Prove that the conditional "All dodecagons must have eleven sides" is false by a counterexample.​

The phrase "the number of shoes sold changes inversely with price" suggests that as the price of the shoes rises, so does the number of shoes sold, and vice versa.

We know that 2000 shoes can be sold for $250 in this circumstance. Using the inverse variation formula, we can write: k/Price = number of shoes sold where k is a proportionality constant. We may use the following information to calculate the value of k: 2000 = k/250 When we multiply both sides by 250, we get: k = 500000 In this case, the equation for the inverse variation is: Price/number of shoes sold = 500000 We may use this equation to compute the number of shoes sold at various prices. For instance, if the price is If the price is $300, the number of shoes sold is: The number of shoes sold is 500000/300, which is 1666.67. As a result, at a price of $300, about 1666.67 pairs of shoes would be sold.

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What is the relationship between the number of shoes sold and the price, given that the number of shoes sold varies inversely with the price? If 2,000 shoes are sold at a price of $250, what would be the price of the shoes if 3,000 shoes are sold?

Answer:

B is the answer

Step-by-step explanation:

The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).

The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.

To express this probability as a fraction, we can use the formula:

Probability of winning = 1 / (odds + 1)

Plugging in the given odds, we get:

Probability of winning = 1 / (16 + 1)

Probability of winning = 1/17

In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.

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The height RT from R to PQ is approximately 3.16 cm.

To find the area of triangle PQR, we can use the formula:

Area = 1/2 * base * height

Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.

Area of PQR = 1/2 * PQ * PS

Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:

[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]

[tex]Area of PQR = 22.5 cm^2[/tex]

Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].

To find the height RT from R to PQ, we can use the Pythagorean theorem.

Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.

Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).

Using the sine function, we can find the length of PT:

sin(69.3) = PT / 7.5

PT = 7.5 * sin(69.3)

PT ≈ 6.93 cm

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

[tex]RT^2 + PT^2 = PR^2[/tex]

[tex]RT^2 = PR^2 - PT^2[/tex]

[tex]RT^2 = 7.5^2 - 6.93^2[/tex]

RT ≈ 3.16 cm

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Strings of 6 letters of the English alphabet containing one vowel: 2,832,240, exactly two vowels: 2,233,200, at least one vowel: 10,919,736, least two vowels: 8,087,496 and number of strings of length n with exactly k vowels: nCk * 5Ck * 21^(n-k)

There are 26 letters in the English alphabet, out of which 5 are vowels (A, E, I, O, U). To find the number of strings of 6 letters of the English alphabet that contain one vowel, we can choose the position of the vowel in 6C1 ways and fill the remaining positions with any of the 21 consonants in 21C5 ways.

Therefore, the total number of such strings is 6C1 * 21C5 = 2,832,240.

To find the number of strings with exactly two vowels, we can choose the positions of the vowels in 6C2 ways and fill them with any of the 5 vowels in 5C2 ways. We can fill the remaining positions with any of the 21 consonants in 21C4 ways.

Therefore, the total number of such strings is 6C2 * 5C2 * 21C4 = 2,233,200.

To find the number of strings with at least one vowel, we can subtract the number of strings with no vowels from the total number of strings. The number of strings with no vowels is 21^6 (since there are 21 consonants and we can choose any of them for each of the 6 positions).

Therefore, the number of strings with at least one vowel is 26^6 - 21^6 = 10,919,736.

To find the number of strings with at least two vowels, we can subtract the number of strings with one vowel or no vowel from the total number of strings. The number of strings with one vowel is 2,832,240 (as we found earlier) and the number of strings with no vowels is 21^6.

Therefore, the number of strings with at least two vowels is 26^6 - 2,832,240 - 21^6 = 8,087,496.

To find the number of strings of length n with exactly k vowels, we can choose the positions of the k vowels in nCk ways and fill them with any of the 5 vowels in 5Ck ways. We can fill the remaining positions with any of the 21 consonants in 21^(n-k) ways.

Therefore, the total number of such strings is nCk * 5Ck * 21^(n-k).

Hence, the number of strings of 6 letters of the English alphabet containing one vowel is 2,832,240, while the number of strings with exactly two vowels is 2,233,200. The number of strings with at least one vowel is 10,919,736, and the number of strings with at least two vowels is 8,087,496.

Finally, the number of strings of length n with exactly k vowels is nCk * 5Ck * 21^(n-k).

