Jules owns a square plot of land that measures 30 yards on each side. He plans to divide the land in half by building a fence, as shown by the dotted line below. How many yards of fencing will Jules need?

15 yd
30 yd
30 StartRoot 3 EndRoot yd
30 StartRoot 3 EndRoot yd

There are a total of 90 possible outcomes in this experiment involving three steps.

To find the total number of possible outcomes, you should multiply the number of outcomes for each step because each outcome for step 1 corresponds to each outcome for step 2 and so on. This experiment requires a sequence of three steps. First step can result in 5 possible outcomes, second step can result in 6 possible outcomes, third step can result in 3 possible outcomes. The total number of possible outcomes is the product of the possible outcomes of each step:

Total possible outcomes = 5 x 6 x 3

Total possible outcomes = 90

Therefore, the total number of possible outcomes in this experiment involving three steps is 90.

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Answer:

Step-by-step explanation:

1+1=4x2=8/2=

answer: 4

Answer:

the surface area of the prism is22

The future value οf the accοunt after 2 years is $1,830.28. If Alice depοsits $1,500 intο an accοunt with an interest rate οf 2.5 percent, cοmpοunded quarterly.

An algebraic expressiοn is a mathematical phrase that cοntains variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Tο calculate the future value οf the accοunt after 2 years, we can use the fοrmula fοr cοmpοund interest:

[tex]FV = PV * (1 + r/n)^{(n*t)[/tex]

where:

FV is the future value οf the accοunt

PV is the present value (initial depοsit)

r is the annual interest rate (2.5%)

n is the number οf cοmpοunding periοds per year (4, since it is cοmpοunded quarterly)

t is the number οf years (2)

Plugging in the values, we get:

[tex]FV = 1,500 * (1 + 0.025/4)^{(4*2)[/tex]

[tex]FV = 1,500 * 1.02891^8[/tex]

FV = 1,500 * 1.22019

FV = 1,830.28

Therefοre, the future value οf the accοunt after 2 years is $1,830.28.

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Answer:

a) AB = XY

BC = YZ

CA = XZ

b) <A = <X

<B = <Y

<C = <Z

c) <X= 50°

Since <A= 50° and <A = <X

d) Measure of <C will be

<C + <A = 180°

<C + 50° = 180°

<C = 180° - 50°

<C = 130°

Hope it helps:)

Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.

We need to find the minimum value of the function

f(x,y) = 3x + y

we can use Lagrange multipliers method defining

F(x,y) = f(x,y) - λx g(x,y)  , where g(x,y) = x²+36 x y² - 1, such that

Fx(x,y) = fx(x,y) - λx gx(x,y) = 0

Fy(x,y) = fy(x,y) - λx gy(x,y) = 0

g(x,y)=0

where the sub-indices x and y represent the partial derivatives with respect to x and y, then

fx(x,y) - λx gx(x,y) = 3 - λx(2x) = 0 → x =3/(2xλ)

fy(x,y) - λx gy(x,y) = 1 - λx(36x2xy) = 0 → y =1/(72xλ)

x²+36xy² - 1 = 0 → [3/(2xλ)]²+36*[1/(72xλ)]² - 1 = 0

therefore, Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.

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Answer:

4,25

Step-by-step explanation:

[tex]3 \frac{5}{4} = \frac{17}{4} = 4 \frac{1}{4} = 4.25[/tex]

The probability is (20/60) * (30/60) = 1/6. Hence, the probability that a student randomly selected from a class of 60 students will be a male who has brown hair is (1/6).

The probability that a student randomly selected from a class of 60 students will be a male who has brown hair is (1/6).

Let's analyze each statement

Statement 1: One-half of the students have brown hair.

Statement 2: One-third of the students are males.

To determine the probability of selecting a male student who has brown hair randomly, we need to find the intersection of these two probabilities. That is, we need to find the probability of the number of students who have brown hair and the number of students who are males.From statement 1, the probability of selecting a student with brown hair is 1/2. Therefore, the number of students with brown hair is (1/2) * 60 = 30.

From statement 2, the probability of selecting a male student is 1/3. Therefore, the number of male students is (1/3) * 60 = 20.Since we need to find the probability of selecting a male student who has brown hair randomly, we need to find the probability that the student is male and has brown hair.

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Answer: The distance (x) from the plane to the airport is approximately 2.2 miles.

