In this problem, you will investigate properties of polygons.

a. Geometric

Draw a three-sided, a four-sided, and a five-sided polygon. Label the 3-sided polygon A B C , the four-sided polygon F G H J , and the five-sided polygon P Q R S T . Use a protractor to measure and label each angle.

There are 336 different 5-digit telephone numbers that can be constructed using the digits 0 to 9, starting with "67" and with no repeated digits.

To answer your question, we need to find the number of ways to arrange the remaining three digits after "67" is fixed.

Since we cannot repeat any digit, the first digit has 8 possibilities (0 to 9 except for 6 and 7).

the second digit has 7 possibilities, and the third digit has 6 possibilities.
To find the total number of arrangements, we multiply the number of possibilities for each digit together:

8 × 7 × 6 = 336.
Therefore, there are 336 different 5-digit telephone numbers that can be constructed using the digits 0 to 9, starting with "67" and with no repeated digits.
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The new average salary for the twenty employees is [tex]$83,000[/tex]per year.Hence, the answer is 83,000.

Let's begin by calculating the initial salary of the twenty employees:

Average salary of 20 [tex]employees = $48,000[/tex] per year

Therefore, the total initial salary of the twenty employees = Average salary x [tex]Total number of employees= $48,000 x 20= $960,000[/tex] Now, ten of the employees get a[tex]$22,000[/tex] per year raise.

This means that their new salary will be [tex]$48,000 + $22,000 = $70,000[/tex]

Therefore, the new total salary of these ten employees = [tex]$70,000 x 10 = $700,000[/tex] To calculate the new average salary for all twenty employees, we need to add the new total salary to the total initial salary and then divide by the total number of employees.

New total salary of twenty employees =[tex]$960,000 + $700,000= $1,660,000[/tex] New average salary of twenty employees = New total salary / Total number of employees= [tex]$1,660,000 / 20= $83,000,[/tex]

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If the supply and demand curves in the provided graph represent the market supply and demand for a purely competitive industry, then the demand curve that an individual firm in the industry faces is perfectly elastic.

This is because firms in a perfectly competitive market are price takers. They have to accept the market price because they are too small to influence it. Therefore, the market demand curve is also the demand curve for the firm because it can sell any amount of output at the market price.

The supply curve for the firm is also the marginal cost curve because the firm produces where marginal cost equals the price. Hence, the individual firms in a perfectly competitive industry face a perfectly elastic demand curve, while the market demand curve is downward sloping.

If the supply and demand curves in the provided graph represent the market supply and demand for a purely competitive industry, then the demand curve that an individual firm in the industry faces is perfectly elastic. This is because firms in a perfectly competitive market are price takers.

They have to accept the market price because they are too small to influence it. Therefore, the market demand curve is also the demand curve for the firm because it can sell any amount of output at the market price. The supply curve for the firm is also the marginal cost curve because the firm produces where marginal cost equals the price.

Hence, the individual firms in a perfectly competitive industry face a perfectly elastic demand curve, while the market demand curve is downward sloping.In a perfectly competitive market, an individual firm can sell all of its output at the market price.

Since the market price is fixed, the firm faces a perfectly elastic demand curve. The reason for this is that the firm is too small to influence the market price. Therefore, the market demand curve is also the demand curve for the firm. As for the supply curve for the firm, it is equal to the marginal cost curve because the firm produces where marginal cost equals the price.

If the market price rises, the firm will produce more because it can cover its costs. If the market price falls, the firm will produce less because it will not be able to cover its costs.

Hence, individual firms in a perfectly competitive industry face a perfectly elastic demand curve, while the market demand curve is downward sloping.

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Leo Tolstoy's quote, "I can still make it the real thing -- I can. But what is the real thing?" is a thought-provoking statement that reflects Tolstoy's exploration of the concept of authenticity in his works. In this quote, Tolstoy is questioning the true essence or nature of something, particularly in relation to art or life.

By saying "I can still make it the real thing," Tolstoy implies that he has the ability to create something genuine, to capture the true essence of it. However, he follows it up with the question, "But what is the real thing?" This suggests that he is contemplating what truly defines authenticity and whether it can ever be fully attained.

