♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The answer is that 20 goes into 16 1.25 times.
Explanation: You can use a calculator, and you just divide 20 by 16. Or, you can divide 20 and 16 both by 4. since you are dividing by four, and there are 5 fours in 20, you could know that 5*0.25 is 1.25, which is the answer. The fraction form is 1 1/4.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
20 cannot go into 16 a whole number of times, but in terms of decimal division, 20 goes into 16 exactly 0.8 times.
The question asks how many times 20 can go into 16. In mathematical terms, this is asking for the result of dividing 16 by 20. Since 20 is larger than 16, 20 cannot go into 16 a whole number of times. However, if we are considering division in terms of fractions or decimals, 20 goes into 16 exactly 0.8 times because 16 divided by 20 equals 0.8.
Pleeeeeeease help me
Plz help !! Me with it
Answer:
x=31
Step-by-step explanation:
4+ sqrt (x+5) = 10
Subtract 4 from each side
4 -4+ sqrt (x+5) = 10-4
sqrt(x+5) = 6
Square each side
(sqrt(x+5))^2 = 6^2
x+5 = 36
Subtract 5 from each side
x+5-5 = 36-5
x = 31
Answer: b. 31
Step-by-step explanation:
[tex]4+\sqrt{x+5}=10\\\\\sqrt{x+5}=6\\\\(\sqrt{x+5})^2=(6)^2\\\\x+5=36\\\\x=31\\\\\\Check:\\4+\sqrt{(31)+5}=10\\\\4+\sqrt{36}=10\\\\4+6=10\ \checkmark[/tex]
Create a real life representation of the following multiplication problem. Explain what the result represents in the problem. 2 4 ( 1 /3 ) = 8 the 1/3 is in fraction form
Which correctly describes a cross section of the square pyramid? Check all that apply.
A cross section parallel to the base is a square with side lengths of 2 ft.
A cross section parallel to the base is a square with side lengths of less than 2 ft.
A cross section perpendicular to the base through the top vertex is a triangle with the same dimensions as the triangular sides of the pyramid.
A cross section perpendicular to the base through the top vertex is a triangle with different dimensions than the triangular sides of the pyramid.
A cross section that is perpendicular to the base that does not pass through the top vertex of the pyramid is a trapezoid.
Answer:
acd
Step-by-step explanation:
please give brainly
The Answer is 1, 4, and 5 hope this helps.
Part A: Explain how to determine the value of the vertical translation, d, for the graph of g(x). (2 points)
Part B: Explain how to determine the value of the vertical translation, d, for the graph of f(x) = 2sin(θ + 120°) + 6. (3 points)
Answer:
Part A: Up 9
Part B: Up 6
Step-by-step explanation:
Part A: The graph appears to be a cosine graph since it starts at a peak on the y-axis. Normally a cosine graph starts at (0,1). This graph begins at (0,10). It has been shifted up y a translation by 9.
Part B: Each trig equation has a basic structure f(x) = a sin (x+b) + k where:
a is the vertical stretchb is the horizontal shiftk is the vertical shiftA vertical translation is a vertical shift and is represented by the value in k added outside of the function. In the equation f(x) = 2sin(θ + 120°) + 6, k = 6. The vertical translation is 6.
Find all solutions of sqrt(3)tan(3x) = 0
Answer:
x= nπ/3
Step-by-step explanation:
We are given that: [tex]\sqrt{3}*tan(3x) = 0[/tex]
Divide both sides by [tex]\sqrt{3}[/tex]
=> [tex]\frac{\sqrt{3}*tan(3x)}{\sqrt{3}} = \frac{0}{\sqrt{3}}[/tex]
=> tan(3x) = 0
we know that arctan(0) = nπ
Therefore,
3x = nπ
or
x= nπ/3 (where n belongs to positive and negative integers)
Isaac sold 58 of his baseball cards at a collectors show. If this represented 14.5% of his total collection, how many baseball cards did Isaac have before he sold his cards?
