There were approximately 3.1 × 10⁸ people in the United States of America in 2010. The average person drank 3.3 × 10³ ounces of soda. Approximately how many total ounces of soda were drank in the USA in 2010?

The standard deviation of the Age variable is 8.2195 years. 95% of the data observations fall between 18.8 and 31.1.

1) The standard deviation of the Age variable is 8.2195 years.

2) Between 18.8 and 31.1.

1) To calculate the standard deviation of the Age variable, first calculate the mean of the variable. To do this, add up all of the values and divide by the total number of observations (in this case, 12). The mean is then 24.75. To calculate the standard deviation, subtract the mean from each observation, square the result, and sum the squared differences. Divide the sum by 11 (the total number of observations minus 1), then take the square root of the result. The standard deviation of the Age variable is 8.2195 years.

2) To find the values between which 95% of the data observations fall, calculate the standard deviation multiplied by 1.96. This will give the range for the 95% of the data observations. To find the lower value, subtract the standard deviation multiplied by 1.96 from the mean. For the upper value, add the standard deviation multiplied by 1.96 to the mean. In this case, the lower value is 18.8 and the upper value is 31.1.

The standard deviation of the Age variable is 8.2195 years. 95% of the data observations fall between 18.8 and 31.1.

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The Ordinary integral of the Line integral [tex]\int _c {(y-z)} \, ds[/tex] where C is the helix ⟨7cos t, 7sin t, t⟩ is [tex]\int\limits^0 _{-2\pi} \sqrt{50}{(7sin\ t -t)} \, dt[/tex] and its value in the range -2π ≤ t ≤ 0 is 10√2 π²

We have x = 7cos t, y = sin t and z = t.

We also need ds =[tex]\sqrt{(\frac{dx}{dt})^{2} +(\frac{dy}{dt})^{2} +(\frac{dy}{dt})^{2} }dt[/tex]

     ds  = [tex]\sqrt{(-7sin\ t)^{2} +(7cost\ t)^{2} +(1)^{2} }dt[/tex]

           = [tex]\sqrt{49sin^{2}t +49cos^{2}t+1 }dt[/tex]

           = [tex]\sqrt{49(sin^{2}t +cos^{2}t)+1 }dt[/tex]

     ds  = [tex]\sqrt{50}dt[/tex]

Now,  [tex]\int _c {(y-z)} \, ds[/tex] =  [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]

Evaluating the integral [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]

[tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]   =  [tex]\sqrt{50}\ {[-7cos\ t -\frac{t^{2} }{2} ]}\limits^0 _{-2\pi}[/tex]

                                     =  [tex]\sqrt{50}\ {[-7+7+2\pi ^{2}]}[/tex]

                                     =  [tex]10\sqrt{2}\pi ^{2}}[/tex]

The question is incomplete, the complete question is

" Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.[tex]\int _c {(y-z)} \, ds[/tex] ; C is the helix ⟨7cos t, 7sin t, t⟩, for -2π ≤ t ≤ 0 "

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The credit term 3/15, n/45 states that the buyer will receive a 3% discount if the payment is made within 15 days. Otherwise, full payment is expected within 45 days from the invoice date.

This term can be expressed as a formula and calculation as follows:

Discount = 3% of Invoice Total

Payment due within 15 days = Invoice Total - Discount

Payment due within 45 days = Invoice Total

For example, if the invoice total is $500, then the buyer will receive a 3% discount (Discount = 3% x $500 = $15) if the payment is made within 15 days. The payment due within 15 days is then equal to the invoice total minus the discount ($500 -$15 = $485). On the other hand, if the payment is not made within 15 days, the buyer is expected to pay the full invoice total within 45 days ($500).

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The function's domain and range are [tex]$x \leq-2, f(x) \leq-8$[/tex]. a part of the job

[tex]$f(x)=-\frac{8}{6}(x+2)^2-8$[/tex] .

