In the above scenario, it can be estimated with 95% confidence that the true proportion of young adult novels that include a love triangle are between 0.6854 and 0.8890
How is this so?First we compute the Point Estimate
PE = 59/75 = 0.7867
Next we compute the standard error
SE = √((- - hat x (1 - p- hat) )/n)
= √( (o.7867 x (1 - 0.7867 ))/ 75
= 0. 509
Since the expected confidence level is 95%,
Margin of error = t - critical x S E
= 1.99 x 0.0509
= 0.101291
Thus,
point estimate ± margin of error
0.7867 ± 0.1013
(0.6854, 0.8880)
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Are the ratios 6:7 and 1:2 equivalent?
Answer:
No
Step-by-step explanation:
If you divide 6 by 7, it is not equal to the number you get when you divide 1 by 2, therfore making them not equavalent.
~~~Harsha~~~
Answer:
No, the are not equivalent
Step-by-step explanation:
The ratios 6:7 & 1:2 are already in their simplest form, meaning we can't simple them anymore.
6:7 ≠ 1:2
Plot and connect the points A (6, -7), B (1, -7), C (1, -4), D (3, -2), E (7. -2), F (7,-4), and find the length of AB.
OA. 6 units
O B.
7 units
O C.
5 units
D. 8 units
Using distance formula, the distance between AB is 5 units and the graph of the coordinates from A to F are attached below
What is the length of ABTo find the length of AB, we have to use distance formula which is given as
AB = √(x₂ - x₁)² + (y₂ - y₁)²
substituting the values into the equation;
AB = √(1 - 6)² + (-7 - (-7))²
AB = 5
The length of line AB is 5 units
To plot the points from A to F, we have to use a graphing calculator, input the points and draw all lines
Kindly find the attached graph of all the coordinates from A to F below
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units Answer:
5
Step-by-step explanation:
The vertices of a figure are given. Rotate the figure as described. Find the coordinates of the image.
E(−4, 1), F(−3, 3), G(−2, 3), H(−1, 1)
180°
about the origin
If f(1)=4 and f(n)=-3f(n-1) , then find the value of f(6).
the value of f(6) is -972.To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:
4, -12, 36, -108, 324, -972, ...
How to solve the question?
We can use the recursive formula given to find the value of f(6). Let's start by calculating f(2):
f(2) = -3f(1) = -3(4) = -12
Next, we can calculate f(3) using the same formula:
f(3) = -3f(2) = -3(-12) = 36
We can continue this process for f(4) and f(5):
f(4) = -3f(3) = -3(36) = -108
f(5) = -3f(4) = -3(-108) = 324
Finally, we can use the formula to find f(6):
f(6) = -3f(5) = -3(324) = -972
Therefore, the value of f(6) is -972.
To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:
4, -12, 36, -108, 324, -972, ...
Each term in the sequence is obtained by multiplying the previous term by -3. We can see that the sequence alternates between positive and negative values, with the magnitude of each term growing rapidly. By the time we reach f(6), the magnitude has grown to 972, and the negative sign indicates that the term is negative. Thus, f(6) is equal to -972.
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The standard form of the equation of a circle is (x−5)2+(y−6)2=1.
What is the general form of the equation?
Responses
x2+y2+10x+12y+62=0
x squared plus y squared plus 10 x plus 12 y plus 62 equals 0
x2+y2−10x−12y+60=0
x squared plus y squared minus 10 x minus 12 y plus 60 equals 0
x2+y2−10x−12y−62=0
x squared plus y squared minus 10 x minus 12 y minus 62 equals 0
x2+y2+10x+12y+60=0
The general form of the equation is x² + y² - 10x - 12y + 60 = 0.
How find the general form of the equation of a circle?The general form of the equation of a circle is given by:
x² + y² + Cx + Dy + E = 0
Where C, D and E are constant
Given the standard form of the equation of a circle as (x−5)² + (y−6)² = 1, we can rewrite it as follow:
(x−5)² + (y−6)² = 1
(x² - 10x + 25) + (y² - 12y + 36) = 1 (Expand the brackets)
x² + y² - 10x - 12y + 25 + 36 - 1 = 0
x² + y² - 10x - 12y + 60 = 0
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what is 6.9cm *10000000m
The value of the product is 6.9 × 10⁵ m
How to determine the productIt is important to note that to determine the product of two different measurements, we need to make sure they have the same units.