Answer:
[tex]400\ cards[/tex]
Step-by-step explanation:
Let
x------> amount of baseball cards Isaac had before he sold
we know that
[tex]14.5\%=14.5/100=0.145[/tex]
so
[tex]0.145x=58[/tex]
Solve for x
[tex]x=58/0.145[/tex]
[tex]x=400\ cards[/tex]
Which is a solution to the equation |10-5y| = 20
Answer:
The correct answer option is a) y =2.
Step-by-step explanation:
We are given the following equation and we are to find the solution of this equation:
[tex] | 1 0 - 5 y | = 2 0 [/tex]
Here, the expression [tex]10-5y[/tex] is given in a modulus, which means that its value cannot be negative.
[tex] 1 0 - 5 y = 2 0 [/tex]
[tex] -5 y = 2 0 - 1 0 [/tex]
[tex] -5 y = 1 0 [/tex]
Ignoring the negative sign because of mod.
[tex]y=\frac{10}{5}[/tex]
y = 2
The equation |10-5y| = 20 has two solutions, which are y = -2 and y = 6. These solutions are obtained by considering the two possible scenarios due to the absolute value.
The equation provided is |10-5y| = 20. To solve the equation, we need to consider the absolute value conditions separately. Since absolute value represents distance, it can be equal to the positive or negative of the number within the absolute value. Therefore, we have two cases to solve:
10 - 5y = 20
10 - 5y = -20
Solving the first case:
-5y = 20 - 10
-5y = 10
y = -2
Solving the second case:
-5y = -30
y = 6
Thus, the solutions to the equation are y = -2 and y = 6.
How to we find the some of x+5 and 2x+3
Answer:
[tex]\boxed{\bold{3x+8}}[/tex]
Step By Step Explanation:
Remove Parenthesis: (a) = a
[tex]\bold{x+5+2x+3}[/tex]
Group Like Terms
[tex]\bold{x+2x+5+3}[/tex]
Combine Similar Elements: [tex]\bold{x+2x=3x}[/tex]
[tex]\bold{3x+5+3}[/tex]
Add: [tex]\bold{5+3=8}[/tex]
[tex]\bold{3x+8}[/tex]
➤ [tex]\boxed{\bold{Mordancy}}[/tex]
Answer:
3x + 8
Step-by-step explanation:
x + 5 + 2x + 3
You have to add like terms. You can't add x and 5 or 2x and 3.
x + 2x is like 2x + 2x, so 3x
5 + 3 is 8, so 3x + 8 is the answer.
This system of equations has infinitely many solutions. Which of the following statements is NOT true?
Answer:
The graphs of the equations are parallel lines.
Step-by-step explanation:
Parallel lines have no solution, not infinitely many solutions. When graphed, infinitely many solutions will appear as the same line.
Answer:
The graphs of the equations are parallel lines.
Step-by-step explanation:
A parabola has zeros at (5,0) and (-3,0) and passes through point (6,18) determine the axis of symmetry
Answer:
The axis of symmetry is [tex]x=1[/tex]
Step-by-step explanation:
we know that
In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex
In this problem we have a vertical parabola open upward
The x-coordinate of the vertex is equal to the midpoint between the zeros of the parabola
so
[tex]x=\frac{5-3}{2}=1[/tex]
therefore
The axis of symmetry is [tex]x=1[/tex]
Cesar bought 2 bottles of juice that each hold 2 quarts and another bottle that hold 1 1/2 gallons of juice. How many quarts of juice did he buy?
Answer:
10
Step-by-step explanation:
1 gallon = 4 quarts
1.5 gallon = 1.5 * 4 quarts = 6 quarts
2 quarts + 2 quarts + 6 quarts = 10 quarts
Will a set of data always have a mode? Explain your answer.
no, if the each item only occurs once the set will not have a mode. Mode is an item that occurs more number of times in a distribution.
Answer: No
Step-by-step explanation: Unlike the mean and median of a data set, it's completely possible for a data set to have no mode. Remember, the mode is the number that appears most frequently in a data set.
I'll show you an example of a data set that has no mode.
In the image provided, you will see that each of the numbers appear only once. In this situation, we would just write no mode.
Is -16 rational or irrational?
Please help me on this question.
