The demand function for a company's product is P=26e^{-.04q} where Q is measured in thousands of units and P is measured in dollars.
(a) What price should the company charge for each unit in order to sell 2500 units? (Round your answer to two decimal places.) (b) If the company prices the products at $8.50 each, how many units will sell? (Round your answer to the nearest integer.) units

The numerical value of Oz is approximately -1819.86.

Using the chain rule, we have:

[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt\\dz/ds = dz/dy * dy/ds[/tex]

We can calculate each term using the given equations:

dz/dx = 1

dx/dt = 2

dy/dt = 0

dz/dy = cos(y)

dy/ds = 6t

Substituting these values, we get:

[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt = 1 * 2 + cos(y) * 0 = 2\\dz/ds = dz/dy * dy/ds = cos(y) * 6t = 6t * cos(6st)[/tex]

To find дz as/Əz, we need to solve for as in terms of z and s:

z = x + sin(y) = 2t + sin(6st)

x = 2t

y = 6st - 1

Solving for s in terms of t, we get:

s = (y + 1)/(6t)

Substituting this into the equation for z, we get:

z = 2t + [tex]sin(6t(y+1)/(6t)) = 2t + sin(y+1)[/tex]

Taking the partial derivative of z with respect to as, we get:

[tex]дz/Əz = 1[/tex]

B. To find the numerical values of дz and Oz, we need to plug in the given values of x, y, s, and t into our equations. Using the given values, we get:

x = 2t = -964

y = 6st - 1 = -3617

z = x + sin(y) = -964 + sin(-3617) ≈ -964.73

Using the values of s and t, we can find:

s = (y + 1)/(6t) ≈ -0.9985

t = x/2 ≈ -482

Substituting these values into our equation for дz as/Əz, we get:

дz/Əz = 1

Therefore, the numerical value of дz is 1.

Substituting these values into our equation for dz/ds, we get:

dz/ds = 6t * cos(6st) ≈ -1819.86

Therefore, the numerical value of Oz is approximately -1819.86.

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From the given graph, the roots of the quadratic equation, 0 = x² - 6x + 5, is 1 and 5. The correct option is the last option x= 1, 5

From the question, we are to determine the roots of the quadratic equation from the provided graph.

From the given information,

The given quadratic equation is

0 = x² - 6x + 5

The roots of a quadratic function are the values of x where the function equals zero. On a graph, this corresponds to the points where the graph intersects the x-axis.

From the graph, we will read the x-coordinates of the points where the graph intersects the x-axis.

From the given graph, the x-coordinates of the points where the graph intersects the x-axis are 1 and 5

Hence, the roots of the quadratic equation is 1 and 5

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The maximum height of Anna's golf ball is 6.25 feet.

To find the maximum height of Anna's golf ball, we need to determine the vertex of the parabolic equation y = x - 0.04x^2. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, the coefficients a and b are:
a = -0.04
b = 1

Substituting the values into the formula:

x = -1 / (2 * -0.04)
x = -1 / (-0.08)
x = 12.5

Now, we need to find the y-coordinate of the vertex by plugging the x-coordinate back into the equation:

y = 12.5 - 0.04(12.5)^2

y = 12.5 - 0.04(156.25)

y = 12.5 - 6.25

y = 6.25

So, the maximum height of Anna's golf ball is 6.25 feet.

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To find dy/dx, we need to take the derivative of y with respect to x. On evaluating the value of dy/dx is [tex]-9t^{8/9}[/tex]

However, we are given x in terms of t. So first, we need to use the chain rule to find dx/dt:
x = [tex]t^{1/9}[/tex]
dx/dt = (1/9) * [tex]t^{-8/9}[/tex]

Now, we can use the chain rule again to find dy/dt:

y = 9 - t
dy/dt = -1

Finally, we can use the formula for the chain rule to find dy/dx:

dy/dx = (dy/dt) / (dx/dt)
dy/dx = (-1) / ((1/9) * [tex]t^{-8/9}[/tex]
dy/dx = [tex]-9t^{8/9}[/tex]

So, the final answer is dy/dx = [tex]-9t^{8/9}[/tex]
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Answer:

6, 9, 10, 10, 11, 11, 12, 13, 15, 15, 18

Q1 (the first quartile) represents the data point that separates the lowest 25% of the data from the rest of the data. To find Q1, we can use the formula:

Q1 = (n + 1) / 4

where n is the total number of data points.