Tolstoy's inquiry can be interpreted in various ways. It may refer to his own quest for genuine expression in his writing or his exploration of the authenticity of human experiences. It could also be seen as a broader philosophical question about the nature of reality and the search for truth.

Ultimately, Tolstoy's quote invites readers to reflect on the meaning of authenticity and prompts them to consider what constitutes the "real thing" in various aspects of life.

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No, not every five measurements of a quadrilateral can determine a quadrilateral uniquely. The choice of measurements depends on the properties of the quadrilateral.

For instance, the measurements for a parallelogram are different from the measurements for a trapezoid, and so on. Therefore, the five measurements must be selected based on the properties of the quadrilateral in question.

Let's see how five measurements can uniquely determine a quadrilateral?

A quadrilateral has 4 sides and 4 angles. The sum of the angles in a quadrilateral is 360°. Therefore, three of the angles can be measured. The fourth angle can be found by subtracting the sum of the other three angles from 360°. In other words, any three angles of a quadrilateral can determine the fourth angle. This gives us four measurements.

The fifth measurement can be any one of the following:

Diagonal length - A quadrilateral has two diagonals. The length of one diagonal can be measured to give us the fifth measurement. This is useful for quadrilaterals with perpendicular diagonals, such as a rhombus or a square.

Length of one side and two diagonals - This is useful for quadrilaterals with two diagonals that bisect each other at right angles, such as a kite.

Lengths of all four sides - This is useful for quadrilaterals with all four sides of equal length, such as a square or a rhombus.

Lengths of three sides and an angle - This is useful for quadrilaterals with two sides of equal length and two adjacent angles of equal measure, such as an isosceles trapezoid.

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Therefore, the quotient of -(3/8) divided by (5/8) is -3/5.

To find the quotient of -(3/8) divided by (5/8), you need to follow these steps:

Step 1: Invert the divisor (the second fraction) to change the division operation to multiplication. So, (5/8) becomes (8/5).

Step 2: Multiply the dividend (the first fraction) by the inverted divisor. Thus, -(3/8) multiplied by (8/5) is (-3/8) * (8/5).

Step 3: Multiply the numerators (top numbers) to get the new numerator and the denominators (bottom numbers) to get the new denominator. So, (-3 * 8) / (8 * 5) equals -24/40.

Step 4: Simplify the fraction if possible. In this case, you can divide both the numerator and the denominator by 8, resulting in -3/5.

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Answer:

Step-by-step explanation:

4, you could pull out green, blue, red, or yellow

Answer:

14

Step-by-step explanation:

4 + 3 + 2 + 5 = 14

Answer: 14

In both the U.S.A. and England, there are only two days of the year that share the same symbol: May 2 (5/2) and February 5 (5/2).

In the United States, the symbol 5/2 is interpreted as the 5th month and 2nd day, representing May 2. On the other hand, in England, 5/2 denotes the 5th day and 2nd month, indicating February 5. To determine how many days of the year have the same symbol in both countries, we need to find the dates that match.

In the U.S., there are 12 months, so there are 12 possible combinations with 5 as the month. However, only May 2 (5/2) coincides with the English interpretation.

In England, there are 31 days in January, so there is no match with the American format. However, in February, there are 28 days (or 29 in a leap year), and February 5 (5/2) aligns with the American interpretation.

Hence, there are only two days of the year that share the same symbol in both the U.S. and England: May 2 (5/2) and February 5 (5/2).

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The statement "approximately 3.24 billion gallons of water flow over Niagara Falls daily" describes a continuous relationship.

In a continuous relationship, the variable (in this case, the amount of water flowing) can take on any value within a certain range. In contrast, a discrete relationship involves distinct, separate values.

In this case, the amount of water flowing can vary continuously and is not limited to specific, separate values. Therefore, the relationship between the amount of water flowing over Niagara Falls daily and the given value is continuous.

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The expression -x² + 13x - 12 can be factored as (x + 1)(-x + 12).

To factor the expression -x² + 13x - 12, we can use the factoring method. First, we look for two numbers that multiply to give -12 and add up to 13. In this case, the numbers are 12 and -1.