Now, we have that;
6.9cm *10000000m
First, let's convert the centimeters to meters , we have;
1m = 100cm
then, xm = 6.9cm
cross multiply the values
x = 6.9/100
Divide the values
x = 6. 9 × 10⁻²m
Then, we have;
6. 9 × 10⁻² × 10⁷m
Multiply the values and add the exponents
6. 9 × 10⁻²⁺⁷
Add the values
6.9 × 10⁵ m
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The population of wild tigers in Nepal can be modeled by the equation LaTeX: p=130\left(2\right)^x
p
=
130
(
2
)
x
, where x is the number of years since 2009.
Part A
Assuming the population growth rate continues, an equation that represents the number of years from 2009 it will take for the population of wild tigers in Nepal to reach 1,000 can be expressed as LaTeX: x=\log_ba
x
=
log
a
b
, where a and b are >0. What are the values of a and b?
Part B
Approximately how many years from 2009 will it take for the population of wild tigers in Nepal to reach 1,000? Round your answer to the nearest whole number
Part A
According to the equation, the values of a is a = 2009 + f(a) and b is b = 800 + f(b).
Part B
Approximately it takes 8 years from 2009 for the population of wild tigers in Nepal to reach 800.
To find these values, we need to set the equation for the population of wild tigers equal to 800 and solve for x. The equation becomes 800 = 121(2)ˣ.
Taking the logarithm of both sides, we get
=> log(800) = log(121) + x log(2).
Solving for x, we get
=> x = (log(800) - log(121))/log(2).
Moving on to the second part of the problem, we are asked to determine approximately how many years from 2009 it will take for the population of wild tigers in Nepal to reach 800. Using the equation we derived in Part A, we can plug in values of a and use trial and error to find the answer. However, this can be time-consuming.
Instead, we can use a calculator to get an approximate answer. Plugging in the values for log(800) and log(121) into the equation we derived in Part A, we get x = 7.75.
Therefore, it will take approximately 8 years from 2009 for the population of wild tigers in Nepal to reach 800.
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Find an equation for the perpendicular bisector of the line segment whose endpoints
are(-1, , -8) and (5, 4).
An equation in slope-intercept form for the perpendicular bisector of the line segment with endpoints (-1, -8) and K (5, 4) is y = 2x - 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 + 8)/(5 + 1)
Slope (m) = 12/6
Slope (m) = 2.
At data point (-1, -8) and a slope of 2, 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 - (-8) = 2(x - (-1))
y + 8 = 2x + 2
y = 2x - 6.
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23=J+68/5 solve this problem I will give you about 11 points
Answer:
PEMDAS. Division first. 68/5 is 13.6. Subtract 13.6 from 23 and the answer is 9.4. Therefore J = 9.4
Step-by-step explanation:
What is the value of x when -3x + 7x = -12?
A -6/5
B -3
C 6/5
D 4/7
E 3
I NEED AN ANSWER ASAP!
A box measures 48 inches long, 22 1/2 inches wide, and 32 inches high. What is the volume of the box
The volume of the box should be 34,560 cubic inches.
v=l*w*h
v=48*22.5*32
(22 1/2 = 22.5)
v=34,560
graph the solution set of the inequality -6 1/2y+9>-17
The graph of the solution set can be seen in the image at the end.
How to find the solution set for the inequality?Here we have the inequality:
-(6 + 1/2)y + 9 > -17
First, we need to isolate the variable y, then we will get:
9 + 17 > (6 + 1/2)y
26 > 6.5y
26/6.5 > y
4 > y
The graph of this will be an open circle at y = 4, and an arrow that goes to the left, the graph can be seen in the image at the end.
