Anyone who speaks Spanish know how to do this????

The equation of the line given, would be able to graph the function by the given points :

You can graph a linear equation by coming up with values of x and then using the function to solve for a value of y. You can then graph these points on a graph.

The equation, y = 3 / 4 x + 2 means that the y - intercept is 2. This means that one point is ( 0, 2) as x = 0 at the y - intercept.

Pick the value of x = 1:

= 3 / 4 x 1 + 2

= 2. 75

Point = (1, 2.75)

x = 2 :

= 3 / 4 x 2 + 2

= 3. 5

Point = ( 2, 3.5 ).

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The transformations that move figure A onto figure B and then onto figure C is B. Reflection, translation.

Shape transformation is a type of geometric transformation that involves changing the shape of an object. It is a type of transformation that changes the size, orientation, and position of the object while preserving its overall structure. Some examples of shape transformations include scaling, rotation, reflection, shearing, and dilation.

Shape transformation is used in a variety of applications, including computer graphics, image processing, and computer-aided design (CAD). By applying shape transformations, it is possible to modify the appearance of an object or image, to correct distortions or errors, or to generate new versions of the original object or image.

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Image transcribed and completed:

These figures are congruent. Identify the transformations that move figure A onto figure B and then onto figure C.

A. Translation, translation

B. Reflection, translation

C. Rotation, translation

D. Reflection, reflection

The slope of the line passing through the points A(1,0) and B(3,11) is 5.5 as a decimal.

The slope of a line is a measure of how steep the line is and describes the rate at which the line is rising or falling.

It is defined as the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between two points on the line.

The formula for slope is:

slope = (changes in y)/(change in x).

It is typically denoted by the letter "m".

The slope of the line passing through points A(1,0) and B(3,11) is:

Rise / Run = (Y-Coordinate Change) / (X-Coordinate Change).

= (11-0) / (3-1)

= 11/2

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The rectangular (standard) form of the complex number is simply 4.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of trigonometric functions, which are functions that relate the angles of a triangle to the ratios of the lengths of its sides.

The rectangular (standard) form of a complex number is typically written as a + bi, where a and b are real numbers, and i is the imaginary unit (√-1). However, in the case of the given complex number 4(cos 0° + i sin 0°), it can be simplified to 4(1 + 0i), since cosine and sine of 0° are equal to 1 and 0 respectively.

The complex number 4(cos 0° + i sin 0°) can be simplified as:

4(cos 0° + i sin 0°) = 4(1 + 0i)

= 4

Therefore, the rectangular (standard) form of the complex number is simply 4.

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Answer:

  (c)  $461

Step-by-step explanation:

You want the balance in an account in which $450 is earning 2.5% interest compounded daily for one year.

The formula for the account balance is ...

  A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r for t years, compounded n times per year.

The attachment shows the evaluation of this formula with the given numbers put in.

Carl will have $461 in a year.

Pairs of samples in which the selection of people or objects into one sample directly affects or is affected by the selection of people or objects into the other sample are referred to as dependent samples. The correct option is B) dependent samples.

Dependent samples are those where the selection of people or objects in one sample is related to the selection in another sample. For example, a study comparing pre- and post-intervention results of the same group of individuals would have dependent samples.

In statistical analysis, dependent samples require different methods than independent samples, as the relatedness between the samples needs to be taken into account. Understanding the nature of the relationship between the samples is important for drawing accurate conclusions from the data. The correct answers is B).

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Answer:

m=5

b=12

Step-by-step explanation:

the slope is the number before x and y intercept is the integer without variables

Applying the formula for volume of cylinder, we have:

3. a. 14.3 cm.      b. 2.5 cm        c. 88.0 cm

4. a. 2.3 cm.       b. 8.1 cm         c. 1.7 cm.

Question 3. a. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. Rearranging this formula, we get h = V/(πr²).