Domain of [tex]$-\frac{5}{6}(x+2)^2-8:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Range of [tex]$-\frac{5}{6}(x+2)^2-8:\left[\begin{array}{cl}\text { Solution: } & f(x) \leq-8 \\ \text { Interval Notation: } & (-\infty,-8]\end{array}\right]$[/tex]

Axis points of interception [tex]\frac{-5}{6}(x+2)^2-8: \quad[/tex] Y Intercepts: [tex]$\left(0,-\frac{34}{3}\right)$[/tex]

Vertex of [tex]$-\frac{5}{6}(x+2)^2-8:$[/tex] Maximum (-2,-8)

A graph's inflection point is a location where the second derivative changes sign and is equal to 0 or undefined.

If [tex]$f^{\prime \prime}(x) > 0$[/tex] after which f(x) concave upward.

If [tex]$f^{\prime \prime}(x) < 0$[/tex] after which f(x) concave downward.

[tex]$f^{\prime \prime}(x)=-\frac{5}{3}$[/tex]

Therefore the correct answer is Domain [tex]$x \leq-2$[/tex] ,range  [tex]f(x) \leq-8$[/tex] .

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The expression in terms of xx that represents the total amount that Elizabeth paid is - xx + 0.07xx + 0.2(xx + 0.07xx) = 1.47xx

This question uses the concepts of percentages and algebraic expressions.

The expression that is used to calculate the total amount that Elizabeth paid is an example of an algebraic expression.

It uses the percentage tax rate of 7% and the percentage tip rate of 20%, which are both represented by decimal numbers.

Step 1: Calculate the tax by multiplying the subtotal (xx) by the tax rate (0.07): 0.07xx

Step 2: Calculate the tip by multiplying the subtotal (xx) plus the tax (0.07xx) by the tip rate (0.2): 0.2(xx + 0.07xx)

Step 3: Calculate the total by adding the subtotal (xx), the tax (0.07xx), and the tip (0.2(xx + 0.07xx)): xx + 0.07xx + 0.2(xx + 0.07xx)

Step 4: Simplify the expression to 1.47xx.

xx + 0.07xx + 0.2(xx + 0.07xx) = 1.47xx

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Answer:

$427

Step-by-step explanation:

Sam expects to make $7 for every $100 he invests, which is a 7% return. To determine how much he expects to make on an investment of $6100, we can use the following formula:

investment amount * (return rate / 100) = expected return

$6100 * (7 / 100) = $427

So Sam expects to make $427 on an investment of $6100 if he makes $7 for every $100 he invests.

Answer:

$427

Step-by-step explanation:

$6100/$100=61

61 ×7=427

Arrays are a fundamental data structure, and an important part of most programming languages.

Method :

Employ two loops. Pick elements one at a time in the outer loop, and then in the inner loop, compare each element's difference to every other element in the array and the largest difference ever calculated. The application of the aforementioned strategy is seen below:

Here i attached the programs

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The area of the octagon is 40 + 40√(2) in simplest radical form.

What is the area of the octagon?

The area of a regular octagon can be calculated using the formula:

Area = (2 + 4 * √2) * s^2

where s is the length of one of the sides.

An equiangular octagon is an octagon in which all of the angles are congruent. In addition, all the side lengths are also congruent. However, in the case of the side lengths of the octagon are given as 1, 2, 3, 4, 1, 2, 3, and 4 in clockwise order.

To find the area of the octagon, we can use the following formula:

Area = 2(1 + 2 + 3 + 4)(4) * (1 + √(2))/4

Area = 2(10)(4) * (1 + √(2))/4

Area = 80 * (1 + √(2))/2

Area = 40 + 40*√(2)

Hence, the area of the octagon is 40 + 40√(2) in simplest radical form.

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Let's see how the while loop functions for n = 2345. Inside the loop, the reversed number is calculated using the formula reverse = reverse * 10 + remainder. n. n != 0.