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Roll a 5: There is only one way to roll a 5 out of six possible outcomes, so the probability of rolling a 5 is 1/6.

Roll a 6: Similarly, there is only one way to roll a 6 out of six possible outcomes, so the probability of rolling a 6 is 1/6.

Roll a c or 4: There are two ways to roll a 4 (rolling a 4 or rolling a 3) and one way to roll a 3, so there are three ways to roll a 4 or c out of six possible outcomes. Therefore, the probability of rolling a 4 or c is 3/6, simplifying it to 1/2.

Roll an odd number: There are three odd numbers (1, 3, 5) out of six possible outcomes, so the probability of rolling an odd number is 3/6, simplifying to 1/2.

Roll an even number: There are three even numbers (2, 4, 6) out of six possible outcomes, so the probability of rolling an exact number is 3/6 or 1/2.

Roll a number greater than 3: There are three numbers greater than 3 (4, 5, 6) out of six possible outcomes, so the probability of rolling a number greater than 3 is 3/6, which simplifies to 1/2.

Roll an even number less than 5: There is only one number less than 5 (2) out of six possible outcomes, so the probability of rolling an actual number less than 5 is 1/6.

Roll a multiple of 2 (2, 4, 6): There are three multiples of 2 out of six possible outcomes, so the probability of rolling a multiple of 2 is 3/6, simplifying to 1/2.

Roll a factor of 6 (1, 2, 3, 6): There are four factors of 6 out of six possible outcomes, so the probability of rolling a factor of 6 is 4/6, which simplifies to 2/3.

So the probabilities for each event expressed as fractions are:

Roll a 5: 1/6

Roll a 6: 1/6

Roll a 4 or c: 1/2

Roll an odd number: 1/2

Roll an even number: 1/2

Roll a number greater than 3: 1/2

Roll an even number less than 5: 1/6

Roll a multiple of 2: 1/2

Roll a factor of 6: 2/3

Answer:

Step-by-step explanation: Its 6x, you add the 6 + 1 then keep the x.

Answer:

10

Step-by-step explanation:

The mean of a set of numbers is the sum divided by the number of terms.

Answer: 132 cubic centimeters

Step-by-step explanation:

To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.

The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).

The volume of A is:

Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters

The volume of B is:

Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters

So the total volume of the block of clay is:

Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters

Therefore, the volume of the block of clay is 132 cubic centimeters.

Philippe can perform a simulation of rain or no rain for tomorrow by spinning a spinner with two sections labeled "Rain" and "No rain."

The spinner could be divided into two sections, one labeled "Rain" and the other labeled "No rain." To perform the simulation, Philippe would need to give the spinner a spin and observe which section it lands on. If it lands on the "Rain" section, he would consider that as an outcome of rain for tomorrow, and if it lands on the "No rain" section, he would consider that as an outcome of no rain for tomorrow. To make the simulation more accurate, he could repeat the process multiple times and record the number of times the spinner lands on each section.

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The child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.

The given problem requires us to determine the number of milliliters of a liquid medicine that a child should receive in order to obtain a specific dosage of the active ingredient. We are given that the medicine contains 100 mg of the active ingredient in 5 ml.

The child needs to receive 300 mg of the active ingredient, and there are 100 mg of the active ingredient in 5 ml of the medicine. Therefore, the child should be given:

[tex]\frac{300 mg}{100mg/5ml} = \frac{300\text{ mg} \times 5\text{ ml}}{100\text{ mg}} = 15\text{ ml}$$[/tex]

So the child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.

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The probability that the first question she gets right is question number 4, is 0.1054.

Number of options there are for a single query = 4

P(guessing correct answer for a single question) = 1/4

P(guessing correct answer for a single question) = 0.25

Probability of getting correct answer P(correct) = 0.25

Probability of getting wrong answer P(wrong) = 1 - Probability of getting correct answer

Probability of getting wrong answer P(wrong) = 1 - 0.25

Probability of getting wrong answer P(wrong) = 0.75

So, the probability that the first question she gets right is question number 4 = Probability of getting 1st question wrong × Probability of getting 2nd question wrong × Probability of getting 3rd question wrong × Probability of getting 4th question right

The probability that the first question she gets right is question number 4 = 0.75 × 0.75 × 0.75 × 0.25

The probability that the first question she gets right is question number 4 = 0.1055

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The complete question is:

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. (Round your answers to four decimal places.)

What is the probability that the first question she gets right is question number 4?

The two planes will meet 6 hours after they start, i.e. at 3 pm.

