Translate this phrase into an algebraic expression.64 less than twice Greg's heightUse the variable g to represent Greg's height.A+ローロ園×園.x & S?
Answers
Answer
64 < 2g
Explanation
Let Greg's height be g
We need to express in equation form,
64 less than twice Greg's height
Greg's height = g
Twice Greg's height = 2g
64 less than twice Greg's height = 64 < 2g
Hope this Helps!!!
Related Questions
301123233What Happened When the Crossword Puzzle Champion Died?Find the graph of the solution set of each inequality below in the corresponding column of graphs. Notice the letter next to it.Write this letter in each box containing the number of that exercise. Keep working and you will find out about this grave event.x<2(10 x<1 0 4x is less than 2-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2X<2D++++-3 -2 -123-3 -2 -1 0 1 2 33 x>2+ 12 -3 2 A +++ +13 x>-3-3 -2 -1 0 1 2-3 -2 -1 0 1 2 3(5) x 114 #-1 ++++-3 -2 -10 1 2 3x < -1 A+++ 6 0 >-3 -2 -12-3 -2 -1 0 1 2 3x>-1 E+6 0 6 +++-3 -2 -1 0 1 2-3 -2 -1 0 1 2 318 0
Answers
I'm doing it on my notebook, hold on, it's easy
If f(x) is a third degree polynomia function, how many distinct complex roots are possible?
Answers
Complex roots always appear in pairs, actually if a+ib is a root then a-ib is also a root. Then, at most there are 2 complex roots in a third degree polynomial.
how do I write an equation as a multiple of a unit fraction using 3×3/7
Answers
EXPLANATION
An equation can be written as a multiply of a unit fraction using the following relationship:
[tex]x(3\cdot\frac{3}{7})[/tex]Simplify:6.2n - 8.3 + -9.1 + 1.4n
Answers
ANSWER
7.6n - 17.4
EXPLANATION
We have the expression that we want to simplify.
We have:
6.2n - 8.3 + (-9.1) + 1.4n
The first step is to collect like terms:
=> 6.2n + 1.4n - 8.3 - 9.1
Now, simplify:
7.6n - 17.4
That is the answer.
n - 3 over 10 = 3 over 5
Answers
The given expression is
[tex]\frac{n-3}{10}=\frac{3}{5}[/tex]First, we multiply by 10 on each side.
[tex]\begin{gathered} 10\cdot\frac{n-3}{10}=\frac{3}{5}\cdot10 \\ n-3=6 \end{gathered}[/tex]Then, we sum 3 on each side.
[tex]\begin{gathered} n-3+3=6+3 \\ n=9 \end{gathered}[/tex]Therefore, the solution is 9.Use long division to find the quotient. If there is a remainder do not include it in your answer. Recall:dividend\div divisor=quotient (4x^2-10x+6) \div(4x+2) Answer:
Answers
Let's do the division:
Answer: x-3
Solve each inequality). 2|4t-1|+6>20
Answers
To answer this question we will use the following property:
[tex]|a|>b>0\text{ if and only if }a>b\text{ or }a<-b.[/tex]Subtracting 6 from the given inequality we get:
[tex]\begin{gathered} 2|4t-1|+6-6>20-6, \\ 2|4t-1|>14. \end{gathered}[/tex]Dividing the above inequality by 2 we get:
[tex]\begin{gathered} \frac{2|4t-1|}{2}>\frac{14}{2}, \\ |4t-1|>7. \end{gathered}[/tex]Then:
[tex]4t-1>7\text{ or }4t-1<-7.[/tex]Solving the above inequalities we get:
1)
[tex]4t-1>7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1>7+1, \\ 4t>8. \end{gathered}[/tex]Dividing the above by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}>\frac{8}{4}, \\ t>2. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](2,\infty).[/tex]2)
[tex]4t-1<-7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1<-7+1, \\ 4t<-6. \end{gathered}[/tex]Dividing the above result by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}<-\frac{6}{4}, \\ t<-\frac{3}{2}. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](-\infty,-\frac{3}{2}).[/tex]Answer:
[tex](-\infty,-\frac{3}{2})\cup(2,\infty).[/tex]Gregory left a $8 tip on a $46 restaurant bill. What percent tip is that? Give your answer to two decimal places if necessary.