Given,

arr: [7, 234, 58100]

Expected Output:

7 + 432+ 18500 = 18939

Input:

arr: [0, 100, 220]

Expected Output:

0 + 100 + 220 = 320

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The correct option is (c) a Mean of 5 inches with a standard deviation of 5 inches for the question

Given,

         The average height of policemen, μ[tex]_{x}[/tex] = 71 inches

          The standard deviation for policemen, SD[tex]_{x}[/tex] = 4 inches

          The average height of a policewoman, μ[tex]_{y}[/tex] = 66 inches

          The standard deviation for policewomen, SD[tex]_{x}[/tex] = 3 inches

We know that,

When policemen and policewomen have paired, the mean for the difference in height can be given by:

                              μ = μ[tex]_{x}[/tex] - μ[tex]_{y}[/tex]

On substituting the value in the above equation, we get:

                              μ = 71 - 66

                              μ = 5 inches

When policemen and policewomen have paired, the standard deviation for the difference in height can be given by:

                              [tex]SD = \sqrt{SD_{x}^{2} + SD_{y}^{2} } \\\\SD = \sqrt{4^{2} + 3^{2} }\\\\SD = \sqrt{ 16 + 9 }\\\\SD = \sqrt{25}\\\\SD = 5[/tex]

Thus, the required mean is 5 inches and the standard deviation is 5 inches.

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Answer: 26

Step-by-step explanation:

Since we are given the value of y, all we need to do is plug it into the equation and solve it. Make sure if you plug this into a calculator that you put the substituted number in parenthesis that way it squares the number correctly without a negative sign.

(-3)²-5(-3)+2

9 - 5(-3) +2

9 - -15 + 2

9 + 15 + 2

24 + 2

26

Hope this helps!

The area of ∆PQR is 42 [tex]cm^{2}[/tex]

We can use Heron's Formula to find the area of a triangle when we have the length of its three sides. Heron's Formula states that the area of a triangle with sides p, q, and r is:

Heron's Formula :

Area =[tex]\sqrt(s(s-p)(s-q)(s-r))[/tex]

where s is the semi-perimeter of the triangle (half of the perimeter).

In this case, we know that the perimeter of the triangle is 24 cm and p+q = 18 cm, and q+r = 14 cm. We can use these equations to find the length of the third side, r.

p+q+r = 24 cm

r = 24 - (p+q) = 24 - 18 = 6 cm

Now we can use this information to find the semi-perimeter of the triangle:

s = (24 cm) / 2 = 12 cm

Now we can substitute the values of p, q, r, and s into Heron's formula to find the area of the triangle:

Area = √(12 x (12-18) x (12-14) x (12-6))

Area = √(12 x (-6) x (-2) x 6)

Area = √(12 x (-12) x (-12))

Area = √(12 x 144)

Area = √(1728) = 42 [tex]cm^{2}[/tex]

Therefore, the area of ∆PQR is  42[tex]cm^{2}[/tex]

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The cosecant of angle U is csc(U) = 1 / sin(U) = √55 / 4

To find the cosecant of angle U in triangle UTV, we need to find the sine of angle U. To do this, we can use the sides of the triangle that are opposite and adjacent to angle U. In a right triangle, the sine of an angle is equal to the opposite side divided by the hypotenuse.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

[tex]VT^2 + UT^2 = UV^2[/tex]

4^2 + (√39)^2 = UV^2

16 + 39 = UV^2

55 = UV^2

UV = √55

So, the length of the hypotenuse is √55. To find the sine of angle U, we can use the ratio of the opposite side (UT) to the hypotenuse:

sin(U) = UT / UV = 4 / √55

The cosecant of angle U is then:

csc(U) = 1 / sin(U) = √55 / 4.

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The equation as a single logarithm is log(4x)^3)/(4y)^2

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Some properties of logarithm are:

[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]

Log with base e = 2.71828... is written as

[tex]\ln(x)[/tex]

Log with base 10 is written as

[tex]\log(x)[/tex]

Given;

Equation=3log4x-2log4y

=log(4x)^3-log(4y)^2

=log(4x)^3)/(4y)^2

Therefore, the answer of logarithm will be log(4x)^3)/(4y)^2

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Therefore ,as a result, the total surface area is 64 + 16 = 80 square units.

The amount of space it occupies on the surface is a decent indication of its overall size. The complete surroundings is taken into account when calculating the area of a tri shape. Something's total size is determined by its surface area. The volume of water inside a cuboid is equal to the total of the volumes on each and every six of its rectangular sides. To calculate the box's measurements, use the formula below: In 2lh, 2lw, and 2hw, the region is identical (SA). The surface area of the multipurpose shape represents the region.

