Find the area of this shapr

The two statements that completes the above proof are:

ΔABC ~ ΔDEC - Side - Angle - Side Postulate

∠1≅∠2 - Corresponding angles.

The Side-Angle-Side (SAS) postulate states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.

Corresponding angles are equal because of the congruence of the triangles. Two angles are corresponding if they occupy the same relative position in two distinct intersecting lines, such that they are on the same side of the transversal and are in the same position in relation to the intersection. Corresponding angles are equal if the two intersecting lines are parallel.

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Minimum value is 50, maximum value is 66, median is 59, Q1 is 53.5 and Q3 is 65. Box-and-whisker plot:

A box plot, often referred to as a whisker plot, shows the distribution of a continuous variable along with details like the median, quartiles, and outliers. A set of data's variety is shown graphically in this way. The plot, often known as a five-number summary, presents five bits of information. The fundamental benefit of box whisker plots is that the overlap between the distributions of various qualities may be calculated by comparing them side by side.

You must determine the minimum value, maximum value, median, and quartiles in order to create a box-and-whisker plot of the provided data.

The base number is fifty.

The highest number is 66.

You must sort the data from smallest to largest in order to determine the median. The listed data are:

50, 51, 51, 52, 53, 53, 54, 55, 58, 58, 58, 60, 61, 62, 63, 65, 65, 66, 66

The middle value of the ordered data is the median. Finding the average of the two middle values is necessary since the data set (18 values) contains an even number of values:

(58 + 60) ÷ 2 = 59

Divide the ordered data into four equal sections before calculating the quartiles. The median of the lower half of the data set is the first quartile (Q1). The median of the data set's upper half represents the third quartile (Q3).

The data set's lower half consists of:

50, 51, 51, 52, 53, 53, 54, 55

The data set's upper half is as follows:

58, 58, 58, **60**, **61**, **62**, **63**, **65**, **65**, **66**, **66**

First quartile (Q1):

(53 + 54) ÷ 2 = **53.5**

Third quartile (Q3) comprises:

(65 + 65) ÷ 2 = **65**

With all of this knowledge at hand, you can now develop a box-and-whisker plan.

Given below:

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The area swept clean by the rear window wiper blade is approximately 91.37 square inches.

We'll calculate the area swept clean by the rear window wiper blade using the given information.
Convert the angle from degrees to radians:

115 degrees * (π radians / 180 degrees) = (23π/36) radians.
Find the length of the arc that the wiper blade traces out:

Arc length = (radius * angle) = (10 inches * (23π/36) radians) ≈ 20.08 inches.
Calculate the area of the sector formed by the arc and the pivot point:

Sector area = (1/2) * (radius² * angle) = (1/2) * (10 inches² * (23π/36) radians) ≈ 100.42 square inches.
Find the length of the arc that the mounting point of the blade traces out:

Arc length = (radius * angle) = (3 inches * (23π/36) radians) ≈ 6.02 inches.
Calculate the area of the sector formed by this arc and the pivot point:

Sector area = (1/2) * (radius² * angle) = (1/2) * (3 inches² * (23π/36) radians) ≈ 9.05 square inches.
Subtract the smaller sector area from the larger one to get the area swept clean by the wiper blade:

Area swept clean = 100.42 square inches - 9.05 square inches ≈ 91.37 square inches.

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The area swept clean by the rear window wiper blade is approximately 31.53 square inches.

To determine the area swept clean by the rear window wiper blade, we first need to find the length of the arc covered by the blade. We can use the formula:

arc length = radius * angle in radians

To convert the angle from degrees to radians, we multiply by[tex]\pi /180[/tex]:

115 degrees x [tex]\pi /180[/tex] = 2.007 radians

The radius is the length of the wiper arm, which is 13 inches minus the distance from the pivot point to the blade, which is 3 inches. Therefore, the radius is:

13 inches - 3 inches = 10 inches

Now we can calculate the arc length:

arc length = 10 inches x 2.007 radians = 20.07 inches

So the area swept clean by the wiper blade is approximately equal to the area of the sector formed by the arc and the two radii. The formula for the area of a sector is:

area = (angle in radians / [tex]2\pi[/tex]) x [tex]\pi r^2[/tex]

Plugging in values we have:

area = (2.007 / [tex]2\pi[/tex]) x [tex]\pi[/tex][tex](10 inches)^2[/tex] = 31.53 square inches

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Answer:

Population: 21 million; parameter: 57%; sample: 85,349; statistic: 72%.

