Find the slope of the line graphed below.

Answer:

[tex]9\frac{1}{2} cm^2[/tex]

Step-by-step explanation:

The area of the shaded region = area of triangle - area of the rectangle

Base, b of the triangle = 3 + 4 = 7 cm

Ar of triangle = base*height/2

= 7*5/2

= 35/2

[tex]=17\frac{1}{2} cm^2[/tex]

ar of rectangle = length *breadth

= 4*2

= 8 cm²

The area of the shaded region = area of triangle - area of the rectangle

[tex]=17\frac{1}{2} - 8\\\\=9\frac{1}{2} cm^2[/tex]

Answer:

16.5 cm²

Step-by-step explanation:

The shaded area is the area of the triangle minus the area of the rectangle.

A = bh/2 - LW

For the triangle,

b = 3 cm + 4 cm = 7 cm

h = 2 cm + 5 cm = 7 cm

For the rectangle,

L = 4 cm

W = 2 cm

A = bh/2 - LW

A = (7 cm)(7 cm)/2 - (4 cm)(2 cm)

A = 24.5 cm² - 8 cm²

A = 16.5 cm²

A ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

The steps for constructing a copy of an angle:

Step 1: Draw the angle.

Step 2: Place the center of the protractor on the vertex of the angle.

Step 3: Line up the baseline of the protractor with one of the angle's rays.

Step 4: Read the degree measure where the other ray crosses the protractor.

Step 5: Draw a ray from the vertex of the angle to the right.

Step 6: Use a ruler to mark the same distance on the ray that was just drawn.

Step 7: Draw a ray from the vertex through the point just marked on the ray.

This is the copy of the angle's second ray.

Step 8: Use a compass to draw an arc centered at the vertex of the original angle that passes through one of the angle's rays.

Step 9: Without adjusting the compass, draw another arc that intersects the previous arc at a point.

Step 10: Draw a ray from the vertex through the point where the two arcs intersect.

This is the copy of the original angle.

Using a compass, draw an arc centered on the vertex of the original angle passing through one of the angle rays. Place the tip of the

compass on the vertex of the original angle and draw an arc that intersects one of the angle rays.

Draws another arc that intersects the previous arc at a point without adjusting the compass.

Draw a second arc that intersects the first arc at another point, keeping the compass latitude.

Using a ruler or ruler, draw a ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

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Mercury will travel approximately 10800 miles in 6 minutes.

To convert the speed of Mercury from miles per second to miles per minute, we need to multiply the given speed by the number of seconds in a minute, which is 60.

Speed of Mercury in miles per minute = 30 miles/second [tex]\times[/tex] 60 seconds/minute = 1800 miles/minute

Therefore, Mercury travels at a speed of 1800 miles per minute.

To calculate the distance Mercury will travel in 6 minutes at this speed, we can multiply the speed by the time.

Distance traveled by Mercury in 6 minutes = Speed [tex]\times[/tex] Time = 1800 miles/minute [tex]\times[/tex] 6 minutes = 10800 miles

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Answer:

Triangle????????????????? ¿

The year when the population becomes zero is 2020.2

We know that the population decreases at a constant rate, so it is modeled by a line:

y = ax + b

Where a is the slope and b is the y-intercept.

Here we have two points (2010, 5100) and (2012, 4100)

The slope is the quotient between the differences of the y-values and the x-values, then:

a = (4100 - 5100)/(2012 - 2010) = -1000/2 = -500

We can write.

y = -500*x + b

We know that when x = 2010, y = 5100, replacing that we get:

5100 = -500*2010 + b

b = 5100 + 500*2010 = 1,010,100

Then:

y = -500*x + 1,010,100

And it is zero when:

0  = -500*x + 1,010,100

x = 1,010,100/500

x = 2020.2.

That is the year when the pópulation becomes zero.

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The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.

To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.

Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.

Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.

Experimental probability of heads: 160/300 = 0.5333

Experimental probability of tails: 140/300 = 0.4667

Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.

In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.

To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.

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The question probable may be:

Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.

Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

Answer:

6

Step-by-step explanation:

Jabez is correct without calculating the product of 54 x 0.06 correctly because his estimation aligns with the mathematical principle that multiplying a number by a decimal less than 1 will result in a smaller product.

To determine who is correct without calculating the product of 54 x 0.06, we can use estimation.
Jabez estimated that the answer will be less than 54 but greater than 5.4. Let's analyze his estimation. When multiplying a number by a decimal less than 1, the product will always be smaller than the original number. In this case, 54 is the original number. Since 0.06 is less than 1, the product of 54 x 0.06 will definitely be smaller than 54.
On the other hand, Christina thinks the answer will be less than 5.4. Let's analyze her estimation. The original number, 54, is already greater than 5.4. When multiplying it by a decimal less than 1, the product will be even smaller. Therefore, Jabez's estimation is incorrect.
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Answer:

325 Adult tickets were sold.

Step-by-step explanation:

Let's assume the number of adult tickets sold is "x."