Answers
Answer:
17.39%
Step-by-step explanation:
Considering that $46 was the restaurant bill and Gregory left an extra tip of $8, the percent is:
[tex]\begin{gathered} \frac{8}{46}=0.1739\text{ } \\ \end{gathered}[/tex]0.1739 = 17.39%
This tip represents 17.39%.
Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.tan(u) = 13/5, 0 < u < /2
Answers
The first step to answer this question is to find tan(2u) by using the double angle formula:
[tex]\begin{gathered} tan(2u)=\frac{2tan(u)}{1-tan^2(u)} \\ tan(2u)=\frac{2(\frac{13}{5})}{1-(\frac{13}{5})^2} \\ tan(2u)=\frac{\frac{26}{5}}{1-\frac{169}{25}} \\ tan(2u)=\frac{\frac{26}{5}}{-\frac{144}{25}} \\ tan(2u)=-\frac{65}{72} \end{gathered}[/tex]It means that tan(2u) is -65/72.
The next step is to rewrite the equations for sin(2u) and cos(2u) to have them in terms of the least number of variables possible, this way:
[tex]\begin{gathered} sin(2u)=2sin(u)cos(u) \\ sin(2u)=2sin(u)\frac{sin(u)}{tan(u)} \\ sin(2u)=\frac{2sin^2(u)}{tan(u)} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=cos{}^2(u)-sin^2(u) \\ cos(2u)=1-sin^2(u)-s\imaginaryI n^2(u) \\ cos(2u)=1-2sin^2(u) \end{gathered}[/tex]If we rewrite tan(2u) in terms of sin(2u) and cos(2u) we will have:
[tex]\begin{gathered} tan(2u)=\frac{sin(2u)}{cos(2u)} \\ tan(2u)=\frac{\frac{2s\imaginaryI n^{2}(u)}{tan(u)}}{1-2sin^2(u)} \end{gathered}[/tex]We know the values of tan(2u) and tan(u), so we can solve the equation for sin^2(u).
[tex]\begin{gathered} tan(2u)=\frac{2sin^2(u)}{tan(u)(1-2sin^2(u))} \\ -\frac{65}{72}=\frac{2s\imaginaryI n^2(u)}{\frac{13}{5}(1-2s\imaginaryI n^2(u))} \\ -\frac{65}{72}\cdot\frac{13}{5}\cdot(1-2sin^2(u))=2sin^2(u) \\ -\frac{169}{72}(1-2sin^2(u))=2sin^2(u) \\ -1+2sin^2(u)=\frac{72}{169}\cdot2sin^2(u) \\ -1+2sin^2(u)=\frac{144}{169}sin^2(u) \\ 2sin^2(u)-\frac{144}{169}sin^2(u)=1 \\ \frac{194}{169}sin^2(u)=1 \\ sin^2(u)=\frac{169}{194} \end{gathered}[/tex]Using this value we can find the values of sin(2u) and cos(2u):
[tex]\begin{gathered} sin(2u)=\frac{2sin^2(u)}{tan(u)} \\ sin(2u)=\frac{2\cdot\frac{169}{194}}{\frac{13}{5}} \\ sin(2u)=\frac{65}{97} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=1-2sin^2(u) \\ cos(2u)=1-2\cdot\frac{169}{194} \\ cos(2u)=1-\frac{169}{97} \\ cos(2u)=-\frac{72}{97} \end{gathered}[/tex]It means that sin(2u)=65/97, cos(2u)=-72/97 and tan(2u)=-65/72.