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every day ben goes for a 5/6 mile walk and his little sister walk 3/6 mile walk after 11 days how much farther has ben walk than his sister ? between what two whole numbers does your answer lie
The response falls between 3 and 4, as a result of: 11/3 = 3.67 as Ben therefore travelled 3 to 4 miles further than his sister.
what is distance ?In geometry, the separation separating two points is determined by the length of the segment of a straight straight line linking them. In two- or two half space, this is referred to as the Euclidean distance. Distance is a crucial idea that is applied in numerous contexts in real life. For instance, distance is employed in transportation to gauge route length and determine trip times. Distance is a unit of measurement used in sports to indicate how far apart two things are or how long a race is. The measurement of distance to celestial objects is a common practise in many scientific disciplines, including astronomy.
given
Ben covers the following distance after walking 5/6 miles per day for 11 days:
11 days at 5/6 miles each day equal 55/6 miles.
Over the course of 11 days, his sister covered a total distance of:
11 days at 3/6 miles per day equal 33/6 miles.
We must take the distance between them out to determine how much farther Ben went than his sister:
22 miles from 55/6 miles to 33/6 miles.
By multiplying the numerator and denominator by 2, we may reduce the following fraction:
22/6 = 11/3
Ben therefore travelled 11.33 miles further than his sister.
The response falls between 3 and 4, as a result of: 11/3 = 3.67 as Ben therefore travelled 3 to 4 miles further than his sister.
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|4x-4(x+1)|=4
put all answers for x on number line
In the bottom, To see the number line of |4x-4(x+1)|=4.
Absolute Value:The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.
The expression is:
|4x-4(x+1)|=4
First simplify in the absolute value
Distribute
|4x−4x-4|=4
|-4|=4
Taking the absolute value
4 =4
This is always true
X is all real numbers
Pick any value for x and it will be a true statement
Put the value of x=0
|4*0−4(*0+1)|=4
|-4|=4
Let taking a value of x = 5
|4*5−4(5+1)|=4
|20−24|=4
|−4|=4
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write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)
Answer:
y = [tex]-\frac{19}{9} (x+3)^{2} + 5[/tex]
Step-by-step explanation:
The form of a quadratic function is y = a(x-h)^2 + k, where (h, k) is the vertex. From the givens in the problem, we know that (h, k) = (-3, 5), and another point on it will be (x, y) = (0, -14). Plug both of these into the equation to get:
-14 = a(3)^2 + 5
-19 = 9a
a = -19/9
∴ The equation is y = [tex]-\frac{19}{9} (x+3)^{2} + 5[/tex]
Write and solve the inequality.
six less than the product 1/4 of a number n and
is no more than 97.
The solution to the inequality is n ≤ 412.
What is inequality?An inequality is a statement that asserts that two values are not equal. An inequality can be represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
According to question:The inequality can be written as:
(1/4)n - 6 ≤ 97
To solve for n, we will isolate n on one side of the inequality. First, we can add 6 to both sides:
(1/4)n ≤ 103
Then, we can multiply both sides by 4:
n ≤ 412
Therefore, the solution to the inequality is:
n ≤ 412
This means that any number less than or equal to 412 satisfies the original inequality.
For example, "x > 5" is an inequality that states that the value of x is greater than 5. The inequality "y 10" indicates that the value of y is less than or equal to 10.
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If the area was equal to 8w solve to find the values of w.
A=2w^2 - 16w
Answer:
hence the value of w is 12
Step-by-step explanation:
[tex]area = 2 {w}^{2} - 16w \\ by \: the \: question \: if \: area \: is \: equal \: to \: 8w \\ 8w = 2w {}^{2} - 16w \\ 8w + 16w = 2 {w}^{2} \\ 24w = 2 w {}^{2} \\ w = 12[/tex]
Find the area of the shaded region for each composite figure. Round your answer to the nearest tenth, if necessary.
The area of the composite figure for this problem is given as follows:
A = 90 in².
How to obtain the area of the composite figure?The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.