Answer:
rational
Step-by-step explanation:
Any rational number can be expressed in the form
[tex]\frac{a}{b}[/tex] where a, b are integers
- 16 can be expressed as
[tex]\frac{-16}{1}[/tex] ← - 16 and 1 are integers
Hence - 16 is rational
Mr. Coleman is mapping the boundaries of a zoo on a coordinate grid. The zoo's headquarters are located at the origin. The equation is shown below represents two boundaries of the zoo. y=-2x-5 -2x+4y=12 The zoo's entrance is located at the intersection of these two boundaries. Which coordinate grid correctly shown the two boundaries and the zoo's entrance?
Answer:
Option B. The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=-2x-5[/tex] ----> equation A
[tex]-2x+4y=12[/tex] -----> equation B
we know that
To graph the lines, find the intercepts
Remember that
The y-intercept is the value of y when the value of x is equal to zero
The x-intercept is the value of x when the value of y is equal to zero
Equation A
[tex]y=-2x-5[/tex]
For [tex]x=0, y=-5[/tex] ----> y-intercept
For [tex]y=0, x=-2.5[/tex] ----> x-intercept
Equation B
[tex]-2x+4y=12[/tex]
For [tex]x=0, y=3[/tex] ----> y-intercept
For [tex]y=0, x=-6[/tex] ----> x-intercept
Plot the intercepts to graphs the lines
see the attached figure
What is the area of this isosceles triangle.
Answer:
A=672 m²
Step-by-step explanation:
a²+b²=c² (to find h)
14²+b²=50²
196+b²=2,500
b²=2,304
√b²=√2,304
b=48
h=48
(base×height)÷2
(28×48)÷2
1,344÷2
A=672 m²
the town library is raising money by selling old books for $2 each which equation can be used to find the amount of money raised if number of books sold is no let x represent the number of books sold and y represent the number of dollars raised
Answer:
(6550)
Step-by-step explanation:
You can put this solution on YOUR website!
Call the number of hardcover and paperback books, h and p.
Thus
h + p = 8 and the value equation is
4h + 2p = 26
Now multiply the top one by four and subtract from the second one...we get
4h + 2p = 26
-(4h + 4p = 32)
----------------
-2p = -6
p = 3 so that
h = 5 x + y = 8, (1)
4x + 2y = 26, (2)
where x and y are the numbers of hardcover and softcover books respectively.
To solve, multiply the equation (1) by 2 (both sides) and then distract it from the equation (2). You will get
4x - 2x = 26 - 16, or
2x = 10, or x = 5 - the number of hardcover books purchased.
Then from the equation (1) you get y = 3.
Check. 4*x + 2*3 = 4*5 + 2*3 = 26. OK.
Answer:
y=2x
Step-by-step explanation:
Attached, is a picture with all the work!
What is the exact circumference of a circle with a diameter 15 inches
47. 12388980384689 would be the exact circumference of a circle witha diameter of 15 inches :)
Approximately what portion of the beaker is filled?
I would say the answer is A
To find the portion of the beaker filled, consider the total volume of the beaker and the volume up to which it is filled. Perform division and multiply by 100 to get the percentage filled.
Explanation:To determine the portion of the beaker filled, one must first understand the metrics of a beaker. A beaker is a cylindrical container with a flat bottom used to measure liquids. The scale etched on the side of the beaker represents the volume it contains. Suppose the total volume from the bottom up to the line of liquid is 300 mL and the total capacity of the beaker is 500 mL. By performing a simple division, 300 mL divided by 500 mL=0.6. Therefore, approximately 60% of the beaker would be filled. This is an approximate measure and for more accuracy, one should use a graduated cylinder.
Learn more about Beaker volume measurement here:https://brainly.com/question/17248597
#SPJ2
Simplify: 9x3 + 8x2 + 3x2
A. 20x7
B. 9x3 + 11x4
C. 9x3 + 11x2
D. 9x3 + 24x4
Answer:
[tex]\large\boxed{C.\ 9x^3+11x^2}[/tex]
Step-by-step explanation:
[tex]9x^3+8x^2+3x^2\qquad\text{combine like terms}\\\\=9x^3+(8x^2+3x^2)\\\\=9x^3+11x^2[/tex]
A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 3 feet
less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to
the building is 15 feet.