5.True or False: The ordered pair (0, 3) is a solution to the equationy = -5x + 3.
Answers
You have the following equation:
y = -5x + 3
in order to determine if the point (0,3) is solution of the previous equation, replace the values of x = 0 and y = 3, and verify if the equation is consistent, as follow:
3 = -5(0) + 3
3 = 3
the equation is consistent for the given point, then, the point (0,3) is a olution of the given equation
Paul has $50,000 to invest. His intent is to earn 13% interest on his investment. He can invest part of his money at 8% interest and part at 16% interest. How much does Paul need to invest in each option to make a total 13% return on his $50,000?8% interest $ 16% interest $
Answers
Let x be the amount invest at 8%
Let y be the amount invest at 16%
Paul has $50,000 to invest:
[tex]x+y=50,000[/tex]His intent is to earn 13% interest on his investment. He can invest part of his money at 8% interest and part at 16% interest.
[tex]\begin{gathered} 50,000(0.13)=x(0.08)+y(0.16) \\ \\ 6,500=0.08x+0.16y \end{gathered}[/tex]Use the next system of equations to find x and y:
[tex]\begin{gathered} x+y=50,000 \\ 6,500=0.08x+0.16y \end{gathered}[/tex]1. Solve x in the first equation:
[tex]x=50,000-y[/tex]2. Substitute the x in the second equation by the value you get in the previous step:
[tex]6,500=0.08(50,000-y)+0.16y[/tex]3. Solve y:
[tex]\begin{gathered} 6,500=4,000-0.08y+0.16y \\ 6,500=4,000+0.08y \\ 6,500-4,000=0.08y \\ 2,500=0.08y \\ \frac{2,500}{0.08}=y \\ \\ y=31,250 \end{gathered}[/tex]4. Use the value of y to solve x:
[tex]\begin{gathered} x=50,000-y \\ x=50,000-31,250 \\ x=18,750 \end{gathered}[/tex]Solution for the system:
x=18,750
y=31,250
Answer: Paul needs to invers8% interest $18,75016% interest $31,250Find the range of the function for the given domain: {-4, 0, 4}
f(x)=x²-2
O {-14, 2)
O {-14, 2, 18)
O {-2, 14)
O (-18, -2, 14)
Answers
Answer:
{-2,14}
Step-by-step explanation:
f(-4) = f(4) = 14
f(0) = -2
Both circles have the same center. What is the area of the shaded region?10.7 md=26.2 mUse 3.14 for a. Write your answer as a whole number or a decimal rounded to the nearesbundredth
Answers
To determine the area of the shaded region, we would subtract the area of the smaller or inner circle from the area of the bigger or outer circle.
From the information given,
diameter of inner circle = 26.2m
radius of inner circle = diameter/2 = 26.2/2 = 13.1m
B applying the formula for determining the area of a circle which is expressed as
Area = pie * r^2,
pie = 3.14
Area of inner circle = 3.14 * 13.1^2 = 538.86 m^2
Radius of outer circle = 10.7 + 13.1 = 23.8m
Area of outer circle = 3.14 * 23.8^2 = 1778.62m^2
Therefore,
Area of shaded region = 1778.62 - 538.86 = 1239.76m^2
You buy a house for $299,00. If you make a 20% down payment, how much would you pay in total per month for the 30 year loan if you pay $3200/year in taxes, $1050/year in insurance and $28/month forthe home owners association?
Answers
Charlene calculated that the monthly patyment, including interests is $ 692.88.
Taxes = $ 3,200 annually, if we divide it by 12, we will find the monthly amount, this way:
3,200/12 = $ 266.67
Insurance = $ 1,050 annually, if we divide it by 12, we will find the monthly amount, this way:
1,,050/12 = $ 87.50
Home owners association = $ 28
Therefore, the monthly payment would be:
692.88 + 266.67 + 87.50 + 28
You can finish the calculation, Charlene!
how do I do plus 4 with 928 times 90 equal to what plus 57 divided by 134
Answers
What to plus 57 divided by 134 is 83523.57
A group of workers can plant 334 acres in 118 days. What is the unit rate in acres per day? Write your answer as a fraction or a mixed number in simplest form.