The right triangle has a side length of 5 in and an hypotenuse of 13 units, hence the missing side is given as follows:
5² + x² = 13²
25 + x² = 169
x² = 144
x = 12.
Thus the entire base is of:
12 + 4 = 16 in.
Then the figure is composed as follows:
Rectangle of dimensions 3 in and 16 in.Right triangle of sides 12 in and 8 - 3 = 5 in.Rectangle of dimensions 4 in and 3 in.Hence the area is given as follows:
A = 3 x 16 + 0.5 x 12 x 5 + 4 x 3
A = 90 in².
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example of definition of derivative:lim as h approaches 0f(a+h) - f(a) / hThe slope of f(x) = -3x^2 +11 at any value of x
The slope of the function f(x) = -3x^2 +11 at any value of x is given by 6x.
The definition of derivative is given by the limit as h approaches 0 of [f(a+h) - f(a)] / h,
where f(x) is a function and a is a fixed value of x.
To find the slope of the function[tex]f(x) = -3x^2 +11[/tex] at any value of x, we need to use this definition of derivative.
So, let's plug in f(x) = -3x^2 +11 and a = x into the formula.
This gives us:
lim as h approaches 0 of [tex][-3(x+h)^2 + 11 - (-3x^2 + 11)] / h[/tex]
Simplifying this expression, we get:
lim as h approaches 0 of [tex][-3x^2 - 6hx - 3h^2 + 11 + 3x^2 - 11] / h[/tex]
Combining like terms, we get:
lim as h approaches 0 of [tex][-6hx - 3h^2] / h][/tex]
Factoring out an h from the numerator, we get:
lim as h approaches 0 of [-h(6x + 3h)] / h
Canceling out the h in the numerator and denominator, we get:
lim as h approaches 0 of 6x + 3h
Now, we can plug in h = 0 to find the slope of the function at any value of x:
6x + 3(0) = 6x.
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Write a matrix that when multiplied by any point [x/y] would have the effect of rotating the point 90 degrees counterclockwise. Also determine the algebraic effect of performing the transformation on the point A.
The result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].
Define rotationRotation is a transformation in geometry that involves turning or spinning an object around a fixed point called the center of rotation. The center of rotation remains stationary while all the points of the object move along circular paths, at the same angle and distance from the center.
To rotate a point [x/y] counterclockwise by 90 degrees, we can use a 2x2 matrix of the form:
[ 0 -1 ]
[ 1 0 ]
To multiply this matrix by a point [x/y], we can use the following matrix multiplication:
[ 0 -1 ] [ x ] [ -y ]
[ 1 0 ] [ y ] = [ x ]
So, if we have a point [x/y] and we want to rotate it 90 degrees counterclockwise, we can multiply it by the matrix [ 0 -1 ; 1 0 ] to get the new point [-y/x].
To rotate a point 90 degrees counterclockwise using a matrix, we need to represent the point as a column matrix and then multiply it by the 2x2 rotation matrix.
Assuming that the point is [x, y] = [-5, 2], we can represent it as a column matrix:
| -5 |
| 2 |
To rotate the point counterclockwise by 90 degrees, we can use the following 2x2 rotation matrix:
| 0 -1 |
| 1 0 |
Multiplying the rotation matrix by the column matrix representing the point gives:
| 0 -1 | | -5 | | 2 |
| 1 0 | ×| 2 | = | -5 |
So the result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].
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How do you solve this?
Answer:
[tex] \sqrt{ \frac{4}{49 {d}^{4} } } = \frac{2}{7 {d}^{2} } [/tex]
Electric utility poles in the form of right cylinders are made out of wood that costs $25. 97 per cubic foot. Calculate the cost of a utility pole with a diameter of 1. 5 ft and a height of 45 ft. Round your answer to the nearest cent
Rounding to the nearest cent, the cost of the utility pole is $2,061.33 with a diameter of 1. 5 ft and a height of 45 ft.