Here,

Imagine a line running from 8m to 4m at the intersection. As a result, a rectangle and a triangle are formed.

Simple

=> is the square's area

=> 8 *8  = 64 square units.

Use the formula

=> (1/2)b*h to determine the triangle's area 

We need to enter the hieght, which is already known to be 4, and the base, which is already known to be 8, into the equation.

=> Triangle area unit = 1/2 * 8 * 4

Therefore ,as a result, the total area is 64 + 16 = 80 square units.

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[tex](3x+2)(3x^{2} +4)[/tex]

This equation can be solved using the distributive is by multiplying each term by the other term.

First, multiply [tex]3x[/tex] by [tex]3x^{2} +4[/tex]

[tex]3x(3x^{2} +4)=(3x*3x^{2} )+(3x*4)[/tex]

Then, multiply [tex]2[/tex] by [tex]3x^{2} +4[/tex]

[tex]2(3x^{2} +4)=(2*3x^{2} )+(2*4)[/tex]

Summary the two equations

[tex](3x*3x^{2} )+(3x*4)+(2*3x^{2} )+(2*4)[/tex]

The correct expansion of [tex](3x+2)(3x^{2} +4)=(3x*3x^{2} )+(3x*4)+(2*3x^{2} )+(2*4)[/tex] (C)

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Answer:

y = 48

Step-by-step explanation:

14 x 2 = 28

28 + 20 = 48 = y

16 x 2 = 32

80 - 32 = 48 = y

The angles for the triangle are 42°, 68° and 70° and x=21.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As sum of all angles of a triangle is 180°

2x+3x+5+4x-14=180

x=21

hence,

         The angles for the triangle are 42°, 68° and 70° and x=21.

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Right question:-

Angles in the question are 2x°,(3x+5)° and (4x-14)° of a triangle.

B) In a right triangle where a=1 and b=1, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 1^2 + 1^2 = 1+1 =2, so c = √2

C) In a right triangle where a=5 and b=6, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 5^2 + 6^2 = 25+36 =61, so c = √61

If C(x) = 0.001x² + 1000 dollars is the cumulative cost of running the Acme factory, we can find the cumulative profit of the Acme factory by subtracting the cumulative cost from the total revenue. Let's assume that the total revenue is a constant value of R dollars.

Therefore, the cumulative profit function P(x) can be written as:

P(x) = R - C(x)

Where R is the total revenue and x is the number of days since the start of 2018. The unit of the function's output will be dollars, since both the total revenue and the cumulative cost are measured in dollars.

Therefore, P(x) = R - (0.001x² + 1000) dollars

It is important to note that the value of R is not given in the problem statement and it is unknown, thus the function P(x) is not complete without the value of R. In addition, a proper function would have the start date of the factory and the end date, but it's mentioned to be since the start of 2018.

The base of Octagon Towers has 135-degree inside angles on each side.

The formula: can be used to determine the size of each inner angle of a regular octagon.

(n-2) x 180 / n

where n is the polygon's number of sides.

n=8 for Octagon.

As a result, we can change n in the formula to 8:

(8-2) x 180 / 8 = 6 x 180 / 8

The base of the Octagon Towers is a regular octagon, the measure of each interior angle of the base of the Octagon Towers will be

135-degree

The base of Octagon Towers has 135-degree inside angles on each side.

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Full question

Octagon Towers is an octagon-shaped condominium building in Miami, Florida. Assuming the base of the Octagon Towers is a regular octagon, find the measure of each interior angle of the base of the Octagon Towers.

Each interior angle measures?

The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14)  of the graph x is 9/2.

The turning point's x-coordinate will be "9/2."

The answer to the query is

y = [tex]x^{2}[/tex] + bx + c

curving goes by.

(2 , 0)

and,

(0 , 14)

Putting (0, 14) results in

→ 14 = 0 +  0 + c

c = 14

then,

→ y = [tex]x^{2}[/tex] + bx + 14.