According to the given information, the number of student tickets sold is 53 more than the number of adult tickets. Therefore, the number of student tickets sold would be "x + 53."

The total number of tickets sold is the sum of adult tickets and student tickets, which is 703.

So, we can set up the equation:

x + (x + 53) = 703

Simplifying the equation:

2x + 53 = 703

Subtracting 53 from both sides:

2x = 650

Dividing both sides by 2:

x = 325

Therefore, 325 adult tickets were sold for the school play.

Answer:

325 adult tickets were sold

Step-by-step explanation:

First equation:

Thus, the first equation in our system is given by:

A + S = 703

Second equation:

Since there 53 more student tickets sold than adult tickets, the second equation in our system is given by:

S = A + 53  

Method to solve:  Substitution:

Substituting S = A + 53 for S in A + S = 703:

A + A + 53 = 703

(2A + 53 = 703) - 53

(2A = 650) / 2

A = 325

Thus, 325 adult tickets were sold.

Optional Step:  Check the validity of the answer:

Plugging in 325 for A in S = A + 53:

S = 325 + 53

S = 378

Thus, 378 student tickets were told.

Therefore, we've correctly determine the number of adult tickets sold.

The Math Club raised $400.

To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.

Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.

According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.

To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:

Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%

Now we can set up a proportion to determine the amount raised by the Math Club:

(x / $2000) = 20% / 100%

Cross-multiplying:

x = ($2000 * 20%) / 100%

Simplifying:

x = $400

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The expression that What formula(s) below represents the frequency of

that E are Option A, C and E.

A stored expression that can be invoked from other expressions is known as an expression rule. You can use rule inputs in your expression rules to allow you to dynamically alter the data your expression returns.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is called an expression or a mathematical expression.

From the option A, we have [tex]440. 2^{\frac{7}{12} } \\\\[/tex]

Then  this can be written as ; [tex]440 ^{\sqrt[12]{2} }[/tex]

which can be written as [tex]440 .10597^7}[/tex]

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a. The exact volume is V = π(9.5 ft)²(50 ft) = 225π ft³.

b. Rounding the answer to the nearest hundredth, the approximate volume of the silo is 706.50 ft³.

(a) The exact volume of the silo can be found using the formula for the volume of a cylinder, which is V = πr²h,

where r is the radius and h is the height.

Since the diameter is given, we can divide it by 2 to find the radius.

The radius of the silo is 19 ft / 2 = 9.5 ft.

The height of the silo is 50 ft.

Using these values, the exact volume of the silo is:

V = π(9.5 ft)²(50 ft) = 225π ft³.

The approximate volume can be found using the ALEKS calculator, which is not available in this text-based interface.

However, you can use the exact volume calculated above to manually approximate the volume to the nearest hundredth by evaluating the expression using the value of π as approximately 3.14 or 22/7.

(b) Approximate volume using the ALEKS calculator: [Please use an online calculator or a scientific calculator to approximate the value to the nearest hundredth].

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The area of the figure WXYZ which can be calculated as the sum of the area of the composite triangles ΔXYZ and ΔXWZ is 12 square units

Composite figures are figures comprising of two or more regular figures.

The slope of the side WZ = 2/5

The slope of YZ = -2/1 = -2

The slope of WZ is not the negative inverse of the slope of YZ, therefore, the figure WZ is not perpendicular to YZ and the figure is not a rectangle.

Considering the two triangles formed by the diagonal XZ, we get;

The figure XYZW is a quadrilateral, which is a composite figure comprising of two triangles, triangle ΔXYZ and ΔXWZ

Area of triangle ΔXYZ = (1/2) × 6 × 2 = 6 square units

Area of triangle ΔXWZ = (1/2) × 6 × 2 = 6 square units

The area of the figure = Area of triangle ΔXYZ + Area of triangle ΔXWZ

Area of triangle ΔXYZ + Area of triangle ΔXWZ = 6 + 6 = 12 square units

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The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = 3.

Hence the side lengths on the dilated image will be three times the side lengths on the original image.

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The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction [tex]\times[/tex] Total time per revolution = (1.0918 / (2π)) [tex]\times[/tex] 2 minutes

Calculating this expression will give us the answer in minutes.

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The approximate mean of the number of cars sold by the salesman in the past 10 weeks is 4.1.

To find the approximate mean, first, we add all the numbers in the data set, and then we divide that sum by the total number of values in the data set.

The formula for finding the approximate mean is as follows: Approximate mean = sum of the values in the data set / total number of values in the data set.

The following data set is given: Number of cars sold by a salesman in the past 10 weeks: 3, 5, 2, 4, 7, 5, 6, 3, 2, 4.

To find the approximate mean, we first need to add all the values: 3 + 5 + 2 + 4 + 7 + 5 + 6 + 3 + 2 + 4 = 41 The sum of all the values is 41.