The length of the ladder is
Answer:
39 feet
Step-by-step explanation:
From the question;
let length of ladder =x feet
height of ladder will be=x-3 feet
ground distance of ladder bottom to building=15 feet
Applying Pythagorean relation
a²+b²=c²
where a=15 feet b=x-3 feet and c=x feet thus
x²-15²=(x-3)²
x²-225=x²-6x+9
collect like term
x²-x²-225-9=-6x
-234= -6x
x= 39 feet length of ladder
distance from ground to top of ladder= 39-3=36 feet
The length of the ladder is 39 feet.
Explanation:Let's denote the length of the ladder as x. According to the problem, the distance from the ground to the top of the ladder is 3 feetless than the length of the ladder. So, the height from the ground to the top of the ladder is x - 3 feet. The distance from the bottom of the ladder to the building is given as 15 feet. We can set up a right triangle where the ladder is the hypotenuse and solve for x using the Pythagorean Theorem:
x^2 = (x - 3)^2 + 15^2
Expanding and simplifying, we get:
x^2 = x^2 - 6x + 9 + 225
Combining like terms, we have:
0 = -6x + 234
Now, let's solve for x:
6x = 234
x = 39
Therefore, the length of the ladder is 39 feet.
Learn more about length of ladder here:https://brainly.com/question/29013068
#SPJ3
Quien es el padre de la Biologia ?
Answer: Charles Darwin : the father of modern biology. AFP. Charles Darwin , born 200 years ago, put man in his place by including him in the long history of the evolution of species, denying the belief of a divine creation and founding modern biology.
Step-by-step explanation:
I need help with this please
Answer:
[tex]y = x^2 + 6x + 8[/tex]
Step-by-step explanation:
The equation can be written using information from the graph. The vertex of the parabola is (-3,-1). Use the vertex form [tex]y = a(x-h)^2 + k[/tex] by substituting h = -3 and k = -1. The equation becomes [tex]y = a(x--3)^2 + -1[/tex]. It simplifies to [tex]y = a(x+3)^2 - 1[/tex]. To find a, substitute the point (x,y) on the graph into the equation and solve for a. Substitute x = -2 and y = 0.
[tex]0 = a(-2+3)^2 - 1[/tex]
[tex]0 = a(1)^2 - 1[/tex]
[tex]0 = a - 1[/tex]
[tex]1 = a[/tex]
So the equation is [tex]y = (x+ 3)^2 - 1[/tex]. Convert to standard form by distributing the parenthesis and combining like terms.
[tex]y = (x+ 3)^2 - 1\\y = x^2 + 3x + 3x + 9 - 1\\y = x^2 + 6x + 8[/tex]
Which solid figure has two parallel bases that are congruent polygons and rectangular faces joining the bases
A prism is a solid figure that has two parallel congruent sides that are called bases that are connected by the lateral faces that are parallelograms.
Answer:
a prism
Step-by-step explanation:
ap3x
Jesse is baking chocolate chip cookies for a party at school. He leaves 12 at home for his family and brings the remaining 24 cookies to school to share with his classmates.
Which equation can you use to find the total number of cookies n that Jesse bakes?
[tex]\[ n = 12 + 24 \][/tex] equation represents the total number of cookies Jesse.
Let's denote the total number of cookies Jesse bakes as [tex]\(n\)[/tex].
From the given information:
Jesse leaves 12 cookies at home.He brings the remaining 24 cookies to school.The total number of cookies he bakes is the sum of the cookies he leaves at home and the cookies he brings to school. We can represent this situation using an equation:
Total number of cookies baked [tex](\(n\))[/tex] = Cookies left at home + Cookies brought to school
[tex]\[ n = 12 + 24 \][/tex]
This equation represents the total number of cookies Jesse bakes [tex](\(n\))[/tex] as the sum of the cookies left at home (12 cookies) and the cookies brought to school (24 cookies).
Plz help me!!!!!!!!!!!
Answer:
The answer is (-7/2,0).
