find distance between 2 points A(-1,-7), B(-8,7)

In a rhombus, all sides are the same length, and the opposite angles are equal. The diagonals also bisect each other at 90 degrees.

We know that,

A rhombus has two congruent acute and two congruent obtuse angles.

Here we use the terms  x and y to represent the angles.

where x is the acute angle

The angles total 360 degrees.

So far, we have:

2(x+y) = 360

By dividing both sides by 2 , we get,

x + y = 180

We can assume y is 3 times larger than x,

That is y = 3x

As a result, the equation becomes,

x + 3y = 180

Calculate the total

4x = 180

As a result, the acute angle is 45 degrees.

Hence we proved that y is 3 times larger than x.

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Answer:

GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

\(\mu = 3.36, \sigma = 1.2\)

Bottom 33%:

The 33rd percentile(X when Z has a pvalue of 0.33) and below.

So we have to find X when Z = -0.44.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.44 = \frac{X - 3.36}{1.2}\)

\(X - 3.36 = -0.44*1.2\)

\(X = 2.832\)

GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

Answer:

32 percent

Step-by-step explanation:

We can set this up as a fraction: because there are 640 out of 2000, it becomes:

640/2000

We can simplify this to get

320/1000

32/100.

0.32

Since percentages are the decimal of the hundredths place, we get 32 percent.

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Answer:

4

Step-by-step explanation:

kcf

8/9 x 9/2= 72/18

=4

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

5.24

Step-by-step explanation:

Answer:

875,000 x 100 = 875 x __100000__

Answer: 100000

Step-by-step explanation: 875,000 x 100 = 875,00000 and not just add the 0s to number 1 and thats ur answer

Answer:

5.04 seconds

Step-by-step explanation:

Having a graphing tool like )desmos.com) helps, just replace t with x

The values of all 9 angles shown were found using the property of a kite they are:

m∠1=55°

m∠2=35°

m∠3=35°

m∠4=90°

m∠5=55°

m∠6=67°

m∠7=67°

m∠8=23°

m∠9=23°

What is an angle ?

In Kite figure, it is given that:

∠2+∠3 = 70°

Since they are equal so ∠2=∠3=35

∠8+∠9 = 46°

Since they are equal so ∠8=∠9=23°

∠5 = 180-∠3-∠4 = 180-35-90=55°

Similarly, ∠1 = 55°

∠6+∠7 = 180-∠8-∠9 = 180-46 = 134°

Since they are equal

∠6=∠7 = 67°

Therefore, all 9 angles were calculated using property of a kite.

m∠1=55°

m∠2=35°

m∠3=35°

m∠4=90°

m∠5=55°

m∠6=67°

m∠7=67°

m∠8=23°

m∠9=23°

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The rays or line segments are called the sides or legs of the angle, and the distance between the sides at the vertex is called the angle's measure.

Angles are typically measured in degrees or radians, and they can be classified by their measures as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (exactly 180 degrees), reflex (greater than 180 degrees and less than 360 degrees), or full (exactly 360 degrees).

Kites have several properties related to their angles, including:

Two pairs of opposite angles in a kite are congruent. That is, the angles formed between the pairs of congruent sides are equal.

One diagonal of a kite bisects the other diagonal. This means that the diagonal that connects the non-congruent vertices of the kite divides the other diagonal into two equal segments.

The sum of the measures of the two non-congruent angles in a kite is 180 degrees. This is because the kite can be divided into two congruent triangles by drawing the diagonal that bisects the other diagonal, and the sum of the angles in a triangle is always 180 degrees.

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Answer:

The answer would be 536 cones.

Step-by-step explanation:

You have to subtract 164 from 700.

700-164=536.

Answer: 9

Step-by-step explanation:

Past the point of 12 there are a total of 9 plants represented.

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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Step-by-step explanation:

5(x - 3) = 3 + 5x + 3x

5x - 15 = 3 + 8x

5x - 8x = 3 + 15

-3x = 18

x = 18/-3

x = -6

The number in the given word problem is -6.

Thus:

unknown number = x

Therefore:

\(5 \times (x - 3) = 3 + (5x + 3x)\)

\(5x - 15 = 3 + 8x\)

\(5x - 8x= 3 + 15\\\\-3x = 18\\\\\)

\(x = -6\)

Therefore, the value of the number is -6.