Step-by-step explanation: The tangent function relates the opposite side of a right triangle to its adjacent side. In this case, we can use it to find the distance (x) from the plane to the airport.

To calculate x, we first need to convert 500 ft to miles. Since there are 5,280 feet in a mile, 500 ft is equal to 0.0947 miles.

Next, we use the tangent function to find x. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, we know that the angle of descent is 13 degrees and that the opposite side is x (the distance from the plane to the airport), and we just calculated that the adjacent side is 0.0947 miles. So we can set up an equation:

tan(13 degrees) = x / 0.0947 miles

To solve for x, we can multiply both sides by 0.0947 miles:

0.0947 miles * tan(13 degrees) = x

Plugging this into a calculator gives us:

x = 0.023 miles

Finally, we round this value to the nearest tenth of a mile:

x ≈ 2.2 miles

So, the distance from the plane to the airport is approximately 2.2 miles.

Hope this helps, and have a great day!

A number line is a graphical representation of numbers in a linear format. It is a useful tool to help visualize the relative positions of numbers, especially fractions.

To place the fractions 2/3, 1/10, and 7/8 on a number line, we need to first identify their relative positions in terms of magnitude.

Starting at 0 on the number line, we can place 1/10 to the right of 0, followed by 2/3 and then 7/8, in order from left to right. Since 2/3 is greater than 1/10 but less than 7/8, it is placed between these two fractions on the number line. The resulting number line would show the relative positions of these three fractions in relation to each other and to the whole numbers. This can help in comparing and ordering fractions, as well as in visualizing their relative magnitudes.

1/10 = 0.1

2/3 = 0.667

7/8 = 0.875

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Answer:

approaches , and the value of the function approaches as x approaches. Which function could be function f?

A.

B.

C.

D

The probability that the mean gain for the sample was between 400 and 800 is approximately 1 or 100%.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

We can use the central limit theorem to approximate the sampling distribution of the sample mean as normal, with a mean of 651 and a standard deviation of (standard deviation of the population)/√(sample size) = 6/√(34) ≈ 1.03.

Then, we can standardize the values of 400 and 800 using the formula z = (x - μ) / σ, where x is the value of interest, μ is the mean of the sampling distribution, and σ is the standard deviation of the sampling distribution.

For 400:

z = (400 - 651) / 1.03 ≈ -241.75

For 800:

z = (800 - 651) / 1.03 ≈ 143.69

We want to find the probability that the sample mean falls between 400 and 800, which is the same as finding the probability that the standardized value falls between -241.75 and 143.69. We can use a standard normal distribution table or a calculator to find this probability:

P(-241.75 < z < 143.69) ≈ P(z < 143.69) - P(z < -241.75) ≈ 1 - 0 ≈ 1

Therefore, the probability that the mean gain for the sample was between 400 and 800 is approximately 1 or 100%.

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Step-by-step explanation:

law of cosine :

c² = a² + b² - 2ab×cos(C)

c being the side opposite of the angle C. a and b are the other 2 sides.

a)

x² = 7² + 9² - 2×7×9×cos(102) = 49 + 81 - 126×cos(102) =

= 130 - 126×cos(102) = 156.196873...

x = 12.49787474... ≈ 12.5

b)

9² = 5² + 12² - 2×5×12×cos(theta)

81 = 25 + 144 - 120×cos(theta)

81 = 169 - 120×cos(theta)

120×cos(theta) = 88

cos(theta) = 88/120 = 11/15 = 0.733333333...

theta = 42.83342807...° ≈ 42.8°

Answer:

Step-by-step explanation:

Ms Pace:   [tex]\frac{6}{24} \times 100=\frac{1}{4} \times 100=25\%[/tex]

Ms Lee:     [tex]\frac{14}{28} \times 100=\frac{1}{2} \times 100=50\%[/tex]

Difference [tex]=50-25=25[/tex]

Answer:

Roman numerals

Step-by-step explanation:

In a pedigree, Roman numerals are used to represent different generations, while Arabic numerals are used to represent individuals within each generation. For example, the first generation would be represented by Roman numeral I, the second generation by Roman numeral II, and so on. Within each generation, individuals are numbered sequentially using Arabic numerals, starting with 1 for the first individual in the generation.

Answer:

The size by which the shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc. The scale factor is 2:5, this means that 2 feet at the original is 5 feet in new.