Explanation:

The population is the entire group being studied, which in this case is all the residents of Florida, with a total population of 21 million.

The parameter is a numerical summary of the population, which in this case is the proportion of residents who visit a doctor annually and is stated as 57% in the problem.

The sample is a subset of the population that is selected for study, which in this case is the 85,349 adults surveyed by the surveyor.

The statistic is a numerical summary of the sample, which in this case is the proportion of adults in the sample who stated that they have visited a doctor within the past year and is stated as 72% in the problem.

Each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Let's consider the number of ways to seat n couples around a circular table without any restrictions first.

Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,

where we divide by 2n to account for rotations of the same seating arrangement.

Now, let's consider the restriction that no couple can sit together.

We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.

After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.

We can continue this process until all couples are seated.

Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:

[tex](2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)![/tex]

We multiply by[tex]2^{n-1}[/tex] to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Note that reflected seatings are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.

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The correct answer is (c) 1.9

To calculate the test statistic in this example, we can use the formula for a z-test for proportions:

[tex]z = (p - P) / \sqrt{[P(1-P) / n][/tex]

where:

p is the sample proportion of vegetarians (140/1000 = 0.14)

P is the hypothesized population proportion of vegetarians (0.12)

n is the sample size (1000)

Substituting these values into the formula, we get:

[tex]z = (0.14 - 0.12) / \sqrt{[0.12(1-0.12) / 1000][/tex]

z = 0.02 / 0.0110

z = 1.818 (rounded to three decimal places)

Therefore, the test statistic in this example will be approximately equal to 1.818. The answer closest to this value is (c) 1.9

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From the figures, AB is a tangent to the C because they make a right angles (90⁰)

Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.

We shall be determining the angle at C to see if it gives 90⁰

Using trigonometrical ratios of tangent

TanB = Opposite/Adjacent

Tan B. = 4.8/7.2

Tan B = 0.6667

B = Tan⁻¹0.6667

<B = 33.69⁰

Also in the same manner,

TanS = opp/Adj

Tan S = 7.2/4.8

Tan S = 1.5

S = Tan⁺¹1.5

< S = 56.31⁰

Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰

Therefore AB makes tangent at C

20.  

Tan C = Opp/Adj

Tan C = 15/11.2

Tan C = 1.3393

C = Tan⁺¹1.3393

< C = 53.25

Also, Tan B = 11.2/15

Tan B = 0.7467

B = 36.75

<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰

Therefore AB makes a tangent at C

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The standard deviation of a normal distribution group of answer choices is always 1.

In a normal distribution, the standard deviation is a measure of the spread or dispersion of the data. The standard deviation is defined as the square root of the variance, which is the average of the squared differences from the mean.

For a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the area under the curve between any two values represents the probability of getting a value between those two values. This property of the standard normal distribution is useful for calculating probabilities in statistics.

However, for a normal distribution that is not standard, the standard deviation can be any positive value. In this case, the mean and standard deviation defines the shape and location of the distribution. A larger standard deviation indicates that the data is more spread out, while a smaller standard deviation indicates that the data is more tightly clustered around the mean.

Therefore, the standard deviation of a normal distribution group of answer choices can be any positive value, but it is often standardized to 1 for ease of calculation and interpretation.

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The electrician's rate experienced a 25% increase compared to what he charged in the year 2018.

A percentage is a number or ratio expressed as a fraction of 100, used to indicate the portion of something in relation to its whole.

To find the percentage increase in the rate, we need to calculate the difference between the two rates and express it as a percentage of the original rate.

The difference between the two rates is

$12,500 - $10,000 = $2,500

To express this difference as a percentage of the original rate, we need to divide it by the original rate and then multiply by 100:

($2,500 / $10,000) x 100% = 25%

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1. Formula for the area of a sector of a circle, which is  A = (θ/360)π[tex]r^2[/tex] 2. The area of sector HIJ is 2.51 square units. 3. The measure of angle KLM is approximately 0.29 degrees

A circle is a geometric shape consisting of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center).