Now, we can rewrite the expression as follows:

-x² + 12x - x + 13x - 12

Next, we group the terms:

(-x² + 12x) + (-x + 13x) - 12

Now, we can factor out common terms from each group:

x(-x + 12) + 1(-x + 12) - 12

Notice that we have a common binomial factor, (-x + 12), so we can factor it out:

(x + 1)(-x + 12)

Therefore, the expression -x² + 13x - 12 can be factored as (x + 1)(-x + 12).

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The midpoint of the line segment is (-4, 0).

To find the midpoint of a line segment starting from the origin (0, 0) and ending at (-8, 0), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) of a line segment with endpoints (x1, y1) and (x2, y2) are given by:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

In this case, the coordinates of the origin are (0, 0) and the coordinates of the endpoint are (-8, 0). Plugging these values into the midpoint formula, we get:

x = (0 + (-8)) / 2 = -8 / 2 = -4

y = (0 + 0) / 2 = 0 / 2 = 0

Therefore, the midpoint of the line segment is (-4, 0). Option b) (–4, 0) is the correct answer.

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The coordinates of point e are (2/70, -4/35).

To find the weight of point e, we need to use the concept of weighted averages. The weighted average formula is given by:

Weighted average = (weight1 * value1 + weight2 * value2 + ... + weightn * valuen) / (weight1 + weight2 + ... + weightn)

Given that p = (1/10, -2/5), f has a weight of 2, and g has a weight of 5, we can find the weighted average of the coordinates of p.

The weighted average for the x-coordinate of p is calculated as:
(2 * (1/10) + 5 * 0) / (2 + 5) = (2/10) / 7 = 2/70

The weighted average for the y-coordinate of p is calculated as:
(2 * (-2/5) + 5 * 0) / (2 + 5) = (-4/5) / 7 = -4/35

Therefore, the coordinates of point e are (2/70, -4/35).

In conclusion, the weight of point e is not provided in the question. The given information only includes the weights of points f and g.

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To calculate how much farther a point on the outside edge of the CD travels in one revolution than a point 1 cm closer to the center, we can use the formula for the circumference of a circle.

The circumference of a circle is given by the formula:

C = 2πr

where C is the circumference and r is the radius of the circle. In this case, the CD has a diameter of 12 cm, so the radius would be half of that, which is 6 cm.  Using the formula, the circumference of the CD is:

C = 2π(6) = 12π cm.

Now, let's find the circumference of a smaller circle with a radius that is 1 cm closer to the center. The radius would be

6 - 1 = 5 cm.

Using the formula, the circumference of this smaller circle is:

C = 2π(5) = 10π cm.

To calculate how much farther the point on the outside edge travels, we can subtract the circumference of the smaller circle from the circumference of the CD:
12π cm - 10π cm

= 2π cm.
Therefore, a point on the outside edge of the CD travels 2π cm farther in one revolution than a point 1 cm closer to the center.

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Out of the given figures, namely, a square, triangle, a trapezoid, a regular pentagon, and a rhombus, a test would require selecting a figure among these figures.

However, we can understand the nature of each of these figures, their characteristics, properties, and formulas related to them, and determine how to select a figure for the test.The square has four sides and four right angles, with all sides of equal length.

Its formula for area is A = s²,

where s is the length of the sides.

The triangle is a polygon with three sides, with its area calculated as A = (1/2)bh,

where b is the base and h is the height of the triangle.A trapezoid is a quadrilateral with only one pair of parallel sides. Its formula for area is A = [(b1+b2)/2]h,

where b1 and b2 are the lengths of the parallel sides, and h is the height of the trapezoid.

A regular pentagon is a polygon with five sides, with all sides of equal length. Its area formula is A = (1/4)s²√(25+10√5), where s is the length of the sides.

The rhombus has four equal sides, with opposite angles being equal.

Its area formula is A = (1/2) d1d2, where d1 and d2 are the lengths of the diagonals.

Depending on the nature and level of the test, the selection of any of the figures can vary. For example, if the test is related to the calculation of areas, the selection of square, triangle, trapezoid, and rhombus would be more appropriate, while the selection of a regular pentagon can be suitable for a more advanced test.

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The standard deviation can be calculated using the formula: Standard deviation = (pessimistic estimate - optimistic estimate) / 6. Therefore, the standard deviation is 0.67.

The standard deviation is a measure of the spread or variability of a set of data. It quantifies the amount of dispersion or deviation from the average or mean. In this case, we are given a pessimistic estimate of 10 days and an optimistic estimate of 6 days. To calculate the standard deviation, we need to find the difference between these two estimates. The difference is 10 - 6 = 4 days.