Answers
Number of acres = 334
Number of days = 118 days
unit rate = Number of acres/Number of days
Unit rate = 334 acres/114 days
2 is common to both numerator and denominator
Divide both by 2:
Unit rate = 167/57
No other number asides 1 is common to both the numerator and denominator
Hence, the unit rate in acres per day is 167/57
In mixed fraction = 2 53/57
add 3 feet 6 in add 3 feet 6 in + 8 ft 2 in + 4in + 2ft 5in what does that add up to
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We want to find the sum of;
3 feet 6 in + 3 feet 6 in + 8 ft 2 in + 4in + 2ft 5in.
Recall that;
[tex]1\text{ feet = 12 inches}[/tex]Adding we have;
[tex]undefined[/tex]Convert the measurement. 12 in/sec = ft/min
Answers
kmartinez2849, this is the solution:
Let's recall that:
1 inch/second = 5 feet/minute
Thus:
12 inch/second = 5 * 12 feet/minute
12 inch/second = 60 feet/minute
Let's recall that:
1 feet = 12 inches
1 minute = 60 seconds
Therefore:
1 inch/second * 60 = 60 inches/minute
Converting inches to feet
60 inches = 5 feet
In conclusion, 5 feet/minute
How much should be invested now at an interest rate of 6.5% per year, compounded continuously l, to have $3500 in four years.Round your answer to the nearest cent.
Answers
Okay, here we have this:
Considering the provided information we are going to replace in the formula of continuous compound interest:
[tex]\begin{gathered} A=Pe^{rt} \\ 3500=Pe^{(0.065\cdot4)} \end{gathered}[/tex]Now, let's solve for P:
[tex]\begin{gathered} P=\frac{3500}{e^{0.26}} \\ P=$2,698.68$ \end{gathered}[/tex]Finally we obtain that should be invested $2,698.68.
Consider the relation y = −3|x + 5| − 6. What are the coordinates of the vertex?
Answers
Solution:
Given the relation below
[tex]y=-3|x+5|-6[/tex]The general form, an absolute value function is
[tex]y=a|x-h|+k[/tex]The vertex coordinates are (h, k)
Solving to find the vertex below
[tex]\begin{gathered} x+5=x-h \\ 5=-h \\ h=-5 \\ k=-6 \\ (h,k)\Rightarrow(-5,-6) \end{gathered}[/tex]Hence, the coordinates of the vertex is
[tex](-5,-6)[/tex]For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.Part A: Write a function in for the geometric sequence where the first term is 11 and the common ratio is 4 .Part B: Find the first five terms in the geometric function.Part C: In one paragraph, using your own words, explain your work for Step A and Step B.
Answers
Remember that the formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]PART A:
With the data given, the formula for the sequence is:
[tex]a_n=11_{}\cdot4^{n-1}[/tex]PART B:
[tex]\begin{gathered} a_1=11\cdot4^{1-1}\rightarrow a_1=11 \\ a_2=11\cdot4^{2-1}\rightarrow a_2=44 \\ a_3=11\cdot4^{3-1}\rightarrow a_3=176 \\ a_4=11\cdot4^{4-1}\rightarrow a_4=704 \\ a_5=11\cdot4^{5-1}\rightarrow a_5=2816 \end{gathered}[/tex]PART C:
For part A, we took the general formula for the geometric sequence and plugged in the first term and the common ratio provided.
For part B, we replaced n for all the numbers from 1 through 5 to get the first 5 terms of the sequence.