BLANK 1: To solve this problem, we can use the formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex], where θ is the central angle of the sector, r is the radius of the circle, and π is pi (approximately 3.14).

BLANK 2: To find the area of sector HIJ, we need to know the radius of circle I and the measure of angle HIJ. From the given information, we know that circle I has a radius of 8, and angle HIJ is 45 degrees. Therefore, the area of sector HIJ is:

A = (45/360) x 3.14 x [tex]8^2[/tex]

A = 3.14 x 8 x (45/360)

A = 3.14 x 8 x 0.125

A = 2.51 square units (rounded to two decimal places)

Therefore, the area of sector HIJ is 2.51 square units.

BLANK 3: We know that sector KLM has the same area as sector HIJ, and circle L has a radius of 10. Therefore, we can use the formula for the area of a sector of a circle again to find the measure of angle KLM. Let x be the measure of angle KLM in degrees. Then:

A = (x/360) x 3.14 x [tex]10^2[/tex] = 2.51

Simplifying this equation gives:

(x/360) = 2.51/(3.14 x [tex]10^2[/tex])

(x/360) = 0.0008

x = 360 x 0.0008

x = 0.288

Therefore, the measure of angle KLM is approximately 0.29 degrees (rounded to two decimal places).

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Mason's friends do not play video games are 4.

Mason asked some classmates whether they play video games.

The ratio of friends who play video games to everyone he asked is given as some fraction or decimal value.
Let's assume that the ratio is in the form of "x:y",

"x" represents the number of friends who play video games, and "y" represents the total number of friends that Mason asked.
To find out how many of his friends do not play video games,

To subtract the number of friends who play video games from the total number of friends that Mason asked.

This is because the remaining friends who were not counted in the "x" value of the ratio must be those who do not play video games.
So, the number of friends who do not play video games can be calculated as:
Total number of friends - Number of friends who play video games = y - x
The ratio of friends who play video games to everyone he asked is 3:7,

It means that out of 7 friends, 3 play video games, and 4 do not play video games.

The number of friends who do not play video games can be calculated as:
y - x = 7 - 3 = 4  

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Step-by-step explanation:

Given :

d = 3.6m

r = d/2

r = 3.6/2

r = 1.8 m

We know that,

C = 2πr

C = 2 * 22/7 * 1.8

C = 11.3 m

Now,

A = π r²

A = 22/7 × (1.8)²

A = 22/7 × 3.24

A = 10.1 m²

Answer:

The Radius is 1.8, The circumference is 11.3 ,The area is 10.2

Step-by-step explanation:

The radius of a circle from diameter: if you know the diameter d , the radius is r = d / 2 .

To calculate the circumference, you need the radius of the circle: Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation.That's it; you found the circumference of the circle.Or you can use the circle's diameter:Multiply the diameter by π, or 3.14.The result is the circle's circumference.


Diameter of circle= 3.6cm So, radius of circle=3.6/2Radius of circle = 1.8 Now ,Area of circle =πr². [r=radius] so 3.14 times 1.8 times 1.8 and you get 10.17 then round it to the nearest tenth and it is 10.2

39 degrees of freedom will be used to find the t-critical statistic value.

We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.

The degrees of freedom (df) for a t-distribution are calculated as given below:

df = n - 1

where n is the sample size of the problem.

In this case, the sample size is 40, so the degrees of freedom would be:

df = 40 - 1 = 39

Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.

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If M is the midpoint of the leg CG, then the

a) Area of ABD = 18.75 ft^2

b) Area of MOC = 15 ft^2

To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.

First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write

AB/CD = AD/CO

Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:

AB/CD = BC/CO

We also know that the area of AOD is 15 ft^2

Area of ABD/ Area of COD = AB/CD

We can substitute the ratio AB/CD from the similarity relation above to get

Area of ABD/ Area of COD = BC/CO

Since the bases of the trapezoids are parallel

Area of ABD/ Area of COD = BD/CO

Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write

Area of ABD/ Area of COD = 5/3

Area of ABD = 5/8 × Area of COD

We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore

Area of ABD = 5/8 × 30 = 18.75 ft^2

Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.