Substituting the given values, we get:

h = 1600/(π × 6²) ≈ 14.3 cm

Therefore, the height of the cylinder is approximately 14.3 cm.

b. Using the same formula and substituting the given values, we get:

h = 800/(π × 9²) ≈ 2.5 cm

Therefore, the height of the cylinder is approximately 2.5 cm.

c. Since the given values are in meters, we first need to convert the volume to cubic centimeters and the radius to centimeters. 1 m = 100 cm, so 0.2 m = 20 cm. Similarly, 1 m³ = 1,000,000 cm³, so 0.11 m³ = 110,000 cm³.

Using the same formula and substituting the given values, we get:

h = 110,000/(π × 20²) ≈ 88.0 cm

Therefore, the height of the cylinder is approximately 88.0 cm.

Question 4: a. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. Rearranging this formula, we get r = √(V/(πh)).

Substituting the given values, we get:

r = √(725/(π × 20)) ≈ 2.3 cm

Therefore, the radius of the cylinder is approximately 2.3 cm.

b. Using the same formula and substituting the given values, we get:

r = √(9000/(π × 12)) ≈ 8.1 cm

Therefore, the radius of the cylinder is approximately 8.1 cm.

c. Using the same formula and substituting the given values, we get:

r = √(170/(π × 9)) ≈ 1.7 cm

Therefore, the radius of the cylinder is approximately 1.7 cm.

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Equation in cylindrical coordinates: 9ρ * cos(φ) + 6ρ * sin(φ) = 4z

I'd be happy to help you convert the given equation into cylindrical coordinates. The equation you provided is 9x + 6y + z = 5z. First, let's simplify the equation:

9x + 6y + z = 5z
9x + 6y = 4z

Now, let's recall the relationships between Cartesian coordinates (x, y, z) and cylindrical coordinates (ρ, φ, z):

x = ρ * cos(φ)
y = ρ * sin(φ)
z = z

Now, substitute these relationships into the simplified equation:

9(ρ * cos(φ)) + 6(ρ * sin(φ)) = 4z

This is the equation in cylindrical coordinates: 9ρ * cos(φ) + 6ρ * sin(φ) = 4z

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The shortest distance from the point (2,1,1) to the plane x+y-z = 1 is √3/3.

To find the shortest distance from a point to a plane, we can use the formula d = |ax + by + cz + d|/√(a² + b² + c²), where (x, y, z) is any point on the plane and a, b, c, and d are constants obtained from the equation of the plane.

In this case, the equation of the plane is x + y - z = 1. We can rewrite this equation as z = x + y - 1, which means a = 1, b = 1, c = -1, and d = -1.

Now, we can plug in the values for the point (2,1,1) and the constants a, b, c, and d into the formula for distance:

d = |1(2) + 1(1) - 1(1) - 1|/√(1² + 1² + (-1)²)

d = √3/3

Therefore, the shortest distance is √3/3.

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We avoid counting the same set of r items multiple times, which is why the formula p(n,r) = p(r,r) * c(n,r) holds.

To understand why p(n,r) = p(r,r) * c(n,r) intuitively, we need to think about the problem of choosing r items from a set of n items. We can start by choosing r items from the set of n items, which gives us p(n,r) possibilities.

Alternatively, we can first choose r items from the set of n items and then choose r items from this smaller set of r items. The number of ways to do this is p(r,r) * c(n,r).

Intuitively, we can think of this as breaking down the problem into two steps: first choosing r items and then choosing r items from that smaller set. By doing this, we avoid counting the same set of r items multiple times, which is why the formula p(n,r) = p(r,r) * c(n,r) holds.

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Answer:

Step-by-step explanation:

For the equation 16x³ + 16x² + 3x = 0, we can factor out x:

x(16x² + 16x + 3) = 0

Using the quadratic formula, we can solve for the roots of 16x² + 16x + 3:

x = (-16 ± √(16² - 4(16)(3))) / (2(16))

x = (-16 ± √160) / 32

x = (-1 ± √10) / 4

So the solutions to the equation are x = 0 and x = (-1 ± √10) / 4.