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Answer:

A would be correct

Step-by-step explanation:

the answer is A.

Answer:

2) Option D is correct.

f = (15m + 35)

3) Check Explanation

Step-by-step explanation:

The diagram of the question is presented in the attached image to this question

English Translation

Efraín has a rectangular land whose area is (120m² + 280m) as shown in the figure. According to these data, how much does side f measure?

a) 12 m² + 35

b) 15 m + 35 cm

c) 12 m + 35

d) 15 m + 35

3.- A child made four plasticine figures: two quadrangular prisms and two cylinders. In which figure did you occupy the most amount of modeling clay? JUSTIFY YOUR ANSWER

Solution

2) The area of a rectangle is given as

Area = Length × Breadth

Area = (120m² + 280m)

Length = f

Breadth = 8m

(120m² + 280m) = f × 8m

f = (120m² + 280m)/(8m)

f = (15m + 35)

Option D is correct.

f = (15m + 35)

3) For the second question, the images for the question and the dimensions of the figures aren't provided, hence, a very accurate answer can be provided. But without This, we can only speculate.

The figure that would use the most clay is the figure whose volume is the highest if the volumes of each of the figures are calculated.

Volume of a quadrangular prism = (Area of base) × (perpendicular height)

Volume of a cylinder = (Area of base) × (Height) = (πR² × H) = πR²H

So, it is in the evaluation of these volumes that the solution of this question is obtained.

Hope this Helps!!

Answer:

\(Length = 25cm\)

Step-by-step explanation:

Given

Brass Shape: Square

\(Density = 4.2g/cm^3\)

\(Mass = 1.05kg\)

\(Height = 4mm\)

Required

Determine the length of the plate

First, we need to calculate the Volume of the Brass using

\(Density = \frac{Mass}{Volume}\)

Make Volume the subject of formula

\(Volume = \frac{Mass}{Density}\)

Substitute 1.05kg for Mass and 4.2g/cm³ for Density

\(Volume = \frac{1,05\ kg}{4.2\ g/cm^3}\)

Convert 1.05 kg to grams

\(Volume = \frac{1.05 * 1000\ kg}{4.2\ g/cm^3}\)

\(Volume = \frac{1050 \ kg}{4.2\ g/cm^3}\)

\(Volume = \frac{1050 \ kg}{4.2\ g/cm^3}\)

\(Volume = 250cm^3\)

Next is to determine the Area of the brass;

\(Volume = Height * Area\)

Substitute 250cm³ for Volume and 4mm for Height

\(250cm^3 = 4mm * Area\)

Convert mm to cm

\(250cm^3 = 4 * 0.1cm * Area\)

\(250cm^3 = 0.4cm * Area\)

Divide both sides by 0.4cm

\(\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}\)

\(\frac{250cm^3}{0.4cm} =Area\)

\(625cm^2 = Area\)

\(Area = 625cm^2\)

Lastly, we'll calculate the length of the brass

Since the brass is square based;

\(Area = Length^2\)

Substitute 625cm² for Area

\(625cm^2 = Length^2\)

Take square root of both sides

\(\sqrt{625cm^2} = Length\)

\(25cm = Length\)

\(Length = 25cm\)

Hence, the length of the square brass is 25cm

Answer: This is the answer. please give me the brainliest. Thanks

An equation of this line in slope-intercept form is y = x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-1, -2) and a slope of -1, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = -1(x - (-1))  

y + 2 = x + 1

y = x + 1 - 2

y = x - 1

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Complete Question:

Write an equation of a line through point (-1, -2) with a slope of -1.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

a) \(a(t) = t -2.5\)

b) \(x(t) = \frac{1}{6}t^3 -\frac{5}{4}t^2 +2t +2.5\\\)

Part a:

Acceleration is just the derivative of velocity. In this case, we are given how the velocity, \(v(t)\), is defined. If we take the derivative of \(v(t)\) that'll be our acceleration.