In this case, n = 11, so:

Q1 = (11 + 1) / 4 = 3rd data point

So, Q1 is 10.

Q3 (the third quartile) represents the data point that separates the highest 25% of the data from the rest of the data. To find Q3, we can use the formula:

Q3 = 3(n + 1) / 4

In this case:

Q3 = 3(11 + 1) / 4 = 9th data point

So, Q3 is 15.

D4 represents the fourth decile, which is the data point that separates the lowest 40% of the data from the rest of the data. To find D4, we can use the formula:

D4 = (n + 1) / 10 * 4

In this case:

D4 = (11 + 1) / 10 * 4 = 5th data point

So, D4 is 11.

D Assimilation represents the data point that is closest to the mean (average) of the data. To find D Assimilation, we first need to find the mean of the data:

Mean = (6 + 9 + 10 + 10 + 11 + 11 + 12 + 13 + 15 + 15 + 18) / 11 = 12

The data point closest to the mean is 12, so:

D Assimilation = 12

Pss (the range) represents the difference between the largest and smallest data points. In this case:

Pss = 18 - 6 = 12
6  9  10 10 11 11 12 13 15 15 18

                             Dss=12

   Q1=10       Q3=15

       D4=11

Step-by-step explanation:

Answer:

a = 16

b = 8z

Step-by-step explanation:

Expanding the given expression, we get:

(4y + z)^2 = (4y + z) × (4y + z)

= 16y^2 + 8yz + z^2

Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:

a = 16

b = 8z

Therefore, the value of a is 16 and the value of b is 8z.

Bank B is offering a lower interest rate and will result in a lower total cost over the 20-year period. Even though the monthly payment is slightly lower with Bank B, Trevor should choose Bank B because he will save money in the long run due to the lower interest rate.

To compare the two mortgage options, Trevor needs to consider both the interest rate and the monthly payment amount.

Bank A offers a 5% interest rate with a monthly payment of $791.95. The total amount he will pay over 20 years is:

$791.95 x 12 months/year x 20 years = $190,068

Bank B offers a 4.75% interest rate with a monthly payment of $775.47. The total amount he will pay over 20 years is:

$775.47 x 12 months/year x 20 years = $186,113.60

So, in this case, Bank B is offering a lower interest rate and will result in a lower total cost over the 20-year period. Even though the monthly payment is slightly lower with Bank B, Trevor should choose Bank B because he will save money in the long run due to the lower interest rate.

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Answer: We can check whether the expression (x + 18) is a factor of x² - 324 by dividing x² - 324 by (x + 18) using polynomial long division or synthetic division.

Using polynomial long division:

x + 18 │x² + 0x - 324

       -x² - 18x

       ----------

        18x - 324

        18x + 324

        ----------

            0

Since there is no remainder, we can see that (x + 18) is indeed a factor of
x² - 324.

The parabola has an axis of symmetry x=22, vertex at (22, 2), and opens downward.

Given the focus (22, 3) and directrix y=1, we can determine the following:

a. Axis of symmetry: Since the parabola is vertical (directrix is horizontal), the axis of symmetry will be a vertical line passing through the focus. So, x=22 is the axis of symmetry.

b. Vertex: The vertex is the midpoint between the focus and the directrix. To find the vertex, average the y-coordinates of the focus and the directrix. Vertex = (22, (3+1)/2) = (22, 2).

c. Direction: If the focus is above the directrix, the parabola opens upward. If the focus is below the directrix, the parabola opens downward. In this case, the focus (22, 3) is above the directrix y=1, so the parabola opens downward.

