Simplify
21x®y:
14x’yº
PLEASE HELPPPP

Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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When we compared equations of the height and when the ball will be at rest, the time is 0 seconds

To determine when the ball will hit the ground, we need to find the time at which the height (h) is equal to zero.

Given the equation h = -3.2t, we substitute h with 0 and solve for t:

From the linear equation;

2 + 12.8t + 1;

0 = -3.2t

Dividing both sides by -3.2:

0 / -3.2 = t

t = 0

So, the ball will hit the ground at t = 0 seconds.

However, let's verify this result by checking if there are any other solutions when h = 0:

0 = -3.2t

Dividing both sides by -3.2:

0 / -3.2 = t

t = 0

Since we get the same solution, t = 0, we can conclude that the ball will hit the ground at t = 0 seconds.

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Answer:

x+18

Step-by-step explanation:

Let's simplify step-by-step.

2x+8−x+10

=2x+8+−x+10

Combine Like Terms:

=2x+8+−x+10

=(2x+−x)+(8+10)

=x + 18

The degrees of freedom for this test can be calculated using the formula: degrees of freedom = sample size - 1.

In this case, the sample size is 150 students. Therefore, the degrees of freedom can be calculated as:

Degrees of freedom = 150 - 1 = 149.

So, the degrees of freedom for this test is 149.

Degrees of freedom represent the number of independent pieces of information available in the sample. In statistical hypothesis testing, degrees of freedom play a crucial role in determining the critical values and the appropriate distribution to use for making inferences. It is important to correctly determine the degrees of freedom to ensure the accuracy of the test results and to make appropriate statistical conclusions.

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Therefore, the steady-state responseusing Laplace theorem ia `Yss(t)` of the system is

\((1/4)sin(4t) + (5/8)sin(8t) + (0.015)sin(12t) + (0.01)sin(16t).Answer: `Yss(t) = (1/4)sin(4t) + (5/8)sin(8t) + (0.015)sin(12t) + (0.01)sin(16t)`\)

Given the transfer function of the system and the input frequency as follows:\(0.5y+5y = f(t)where f(t) = sin(4t) + 4sin(8t) + 0.04sin(12t) + 0.06sin(16t)\)

We have to find the steady-state response \(`Yss(t)`\) of the system.

Let's start the solution: Take Laplace transform on both sides of the given equation.\(`(0.5y + 5y)(L) = f(t)(L)`\)

By using linearity of Laplace transform:`\(L(0.5y) + L(5y) = L(f(t))``0.5L(y) + 5L(y) = L(sin(4t)) + 4L(sin(8t)) + 0.04L(sin(12t)) + 0.06L(sin(16t))`\)We know that the Laplace transform of sin(at) is given by:\(`L(sin(at)) = (a) / (s² + a²)`\)

Putting values of Laplace transform of input f(t) into the above equation.\(`0.5L(y) + 5L(y) = (4) / (s² + 16) + 4(8) / (s² + 64) + 0.04(12) / (s² + 144) + 0.06(16) / (s² + 256)`\)

Let's solve for \(L(y).`0.5L(y) + 5L(y) = 0.25 / (s² + 4²) + 1.25 / (s² + 8²) + 0.03 / (s² + 12²) + 0.04 / (s² + 16²)`\)

Factorizing the denominator, we get:  \(`L(y) = [0.25 / (s² + 4²) + 1.25 / (s² + 8²) + 0.03 / (s² + 12²) + 0.04 / (s² + 16²)] / (0.5 + 5)`\)

Evaluating the above expression we get:  \(`L(y) = [0.25 / (s² + 4²) + 1.25 / (s² + 8²) + 0.03 / (s² + 12²) + 0.04 / (s² + 16²)] / 5.5`\)

We know that the inverse Laplace transform of \(`1 / (s² + a²)` is given by: `L⁻¹[1 / (s² + a²)] = (1 / a) sin(at)`\)

Using the above formula and taking inverse Laplace transform on L(y), we get\(:`y(t) = L⁻¹[L(y)]``y(t) = (1/4)sin(4t) + (5/8)sin(8t) + (0.015)sin(12t) + (0.01)sin(16t)`.=\)