Two planes leave at 9 am from airports that are 2700 miles apart and fly towards each other at a speed of 200 mph and 250 mph. At what time will they pass each other?

Let's assume the planes A and B leave the two airports that are 2700 miles apart at the same time. The speed of the first plane is 200 mph and the speed of the second plane is 250 mph. To find out the time at which they pass each other, we need to calculate the distance between them and divide it by the sum of their speeds.

Distance traveled by the first plane in time t1 is equal to 200t1.Distance traveled by the second plane in time t2 is equal to 250t2.The distance covered by the first plane and the second plane together will be 2700 miles.Time taken by both the planes to meet can be calculated as below:

t1 + t2 = 2700/(200+250) = 6 hoursAs both the planes start at 9 am, they will meet each other after 6 hours of their journey. Therefore, they will pass each other at 3 pm. This is the required answer. Explanation: So, the two planes will meet 6 hours after they start, i.e. at 3 pm.

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Step-by-step explanation:

Diameter = 10 units then radius, r = 5 inches

Cylinder's  base AREA = pi r^2 = pi (5)^2 = 25 pi = 78.54 units^2

Base area * height = volume = 25 pi * 4 = 100 pi =314.2 units^3

If a car traveling at 40 mph requires 80 feet to stop, the stopping distance S of a car varies directly as the square of its speed v and is equal to 180 feet.


Given, the stopping distance S of a car varies directly as the square of its speed v. So the relation can be represented as,

S ∝ v2

Here, the constant of proportionality is k.

S = kv2 ——— (1)

Given, when the speed v = 40 mph, stopping distance s = 80 feet.

Therefore, from equation (1), we have

80 = k × 402

k = 80/1600

k = 0.05

Hence, the relation between the stopping distance S and the speed v of the car can be given as

S = 0.05v2

To find the stopping distance S of the car at speed v = 60 mph, substitute v = 60 in the above equation.

S = 0.05 × 602

S = 0.05 × 3600

S = 180 feet

Therefore, the stopping distance of a car traveling at 60 mph would be 180 feet.


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Answer:

  4/33

Step-by-step explanation:

You want to write 0.1212...(repeating) as a simplified fraction.

A repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.

Here, there are 2 repeating digits, so the basic fraction is ...

  12/99

This can be reduced by removing a factor of 3 from numerator and denominator:

  [tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]

__

Additional comment

Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.

  0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99

Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.

You can also approach this by writing the number as a continued fraction. The basic form is ...

  [tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]

where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.

A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.

Answer:

what's your exact question

Answer:

can u pls type the full question

Let's assume that each van and each bus can carry "x" number of students.

Let's assume there are "x" students in each van and each bus. Therefore, the total number of students in High School A's senior class is 8x + 8x = 16x. We know that the total number of students in High School A's senior class is 240, so we can set up an equation:

16x = 240

Solving for x, we get:

x = 15

So, each van and each bus had 15 students in it for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 1x = 5x. We know that the total number of students in High School B's senior class is 54, so we can set up an equation:

5x = 54

Solving for x, we get:

x = 10.8

Since the number of students must be a whole number, we can round up to 11. Therefore, each van and each bus had 11 students in it for High School B's senior class.

Therefore, the total number of students in High School A's senior class is 1x + 6x = 7x. We know that the total number of students in High School A's senior class is 372, so we can set up an equation:

7x = 372

Solving for x, we get:

x = 53

Therefore, each van and each bus can carry 53 students for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 12x = 16x. We know that the total number of students in High School B's senior class is 780, so we can set up an equation:

16x = 780

Solving for x, we get:

x = 48.75

Since the number of students must be a whole number, we can round up to 49. Therefore, each van and each bus can carry 49 students for High School B's senior class.

Let's assume that the price of one senior citizen ticket is "s" and the price of one child ticket is "c". Therefore, we can set up two equations based on the given information:

[tex]3s + 9c = 75[/tex]

[tex]8s + 5c = 67[/tex]

We can solve these equations simultaneously to find the values of "s" and "c". One way to do this is to multiply the first equation by 8 and the second equation by 3, so that we can eliminate "c" and solve for "s":

[tex]24s + 72c = 600[/tex]

[tex]24s + 15c = 201[/tex]

Subtracting the second equation from the first, we get:

57c = 399

Solving for "c", we get:

c = 7

Substituting this value into one of the original equations, we can solve for "s":

[tex]3s + 9(7) = 75[/tex]

[tex]3s + 63 = 75[/tex]

[tex]3s = 12[/tex]

[tex]s = 4[/tex]

Therefore, one senior citizen ticket costs $4 and one child ticket costs $7.