To calculate the cost of a utility pole, we first need to find its volume, which is the product of its height and the cross-sectional area of its base. Since the pole is in the form of a right cylinder, the cross-sectional area of its base is a circle with radius equal to half the diameter, which is 0.75 ft. Therefore, the cross-sectional area is:
Area = πr^2 = π(0.75)^2 = 1.767 ft^2
The volume of the pole is then:
Volume = Area x Height = 1.767 x 45 = 79.515 ft^3
Finally, we can calculate the cost of the pole by multiplying its volume by the cost per cubic foot of wood:
Cost = Volume x Cost per cubic foot = 79.515 x $25.97 = $2,061.33
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I need help on this question
Answer:
Step-by-step explanation:
I think it’s b
Which statement is true?
f 0.09>78
g 8.0×10-3>6%
h 78<8.0×10-3
j 6%<0.09
Answer:g maybe
Step-by-step explanation:
An official NHL hockey puck is shaped like a cylinder with a diameter of 3 inches and a volume of 7.1 cubic inches. What is the height of a hockey puck?
Answer: the height of the hockey puck is approximately 0.835 inches.
Step-by-step explanation: The formula for determining the volume of a cylinder is as follows:
The formula for the volume (V) of a cylinder can be expressed mathematically as V = πr2h, where r represents the radius of the cylinder's base and h represents the height of the cylinder. This formula is derived from the concept that the volume of a cylinder can be calculated by multiplying the area of its base (which is represented by the term πr2) by its height (h).
The present study utilizes the conventional nomenclature in which V denotes the volume, r represents the radius, and h stands for the height.
As the diameter of the hockey puck is measured to be 3 inches, it follows that the radius is equivalently calculated as 1.5 inches, or precisely half of the diameter.
It is established that the hockey puck has a volume of 7.1 cubic inches; accordingly, by substituting these known values into the relevant formula and performing the appropriate calculations, the measurement of h may be ascertained.
The expression 7.1 = π(1.5)^2h can be reformulated in a more academic manner. It can be said that the equation represents the mathematical relationship between the volume of a cylinder and its dimensions, wherein the value of 7.1 denotes the volume of the cylinder, whereas π, 1.5, and h refer to the mathematical constants of pi, radius, and height, respectively. Thus, the formula can be expressed as V = πr^2h, where V represents the volume of the cylinder, r denotes the radius, and h denotes the height.
The process of reducing something to its simplest form. Rewritten: The act of simplification involves distilling a concept or idea to its most basic, essential components. This process aims to facilitate a clear and concise understanding of the subject matter, allowing for greater comprehension and ease of communication.
The numerical expression 7.1 = 2.25πh can be written in a more formal and academic manner. Specifically, the equation can be rephrased as an algebraic relationship between the variables involved. More concisely, the equation describes the result of a multiplication between the constant factor 2.25π and the variable h, which according to the equation equals 7.1. As such, it can be represented by the following expression: 2.25πh = 7.1
Dividing each side by 2.25π is a logical mathematical operation utilized to simplify an equation or expression.
The aforementioned equation may be expressed in an academic tone as follows: The value of h is equivalent to the quotient obtained from dividing 7.1 by 2.25 times the mathematical constant π.
The employment of a calculator to compute the aforementioned expression:
The observed value of h is approximately equal to 0.835 inches.
brainliest+100 points
Find the entire perimeter of the entire floor
If three squares have sides that make an acute triangle, then the sum of the areas of the two small squares...
If three squares have sides that make an obtuse triangle, then the sum of the areas of the two small squares...
If three squares have sides that make a right triangle, then the sum of the areas of the two small squares...
The Pythagorean Theorem can be utilized in any situation to establish a connection between the side lengths of the squares and the sort of triangle that results.
What is the Pythagorean Theorem?Let's use the notation "a, b, and c" to indicate the three squares' side lengths, where "a" stands for the shortest side, "b" for the midpoint, and "c" for the longest side.
The area of the largest square (c), which is created by the hypotenuse of the triangle, is equal to the sum of the areas of the two smaller squares when three squares' sides form an acute triangle.
The areas of the two smaller squares (a and b) formed by the two larger squares (a and b) are equal when three squares have sides that form an obtuse triangle.