Hence, the steady-state response of the given system is:\(`Yss(t) = (1/4)sin(4t) + (5/8)sin(8t) + (0.015)sin(12t) + (0.01)sin(16t)`\)

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\(\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}\)

\(:\implies\sf{ \frac{36}{x} = - 9} \\ \\ :\implies\sf{ \frac{36}{ 9} = -x} \\ \\ :\implies\sf{4 = -x} \\ \\ :\implies\sf{x = -4}\)

Answer:

-18+ 13

-6 + 1

-20 + 15

-7 + 2

Step-by-step explanation:

Answer: $364

Step-by-step explanation:

\(\displaystyle\\ \$260+\frac{40\%(\$260)}{100\%} =\\\\ \$260+\frac{\$10400}{100}=\\\\ \$260+\$104=\\\\\$364\)

The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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The answer that describes the polygon RSTU is as follows:

A quadrilateral is a polygon with 4 sides. Therefore, let's use the properties to find the name of the shape  RSTU as follows:

The polygon has 4 sides therefore, it is a quadrilateral.

The quadrilateral has opposite side parallel to each other. The opposite sides are RS and TU.

A trapezoid is a quadrilateral with only one pair of opposite side parallel to each other.

Therefore, the shapes that defines the polygon are as follows:

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Answer:

Domain of the given function is all real numbers i.e. R.

Step-by-step explanation:

It is given that the given graph is a V shaped graph.

It is crossing x - axis at \((-2,0)\)

then y-axis at \((0,-2)\) and

then again x - axis at \((2,0)\).

If we try to plot the graph, the graph will be like it comes down from the negative x axis side and then intersect x axis at \((-2,0)\), then intersects y axis at \((0,-2)\)  and then rises towards the right side (i.e. positive x axis) intersecting the positive x axis at \((2,0)\).

Please find attached graph for the same.

This graph denotes the following function:

\(y=f(x)=|x|-2\)

Domain of a function \(y =f(x)\) is the values of \(x\) that can be provided to the function.

Here function is a modulus function and from graph we can easily infer that it can have any Real Number, R as its input.

Modulus function has R as its domain.

So, the answer is:

Domain of given function is all Real Numbers, R

Answer:

A on edg. all real numbers

Step-by-step explanation:

The limit of (f(x) + 1) / sin(x) as x approaches 0 is 0, the approximation for f(1/2) using Euler's method with two steps is 19/32 and the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1.

(a) To find the limit of (f(x) + 1) / sin(x) as x approaches 0, we can first rewrite the given differential equation as:

dy / dx = y²  (2x + 2)

Separating variables, we get:

dy / y²  = (2x + 2) dx

Integrating both sides, we have:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side gives:

-1 / y = x²  + 2x + C1

where C1 is the constant of integration.

Since we have the initial condition f(0) = -1, we substitute x = 0 and y = -1 into the above equation:

-1 / (-1) = 0²  + 2(0) + C1

1 = C1

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Now, to find the limit (f(x) + 1) / sin(x) as x approaches 0, we substitute x = 0 into the particular solution equation:

f(0)(0²  + 2(0) + 1) + 1 = 0

-1(0) + 1 = 0

1 = 0

Therefore, the limit of (f(x) + 1) / sin(x) as x approaches 0 is 0.

(b) Using Euler's method, we approximate the value of f(1/2) starting at x = 0 with two steps of equal size. Let's choose the step size h = 1/4.

First step:

x0 = 0, y0 = f(0) = -1

Using the differential equation, we have:

dy / dx = y²  (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (-1)²  (2(0) + 2) (1/4)

Δy ≈ 1/2

Next, we update the values:

x1 = x0 + Δx = 0 + 1/4 = 1/4

y1 = y0 + Δy = -1 + 1/2 = 1/2

Second step:

x0 = 1/4, y0 = 1/2

Using the differential equation again:

dy / dx = y^2 (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (1/2)²  (2(1/4) + 2) (1/4)

Δy ≈ 3/32

Updating the values:

x2 = x1 + Δx = 1/4 + 1/4 = 1/2

y2 = y1 + Δy = 1/2 + 3/32 = 19/32

Therefore, the approximation for f(1/2) using Euler's method with two steps is 19/32.

c)To find the particular solution to the differential equation dy/dx = y^2 (2x + 2) with the initial condition f(0) = -1, we can solve the separable differential equation.