Therefore the new base is 18 x 5/2 = 45 feet

The new height  = 7 x 5/2 = 17.5 feet

The area of a triangle = ½ base x height

There's the area of the old deck = 1/2 × 18 × 7 = 63 square feet the area of the new deck = 1/2 × 45 × 17.5 = 393.75 square feet.

The scale factor = 2/5 = 1/2.5

and the ratio of the area 1/6.25 .i.e 63/393.75 This means the area of the new deck is twice or double of the old deck.

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By answering the presented question, we may conclude that As a result, function the solution is y = x/3.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

A direct variation function has the formula y = kx, where k is the proportionality constant. We may utilise the supplied coordinates (-9, -3) and (-12, -4) to obtain k as follows:

(using the point (-9, -3)) -3 = k(-9)

-4 = k(-12) (using the coordinates -12, -4)

When we solve for k in both equations, we get:

k = -3/9 = -1/3 \sk = -4/-12 = 1/3

We made a mistake in one of the equations since the values of k are not the same. The first equation is clearly erroneous since it suggests k = -1/3, which is not the same as k = 1/3 from the second equation. As a result, the proper equation for the direct variation function is:

y = (1/3)x

As a result, the solution is y = x/3.

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Answer:

Step-by-step explanation:

they wrote the answer already^

The composition of transformations that map ABCD to EHGF is: reflect over the x-axis, then translate (x + 3. y + 1).

In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

Since triangle ABCD was reflected over the x-axis, the coordinate A of triangle ABCD can be calculated as follows;

(x, y)            →      (x, -y)

A (-5, 2)      →      (-5, -(2)) = (-5, -2)

For the translation, we have:

(x, y)            →       (x + a, y + b)

A (-5, -2)           →      E (-2, 1)

-5 + a = -2

a = -2 + 5

a = 3

-2 + b = -1

b = -1 + 2

b = 1

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The probability that a randomly selected region had exactly three hits is approximately 0.139.

In this problem, we can use the Poisson probability distribution formula to find the probability of a randomly selected region having exactly three hits.

The Poisson probability distribution formula is:

P(x) = (e^(-μ) * μ^x) / x!

Where:

P(x) is the probability of x occurrences of an event.

μ is the mean number of occurrences of the event in a given interval.

x is the number of occurrences of the event.

e is the mathematical constant e, approximately equal to 2.71828.

To apply this formula to the problem at hand, we need to determine the values of μ and x.

Since there were a total of 515 bombs that hit the 573 regions, we can calculate the average number of bombs that hit each region:

μ = total number of bombs / number of regions

μ = 515 bombs / 573 regions

μ = 0.8993

Therefore, the mean number of hits per region is 0.8993.

To find the probability that a randomly selected region had exactly three hits, we can plug in x = 3 into the Poisson probability distribution formula:

P(3) = (e^(-0.8993) * (0.8993)^3) / 3!

P(3) ≈ 0.139

Therefore, the probability that a randomly selected region had exactly three hits is approximately 0.139.

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Answer: There are 2 common tangents, they are external

Step-by-step explanation:

I just learned this lesson in my Geometry class trust

The area of the given figure consisting of rectangle and triangles is 51.5 square feet.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm² and m² are used to measure area.

We must first calculate the areas of each form in the figure in order to obtain the total area.

Let's start by calculating the rectangle's area:

Area = length x width

Area = 11ft x 4ft

Area = 44ft²

The area of the two right triangles should now be determined.

Triangle 1:

Area = (base x height) / 2

Area = (2ft x 3ft) / 2

Area = 3ft²

Triangle 2:

Area = (base x height) / 2

Area = (3ft x 3ft) / 2

Area = 4.5ft²

The total area of the figure can now be calculated by adding the areas of the three shapes:

Total Area = Area of Rectangle + Area of Triangle 1 + Area of Triangle 2

Total Area = 44ft² + 3ft² + 4.5ft²

Total Area = 51.5ft²

Therefore, the area of the figure is 51.5 square feet.