Recall:

\(\frac{\mathrm{d}}{\mathrm{d}x}(x^n) = nx^{n -1}\\\)

\(\frac{\mathrm{d}}{\mathrm{d}x}(f(x) +g(x)) = \frac{\mathrm{d}}{\mathrm{d}x}(f(x)) +\frac{\mathrm{d}}{\mathrm{d}x}(g(x))\\\)

\(\frac{\mathrm{d}}{\mathrm{d}x}(a \cdot f(x)) = a \cdot \frac{\mathrm{d}}{\mathrm{d}x}(f(x))\\\)

Let \(a(t)\) be the acceleration. Solving for \(a(t)\):

\(v(t) = 0.5t^2 -2.5t +2 \\ \frac{\mathrm{d}}{\mathrm{d}t}(v(t)) = \frac{\mathrm{d}}{\mathrm{d}t}(0.5t^2 -2.5t +2) \\ a(t) = \frac{\mathrm{d}}{\mathrm{d}t}(0.5t^2) -\frac{\mathrm{d}}{\mathrm{d}t}(2.5t) +\frac{\mathrm{d}}{\mathrm{d}t}(2) \\ a(t) = 0.5\frac{\mathrm{d}}{\mathrm{d}t}(t^2) -2.5\frac{\mathrm{d}}{\mathrm{d}t}(t) +\frac{\mathrm{d}}{\mathrm{d}t}(2) \\ a(t) = 0.5(2t) -2.5 +0 \\ a(t) = t -2.5\)

Part b:

Position is the same thing as displacement (Although they are fundamentally different but it's okay to treat them as similar things in this case). Displacement is just the integral of velocity. If we take the integral of \(v(t)\) that'll be our displacement.

Please refer to my Answer from this question to know the needed information of integrals to solve: brainly.com/question/24687635

Recall:

\(\int (a \cdot f(x)) \mathrm{d}x = a\int f(x) \mathrm{d}x\\\)

\(\int (f(x) +g(x)) \mathrm{d}x = \int f(x) \mathrm{d}x +\int g(x) \mathrm{d}x\\\)

Let \(x(t)\) be our position. Solving for \(x(t)\):

\(v(t) = 0.5t^2 -2.5t +2 \\ \int v(t) \mathrm{d}t = \int (0.5t^2 -2.5t +2) \mathrm{d}t \\ x(t) = \int (0.5t^2) \mathrm{d}t -\int (2.5t) \mathrm{d}t +\int (2) \mathrm{d}t \\ x(t) = 0.5\int (t^2) \mathrm{d}t -2.5\int (t) \mathrm{d}t +\int (2) \mathrm{d}t \\ x(t) = 0.5(\frac{t^3}{3}) -2.5(\frac{t^2}{2}) +2t +C \\ x(t) = \frac{1}{6}t^3 -\frac{5}{4}t^2 +2t +C\)

We still have to solve for \(C\). We are given that at \(t = 0\), \(x(t) = 2.5\). We can therefore write the equation: \(x(0) = 2.5\) or \(\frac{1}{6}(0)^3 -\frac{5}{4}(0)^2 +2(0) +C = 2.5\\\).

Solving for \(C\):

\(\frac{1}{6}(0)^3 -\frac{5}{4}(0)^2 +2(0) +C = 2.5\\ 0 -0 +0 +C = 2.5 \\ C = 2.5\)

We can also write the equation:

\(x(t) = \frac{1}{6}t^3 -\frac{5}{4}t^2 +2t +2.5\\\)

Im sure it's -3    Because well thats what  i got

Answer:

Area of Parallelogram Using Diagonals ; Using Base and Height, A = b × h ; Using Trigonometry, A = ab sin (x) ; Using Diagonals, A = ½ × d1 × d2 .....

Using Diagonals: A = ½ × d1 × d2 sin (y)

Using Base and Height: A = b × h

Using Trigonometry: A = ab sin (x)

Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer:

Explanation:

The volume of the triangular prism:

The base area of the prism = 1/2 x 4 x 6 = 12 ft2

Height = 6 ft

The volume of the triangular prism = 12 x 6 = 72 ft3

The volume of the rectangular prism:

The base area of the prism = 4 x 6 = 24 ft2

Height = 12 ft

The volume of the triangular prism = 12 x 24 = 288 ft3

Volume of the composite figure = (288 + 72)ft3 = 360 ft3

Step-by-step explanation:

There is a probability of 94/315 that the problem will be solved.

We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.

The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.

The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.

The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.

The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.

To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:

2/7 + 4/7 + 4/9 = 94/315

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