Answer: [tex]\bold{x=\{0,-\dfrac{7}{2}\}}[/tex]
Step-by-step explanation:
[tex](x+2)(2x+3)=6\\\\\text{Expand:}\\2x^2+3x+4x+6=6\\\\\text{Simplify (add like terms):}\\2x^2+7x+6=0\\\\\text{Subtract 6 from both sides:}\\2x^2+7x=0\\\\\text{Factor out the common term:}\\x(2x+7)=0\\\\\text{Apply the Zero Product Property:}\\\boxed{x=0}\qquad 2x+7=0\\\\.\qquad \qquad 2x=-7\\\\.\qquad \qquad \boxed{x=-\dfrac{7}{2}}[/tex]
PLZ HELP URGENT!!!! Valentin is deciding where to buy computer glasses. Each store offers a 1-year loan for $750 but with different interest rates and fees. Which is the best way for Valentin to choose the $750 loan that will cost him the LEAST?
A:Choose the loan with the lowest Annual Percentage Rate (APR).
B:Choose the loan with the lowest interest rate.
C:Choose the loan with the highest interest rate.
D:Choose the loan with the lowest fees.
Answer:
b on edg 2021
Step-by-step explanation:
Answer:
A:Choose the loan with the lowest Annual Percentage Rate (APR).
Step-by-step explanation:
i got it right on imagine math
How do I find Trig ratios
Trig ratios can only be used on right triangles with acute measures.
If given an angle and there are adjacent and opposite sides, then use tan(opposite/adjacent)
If given an angle and there is an adjacent side and a hypotenuse, then use cosine(adjacent/hypotenuse)
If given an angle and there is an opposite and adjacent side, then use sin(opposite/hypotenuse)
A common mnemonic device used to memorize the trig rules is SOH-CAH-TOA
Trig ratios refer to the ratios of sides of a right triangle expressed about an angle. These include sine (sin), cosine (cos), and tangent (tan), as well as their reciprocals cosecant (csc), secant (sec), and cotangent (cot). They are fundamental in many real-world applications, including engineering, navigation, and physics.
Explanation:The trigonometric ratios are ratios of sides of a right triangle. Specifically, we have the following respected relations between angles and sides: Sine (sin) is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Tangent (tan) is the ratio of the opposite side's length to the adjacent side's length. This is also equivalent to sin/cos. Respective reciprocal ratios are: cosecant (csc), secant (sec), and cotangent (cot).
These trig ratios allow us to determine distances, angles, and other aspects within a right triangle or representation of a circle.
For example, suppose we have a right triangle where the angle A is 30°, and the hypotenuse (the side opposite the right angle) is 10. In that case, we can determine the length of the opposite side by using the sin ratio, which is sin(30°) = Opposite/Hypotenuse. Solving, we get Opposite = sin(30°) * 10.
How do these trig ratios apply to real-world examples? Consider a ladder leaning against a wall, creating a right triangle with the ground. With the angle made at the ground and the length of the ladder, we can figure out how high up the ladder reaches on the wall using sin or how far from the base of the ladder's base should be placed using cos.
In conclusion, understanding trig ratios is an essential part of trigonometry and has numerous practical applications in real life, from construction and engineering to navigation and physics.