Separating variables, we have:

dy / y² = (2x + 2) dx

Integrating both sides:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side:

-1 / y = x²  + 2x + C

where C is the constant of integration.

To find the particular solution, we substitute the initial condition f(0) = -1:

-1 / (-1) = 0²  + 2(0) + C

1 = C

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Therefore, the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1

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The answer of the given question is inferential statistics.

The mathematical procedures used to assume or understand predictions about the whole population, based on the data collected from a random sample selected from the population, are called inferential statistics.

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The mathematical procedures used to assume or understand predictions about the whole population based on data collected from a random sample selected from the population are called statistical inference techniques.

Statistical inference involves drawing conclusions, making predictions, and testing hypotheses about population parameters based on sample data. These techniques include methods such as estimation, hypothesis testing, confidence intervals, and regression analysis.

By using statistical inference, we can generalize findings from the sample to make inferences about the larger population, allowing us to make informed decisions and draw meaningful conclusions based on the available data.

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Answer:

HARAMBE KNOWS THE ANSWER!!!!!!!!!!!!!!1111Write an essay of at least 250 words that summarizes the main points of the essay by Langston Hughes. Use the information you gathered from your literary analysis to help with your summary. Be sure to create an outline and structure your essay with a thesis statement and supporting details..

Step-by-step explanation:

Answer:

Step-by-step explanation:

The recursive formula for a geometric sequence is a formula that relates each term to the preceding term(s). In a geometric sequence with a common ratio of r, the recursive formula is typically of the form: an = r * an-1.

Let's analyze the given options:

A. an = 38-1/2: This is not a valid recursive formula for a geometric sequence as it does not involve a common ratio.

B. an = 3 * 233-1/3: This is not a valid recursive formula for a geometric sequence as it does not follow the format an = r * an-1.

C. an = 23-1: This is not a valid recursive formula for a geometric sequence as it does not involve a common ratio.

D. an = 8/11 * an-1: This is a valid recursive formula for a geometric sequence as it follows the format an = r * an-1, where the common ratio is 8/11.

Based on the analysis, the recursive formula that applies to the given geometric sequence is:

D. an = 8/11 * an-1.

Note: The options "39," "2'4'1," "3 = 233-1/3," and "2/3" are not valid recursive formulas for a geometric sequence.

Answer:

Pl

Step-by-step explanation:

Please where is the equating

Answer:

(B)\(2^1\)

Step-by-step explanation:

We are to simplify the given expression: \(\dfrac{2^2 \cdot 2^3}{2^4}\)

Step 1: Apply the addition law of indices to simplify the numerator.

\(\text{Addition Law: }a^x \cdot a^y=a^{x+y}\)

Therefore:

\(\dfrac{2^2 \cdot 2^3}{2^4} \\\\=\dfrac{2^{2+3}}{2^4}\\\\=\dfrac{2^5}{2^4}\)

Step 2: Apply the Subtraction law of indices to simplify the expression

\(\text{Subtraction Law: }a^x \div a^y=a^{x-y}\\\\\implies \dfrac{2^5}{2^4} =2^{5-4}\\\\=2^1\)

The correct option is B.

Answer:

about +–1%; between 46.5% and 47.5%

Step-by-step explanation:

The roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

The equation is given as:

x^2 + (1 - k).x+k-3 = 0

For an equation to have real root, then the following must be true:

\(b^2 \ge 4ac\)

In x^2 + (1 - k).x+k-3 = 0, we have:

a = 1

b = 1 - k

c = k - 3

So, we have:

\((1 - k)^2 \ge 4 * 1 * (k - 3)\)

Evaluate

\(1 - 2k + k^2 \ge 4k - 12\)

Collect like terms

\(k^2 - 2k - 4k + 1 + 12 \ge 0\)

\(k^2 - 6k + 13 \ge 0\)

Using a graphing calculator, the value of k is all real numbers

Hence, the roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k

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Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Step-by-step explanation:

To solve this problem, we need to find the scale factor that will allow us to enlarge the 12" x 9" painting to fit the 24' x 16' wall.