Since the range between the optimistic and pessimistic estimates is 6 days, we divide the difference by 6 to normalize it. So, 4 / 6 = 0.67.

Therefore, the standard deviation is 0.67. This means that the actual value is likely to deviate from the average estimate by approximately 0.67 days. A smaller standard deviation indicates less variability, while a larger standard deviation indicates more variability.

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Each one of the following is classified as:

7. -15 = Integer

8. 5/4 = rational number

9. 0.48 = Rational number

10. 32 = Whole number

To classify each of the given numbers, let's understand the definitions of whole numbers, integers, and rational numbers:

1. Whole numbers: These are non-negative numbers that do not include fractions or decimals. Examples of whole numbers are 0, 1, 2, 3, etc.

2. Integers: These include both positive and negative whole numbers, as well as zero. Examples of integers are -3, -2, -1, 0, 1, 2, 3, etc.

3. Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Rational numbers include integers as well as fractions. Examples of rational numbers are -2/3, 1/4, 0.5, 2, etc.

Now, let's classify each of the given numbers:

7. -15: This is an integer because it is a negative whole number.

8. 5/4: This is a rational number because it can be expressed as a fraction, where the numerator and denominator are both integers.

9. 0.48: This is a rational number because it can be expressed as a fraction. We can write it as 48/100, which can be simplified to 12/25.

10. 32: This is a whole number because it is a positive whole number.

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To find P(Y ≤ X + 1), we need to set up a double integral with the correct limits. First, let's sketch out the region using the support from part a.

From part a, we know that the region is defined by the inequalities 0 ≤ X ≤ 1 and 0 ≤ Y ≤ X. This forms a triangular region in the XY-plane.

To set up the double integral, we integrate over this region. The limits for the outer integral will be from 0 to 1, which corresponds to the limits of X.

For the inner integral, the limits will be from 0 to X + 1, since we want to find P(Y ≤ X + 1). This corresponds to the limits of Y.

Therefore, the double integral that needs to be solved is ∫∫R f(x, y) dy dx, with the limits of integration as follows:

Outer integral limits: 0 to 1 (X)
Inner integral limits: 0 to X + 1 (Y)

In conclusion, to find P(Y ≤ X + 1), you need to set up the double integral ∫∫R f(x, y) dy dx, with the limits as mentioned above.

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By considering the elements in set A, Thomas can gain insights into the diversity of experiences and preferences within his family when it comes to living arrangements after high school.

Set A represents the number of different places where nine of Thomas' family members have lived after high school. The set A consists of unique values that indicate the number of locations each family member has lived in. Each element of set A represents a specific count, reflecting the diversity in the experiences of Thomas' family members regarding their living arrangements after high school.

Set A is a collection of values that represent the number of different places where each family member has lived after high school. The elements of set A could include values such as 0, 1, 2, 3, and so on, depending on the range of experiences within Thomas' family.

For instance, if one family member has only lived in their hometown after high school, their corresponding element in set A would be 1. On the other hand, if another family member has lived in three different cities, their element in set A would be 3.

By considering the elements in set A, Thomas can gain insights into the diversity of experiences and preferences within his family when it comes to living arrangements after high school. The set A provides a comprehensive overview of the number of different places each family member has chosen to reside in, allowing Thomas to explore various perspectives and make informed decisions about his own future living choices.

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The result when the number 31 is increased by 8% and rounded to the nearest tenth is 33.5.

To find the result when the number 31 is increased by 8%, we can calculate 8% of 31 and add it to 31.

8% of 31 can be found by multiplying 31 by 0.08:

8% of 31 = 31 * 0.08 = 2.48

Now, we add this result to 31:

31 + 2.48 = 33.48

Rounding this answer to the nearest tenth, we get:

33.5

Therefore, the result when the number 31 is increased by 8% and rounded to the nearest tenth is 33.5.

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Los Angeles, California, has an average daily temperature between 70 degrees F and 80 degrees F throughout most of the year. There's very little rainfall except for during a rainy season beginning in the fall. This describes the city's climate.