Next, we need to divide this sum by the total number of values in the data set. In this case, the total number of values is 10. Therefore, the approximate mean for the given data set is: Approximate mean = 41 / 10 = 4.1

Therefore, the approximate mean of the number of cars sold by the salesman in the past 10 weeks is 4.1.

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Answer:

(-3, -2) ∪ (1, ∞)

Step-by-step explanation:

Given inequality:

[tex]\dfrac{x^2+5x+6}{x-1} > 0[/tex]

Begin by factoring the denominator:

[tex]\begin{aligned}x^2+5x+6&=x^2+2x+3x+6\\&=x(x+2)+3(x+2)\\&=(x+3)(x+2)\end{aligned}[/tex]

Therefore, the factored inequality is:

[tex]\dfrac{(x+3)(x+2)}{x-1} > 0[/tex]

Determine the critical points - these are the points where the rational expression will be zero or undefined.

The rational expression will be zero when the numerator is zero:

[tex](x+3)(x+2)=0 \implies x=-3,\;x=-2[/tex]

Therefore, -3 and -2 are critical points.

The rational expression will be undefined when the denominator is zero:

[tex]x-1=0 \implies x=1[/tex]

Therefore, 1 is a critical point.

So the critical points are -3, -2 and 1.

Create a sign chart, using open dots at each critical point (the inequality is greater than, so the interval doesn't include the values).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

Chosen test values: -4, -2.5, 0, 2

For each test value, determine if the function is positive or negative:

[tex]x=-4 \implies \dfrac{(-4+3)(-4+2)}{-4-1} = \dfrac{(-)(-)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]

[tex]x=-2.5 \implies \dfrac{(-2.5+3)(-2.5+2)}{-2.5-1} = \dfrac{(+)(-)}{(-)}=\dfrac{(-)}{(-)}=+[/tex]

[tex]x=0 \implies \dfrac{(0+3)(0+2)}{0-1} = \dfrac{(+)(+)}{(-)}=\dfrac{(+)}{(-)}=-[/tex]

[tex]x=2 \implies \dfrac{(2+3)(2+2)}{2-1} = \dfrac{(+)(+)}{(+)}=\dfrac{(+)}{(+)}=+[/tex]

Record the results on the sign chart for each region (see attached).

As we need to find the values for which the rational expression is greater than zero, shade the positive regions on the sign chart (see attached). These regions are the solution set.

Remember that the intervals of the solution set should not include the critical points, as the critical points of the numerator make the expression zero, and the critical point of the denominator makes the expression undefined. The intervals of the solution set are those where the rational expression is greater than zero only.

Therefore, the solution set is:

-3 < x < -2  or  x > 1

As interval notation:

(-3, -2) ∪ (1, ∞)

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"The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

There are three commonly-used forms of quadratics:

Standard Form: y = a x 2 + b x + c y= [tex]ax^2+bx+c y=ax2+bx+c.[/tex]

Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y= a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)

Vertex Form: y = a ( x − h ) 2 + k y= [tex]a(x-h)^2+k y=a(x−h)2+k.[/tex]

Quadratic functions can be represented symbolically by the equation, y(x) = ax2 + bx + c, where a, b, and c are constants, and a ≠ 0. This form is referred to as standard form.

The statement "The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.

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The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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Answer:

answer is 42

Step-by-step explanation:

use the distance formula and it's simple afterwards. I am pretty sure the answer is correct but let me know if you need more help

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of [tex]f(x)=(x-1)(x+7)[/tex] has clear zeroes at [tex]x=1[/tex] and [tex]x=-7[/tex], showing that [tex]f(x) > 0[/tex] when [tex]x < -7[/tex] and [tex]x > 1[/tex]. To determine where the vertex is, we can complete the square:

[tex]f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16[/tex]

So, we can see the vertex is (-3,-16), meaning that where [tex]x > -3[/tex], the function will be increasing on that interval

Answer:

-13/60

Step-by-step explanation:

trust me

Answer:

C

Step-by-step explanation:

just look at point A and the difference to A'.

A was moved 2 units to the left and 4 units up to get A'.

and the same happened, of course, to all other points of the triangle.

so, C is correct.

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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Based on unit conversions, the number of customers that would seat at each table is 12 persons.

The number of customers per table can be determined using unit conversions, which involve multiplication and division.

In this situation, the total available space per table is converted to squared inches from squared feet, and divided by the required table space per customer.

Conversely, the required table space per customer can be converted to squared feet and the result used to divide the total available space per table.

The required table space per customer = 300 in²

The total available space (area) per table = 300 ft²

1 foot = 12 inches

300 ft² = 3,600 in² (12 x 300)

The number of customers per table = 12 (3,600 ÷ 300)

OR:

300 in² = 25 ft² (300 ÷ 12)

The number of customers per table = 12 (300 ÷ 25)

Thus, using unit conversions, we expect the restaurant owner to seat 12 customers per table.

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The area occupied by each table is 300 ft².