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[tex]\sf Let \ d_1 \ and \ d_2 \ be \ the \ lengths \ of \ the \ sides \ of \ diagonals.[/tex]

[tex]\sf Given \ that \ d_1=8 \ cm[/tex]

[tex]\sf And \ d_2=10 \ cm[/tex]

[tex]\therefore\sf Area \ of \ rhombus=\dfrac{1}{2} (d_1)(d_2)=\dfrac{1}{2}(8)(10)=40 \ cm^2[/tex]

[tex]\rightarrow\boxed{\sf Area \ of \ rhombus=40 \ cm^2}[/tex]

Answer:

D. 4π

Step-by-step explanation:

Circumference: C = 2πr = 2π(8) = 16π

The distance = 1/4 circumference (angle is 90 degrees)

=> distance = 16π/4 = 4π

The correct answer is e. 2/7.

To evaluate this line integral, we need to parameterize the curve given by the parabola y = x from (1, 1) to (-1, 1).

Let's let x = t and y = t, where t goes from 1 to -1. Then we can rewrite the integral as follows:

[tex]\int\ C (x - y)\dx + (y \sin y)\dy[/tex]

[tex]= \int\limits^1_{-1} {[(t - t)dt + (t sin t)}\,dt}[/tex]

[tex]= \int\limits^1_{-1} { (t \sin t)} \, dt[/tex]

We can evaluate this integral using integration by parts:

Let u = t and [tex]dv = sin t\ dt[/tex]. Then [tex]du/dt = 1[/tex] and v = -cos t.

Using the formula for integration by parts, we have:

[tex]\int\limits^1_{-1} { (t \sin t)}\, dt = -t \cos t |_{-1}^{1} + \int\limits^1_{-1} { cos t}\, dt[/tex]

= -cos(-1) + cos(1) + sin(-1) - sin(1)

= 2sin(1) - 2cos(1)

Therefore, the value of the line integral is:

[tex]S_c(x - y)dx + (y \sin y)dy = 2\sin(1) - 2\cos(1)[/tex]

Hence, the correct answer is e. 2/7.

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The amount for the fencing cost  is $903. 36

From the information given, we have that the shape of the garden is  semi -circle.

Now, the formula that is used for calculating the circumference of a semicircle is expressed as;

C = πr + 2r

Given that the parameters of the equation are;

From the information given,

Substitute the values, we have;

Circumference = 3.14(19) + 2(19)

expand the bracket

Circumference = 59. 66 + 38

Add the values

Circumference = 97. 66 feet

Then,

if 1 feet = $9.25

Then, 97. 66 feet = x

x = $903. 36

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Area of sector NPQ ≈ 127.23 square units

To find the area of the sector NPQ, we first need to find the measure of the central angle that defines the sector. We know that the measure of the angle NPQ is 104 degrees, but we need to find the measure of the central angle that includes this arc.

Since NP is a radius of the circle, we know that triangle NQP is an isosceles triangle, with angles NQP and PNQ each measuring (180 - 104)/2 = 38 degrees. Therefore, the measure of the central angle that includes arc NPQ is 2 * 38 + 104 = 180 degrees.

The area of the sector NPQ is then a fraction of the total area of the circle, where the fraction is equal to the ratio of the central angle to the total angle around the circle. Since the total angle around a circle is 360 degrees, the fraction of the circle's area covered by the sector is:

180 degrees / 360 degrees = 1/2

Therefore, the area of the sector NPQ is equal to half the area of the circle with radius 9 units:

Area of sector NPQ = (1/2) * π * 9^2 = 40.5π

Rounding to the nearest hundredth, the area of the sector NPQ is approximately:

Area of sector NPQ ≈ 127.23 square units

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The coordinates of transforming image of the vertices of the triangle ABC are A' (1, -1) ,B' (3, 1) , and C' (1, 4).