If three squares have sides that make a right triangle, then the sum of the areas of the two small squares is equal to the area of the largest square (c) formed by the hypotenuse of the right triangle.
In all cases, the Pythagorean Theorem can be used to determine the relationship between the side lengths of the squares and the type of triangle formed.
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Billy has a credit card with a current balance of $3,500 and a 16% APR. With his current monthly payment, he will be able to pay off this debt in 15 months. But Billy just learned that he is getting a raise at work. If he puts all of the extra income from his raise into his monthly credit card payment, how much additional monthly income would he require from his raise to pay off the credit card in 12 months? a. $58.57 b. $171.37 c. $258.99 d. $317.56
Answer:
a. $58.57
Step-by-step explanation:
Billy is in a pickle. He has a credit card debt of $3500 with a 16% annual interest rate, and he wants to pay it off in a year. He also wants to ask his boss for a raise, but he doesn't know how much to ask for. Luckily, he has a friend who is good at math and can help him out.
The friend tells Billy that we need to use the formula for the monthly payment of a credit card debt, which is:
P = (r / 12) * B / (1 - (1 + r / 12)^(-n))
where P is the monthly payment, r is the annual interest rate, B is the current balance, and n is the number of months to pay off the debt.
Using this formula, the friend calculates how much Billy is currently paying and how much he would need to pay to clear his debt in 12 months. The friend also finds the difference between these two payments, which is the amount of extra income Billy would need from his raise.
The friend shows Billy the calculations and says:
"Here you go, Billy. You are currently paying $280.42 per month to pay off your debt in 15 months. If you want to pay it off in 12 months, you would need to pay $331.79 per month. That means you would need an additional monthly income of $51.37 from your raise. The closest answer choice to this amount is a. $58.57, so this is the best option."
Billy thanks his friend and says:
"Wow, you are amazing! Thank you so much for helping me out. I'm going to ask my boss for a raise right now. Wish me luck!"
The friend wishes Billy good luck and hopes that he will get his raise and pay off his debt soon.
Mendel is back at it with another genetics experiment. This time he needs to partition a
rectangular garden into 4 parts by constructing three additional fences parallel to one of the
sides, in addition to fencing the perimeter. What is the minimum amount of fencing (in
meters) he will need to enclose 2500 m2?
The minimum amount of fencing Mendel will need to enclose 2500 m² = 317 meters
Let's assume that x represents the length of and y represents the width of the rectangular garden.
Using the formula for tha area of rectangle, the area of the garden would be,
A = length × width
A = xy
Here, A = 2500 m²
so, 2500 = xy
⇒ y = 2500/x
Using the formula for the perimeter of the rectangle, the perimeter of the garden would be,
P = 2x + 2y
But a rectangular garden is partitioned into 4 parts by constructing three additional fences parallel to one of the side.
So, the perimeter would be,
P = 2x + 5y
sides, in addition to fencing the perimeter.
P = 2x + 5(2500/x)
P = 2x + (12500/x)
Consider the derivative of P(x) with respect to x.
P'(x) = 2 - 12500/x²
To find the minimum value consider P'(x) = 0
2 - 12500/x² = 0
2 = 12500/x²
x² = 12500/2
x² = 6250
x = 79.05 m
and y = 2500/79.05
y = 31.63 m
So, the minimum amount of fencing would be,
P = 2x + 5y
P = 2(79.05) + 5( 31.63 )
P = 316.25 meters
P ≈ 317 meters
The minimum amount of fencing need to enclose 2500 m² = 316.25 meters
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What is the value of the following expression?
2 + [(15 + 3) × 2]
Step-by-step explanation:
The value of the expression can be calculated using the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
The expression is:
2 + [(15 + 3) × 2]
According to PEMDAS, we should first evaluate the expression within the parentheses:
15 + 3 = 18
So, the expression becomes:
2 + [18 × 2]
Next, we perform the multiplication:
18 × 2 = 36
Now, we substitute the result back into the original expression:
2 + 36
Finally, we perform the addition:
2 + 36 = 38
So, the value of the given expression is 38.