First, we need to convert all the units to the same system. Let's convert the painting size to feet:

12 inches = 1 foot (since there are 12 inches in a foot)

9 inches = 0.75 feet (since 9/12 = 0.75)

So the size of the painting in feet is 1 foot by 0.75 feet.

Next, we can find the scale factor by dividing the size of the wall by the size of the painting:

Scale factor = (24 feet) / (1 foot) = 24

Scale factor = (16 feet) / (0.75 feet) = 21.33 (rounded to two decimal places)

We use the smaller of the two scale factors, which is 21.33, to ensure that the painting will fit within the dimensions of the wall.

Finally, we can find the size of the enlarged painting by multiplying the original size by the scale factor:

Width of enlarged painting = 1 foot x 21.33 = 21.33 feet

Height of enlarged painting = 0.75 feet x 21.33 = 15.99 feet

Therefore, the largest possible complete design that can be painted on the 24' x 16' wall is approximately 21.33 feet by 15.99 feet, using a scale factor of 21.33.

Answer:

the largest possible complete design that can be painted on the 24' x 16' wall is 21' x 15.75'

Step-by-step explanation:

Here, the double prime (double commas) ('') mean inches and the single prime(single comma) (') means foot.

So, the painting is (12" )(9") so it is 12 inches by 9 inches.

While the wall is (24')(16') so it is 24 feet by 16 feet.

We have to find the largest possible complete design that can be painted on the wall

Now, since 12 inches = 1 foot

And for the design to be complete, the design must fit on the wall

now, for every 12 inches we add to the height (the first part i.e 24)

We add 9 inches to the width (the 2nd part i.e. 16)

starting from one side,

we have,

(12 inch)(9 inch) = (1 feet)(9/12 feet)

(12 inch)x(9 inch) = (1 feet)x(3/4 feet)  (i)

where we get the 2nd term, 9/12 as follows,

Since,

\(12 \ inches = 1 foot\\so, \\1 \ inch = (1/12) feet\\and,\\9 \ inches = 9/12 \ feet\)

Now, 9/12 = 3/4

so, 9 inches = 3/4 feet

We have obtained the required ratio, we just now check how far this ratio can go until we exceed the limit of the wall, 24 feet by 16 feet,

so, for example,

Now, this means that when we increase the height by 12 inches = 1 foot,

we also have to increase the width by 3/4 feet = 9 inches

so, if we muliiply the height by 2, we also multiply the width by 2 to get,

(24 inch)x(18 inch) = (2 ft) x (3/2 ft)

now, (2 ft) x (3/2 ft) is smaller than (24 ft) x (16 ft),

Similarly, If we multiply the height by 24, we also have to multiply the width by 24, in which case we get,

24 ft by 24(3/4)ft

(24 ft) x (18 ft) which is greater than the allowed, (24 ft) x (16 ft) (i.e. 18 > 16)so this design cannot fit on the wall

(24 ft) x (18 ft) cannot be painted on the wall since the wall is smaller,

Trying 23, we get,

(23 ft) x (23(3/4) ft) = (23 ft) x (17.25 ft) which is still greater

so we try 22,

(22 ft) x (22(3/4) ft) = (22 ft) x (16.5 ft) which is Still greater

We try 21 to get,

(21 ft) x (21(3/4) ft) = (22 ft) x (15.75 ft) Which is smaller than the wall

So, the largest possible complete design that can be painted on a 24' x 16' wall is 22' x 15.75'

Doing this in another way,

1 inch = 1/12 feet

9 inches = 3/4 feet

We have to find the greatest possible ratio between the height and width of the painting that can be fitted on the wall,

the ratio is height/width = 12 inches/9 inches = 1 ft/(3/4 ft)

and this has to be the greatest ratio less than 24 ft/(16 ft)

If we multiply and divide the ratio by 21, we get,

\(21 \ ft/((21)(3/4\ ft))\)

which gives,

21 ft/ 15.75 ft

or in the other form, the painting is 21' x 15.75' < 24' x 16' (both 21' < 24' and 15,75' < 16')

But if we multiply by 22,

we get

22 ft /(22)(3/4) ft  

in the other form, the ratio is 22' x 16.5'

but since 16.5' is greater than 16',

the 22' x 16.5' design cannot be painted on the wall ( the wall has too little width 16' instead of 16.5')

So, the largest possible complete design that can be painted on the 24' x 16' wall is 21' x 15.75'

Answer:

Hi there.....