The climate in Los Angeles can be characterized as a Mediterranean climate. This type of climate is typically found in areas close to the ocean, with dry summers and mild, wet winters. The average daily temperature range of 70-80 degrees F indicates the warm and mild nature of the climate.

The limited rainfall throughout most of the year suggests a dry climate, with the exception of the rainy season in the fall. This seasonal pattern is common in Mediterranean climates, where the majority of rainfall occurs during the cooler months.

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The statement "The center of a trapezoid is the perpendicular distance between the bases" is false.

To make the statement true, we need to replace the underlined term. The correct term should be "midsegment" instead of "perpendicular distance between the bases."

The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides. It is parallel to the bases and its length is equal to the average of the lengths of the bases.

Here's a step-by-step explanation:

1. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

2. The bases of a trapezoid are the parallel sides.

3. The midsegment of a trapezoid connects the midpoints of the non-parallel sides.

4. The midsegment is parallel to the bases and its length is equal to the average of the lengths of the bases.

5. Therefore, the statement "The center of a trapezoid is the perpendicular distance between the bases" is false.

6. To make it true, we should replace "perpendicular distance between the bases" with "midsegment".

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The dimensions of the rectangular window are 42 inches by 1.6 times 42 inches, which is 67.2 inches.

To find the dimensions of the rectangular window, we can set up an equation using the given ratio and area. Let's call the shorter side of the window x.
According to the ratio, the longer side of the window would be 1.6x.
The area of a rectangle is calculated by multiplying the length by the width.

So, we can set up the equation:
x * 1.6x = 2822.4
Simplifying this equation,

we get:
1.6x² = 2822.4
Dividing both sides of the equation by 1.6, we have:
x² = 1764
Taking the square root of both sides, we find:
x = 42
Therefore, the dimensions of the rectangular window are 42 inches

by 1.6 times 42 inches,

which is 67.2 inches.

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The dimensions of the window are approximately 67.2 inches for the length and 42 inches for the width.

The ratio of the lengths of the sides of the rectangular window is 1.6 to 1.

Let's represent the length as 1.6x and the width as x.

The area of the window is given as 2822.4 in².

To find the dimensions of the window,

we can use the formula for the area of a rectangle:

area = length × width.

Substituting the given values, we have:

2822.4 = (1.6x)(x)

To solve this equation, we can multiply 1.6x by x, giving us:

2822.4 = 1.6x²

Now, let's solve for x by dividing both sides of the equation by 1.6:

x² = 2822.4 / 1.6

x² = 1764

Taking the square root of both sides, we find:

x = √1764

x = 42

Now that we have the value of x, we can find the length and width of the window.

The length is 1.6 times the width, so:

Length = 1.6x = 1.6 * 42 = 67.2

Width = x = 42

Therefore, the dimensions of the window are approximately 67.2 inches for the length and 42 inches for the width.

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According to the given statement the number of sides in the polygon is: n = 12. So, the polygon has 12 sides.

To find the number of sides in a regular polygon, we can use the formula:
Sum of interior angles = (n-2) × 180 degrees,
where n represents the number of sides in the polygon.
Given that the sum of the interior angles is 1800 degrees, we can substitute this value into the formula:
      1800 = (n-2) × 180.
To solve for n, we can divide both sides of the equation by 180:
      1800 / 180 = n - 2.
Simplifying the equation gives:
       10 = n - 2.
To isolate n, we can add 2 to both sides:
       10 + 2 = n.
Therefore, the number of sides in the polygon is: n = 12.
So, the polygon has 12 sides.

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The digital signature approach uses an algorithm that is designed to provide only the authentication function.

To elaborate, a digital signature is a cryptographic technique used to verify the authenticity and integrity of digital documents or messages. It involves the use of a specific algorithm that generates a unique digital signature for each document or message. This digital signature serves as a form of authentication, ensuring that the document or message has not been tampered with and can be trusted.

In summary, the digital signature approach focuses on providing the authentication function by using a specific algorithm to generate unique digital signatures for documents or messages.

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Yes, the given transformation is found to be  linear.

To determine if a transformation is linear, we need to check two conditions: preservation of addition and preservation of scalar multiplication.

For the preservation of addition, let's consider two arbitrary vectors u and v in R^2.

The transformation Lwt translates each vector up by 3 units.

