centimeters = 10 millimeters

0.4 centimeters= 4 miliimeters