In triangle ABC,

Coordinates of the vertices of triangle ABC are,

A(-1,1), B(1,3) and C(4,1)

The transformation T y=x reflects the points across the line y=x.

The image of each point, we simply swap the x and y coordinates of each point.

So, applying the transformation T y=x to the vertices of triangle ABC, we get,

A' = (-1, 1) → (1, -1)

B' = (1, 3) → (3, 1)

C' = (4, 1) → (1, 4)

This implies,

The image of triangle ABC under the transformation T y=x is triangle A'B'C', where,

A' is located at (1, -1)

B' is located at (3, 1)

C' is located at (1, 4)

Therefore, in triangle ABC labeling the coordinates of the vertices of A'B'C'  after transformation are as follows,

A' (1, -1)

B' (3, 1)

C' (1, 4)

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The above question is incomplete, the complete question is:

Triangle ABC has vertices A(-1,1), B(1,3) and C(4,1). The image of ABC after the transformation T y=x is A’ B’ C’. State and label the coordinates of A’ B’ C’.

Answer:

Step-by-step explanation:

In option (a), sin(t) < 0 and cos(t) < 0, In trigonometry, the terminal point of an angle t is the point on the unit circle where the angle intersects with the circle.

The position of the terminal point determines the quadrant in which the angle lies.

To determine the quadrant, we need to look at the signs of the sine and cosine functions. In quadrant I, both sine and cosine are positive. In quadrant II, sine is positive and cosine is negative. In quadrant III, both sine and cosine are negative. In quadrant IV, sine is negative and cosine is positive.

In option (a), sin(t) < 0 and cos(t) < 0, both the sine and cosine functions are negative. This means that the terminal point lies in quadrant III.

In option (b), sin(t) > 0 and cos(t) < 0, the sine function is positive and the cosine function is negative. This means that the terminal point lies in quadrant II.

In option (c), sin(t) > 0 and cos(t) > 0, both the sine and cosine functions are positive. This means that the terminal point lies in quadrant I.

In option (d), sin(t) < 0 and cos(t) > 0, the sine function is negative and the cosine function is positive. This means that the terminal point lies in quadrant IV.

In summary, the signs of the sine and cosine functions can be used to determine the quadrant in which the terminal point lies.

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The expression that represents the length (in feet) of the world's longest glass-bottom bridge is 4.3x+550.4.

Let's denote the length of the Coiling Dragon Cliff Skywalk as y (in feet). According to the given information, we have:

y = x + 128

The length of the world's longest glass-bottom bridge is 4.3 times longer than the Coiling Dragon Cliff Skywalk, so we can write an expression for it as:

Length of the longest glass-bottom bridge = 4.3 * y

Now, we can substitute the expression for y from the first equation:

Length of the longest glass-bottom bridge = 4.3 * (x + 128)

To simplify, distribute the 4.3:

Length of the longest glass-bottom bridge = 4.3x + 550.4

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1 hour =60 minutes

Step-by-step explanation:

Let M be the time in minutes . T be temperature in Farhenheit. From 45th min to end of the hour there remains a steady temperature. after that gyms starts to cools down . For time 45≤M≤60, Temperature T=77oF.To find a) Is M a function of T ? we know that Temperature changes with respect to time . So M is independent variable and T is dependent variable . so M cannot be a function of T .

To find the limit of (7x3)/(4x2-2x+10) as x approaches infinity, we need to divide the highest power of x in the numerator and denominator, which is x3, by the highest power of x in the denominator, which is x2. This gives us: (7x3)/(4x2-2x+10) = (7/4)x

As x approaches infinity, the value of (7/4)x also approaches infinity. Therefore, the limit of (7x3)/(4x2-2x+10) as x approaches infinity is infinity.

To find the limit of (7x^3)/(4x^2-2x+10) as x approaches infinity, we'll first look at the highest powers of x in the numerator and denominator.