Let x be the length of OC, and let y be the length of OG. Then we have

Area of MOC/ Area of MOG = x/y

Also, since M is the midpoint of CG, we have

x = 2y

Substituting this into the first equation, we get

Area of MOC/ Area of MOG = 2

We know that the area of MOG is half the area of AOD, so

Area of MOG = 15/2 ft^2

Therefore, we have

Area of MOC = 2 × Area of MOG = 15 ft^2

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a) x= 20, y=20√3 b) x=2, y=2/√3 c) x=9, y=√162 is the correct answer.

Right triangle is that triangle in which one angle has to be 90 degree.The side opposite the right angle is called the hypotenuse, while the other two sides are called legs. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

a)sinα= perpendicular/hypotenuse

sin30°=x/40

1/2=x/40

2x=40

x=20

tanα= perpendicular/base

tan30°=x/y=20/y

1/√3=20/y

y=20√3

b) tanβ=⊥/base

tan60°=2√3/x

x√3=2√3

x=2

tanγ=⊥/base

tan30°=y/x=y/2

1/√3=y/2

y=2/√3

c) tanω=⊥/base

tan45°=9/x

1=9/x

x=9

y²=9²+x²

y²=81+81

y=√162

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The value of function k(f(x)) is 12x³ + 32x - 8.

Function composition is a way to combine two or more functions to form a new function. In this case, we are given two functions f(x) and k(x), and we need to find the value of k(f(x)), which means we need to apply the function k(x) to the output of the function f(x).

Here we have

Functions f(x)= 3x³ +8x -2 and k(x) = 4x

To find k(f(x)), we need to substitute the expression for f(x) into k(x) wherever we see x. So, we have:

k(f(x)) = 4(f(x)) = 4(3x³ + 8x - 2)

We can simplify this expression by distributing the 4:

k(f(x)) = 12x³ + 32x - 8

Therefore,

The value of function k(f(x)) is 12x³ + 32x - 8.

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Answer:

-6/7

Step-by-step explanation:

Answer:

4x - y = 2,

Step-by-step explanation:

The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, we are given that the line passes through the points (4, -3) and (12, 1). The slope of the line is then m = (1 - (-3)) / (12 - 4) = 1/4.

Substituting the slope and the point (4, -3) into the point-slope form of the equation, we get y - (-3) = 1/4(x - 4). Simplifying, we get y + 3 = 1/4x - 1.

To convert the equation to standard form, we multiply both sides of the equation by 4. This gives 4y + 12 = x - 4. Simplifying, we get 4x - y = 8.

Therefore, the standard form of the equation of the line is 4x - y = 8.

Answer:

[tex]2((1 \frac{1}{3} )(1 \frac{1}{2} ) + (1 \frac{1}{2} )(5) + (1 \frac{1}{3}) (5))[/tex]

[tex]2(( \frac{4}{3} )( \frac{3}{2} ) + ( \frac{3}{2} )(5) + ( \frac{4}{3} )(5))[/tex]

[tex]2(2 + \frac{15}{2} + \frac{20}{3} )[/tex]

[tex]2( \frac{12 + 45 + 40}{6} )[/tex]

[tex] \frac{97}{3} = 32 \frac{1}{3} [/tex]

The surface area of this rectangular prism is 32 1/3 square feet.

Step-by-step explanation:

For right triangles     tan B = opposite leg / adjacent leg

tan B = 3/4  

arctan (3/4) = B = 36.87 degrees

75% of the data lies below 81.5.

In a box plot, the box represents the middle 50% of the data, with the lower edge of the box (the "whisker") representing the 25th percentile and the upper edge of the box (the other "whisker") representing the 75th percentile.

Since the lower edge of the box is at 75, we know that at least 25% of the data lies below 75. Similarly, since the upper edge of the box is at 82, we know that at least 25% of the data lies above 82. Therefore, the middle 50% of the data lies between 75 and 82.