Putting in (2, 0) gives us

→0 = 4 + 2b + 14

-2b = 18

b =  - 18 /2

= -9

then,

→ y = [tex]x^{2}[/tex] - 9x + 14.

the discovery of

→ dy / dx = 0

dy/dx = 2x - 9

turning point

→ dy / dx = 0

2x - 9 = 0

x = 9/2.

The curve intersects

The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14)  of the graph x is 9/2.

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Answer:

-1/2

Step-by-step explanation:

first u would label ur x and ys 2,6 would be x1, y1 then u would put 8,4 would be x2 and y2 . You would put 4-6 as y2 - y1  and 8-2 as x2 - x1 to get -2 divided by 4 to get your -1/2

Students that ran faster than Amy are Chris and Ethan.

Speed is the ratio between distance and time. The formula for speed

v = d ÷ t

Amy's speed

Brian's speed

Chris's speed

Ethan's speed

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P (W or Z) if W and Z are independent, would be 0.673.

Independent events are the events that the outcome of one event does not affect the outcome of the other event, so the probability of one event happening doesn't change the probability of the other event happening.

If W and Z are independent, it means that the probability of W occurring has no effect on the probability of Z occurring, and vice versa.

In this case P(W or Z) can be calculated using the formula for the probability of the union of two independent events:

P(W or Z) = P(W) + P(Z) - P(W and Z)

P(W and Z) = P(W) x P(Z)

= 0.42 x 0.35

= 0.147

Therefore:

P(W or Z) = P(W) + P(Z) - P(W and Z)

= 0.42 + 0.35 - 0.147

= 0.673

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The original dimension of the metal is width = 21 and length = 41 before cutting off the squares.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

Let us suppose the width of the rectangular metal = w.

Then the length of the rectangular metal is = 20 + w

Given that squares of 4in are cut from the four corners, then the new width and length will be:

width = w - 8

length = 20 + w - 8

The height of the rectangular metal when the flaps are folded are 4 in.

The volume of the rectangular prism is:

V = (l)(w)(h)

Substituting the value of V = 1716, width = w - 8, length = 20 + w - 8, and h = 4 we have:

1716 = (w - 8)(20 + w - 8)(4)

1716 = 80w + 4w^2 - 32w - 640 - 32w + 256

1716 = 4w^2 + 16 w - 384

4w^2 + 16w -384 - 1716 = 0

4w^2 + 16w - 2100 = 0

w^2 + 4w - 525 = 0

w^2 + 25w - 21w - 525 = 0

w(w + 25) - 21 (w + 25) = 0

(w - 21) (w + 25) = 0

w = 21

w = -25

The dimensions of the box cannot be negative hence, the width is 21.

length = 20 + 21

length = 41

The original dimensions of the metal is width = 21 and length = 41 before cutting off the squares.

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The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.

Given data :

calculate a 95% two-sided confidence interval on the mean for women and men separately :

A) The confidence interval for women: [1711.70] <u< [1894.10]

Women = [tex]\frac{1674+ 1622 + 1637 + 1838 + 1964 + 1836 + 1728 +1913 + 1885 + 1932}{10}[/tex] = 1802.9

B) B) The confidence interval for men: [2096.50] <u< [2513.80]  

Men =   [tex]\frac{1852 + 2403 + 2383 + 2336 + 2597 + 2581 + 2169 + 2120}{8}[/tex] =  2305.125

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The slope of the graph changes from -3 to 3 and the y-intercept changes from -2 to -4.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The given equations are f(x)= -3x-2 to f(x)=3x-4.

The slope of the equation changes from -3 to 3 which is shown in the graph similarly the y-intercept of the graph changes from -2 to -4.

The graph of the two lines f(x)= -3x-2 and f(x)=3x-4 is attached with the answer below.

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The required correct way of division has been shown, as per the long division.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
The questions seem to be incomplete, so we assume the number 729 that Allie divides it by the number 9.
According to the question,
Long division,

9 ] 729  [8 1
   - 72
---------------
       0 9
        - 9
---------------
          0

Thus, the required correct way of division has been shown, as per the long division.

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