In this case, the highest power of x in the numerator is x^3, and in the denominator, it's x^2. Since the highest power of x in the numerator is greater than that in the denominator, the limit will go to infinity (or -infinity) depending on the coefficients of the highest powers.

For this function, the coefficients are positive (7 for x^3 and 4 for x^2), so the limit as x approaches infinity will be positive infinity.

Your answer: The limit of (7x^3)/(4x^2-2x+10) as x approaches infinity is positive infinity.

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The difference in measures of center as a multiple of the measure of variation can be expressed using the coefficient of variation.

To express the difference in measures of center as a multiple of the measure of variation, you can use the coefficient of variation (CV).

The CV is calculated by dividing the standard deviation (measure of variation) by the mean (measure of center), and then multiplying by 100 to express the result as a percentage.

For example, if the standard deviation of one dataset is 5 and the mean is 10, the CV would be 50%. If the standard deviation of another dataset is 2 and the mean is 8, the CV would be 25%.

To express the difference in measures of center as a multiple of the measure of variation between these two datasets, you would calculate the difference in their means (10-8=2) and divide it by the CV of the combined dataset ((5/10 + 2/8)/2 = 47.5%).

Therefore, the difference in measures of center is approximately 0.042 times the measure of variation (2/47.5%).

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Answer:

Rate: 36:3

Unit Rate: 12:1

Step-by-step explanation:

31.8 kilograms is equivalent to 31,800 grams.

The correct answer is (D) 31,800 grams.

To convert kilograms to grams, we multiply the number of kilograms by 1000. So, to convert 31.8 kilograms to grams, we can use the following formula:

31.8 kilograms x 1000 grams/kilogram = 31,800 grams

Therefore, 31.8 kilograms is equivalent to 31,800 grams.

To convert kilograms to grams, we need to multiply the number of kilograms by 1000 because there are 1000 grams in one kilogram. In this case, Eddie's dog weighs 31.8 kilograms. To find out how many grams this is, we simply multiply 31.8 by 1000, which gives us 31,800 grams. Therefore, 31.8 kilograms is equivalent to 31,800 grams. It's important to understand the basic metric system conversions, like kilograms to grams, as they are commonly used in everyday life, particularly when it comes to measuring weight. Knowing how to make these conversions can be helpful in many different situations, from cooking and baking to medical and scientific contexts.  

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The volume of the pyramid with a square base of side length 11.8 ft and a height of 5.2 ft is 240.0 cubic feet.

To find the volume of a pyramid with a square base of side length 11.8 ft and a height of 5.2 ft, you can use the following formula:

Volume = (1/3) × Base Area × Height

1: Find the base area.

The base is a square with a side length of 11.8 ft, so the area of the base is:

Base Area = Side Length × Side Length

Base Area = 11.8 ft × 11.8 ft

Base Area ≈ 139.24 square ft

2: Find the volume.

Now, use the formula to find the volume:

Volume = (1/3) × Base Area × Height

Volume = (1/3) × 139.24 sq ft × 5.2 ft

Volume ≈ 240.0368 cubic ft

3: Round your answer to the nearest tenth.

Volume ≈ 240.0 cubic ft

So, the volume of the pyramid is approximately 240.0 cubic feet.

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The explicit formula for the given sequence is An = 256 * (0.25)ⁿ⁻¹, where n is the term number. Using this formula, we can generate the first five terms of the sequence as follows:

A1 = 256 * (0.25)¹⁻¹ = 256 * 1 = 256
A2 = 256 * (0.25)²⁻¹ = 256 * 0.25 = 64
A3 = 256 * (0.25)³⁻¹ = 256 * 0.0625 = 16
A4 = 256 * (0.25)⁴⁻¹ = 256 * 0.015625 = 4
A5 = 256 * (0.25)⁵⁻¹ = 256 * 0.00390625 = 1

In simpler terms, the explicit formula for the given sequence is found by multiplying the first term by the common ratio raised to the power of n-1, where n is the term number. This results in a decreasing sequence as the common ratio is less than 1. The first five terms of the sequence are 256, 64, 16, 4, and 1, respectively.