To find the value that 75% of the data lies below, we need to find the 75th percentile. Since the line in the box is at 79, we know that 50% of the data lies below 79. Therefore, we need to find the value that is greater than 79 and such that 75% of the data lies below it.

We can use the length of the box (82 - 75 = 7) to find the size of each quartile. Since the middle 50% of the data lies in the box, each quartile contains 25/2 = 12.5% of the data.

To find the value that 75% of the data lies below, we need to add 12.5% to 50% (which is the location of the line in the box). Therefore, we need to find the value that is greater than 79 and such that 62.5% of the data lies below it.

Since the length of the number line is 87 - 69 = 18, each tick mark represents 0.5 units. Therefore, to find the tick mark that corresponds to the 62.5th percentile, we can add 0.5 units for every 12.5% increase. Starting from 79, we need to add 0.5 x 5 = 2.5 units to reach the tick mark that corresponds to the 62.5th percentile. Therefore, the value that 75% of the data lies below is:

79 + 2.5 = 81.5

So, 75% of the data lies below 81.5.

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Answer:

The lower quatile (Q1), and it is 79

Step-by-step explanation:

If you were to pick 84 that would be 100%

Value of the z-test statistic is 1.20.

To find the value of the z-test statistic, we need to calculate the sample proportion and the standard error of the proportion.

The sample proportion is:

p⁻ = 92/400 = 0.23

The standard error of the proportion is:

SE = √[(pq)/n] = √[(0.20.8)/400] = 0.025

where p = 0.2 and q = 0.8.

Now we can calculate the z-test statistic:

z = (p⁻ - p)/SE = (0.23 - 0.2)/0.025 = 1.2

Therefore, the value of the z-test statistic is 1.20.

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If a hypothesis test is performed that fails to reject the null hypothesis, it means that the evidence provided by the sample data is not strong enough to support the alternative hypothesis.

In the case of the landscaping company, it would mean that there is not enough evidence to support the claim that at least 90% of workers arrive on time.

Therefore, the null hypothesis that the proportion of workers arriving on time is less than 90% cannot be rejected at the chosen significance level.

However, it is important to note that failing to reject the null hypothesis does not necessarily mean that the null hypothesis is true, but rather that there is not enough evidence to support the alternative hypothesis.

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The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

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Step-by-step explanation:

18-2x<3(2x-1)-3

21-2x<6x-3

24<8x

3<x

Interval notation

(3, ∞)

For all given Quadrilaterals none has enough information provided in the problem to definitively say - if they are a parallelogram.Hence, option E is correct for all.

If a quadrilateral is a parallelogram, it satisfies the following properties:

It is important to note that in order to definitively conclude that a quadrilateral is a parallelogram, all four properties must be satisfied. If only one or some of the properties are met, it does not necessarily guarantee that the quadrilateral is a parallelogram.

Figure 1-: Adjacent angles are 105 and 75 degrees, which satify the condition of opposite angles being equal but except this no other information is provided, Hence, we don't have enough information to say figure 1 is a parallelogram.

Figure 2-: Diagonals bisect each other and make angle 65 degree with each other. Given that Diagonal 1 bisects Diagonal 2 and the opposite sides of the quadrilateral are equal, by using SAS criterion, the congruency of triangles formed by the diagonals can be derived to say that the opposite angles of the quadrilateral are also equal . However, we still need more information about parallelism of sides to definitively say given quadrilateral is a parallelogram.

Figure 3-: One pair of opposite side is equal in length ,while other pair of line is parallel to each other.This information is insufficient to determine if given quadrilateral is a parallelogram.

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The height of the pyramid whose volume is already given would be = 1,440,000 ft

To calculate the height of the pyramid, the formula of the Volume of the pyramid should be used.

Volume = 1/3lwh

where l = base length = 8h-30 ft= 3.75 ft

w = base width= 8h+20 ft = -2.5 ft

h = h ft

The volume of the pyramid = 4,500,000 cubic feet

4,500,000 = 1/3 × (3.75)(-2.5)h

Make h the subject of formula;

h = 4500000×3/3.75×(-2.5)

h = 13500000/9.375

h = 1,440,000 ft.

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Answer:

see what you got to do is you have to find n