Let's assume that the speed of the boat in still water is "b" and the speed of the current is "c".

Therefore, we can set up two equations based on the given information:

[tex]336 = (b + c) * 12[/tex]

[tex]336 = (b - c) * 14[/tex]

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Thus, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

The ratio of the scale of an original thing to a new object that is a representation of it but of a variable size is known as a scale factor (bigger or smaller).

The procedures below can be used to increase form A by a scale factor of 3.5 with the centre of enlargement at (8,-7).

Transform the square so that its origin is where the centre of enlargement is (0,0).

To do this, we deduct each vertex's coordinates from the centre of enlargement (8,-7):

A = (4 - 8, -3+ 7) = (-4, 4)

B = (6 -8, -3 + 7) = (-2, 4)

C = (6 - 8, -5 + 7) = (-2, 2)

D = (4 - 8, -5 + 7) = (-4, 2)

Multiply the coordinates of the each vertex by the scaling factor (3.5) to enlarge the translated square:

A = (-14, 14)

B = (-7, 14)

C = (-7, 7)

D = (-14, 7)

By adding those coordinates of the centre of the enlargement (8,-7) to each vertex, move the square from its larger state back to its original one:

A = (-14 + 8, 14-7) = (-6, 7)

B = (-7 + 8, 14-7) = (1, 7)

C = (-7 + 8, 7-7) = (1, 0)

D = (-14 + 8, 7-7) = (-6 ,0)

As a result, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

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Answer: 16x+3x^3−8

Please mark me brainliest :)

Answer: 30

180 - x = 180 - 2x + 30

x = 30

Answer:

The measure of the unknown angle is 30°.

Step-by-step explanation:

Let the measure of the unknown angle be x°.

Supplementary angles are two angles whose measures sum to 180°.

Complementary angles are two angles whose measures sum to 90°.

Therefore, the supplement of x° is (180 - x)°, and its complement is (90 - x)°.

Given that the supplement is 30° more than twice its complement:

(180 - x)° = 2(90 - x)° + 30°

To find the measure of the angle, solve the equation:

⇒ (180 - x)° = (180 - 2x)° + 30°

⇒ 180° - x° = 180° - 2x° + 30°

⇒ 180° - x° = 210° - 2x°

⇒ 180° - x° + 2x° = 210° - 2x° + 2x°

⇒ 180° + x° = 210°

⇒ 180° + x° - 180° = 210° - 180°

⇒ x° = 30°

Therefore, the measure of the unknown angle is 30°.

The equation that represents the relationship between the number of hours needed to complete a trip, h, and the driving speed, s, is h = 5/s. This means that the number of hours needed to complete the trip is inversely proportional to the driving speed.

When the driving speed is 60 miles per hour, the number of hours needed to complete the trip is 5 (h = 5/60). If the driving speed is increased to 90 miles per hour, the number of hours needed to complete the trip is 5/90 (h = 5/90).

In general, as the driving speed increases, the number of hours needed to complete the trip decreases.

To summarize, the equation that represents the inverse relationship between the number of hours needed to complete a trip and the driving speed is h = 5/s. This equation can be used to determine the number of hours needed to complete a trip at any given speed.

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The rate of change of the area of a circle when the radius is 4 cm is 4π cm2/sec.

This can be calculated using the formula for the area of a circle (A = πr2) and the chain rule for derivatives. The chain rule states that when the radius (r) changes, the area of a circle (A) is equal to 2πr times the rate of change of the radius (dr/dt).

Therefore, the rate of change of the area of a circle when the radius is 4 cm is equal to 2π(4 cm) × (0.5 cm/sec) = 4π cm2/sec.

Note that if the rate of change of the radius were different, the rate of change of the area would also be different. This formula can be used to calculate the rate of change of the area of a circle at any given radius, as long as the rate of change of the radius is known.

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The triangle has sides; a = 11.3 ft, b = 9.03 ft, and c = 12.9 ft. 1

Angles of approximately A = 59°, B = 51°, and C = 70°

Triangle is a shape of three line segments these segments have three points which crosses it.