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1. The area of the shaded region is

2. percentage of the shaded part is 89.6%

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of the shaded part = area of the rectangle - area of unshaded part

Area of rectangle = 7× 11 = 77 unit²

area of rectangle = 1/2 bh

= 1/2 × 4 × 4

= 1/2 × 8

= 4 unit²

area of second triangle = 4 units²

area of unshaded part = 4+4 = 8 units²

area of shaded part = 77-8 = 69units²

2. percentage of the rectangle shaded = 69/77 × 100

= 6900/77 = 89.6%

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Answer:

im gooder like that

Step-by-step explanation:

3z*5=15z

15z+4z-7

19z-7  

The largest box of soup will hold about 120 ounces or 221 cubic inches of soup.

Since the scale factor is 2, the volume of the largest box will be 2^3 = 8 times the volume of the smallest box. Therefore, the volume of the largest box will be 8 x 15 cubic inches = 120 cubic inches. To find the dimensions of the largest box, we need to find the cube root of 120 cubic inches, which is approximately 5.87 inches.

Since the smallest box has no shape restrictions, we can assume that the largest box will also have a rectangular shape. Therefore, a set of dimensions for the largest box could be 5.87 inches x 5.87 inches x 5.87 inches, or rounded to the nearest tenth, 5.9 inches x 5.9 inches x 5.9 inches.

This would result in a volume of approximately 221 cubic inches, which is about 120 ounces of soup.

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The missing number for box a transaction amount account balance are a = 10, b = 210, c = 210.

Using the information provided in the table, we can fill in the missing numbers as follows:

For transaction 3: The account balance after transaction 2 was $100, and transaction 3 had an amount of $90. Therefore, the account balance after transaction 3 is $190. Hence, the missing number in box a is 190.

For transaction 4: The account balance after transaction 3 was $190, and transaction 4 had an amount of -$200. Therefore, the account balance after transaction 4 is -$10. Hence, the missing number in box b is -10.

For transaction 5: The account balance after transaction 4 was -$10, and transaction 5 had an amount of $c. Therefore, the account balance after transaction 5 is 0. Hence, the missing number in box c is 10.

Therefore, the completed table is:

transaction amount account balance

1 150 150

2 50 100

3 90 190

4     -200-10

5 10 0

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The evaluation of the triple integral ∫∫∫E 4[tex]x^{2}[/tex] + 3dV is  (38/15)ππ

To evaluate the triple integral ∫∫∫E 4x^2 + 3dV in spherical coordinates, we need to express the integrand and the volume element dV in terms of the spherical coordinates ρ, θ, and φ.

The volume element dV in spherical coordinates is given by:
dV =  sin φ dρ dθ dφ
where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.
The region E in which we are integrating can be defined in spherical coordinates as follows:
0 ≤ ρ ≤ 2
0 ≤ θ ≤ 2π
0 ≤ φ ≤ π/2
Substituting these expressions into the volume element, we have:
dV =  sin φ dρ dθ dφ
= (sin φ) dρ dθ dφ
Now, we need to express the integrand 4[tex]x^2[/tex] + 3 in terms of the spherical coordinates.

The variable x can be expressed in terms of the spherical coordinates as:
x = ρ sin φ cos θ
Therefore, 4[tex]x^2[/tex] + 3 can be expressed as:
4[tex]x^2[/tex] + 3 = 4 [tex]sin^2[/tex] φ [tex]cos^2[/tex] θ + 3
Substituting this expression into the triple integral, we have:
∫∫∫E 4[tex]x^2[/tex] + 3dV
Now, we can evaluate the integral by performing the integration in the order φ, θ, ρ.
= (8/15)π + 2π
= (38/15)ππ

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A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:

1/8 = 0.125 = 12.5%.

The experimental probabilities are obtained considering the trials, hence:

The more trials, the closer the experimental probability should be to the theoretical probability.

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