So I am struggling in math and I could use some help to try and get through it
Answers
Given the functions:
[tex]\begin{gathered} f(x)=-5x+2 \\ g(x)=-2x²-3 \end{gathered}[/tex]to find f(7), we can make x = 7 on the function f to get the following:
[tex]\begin{gathered} f(7)=-5(7)+2=-35+2=-33 \\ \Rightarrow f(7)=-33 \end{gathered}[/tex]in a similar way, we can find g(5) by making x = 5 on the function g:
[tex]\begin{gathered} g(5)=-2(5)²-3=-2(25)-3=-50-3=-53 \\ \Rightarrow g(5)=-53 \end{gathered}[/tex]therefore, f(7) = -33 and g(5) = -53
Use this graph of y = 2x2 - 12x + 19 to find the vertex. Decide whether thevertex is a maximum or a minimum point.TV-5O A. Vertex is a minimum point at (1,3)B. Vertex is a minimum point at (3,1)C. Vertex is a maximum point at (1,7)D. Vertex is a maximum point at (3,1)
Answers
For a parabola, the vertex is the critical point, in other words, it is the maximum or the minimum of the function.
From the graph, we can see that the minimum (the minimum value of y) of the graph is 1. The vertex is the point (3,1).
Moreover, as we mentioned the vertex is always the minimum or the maximum, in this case, it is the minimum since the rest of the graph is 'above' that point.
The answer is option B. Vertex is a minimum point at (3,1)
what is the value of B ( area of the base) for the following triangular prism?40 ft^248 ft^260 ft^224ft^2
Answers
SOLUTION:
The base of the prism is a triangle and the formula for finding the area of a triangle is "half base multiplied by height".
From the figure of the prism given the base and height of the triangle is 6 ft and 8 ft.
[tex]\begin{gathered} \frac{1}{2\text{ }}\text{ x 6 x 8} \\ \\ \frac{48}{2} \\ \\ 24ft^2 \end{gathered}[/tex]CONCLUSION:
The area of the base of the given triangular prism is 24 squared feet ( the fourth option).
Erica's marks in eight consecutive mathematics examinations were:94,83,75,52,71,68,75,49
Answers
(a) The total marks Erica scored is the sum of the given marks:
total = 94 + 83 + 75 + 52 + 71 + 68 +75 + 49 = 567
(b) The mean is given by the quotient between the total and the number of marks, as follow:
mean = 567/8 = 70.875
Evaluate the expression and leaving your answer in polar form.
Answers
Complex numbers z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex] are the square roots of the complex number in polar form.
How to find the square root of a complex number in polar form
In this problem we find a complex number in polar form, that is, a complex number of the form:
z = r · [tex]e^{i\,\theta}[/tex]
Where:
r - Norm of the complex number.θ - Direction of the complex number, in radians.The square root of this number can be found by means of the De Moivre's theorem:
[tex]\sqrt{z} = \sqrt{z} \cdot e^{i\,\left(\frac{\theta + 2\pi\cdot k}{n} \right)}[/tex], for k = {0, 1}
If we know that z = 36 and θ = 17π / 10, then the roots of the complex number are:
z₁ = 6 · [tex]e^{i\,\frac{\frac{17\pi}{10}}{2} }[/tex]
z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex]
z₂ = 6 · [tex]e^{\frac{\frac{17\pi}{10} + 2\pi }{2} }[/tex]
z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex]
The solutions are z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex].
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2.Flight of a Model Rocket A model rocket is launched from the ground with veloc-ity 48 ft per sec at an angle of 60° with respect to the ground.(a) Determine the parametric equations that model the path of the projectile.(b) Determine the rectangular equation that models the path of the projectile.(c) Determine approximately how long the projectile is in flight and the horizontaldistance covered.
Answers
The parametric equation for the rocket is given by
x = 24 t and y = 24√3 t
Given velocity = 48 ft per sec
∅ = 60°
Distance = speed × time
d = 48t
Displacement along the x-axis
= v cos ∅
= 48× t ×cos60°
=24 t
displacement along the y axis
= v sin ∅
=48 t sin 60°
=24√3 t
In mathematics, a parametric equation represents a set of numbers as functions between one or maybe more independent variables, often known as parameters.