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The area of the rectangle is 41 square units

The area of a composite figure, you must first break it down into simpler shapes. Then, you can find the area of each shape and add them together to get the total area of the composite figure.
Let's say our composite figure consists of a rectangle and a triangle. To find the area, we need to find the area of the rectangle and the area of the triangle separately, and then add them together.
To find the area of the rectangle, we need to know its length and width. Let's say the length is 8 units and the width is 4 units. The formula for the area of a rectangle is length x width, so the area of our rectangle is:
[tex]8 x 4 = 32 square units[/tex]
Now, let's find the area of the triangle. To do this, we need to know its base and height. Let's say the base is 6 units and the height is 3 units. The formula for the area of a triangle is 1/2 x base x height, so the area of our triangle is:
[tex]1/2 x 6 x 3 = 9 square units[/tex]
Now that we have the area of both the rectangle and the triangle, we can add them together to find the total area of the composite figure:
[tex]32 + 9 = 41 square units[/tex]
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The critical z-value using a z-table or calculator:

Critical z-value = ±2.576.

What is null hypothesis's?

A null hypothesis is a statement or assumption that there is no significant difference or relationship between two or more variables or groups. In statistical hypothesis testing, the null hypothesis is usually denoted as H0 and is tested against an alternative hypothesis (Ha), which is the hypothesis that there is a significant difference or relationship between the variables or groups being studied.

According to the question:
(a) The null hypothesis is that there is no significant difference in the average amount of money spent per day between the two groups. The alternative hypothesis is that there is a significant difference in the average amount of money spent per day between the two groups.

Since we are not given any information about the direction of the difference, we will use a two-tailed test. The appropriate test to use in this situation is the two-sample t-test.

(b) To find the critical z-value, we first need to calculate the degrees of freedom for the test:

df = (n1 + n2 - 2) = (25 + 27 - 2) = 50

Using a significance level of 0.01, we find the critical z-value using a z-table or calculator:

Critical z-value = ±2.576

(c) To find the test value, we will first calculate the pooled standard deviation using the formula:

[tex]sp = \sqrt{((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)}[/tex]

where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes. Substituting the given values, we get:

[tex]sp = \sqrt{((24 * 5.3^2) + (26 * 6.8^2)) / 50} = 6.083[/tex]

Next, we calculate the t-value using the formula:

[tex]t = (x1 - x2) / (sp * \sqrt{1/n1 + 1/n2})[/tex]

where x1 and x2 are the sample means. Substituting the given values, we get:

[tex]t = (38.6 - 37.4) / (6.083 * \sqrt{1/25 + 1/27}) = 1.213[/tex]

Since the absolute value of the test value is less than the critical z-value, we fail to reject the null hypothesis. Therefore, we cannot conclude that there is a significant difference in the average amount of money spent per day between the two groups.

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To solve this expression, we can use the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right).

Following this order, we first need to evaluate the exponent, which gives:

1000^3 = 1,000,000,000

Then, we can substitute this value back into the expression:

1000 + 1000^3 = 1000 + 1,000,000,000 = 1,000,000,000 + 1000 = 1,000,001,000

Therefore, 1000 + 1000^3 equals 1,000,001,000.

Answer: 8000000000

Step-by-step explanation:

The coordinates of the vertex B' are (-2, -3)

The term vertices (singular: vertex) refers to the points where the sides or edges of a geometric shape or object meet.

The coordinates vertex B', we need to reflect the point B (-2, 5) across the line y = 1.

The line y = 1 is the horizontal line passing through (0, 1). The reflection of a point (x, y) across this line will have the same x-coordinate but a y-coordinate that is the same distance from the line y = 1 as the original point, but in the opposite direction.

So, the y-coordinate of the reflected point B' will be:

y-coordinate of B' = 1 - (y-coordinate of B - 1)

y-coordinate of B' = 1 - (5 - 1) = -3

Therefore, the coordinates of B' are (-2, -3).

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Therefore, the angle V in parallelogram WXUV is 100 degrees. Therefore, the angle L in parallelogram LMJK is 98 degrees. Therefore, the length of side SP in parallelogram SRQP is 26 units. Therefore, the length of side FC in parallelogram FCDE is 12.6 units.

A parallelogram is a quadrilateral (a four-sided polygon) with two pairs of parallel sides. In other words, the opposite sides of a parallelogram are parallel and congruent (equal in length). The properties of a parallelogram include:

Opposite sides are parallel and congruent

Opposite angles are congruent (equal in measure)

Consecutive angles are supplementary (add up to 180 degrees)

Diagonals bisect each other (divide each other into two equal parts)

Some common examples of parallelograms include rectangles, rhombuses, and squares. A rectangle is a parallelogram with four right angles, a rhombus is a parallelogram with four congruent sides, and a square is a parallelogram with four congruent sides and four right angles.