For the equation 4x^2 - 9 = 0:

We can first add 9 to both sides:

4x^2 = 9

Then divide both sides by 4:

x^2 = 9/4

Finally, take the square root of both

Answer:

B

Step-by-step explanation:

The angle opposite of y would have the same value.  That would make that angle 110.  That angle and the x would make a straight line.  The measurement of a straight line is 180.  180 - 110 = 70. Angle x would be 70.

Helping in the name of Jesus.

Answer:

B) 70⁰

Step-by-step explanation:

Opposite angles of a paralellogram are equal, so the inside angle of the paralellogram is also 110⁰. x+110 must add up to 180⁰, so x=70⁰.

Hope this helps!

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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The general solution of the given higher-order differential equation y''' − 3y'' − 4y' = 0 is y(x) = c₁ + c₂ e^(4x) + c₃ e^(-x)

To find the general solution of the given differential equation, we start by assuming a solution of the form y(x) = e^(rx), where r is a constant.

Substituting this into the differential equation, we get:

r^3 e^(rx) - 3r^2 e^(rx) - 4r e^(rx) = 0

Factoring out e^(rx), we get:

r^3 - 3r^2 - 4r = 0

Simplifying by factoring out an r, we have:

r(r^2 - 3r - 4) = 0

The roots of this equation are r = 0, r = 4, and r = -1.

Therefore, the general solution is a linear combination of the three solutions:

y(x) = c₁ e^(0x) + c₂ e^(4x) + c₃ e^(-x)

Simplifying, we get:

y(x) = c₁ + c₂ e^(4x) + c₃ e^(-x)

Where c₁, c₂, and c₃ are arbitrary constants determined by any initial or boundary conditions given in the problem.

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Complete question is:

Find the general solution of the given higher-order differential equation.

y''' − 3y'' − 4y' = 0

y(x) =

The area of the sector bounded by a 144° arc in a circle with a radius of 5 meters is 10π square meters.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.

The area of a sector can be calculated using the formula:

Area of sector = (θ/360) x πr²

where θ is the angle of the sector and r is the radius of the circle.

In this case, θ = 144° and r = 5 m, so:

Area of sector = (144/360) x π(5)²

= (2/5) x π(25)

= 10π

Therefore, the area of the sector bounded by a 144° arc in a circle with a radius of 5 meters is 10π square meters.

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Contingency tables are used for summarizing data at the Nominal and Ordinal levels.

In a contingency table, the joint events are mutually exclusive because they consist of unique combinations of individual events that are mutually exclusive. For an individual to be described by one of the joint events, the individual must be described using each of the two attributes measured in the table. Since the possibilities for each of the two attribute are mutually exclusive, there can be only one way for an individual to be labeled with each pair of attributes. Therefore there can only be one joint event in the table that describes the individual.

Nominal and ordinal levels of measurement are two types of categorical data in statistics.

Nominal data is the lowest level of measurement and refers to data that can be placed into categories but cannot be ordered. For example, colors, gender, and yes or no responses are all examples of nominal data.

Ordinal data, on the other hand, refers to data that can be placed into categories and can also be ordered. For example, letter grades (A, B, C, etc.), socioeconomic status (low, medium, high), and levels of education (elementary, high school, college) are all examples of ordinal data.

It's important to note that while ordinal data can be ordered, the distance between categories is not necessarily equal. For example, the difference between an A and a B grade may not be the same as the difference between a B and a C grade.

Understanding the level of measurement is important when choosing statistical analyses, as different tests are appropriate for different levels of measurement.

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The expression is evaluated as 12

Algebraic expressions are defined as expressions that are composed of terms, variables, constants, coefficients and factors.

Algebraic expressions are also composed of arithmetic operations, such as;

From the information given, we have that;

y²+4y-2

To determine the expression for y = 7

Substitute the value

(7)² - 4(7) - 2

expand the bracket and find the square

49 - 35 - 2

subtract the values

12

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According to the recursive definition for the length of a string, the length |001| is 3. The term "recursive" refers to a process that defines something in terms of itself, "length" refers to the number of characters in the string, and "string" is a sequence of characters. In this case, the string "001" has three characters (0, 0, and 1), so its length is 3.