When equations are used to indicate the dimensions of the constituent parts of a geometric object, such as a curve or surface, they are collectively referred to as the parametric representation (alternatively written as parametrization) of the object.
b) now we will use the parametric equation to calculate the rectangular equation.
we know that x = 24t and y = 24√3 t
again, x/24 = y/24√3
or, √3x = y
c) Hence we can see that the parametric equation for the projectile is given by x = 24 t and y = 24√3 t and the rectangular equation is given by
√3x = y .
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A professor had students keep track of the social relations for a week and a number of social directions over the weekend and following the distribution how many students had at least 75 social interactions in the week?
Answers
Answer: 12 students
Since we need to find how many students had at least 75 social interactions in the week, we will add up all the frequencies from at least 75 interactions. Looking at the given table, that would be 3, 6, 1, and 2.
Adding them up together and we will get:
[tex]3+6+1+2=12[/tex]Therefore, 12 students had at least 75 social interactions in the week.
There are 25
students in an
Algebra class. 9 of
them got an A on
the test. What
percent of them
scored an A?
Answers
Answer:
36%
Step-by-step explanation:
First, you would write that as a fraction, which would be 9/25. Then, you'd convert the fraction to a percentage by getting the denominator to 100. Multiply the numerator and denominator by 4 to achieve this. The answer would be 36/100, which translates to 36%.
The organizer of a conference is selecting workshops to include. She will select from 6 workshops about chemistry and 7 workshops about biology. In how many ways can she select 4 workshops if 2 or fewer must be about chemistry?
Answers
Given that there are 6 workshops about chemistry and 7 workshops about biology.
So the total number of workshops available are,
[tex]\begin{gathered} =6+7 \\ =13 \end{gathered}[/tex]The number of ways of selecting 'r' objects from 'n' distinct objects is given by,
[tex]^nC_r=\frac{n!}{r!\cdot(n-r)!}[/tex]The total number of ways of selecting 4 workshops having no workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 0 chemistry)}=^7C_4 \\ n(\text{ 0 chemistry)}=\frac{7!}{4!\cdot(7-4)!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5\cdot4!}{4!\cdot3!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5}{3\cdot2\cdot1} \\ n(\text{ 0 chemistry)}=35 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 1 workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 1 chemistry)}=^7C_3\cdot^6C_1 \\ n(\text{ 1 chemistry)}=\frac{7!}{3!\cdot(7-3)!}\cdot\frac{6!}{1!\cdot(6-1)!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4\cdot3!}{3!\cdot4!}\cdot\frac{6\cdot5!}{1!\cdot5!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4}{4\cdot3\cdot2\cdot1}\cdot6 \\ n(\text{ 1 chemistry)}=210 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 2 workshops about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 2 chemistry)}=^7C_2\cdot^6C_2 \\ n(\text{ 2 chemistry)}=\frac{7!}{2!\cdot(7-2)!}\cdot\frac{6!}{2!\cdot(6-2)!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6\cdot5!}{2!\cdot5!}\cdot\frac{6\cdot5\cdot4!}{2!\cdot4!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6}{2\cdot1}\cdot\frac{6\cdot5}{2\cdot1} \\ n(\text{ 2 chemistry)}=315 \end{gathered}[/tex]Consider that the number of ways to select 4 workshops if 2 or fewer must be about chemistry, will be equal to the sum of the individual cases when the number of chemistry workshops in the selection are either 0 or 1 or 2.
This can be calculated as follows,
[tex]\begin{gathered} \text{ Total}=n(\text{ 0 chemistry)}+n(\text{ 1 chemistry)}+n(\text{ 2 chemistry)} \\ \text{Total}=35+210+315 \\ \text{Total}=560 \end{gathered}[/tex]Thus, the total number of ways is 560.