Therefore,

Lwt(u+v) = (u+v) + (3,3)

= (u + (3,3)) + (v + (3,3))

= Lwt(u) + Lwt(v).

For the preservation of scalar multiplication, let's consider an arbitrary vector u in R^2 and a scalar c. The transformation Lwt translates the vector u up by 3 units.

Therefore,

Lwt(cu) = cu + (3,3)

= c(u + (3,3))

= cLwt(u).

Since both conditions hold true, the transformation Lwt is linear.

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The graph will show a linear relationship, where the distance increases steadily as time increases.

To complete the table and graph, we need to determine the relationship between distance and time based on the given information.

Given:

Time taken = 5 minutes

Distance travelled = 13 kilometers

Since the distance is proportional to the time taken, we can set up a proportion to find the constant of proportionality:

Distance / Time = Constant

Let's calculate the constant of proportionality:

13 kilometers / 5 minutes = 2.6 kilometers/minute

Now, we can complete the table and graph:

| Time (minutes) | Distance (kilometers) |

|---------------|----------------------|

| 5              | 13                     |

| 10             | 26                    |

| 15             | 39                    |

| 20            | 52                    |

| 25            | 65                    |

To graph the data, we can plot the points (5, 13), (10, 26), (15, 39), (20, 52), and (25, 65) on a coordinate plane with time on the x-axis and distance on the y-axis. Connect the points with a straight line to represent the constant speed of the train.

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Using the formula to calculate the length of arcs, the approximate length of boundary ABCD is 23.1

The arc length is defined as the interspace between the two points along a section of a curve.

The formula for calculating arc length is :[tex]2\pi r*\frac{theta}{360}[/tex]

DC = 5

AB = 5

AD = [tex]2*\frac{22}{7} *5*\frac{30}{360} = 2.619[/tex]

BC = [tex]2*\frac{22}{7} *5*\frac{120}{360} = 10.4762[/tex]

Length of ABCD = AB + BC +CD + AD = 23.1

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To predict how many metric tons of pork will be produced in 2025 using your linear model, you will need the equation of your linear model and the value of the independent variable (year) for 2025.

Let's say your linear model equation is: Pork Production = a + b * Year

To predict the pork production in 2025, substitute the value of 2025 for the Year variable in the equation and solve for the Pork Production variable.

For example, if your linear model equation is: Pork Production = 100 + 3 * Year, substitute 2025 for Year:

Pork Production = 100 + 3 * 2025

Simplify the equation:

Pork Production = 100 + 3 * 2025
Pork Production = 100 + 6075
Pork Production = 6175

Therefore, your linear model predicts that approximately 6175 metric tons of pork will be produced in 2025.

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The question is that the number of particles of contamination per pound of material is modeled variable  by a Poisson random variable with a mean of 0.01 particle per pound.

This means that on average, there are 0.01 particles of contamination per pound of material.To study the raw materials for contamination, the number of particles per pound is observed and analyzed. This information helps determine the level of contamination in the raw materials and allows for appropriate actions to be taken if necessary.

By using a poisson random variable, it is possible to calculate the probability of a certain number of particles per pound occurring. This can help in assessing the likelihood of contamination and making informed decisions based on the observed data.In summary, raw materials are studied for contamination using a poisson random variable with a mean of 0.01 particle per pound. This allows for the analysis of the number of particles of contamination per pound and helps in assessing the level of contamination in the raw materials.

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When three standard six-faced dice are rolled, the probability that the sum of the three numbers rolled is 9 is equal to 10/216 or 5/108.

Total number of ways three dice can be rolled = 6 × 6 × 6 = 216.

Each dice can have any number from 1 to 6. The probability of rolling a particular number on a dice = 1/6.

The probability of rolling a particular number on three dice = (1/6) × (1/6) × (1/6) = 1/216.

In order to get a sum of 9, there are four combinations that can be rolled:

3 + 3 + 3 = 9

3 + 4 + 2 = 9

3 + 5 + 1 = 9

4 + 3 + 2 = 9

The probability of rolling any of these combinations = probability of rolling 3-3-3 + probability of rolling 3-4-2 + probability of rolling 3-5-1 + probability of rolling 4-3-2

= (1/216) + (3/216) + (3/216) + (3/216)

= 10/216 or 5/108.

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