According to the recursive definition for the length of a string, |001| is 3. The length of a string is defined as 0 if the string is empty, and 1 plus the length of the string without its first character if the string is not empty. In this case, the string "001" is not empty, so its length is 1 plus the length of the string "01" without its first character. Since the string "01" is also not empty, its length is 1 plus the length of the string "1" without its first character. Finally, the string "1" is a single character and has a length of 1, so the total length of "001" is 1 + 1 + 1 = 3.
Recursion is the process of calling itself. This process provides a way to break complex problems into simpler processes that are easier to solve. Recursion can be a bit confusing. The best way to determine how it works is to experiment with it.

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The solution to the 1-dimensional heat equation problem with the given initial and boundary conditions is [tex]u(x, t) = \sum_{n=1}^\infty \frac{(-1)^n}{n\pi} \sin\left(\frac{n\pi x}{5}\right) e^{-(n\pi)^2 \frac{2t}{25}}[/tex].

We are given the one-dimensional heat equation:

[tex]\frac{\partial u}{\partial t} = 2 \frac{\partial^2 u}{\partial x^2}[/tex]

We need to find the solution u(x, t) subject to the initial condition u(x, 0) = f(x) and boundary conditions u(0, t) = u(5, t) = 0 for t > 0.

To solve this problem, we use separation of variables:

u(x, t) = X(x)T(t)

Substituting this into the heat equation and dividing by u(x, t), we obtain:

[tex]\frac{1}{T(t)}\frac{dT}{dt} = \frac{2}{X(x)}\frac{d^2X}{dx^2}[/tex]

Both sides are equal to a constant, which we denote by -λ². We then obtain two ordinary differential equations:

[tex]\frac{d^2X}{dx^2} + \lambda^2X = 0[/tex]

[tex]\frac{1}{T} \frac{dT}{dt} = -\frac{\lambda^2}{2}[/tex]

The general solution to the first equation is:

[tex]X(x) = A \sin\left(\frac{\pi x}{L}\right) + B \cos\left(\frac{\pi x}{L}\right)[/tex]

where L = 5 is the length of the interval and A, B are constants determined by the boundary conditions.

The second equation has the solution:

[tex]T(t) = Ce^{-\lambda^2t/2}[/tex]

where C is a constant determined by the initial condition.

The general solution to the heat equation is then:

[tex]u(x,t)=\sum\limits_{n=1}^{\infty}\left(A_n\sin\left(\frac{n\pi x}{5}\right) + B_n\cos\left(\frac{n\pi x}{5}\right)\right)e^{-\frac{n^2\pi^2t}{5^2}}[/tex]

where the sum is taken over all positive integers n.

Using the initial condition, we can determine the coefficients A_n and B_n as:

A_n = [tex](-1)^n \frac{(4n\pi\sin(n\pi) - 3\sin(2n\pi))}{n^3\pi^3}[/tex]

B_n = 0

Therefore, the solution to the given problem is:

[tex]u(x, t) = \sum_{n=1}^\infty \frac{(-1)^n}{n\pi} \sin\left(\frac{n\pi x}{5}\right) e^{-(n\pi)^2 \frac{2t}{25}}[/tex]

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To obtain an orthonormal basis, we normalize each vector of B' to obtain:

e1 = (0,1/√2,1/√2)

e2 = (1/√2,-1/√6,1/√6)

e3

(a) Let B = {(1,-1), (2, 1)} be a basis of R². To obtain an orthogonal basis B' of R² using the Gram-Schmidt process, we first normalize the first vector of B to obtain:

v1' = (1/√2)(1,-1) = (cos(π/4), -sin(π/4))

Then, we subtract the projection of the second vector onto v1' from v2 to obtain an orthogonal vector v2':

v2' = (2,1) - proj_v1'(2,1) = (2,1) - ((2+1)/2)(cos(π/4),-sin(π/4)) = (1/√2)(3,1)

Thus, an orthogonal basis of R² is B' = {(cos(π/4), -sin(π/4)), (1/√2)(3,1)}. To obtain an orthonormal basis, we normalize each vector of B' to obtain:

e1 = (1/√2)(cos(π/4), -sin(π/4)) = (cos(π/4)/√2, -sin(π/4)/√2)

e2 = (1/√10)(3,1)

Therefore, an orthonormal basis of R² with respect to B is {e1, e2}.