Step-by-step explanation:

This is ur answer......

1, 3, 5, 7, 9, 11, 13, 15.................39

Therefore the total sum = 400

hope it helps you,

mark me as the brainliest....

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Answer:

400

Step-by-step explanation:

These are the first 20 odd numbers

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39

Put them in a calculator and you get: 400

The function is decreasing.

The domain is the set of x-values.

The range is the set of y-values.

Step-by-step explanation:

The spherical and Cartesian coordinates are related by the equations,

x = ρ sin(φ) cos(θ)

y = ρ sin(φ) sin(θ)

z = ρ cos(φ)

Here, x, y and z represent the coordinates of the center of the sphere on x, y and z axes respectively.

Now, multiply the given surface equation by ρ.

ρ² = ρsin(θ) sin(φ)

We have, ρ² = x² + y² + z².

Substitute this value in above equation and also replace the RHS by y coordinate.

x² + y² + z² = y

Now, simplify the above equation.

x² + y² - y + z² = 0

x² + y² - 2y½ + (1/2)² + z² = (1/2)²

x² + (y - 1/2)² + z² = (1/2)² ...(1)

The general form of equation of sphere is,

(x - a)² + (y - b)² + (z - c)² = r²

Here, a, b, c are the coordinates of the center of the sphere on x, y, z axes respectively and r is the radius of the sphere.

Compare equation (1) with the general form of equation of sphere. Therefore we get,

Therefore, the radius of the sphere is 1/2 and center of sphere is at (0, 1/2, 0).

Thus, The given equation represents - a sphere of radius 1/2 centers at (0, 1/2, 0).

Answer:

x=3,y= -4

Step-by-step explanation:

ii) x-2y=11

x=11+2y-----(i)

Now,

i) -7x-2y= -13

or, -7(11+2y)-2y= -13

or, -77-14y-2y = -13

or -14y-2y = -13+77

or -16y = 64

or y =64÷(-16)

:: y = -4

Again,

(ii) x-2y= 11

or x-2(-4)= 11

or x+8 = 11

or x = 11-8

:: x = 3

Ok, here are the steps to determine how many points should be below the trend line:

1) There are 4 points above the trend line.

2) If the points are distributed randomly and evenly on both sides of the trend line, then there should be approximately the same number of points above and below the line.

3) Since there are 4 points above the line, there should be around 4 points below the line as well.

Therefore, the answer is that about 4 points should be below the trend line.

The probability that at least two ladies choose the same type of overcoat is approximately 0.8869, or 88.69%.

To find the probability that at least two ladies choose the same type of overcoat, we can use the concept of complementary probability. We'll calculate the probability that all ladies choose different types of overcoats and then subtract it from 1.

The first lady can choose any of the 14 different styles of overcoats, so the probability of her selecting a unique style is 14/14 = 1.

For the second lady, there are now 13 remaining styles out of 14 to choose from. The probability of her selecting a unique style is 13/14.

Similarly, for the third lady, there are 12 remaining styles out of 14 to choose from. The probability of her selecting a unique style is 12/14.

We continue this process until the eighth lady makes her selection. The probability of her selecting a unique style is 7/14.

To find the probability that all ladies choose different types of overcoats, we multiply the individual probabilities together:

P(all unique) = (1 * 13/14 * 12/14 * 11/14 * 10/14 * 9/14 * 8/14 * 7/14)

Now, to find the probability that at least two ladies choose the same type of overcoat, we subtract the probability of all unique selections from 1:

P(at least two choose the same) = 1 - P(all unique)

P(at least two choose the same) = 1 - (1 * 13/14 * 12/14 * 11/14 * 10/14 * 9/14 * 8/14 * 7/14)

P(at least two choose the same) ≈ 1 - 0.1131

P(at least two choose the same) ≈ 0.8869

Therefore, the probability that at least two ladies choose the same type of overcoat is approximately 0.8869, or 88.69%.

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Answer:

800

Step-by-step explanation:

28/100 =224/x

28x/28 = 22400/28