The Law of Cosines states that;

c² = a² + b² - 2ab Cos(C)

put values;

12.9² = 11.3² + b² - 2(11.3)(b) Cos(C)

166.41 = 127.69 + b² - 22.6b Cos(C)

b² - 22.6b Cos(C) - 38.72 = 0

We know the quadratic formula, solve it for value of b:

b = [-22.6 Cos(C) ± [tex]\sqrt{(22.6Cos(C))^2 - 4*1*(-38.72)))[/tex]] / (2×1)

b = -11.3 Cos(C) ± [tex]\frac{\sqrt{510.76 Cos^2(C) + 154.88}}{2}[/tex]

To solve for the angles A and C, we can use the Law of Sines, which states that for any triangle with sides of lengths a, b, and c, and its opposite angles which are A, B, and C, So the equation is:

sin(A)/a = sin(B)/b = sin(C)/c

We know that c = 12.9 ft and a = 11.3 ft, and we have just found b, so we can use the Law of Sines to solve for the angles A and C.

sin(A)/11.3 = sin(C)/12.9

sin(A) = (11.3/12.9)sin(C)

sin(A) = 0.875969

A = [tex]Sin^{-1}(0.875969)[/tex]

A ≈ 59° (rounded to the nearest minute)

Now we can use the fact that the sum of the angles in a triangle is 180° to solve for C:

C = 180° - A - B

C = 180° - 59° - [tex]Sin^{-1}[/tex]([22.6cos(C) ± [tex]\sqrt{(511.56 - 154.88 Cos^2(C)) }[/tex]] / 2)

We can use a numerical solver to find the value of C that satisfies this equation. One possible value for C is:

C ≈ 70° (rounded to the nearest minute)

Finally, we can use the Law of Sines again to find the other angle B:

Sin(B)/b = sin(C)/c

Sin(B) = (b/12.9)sin(C)

Sin(B) = (b/12.9)sin(70°)

B = [tex]Sin^{-1}[/tex]((b/12.9)sin(70°))

By putting the value of b,

B ≈ 51° (rounded to the nearest minute)

Therefore, the triangle has sides of lengths 11.3 ft, approximately 9.03 ft, and 12.9 ft, and angles of approximately 59°, 51°, and 70°.

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We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.

The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.

To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.

Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.

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B. The probability of an outcome is between 0 and 1. C. The sum of the probabilities of all possible outcomes is 1.

Option B is correct because probability values must be between 0 and 1.

Option C is correct because the sum of the probabilities of all possible outcomes must equal 1.

Option A is incorrect because it is not necessary for half of the possible outcomes to have probabilities greater than 0.5.

Option D is incorrect because the distribution does not have to be symmetrical.

Option E is incorrect because the outcomes can have common events and can be dependent.

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The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.

An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.

Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.

Angle ABC = Angle ABD + Angle ACD

replacing the specified values:

110° = Angle ABD + 75°

Simplifying:

Angle ABD = 110° - 75°

Angle ABD = 35°

Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:

AC / CD = AB / BD

replacing the specified values:

AC / 10 = 16 / 8

Simplifying:

AC = 20

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Complete Question:

Find the angle ∠ABD jn the given figure

Answer:

16

Step-by-step explanation:

When we divide the entire equation by 1/-2 to get rid of the coefficient of n we get n = 16.

The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is [tex]\frac{7}{12}[/tex] , where 7 and 12 are relatively prime positive integers. The answer is 7+12=19.

The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is 1 minus the probability that no diameter of the circle has two girls sitting on opposite ends of the diameter.

There are

[tex]{10\choose5}[/tex] =252

ways to seat the five girls and five boys.

There are 5 ways to choose a diameter of the circle.

Once this diameter is fixed, there are [tex]{5\choose2}[/tex] = 10 ways to choose a pair of seats on the diameter to place two girls (in the order in which they appear counterclockwise).

There are 5!=120 ways to seat the remaining 3 girls and 5 boys such that no two girls sit on the same diameter.

Hence, there are [tex]5\cdot10\cdot120[/tex] =6000 valid seatings that satisfy the condition in the question.

Thus, the desired probability is 1 - [tex]\frac{6000}{252}[/tex] = [tex]\frac{7}{12}[/tex], as stated above.

Thus, the answer is 7+12 = [tex]\boxed{19}[/tex]

For similar question on probability

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Answer:

Step-by-step explanation:

[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]    

[tex]7 (x+\frac{9}{28} )=60[/tex]     (multiplied both sides by 3)

[tex]x+\frac{9}{28} =\frac{60}{7}[/tex]          (divided both sides by 7)

[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex]     (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)