(b) Let B = {(0, 1, 1), (1, 1, 1), (1, −2, 2)} be a basis of R³. To obtain an orthogonal basis B' of R³ using the Gram-Schmidt process, we first normalize the first vector of B to obtain:

v1' = (0,1/√2,1/√2)

Then, we subtract the projection of the second vector onto v1' from v2 to obtain an orthogonal vector v2':

v2' = (1,1,1) - proj_v1'(1,1,1) = (1,1,1) - ((0+1/√2+1/√2)/2)(0,1/√2,1/√2) = (1,-1/√2,1/√2)

Finally, we subtract the projections of the third vector onto v1' and v2' from v3 to obtain an orthogonal vector v3':

v3' = (1,-2,2) - proj_v1'(1,-2,2) - proj_v2'(1,-2,2) = (1,-2,2) - ((0-2/√2+2/√2)/2)(0,1/√2,1/√2) - ((1-1/√2+1/√2)/3)(1,-1/√2,1/√2) = (1/√6,-1/√6,2/√6)

Thus, an orthogonal basis of R³ is B' = {(0,1/√2,1/√2), (1,-1/√2,1/√2), (1/√6,-1/√6,2/√6)}. To obtain an orthonormal basis, we normalize each vector of B' to obtain:

e1 = (0,1/√2,1/√2)

e2 = (1/√2,-1/√6,1/√6)

e3

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Slope = -11

Y-intercept = (0, 199)

What is a linear function?

A function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.

Here, we have

Given: A man has a starting weight of 199 pounds and is losing 11 pounds each month. Model his weight with a linear function.

Linear function: y = mx+b

m = a number of months and W = man's weight.

Man's starting weight = 199 pounds.

w = -m(11) + b = 199

w = -0(11) + b = 199

b = 199

w = -11m + 199

Slope = -11

Y-intercept = (0, 199)

Hence, Slope = -11

Y-intercept = (0, 199)

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In the given set option (1) This triangle is not a right triangle.(2) This triangle is a right triangle.

A right triangle is a three sided figure with one angle equal to 90 degrees. A 90 degree angle is called a right angle and that is where the right triangle gets its name.

To determine whether a set of side lengths forms a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (also known as the hypotenuse).

(1) In this case, the given side lengths are 10m, 11m, and 15m. Let's check if they satisfy the Pythagorean theorem:

10² + 11² = 100 + 121 = 221

15²= 225

Since 221 is not equal to 225, the side lengths of 10m, 11m, and 15m do not form a right triangle. Therefore, we can conclude that this triangle is not a right triangle.

To determine whether a set of side lengths forms a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (also known as the hypotenuse).

(2) In this case, the given side lengths are 15m, 8m, and 17m. Let's check if they satisfy the Pythagorean theorem:

15² + 8² = 225 + 64 = 289

17² = 289

Since both sides of the equation are equal, we can conclude that the given side lengths form a right triangle. Therefore, we can say that this triangle is a right triangle.

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Answer:

Step-by-step explanation:

15m 8m 17m is right triangle

10m, 11m, 15m is not a right triangle

In a case whereby there are 5,000 books in the​ town's library. Of​ these, 4,300 are fiction the percent of books that are fiction is 86% and the equation is 4300=(m×5000)

We can represent the percent of the books that are​ fiction  as ( m)

we have the total of 5,000 books

thefrictional book = 4,300

Then m= (4300/5000)

4300=(m×5000)

Percentage =(4300/5000 ×100)

= 86%

Then the expression that fit in is  4300=m×5000 which is the option B is

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missing options:

A. 4,300 = m / 5,000

B. 4,300 = m x 5,000

C. 5,000 = m / 4,300

D. 5,000 = m x 4,300

The catcher has to throw a ball to get out a runner trying to steal second base about 127.3 ft away.