Here,

1. In a parallelogram, opposite angles are equal. Therefore, if angle U is 80 degrees, then angle W must also be 80 degrees.

We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices V and U is 360 - 2*80 = 200 degrees.

Since opposite angles in a parallelogram are equal, the angle at vertex V must also be 100 degrees.

2. In a parallelogram, opposite angles are equal. Therefore, if angle J is 98 degrees, then angle L must also be 98 degrees.

We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices J and K is 360 - 2*98 = 164 degrees.

Since opposite angles in a parallelogram are equal, the angle at vertex M must also be 98 degrees.

3. In a parallelogram, opposite sides are equal in length. Therefore, if side RQ is 26 units, then side SP must also be 26 units.

This is because SRQP is a parallelogram, so side SR is equal in length to side PQ, and side RQ is equal in length to side SP.

4. In a parallelogram, opposite sides are equal in length. Therefore, if side DE is 12.6 units, then side FC must also be 12.6 units.

This is because FCDE is a parallelogram, so side FC is equal in length to side DE, and side DE is equal in length to side FC.

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there are 45,360 distinguishable arrangements of the letters in the word "SASKATOON" and  there are 34,650 distinguishable arrangements of the letters in the word "MISSISSIPPI".

a. SASKATOON:

To determine the number of distinguishable arrangements of the word "SASKATOON", we can use the formula for permutations of indistinguishable objects, which is n!/a!b!c!…, where n is the total number of objects and a, b, c,… are the frequencies of each indistinguishable object. In this case, there are 9 letters in the word "SASKATOON", but some of them are repeated. Specifically, there are 2 S's, 2 A's, and 2 O's. Using the formula, we get:

9!/(2!2!2!) = 9876543/(222) = 45,360

Therefore, there are 45,360 distinguishable arrangements of the letters in the word "SASKATOON".

b. MISSISSIPPI:

To determine the number of distinguishable arrangements of the word "MISSISSIPPI", we can use the same formula for permutations of indistinguishable objects. In this case, there are 11 letters in the word "MISSISSIPPI", but some of them are repeated. Specifically, there are 4 I's, 4 S's, and 2 P's. Using the formula, we get:

11!/(4!4!2!) = 34,650

Therefore, there are 34,650 distinguishable arrangements of the letters in the word "MISSISSIPPI".

In summary, the number of distinguishable arrangements of a word can be found using the formula for permutations of indistinguishable objects, which takes into account the frequency of each repeated letter. By applying this formula to the words "SASKATOON" and "MISSISSIPPI", we find that there are 45,360 and 34,650 distinguishable arrangements, respectively.

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The amount of sand Jamilla have to order to fill the square sandbox with sides 8 1/2 feet long and 2 1/2 feet deep is 180.625 cubic feet of sand.

To calculate the amount of sand that Jamilla should order, you need to calculate the volume of the sandbox. Given that Jamilla is building a square sandbox with sides 8 1/2 feet long and wants to put sand 2 1/2 feet deep in the box. Thus, the volume of the sandbox is calculated as follows:

Volume of the sandbox = Length * Width * Depth

Volume of the sandbox = (8 1/2 feet) * (8 1/2 feet) * (2 1/2 feet)

Converting each mixed fraction to its corresponding improper fraction, we get:

8 1/2 feet = 17/2 feet

2 1/2 feet = 5/2 feet

On simplifying the above equation we get:

Volume of the sandbox = (17/2 feet)² * (5/2 feet)

Volume of the sandbox = (289/4) * (5/2) cubic feet

Volume of the sandbox = 1445/8 cubic feet

Volume of the sandbox = 180.625 cubic feet

Therefore, Jamilla should order 180.625 cubic feet of sand.

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The skyscraper will have 78 floors when it is finished.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Let's assume that the total number of floors in the skyscraper is "x".

According to the problem, the builder has built 1/6 of the floors.

So the number of floors built by the builder is:

= (1/6)x

The problem also tells us that the builder has built 13 floors.

So we can set up the equation:

(1/6) x = 13

To solve for "x", we can multiply both sides by 6:

x = 78

Therefore,Therefore, The skyscraper will have 78 floors when it is finished.

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Answer:A

Step-by-step explanation:

It would have the greatest chance to be the line on the graph