Learn more about Trigonometric Ratios here:https://brainly.com/question/23130410
#SPJ3
Perform the indicated operations; reduce the answer to lowest terms. a. 3⁄10 + 6⁄10 b. 1⁄3 + 1⁄4 + 1⁄6 c. 5⁄6 – 3⁄6 d. 2⁄3 – 6⁄10 e. 4⁄10 × 3⁄7 f. 1⁄6 × 6⁄15 g. 1⁄8 ÷ 4⁄9 h. 1⁄5 ÷ 3⁄4
Answer:
a. 3⁄10 + 6⁄10 = 9/10
b. 1⁄3 + 1⁄4 + 1⁄6 = 3/4
c. 5⁄6 – 3⁄6 = 1/3
d. 2⁄3 – 6⁄10 = 1/15
e. 4⁄10 × 3⁄7 = 6/35
f. 1⁄6 × 6⁄15 = 1/15
g. 1⁄8 ÷ 4⁄9 = 9/32
h. 1⁄5 ÷ 3⁄4 = 4/15
Step-by-step explanation:
a. 3⁄10 + 6⁄10
= 3*1 + 6*1 / 10
= 3+6/10
= 9/10
b. 1⁄3 + 1⁄4 + 1⁄6
since denominators are different we take LCM of 3,4,6 which is 12
= 1*4 + 1*3 + 1*2 / 12
= 4+3+2/12
= 9 ÷ 3 / 12 ÷ 3
= 3 / 4
c. 5⁄6 – 3⁄6
= 5 - 3 / 6
= 2 ÷ 2 / 6 ÷ 2 = 1/3
d. 2⁄3 – 6⁄10
LCM of 3 and 10 is 30
= 2 * 10 - 6 * 3 / 30
= 20 - 18 / 30
= 2 ÷ 2 / 30 ÷ 2 = 1/15
e. 4⁄10 × 3⁄7
= 12 ÷ 2 / 70 ÷ 2 = 6/35
f. 1⁄6 × 6⁄15
= 6 ÷ 6/90 ÷ 6 = 1/15
g. 1⁄8 ÷ 4⁄9
= 1/ 8 * 9/4
=9/32
h. 1⁄5 ÷ 3⁄4
=1/5 * 4/3
= 4/15
a)
[tex]\dfrac{9}{10}[/tex]
b)
[tex]\dfrac{3}{4}[/tex]
c)
[tex]\dfrac{1}{3}[/tex]
d)
[tex]\dfrac{1}{15}[/tex]
e)
[tex]\dfrac{6}{35}[/tex]
f)
[tex]\dfrac{1}{15}[/tex]
g)
[tex]\dfrac{9}{32}[/tex]
h)
[tex]\dfrac{4}{15}[/tex]
Step-by-step explanation:a)
[tex]\dfrac{3}{10}+\dfrac{6}{10}[/tex]
Now, this expression could also be given by:
[tex]=\dfrac{6+3}{10}\\\\=\dfrac{9}{10}[/tex]
b)
[tex]\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{6}[/tex]
On taking the least common multiple of the denominator we have:
[tex]L.C.M\{3,4,6\}=12[/tex]
Hence, we have:
[tex]=\dfrac{1\times 4+1\times 3+1\times 2}{12}\\\\=\dfrac{4+3+2}{12}\\\\=\dfrac{9}{12}\\\\=\dfrac{3\times 3}{3\times 4}\\\\=\dfrac{3}{4}[/tex]
c)
[tex]\dfrac{5}{6}-\dfrac{3}{6}[/tex]
Now, this expression could also be given by:
[tex]=\dfrac{5-3}{6}\\\\=\dfrac{2}{6}[/tex]
which on reducing to the lowest terms is given by:
[tex]=\dfrac{1}{3}[/tex]
d)
[tex]\dfrac{2}{3}-\dfrac{6}{10}[/tex]
on reducing the second term we have:
[tex]=\dfrac{2}{3}-\dfrac{3}{5}[/tex]
Now on simplifying the expression we have:
[tex]=\dfrac{2\times 5-3\times 3}{15}\\\\=\dfrac{10-9}{15}\\\\=\dfrac{1}{15}[/tex]
e)
[tex]\dfrac{4}{10}\times \dfrac{3}{7}[/tex]
We know that:
[tex]\dfrac{4}{10}=\dfrac{2}{5}[/tex]
Hence, we have:
[tex]=\dfrac{2}{5}\times \dfrac{3}{7}\\\\=\dfrac{6}{35}[/tex]
f)
[tex]\dfrac{1}{6}\times \dfrac{6}{15}[/tex]
which on simplifying gives:
[tex]=\dfrac{1}{15}[/tex]
g)
[tex]\dfrac{\dfrac{1}{8}}{\dfrac{4}{9}}[/tex]
which is further written as:
[tex]=\dfrac{1\times 9}{4\times 8}\\\\=\dfrac{9}{32}[/tex]
h)
[tex]\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}[/tex]
which is given by:
[tex]=\dfrac{1\times 4}{3\times 5}\\\\=\dfrac{4}{15}[/tex]
at which value will the graph of y=secx have a zero
Answer:
Step-by-step explanation: 1
Note that y = sec x is equivalent to y = ----------
cos x
Also note that the range of the cos x function is [-1, 1], which means that there is no x value for which sec x has a zero.