Given is a figure of baseball field, we are asked to find the distance between home plate and second base,

Since, the field is a square so all the sides will be equal,

So, using the Pythagorean theorem,

The distance between home plate and second base = √90²+90²

= √8100+8100

= √16200

= 127.3

Hence the catcher has to throw a ball to get out a runner trying to steal second base about 127.3 ft away.

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Answer:

Step-by-step explanation:

0.65 * 10 * 10 * 10 * 10 * 10

You know how to multiply a number by 10^3, so all that's left is to multiply another 10^2

650 * 10 * 10 = 6500 * 10 = 65000

Juan can buy 3 roses and 9 carnations for a total cost of $18, which meets his conditions.

Let x be the number of roses Juan buys and y be the number of carnations he buys.

From the problem statement, we know that:

y = 3x (Juan wants to buy 3 times as many carnations as roses)

3x + 1.5y = 6x (Juan wants to spend all his money on flowers)

Substituting y = 3x into the second equation gives:

3x + 1.5(3x) = 6x

Simplifying this equation gives:

6x = 6x

This equation is true for all values of x, which means there are infinitely many solutions. However, we need to check if there is a viable solution that meets Juan's conditions.

Since Juan wants to spend all his money, we know that the total cost of the flowers must be $18. So we have:

3x + 1.5y = 18

Substituting y = 3x into this equation gives:

3x + 1.5(3x) = 18

Simplifying this equation gives:

6x = 18

x = 3

So Juan can buy 3 roses and 9 carnations for a total cost of $18, which meets his conditions.

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Answer:

It would take 45 minutes to read 27 pages.

Answer: 45

Step-by-step explanation: First, divide twenty by twelve to find out how long it takes to read one page, which I got was 1.66666666666666. Yes, know that is long, but once you multiply that by 27, you would get exactly 45.

Answer:

Step-by-step explanation:

A) The Binomial Theorem states that for any positive integer n, the expansion of (1 + x)^n can be expressed as:

(1 + x)^n = C(n, 0) * 1^n * x^0 + C(n, 1) * 1^(n-1) * x^1 + C(n, 2) * 1^(n-2) * x^2 + ... + C(n, n-1) * 1^1 * x^(n-1) + C(n, n) * 1^0 * x^n

where C(n, k) represents the binomial coefficient, defined as C(n, k) = n! / (k! * (n - k)!), and "!" denotes the factorial operation.

Using the above formula, we can find the first four terms of the polynomial (1 + x)^n:

Term 1: C(n, 0) * 1^n * x^0 = 1 * 1 * 1 = 1

Term 2: C(n, 1) * 1^(n-1) * x^1 = n * x

Term 3: C(n, 2) * 1^(n-2) * x^2 = n * (n - 1) / 2 * x^2

Term 4: C(n, 3) * 1^(n-3) * x^3 = n * (n - 1) * (n - 2) / 6 * x^3

So the first four terms of the polynomial (1 + x)^n are: 1, n * x, n * (n - 1) / 2 * x^2, and n * (n - 1) * (n - 2) / 6 * x^3.

B) When x is less than 1, x^n becomes a smaller and smaller fraction as n increases. This is because each subsequent term in the expansion (1 + x)^n is multiplied by x, making it smaller compared to the previous term. Therefore, as n gets larger, x^n approaches 0 rapidly. In this case, the approximation of (1 + x)^n by 1 + nx becomes more accurate because the higher-order terms involving x^2, x^3, and so on, become negligible. Thus, 1 + nx becomes a good approximation of (1 + x)^n for small values of x. This is known as a linear approximation or a first-order approximation.