Answer:
n is 41.67 degrees
Step-by-step explanation:
At the intersection point of two lines, there are two angles, a and b. The sum of these two angles is 180.
In this question:
One of the angles is (3n - 28)
The other is 83.
Then
[tex]3n - 28 + 83 = 180[/tex]
[tex]3n + 55 = 180[/tex]
[tex]3n = 180 - 55[/tex]
[tex]3n = 125[/tex]
[tex]n = \frac{125}{3}[/tex]
[tex]n = 41.67[/tex]
Carlo buys $14.40 worth of grapefruit. Each grapefruit costs 0.80. (PLz help and yeett) with steps plz
Answer:
a) 18 grapefruits
b) 6 grapefruits
Step-by-step explanation:
a) n = 14.4 / 0.80 = 18 grapefruits
b) n = (14.4 / 3) / 0.8 = 6 grapefruits
A seabird rescue center has a special habitat for birds that will be released soon. The habitat is shaped like a rectangular prism. The habitat has a ground area of 2,000 square meters that is covered in grass and sand. The height of the habitat is 9 meters. What is the volume of the bird habitat? This is not collage level.
Answer:
18,000 Cubic meters
Step-by-step explanation:
Since volume is lwh and the area of the ground is lw and it gives you the height, You just multiply The area of the ground, 2,000 m, and the height, 9, to find the volume. 9 x 2,000= 18,000.
What is the value of 4p − 2, when p = 8? 16 24 30 34
Answer:
30
Step-by-step explanation:
Substitute 8 for p.
4(8)-2=
32-2=
30
Answer: 30
Step-by-step explanation: 4p-2
4(8)- 2
32-2
= 30
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not a question...and scribbles.
data set A is {30, 45, 32, 50, 33, 40, 44, 32}. Data set B is {28, 43, 30, 48, 35, 42, 46, 34}. which statement best compares the two data sets
Answer:
the mean in set B is equal to the mean in set A (option C)
Question:
The question is incomplete as the answer choices were not given.Let's consider the following question:
Data set A is {30, 45, 32, 50, 33, 40, 44, 32}. Data set B is {28, 43, 30, 48, 35, 42, 46, 34}. which statement best compares the two data sets?
a) median for set A is equal to the median for set B
b) Range for set A is greater than range for set B
c) The mean in set B is equal to the mean in set A
Step by step explanation:
We can describe a data set using four ways:
Center, spread, shape and unusual features.
Let's consider the center and spread.
Center: This is the median of the distribution.
Spread: This is the variation of the data set. If the range is wide, the spread is larger and If the range is small, the spread is smaller.
Rearranging the data set:
A = {30, 32, 32, 33, 40, 44, 45, 50}
B = {28, 30, 34, 35, 42, 43, 46, 48}
From the data:
The median for set A = (33+40)/2 = 73/2= 36.5
The median for set B = (35+42)/2 = 77/2= 38.5
Range = highest value - lowest value
The data ranges from 30 to 50 (range = 20) for A
The data ranges from 28 to 48 (range = 20) for B
Mean for set A = (30+32+32+33+40+4445+50)/8 = 306/8 = 38.25
Mean for set B = (28+30+34+35+42+43+46+48)/8= 306/8 = 38.25
In both data set the mean is equal to 38.25.
Therefore the statement that best compares the two data sets is the mean in set B is equal to the mean in set A (C)
Answer:
I think it is The mean for data set B is greater that the mean for data set A
Step-by-step explanation:
if not pls correct me
URGENT PLEASE HELP!!!
The dimensions of a rectangular prism are multiplied by 1/2 (so the sides of the new rectangular prism will all be half). Describe the effect of change on the volume.
a
The volume will be multiplied by 1/8, 1/8 times as large.
b
The volume will be 1/2 as much.
c
The volume will be multiplied by 1/4, 1/4 times as large.
d
The volume will be twice as large.
Answer:
i think the answer is C or D:)
avier is considering two options for college. Option A: Complete the first two years of schooling at a community college and then transfer to a university. Option B: Complete all four years of schooling at the university.
Answer:
kok
Step-by-step explanation:
The diagram above shows
circle ABCD
with Centre E Quadrilateral EADC is a rhombus.
<BAE =<ECB=n and <ABC=m.
find
i) m
ii) n
Answer:
m = 60°n = 30°Step-by-step explanation:
Opposite angles D and E in the rhombus are congruent. The measure of arc ADC is the same as the measure of central angle AEC. The measure of arc ABC is twice the measure of angle AEC, so the measure of arc ABC is twice the measure of arc ADC.
This means that short arcs AB, BC and CA are all 120°. Inscribed angle ABC (angle m) is half that value, or 60°.
Likewise, the angle BAC is 60°. We know that angle EAD is supplementary to angle AEC, so is 180° -120° = 60°. Segment AC bisects this angle, so angle n is 60°/2 = 30° less than angle BAC.
angle m is 60°, angle n is 30°
Please Help With problem 1
Answer:
60
Step-by-step explanation:
To find the volume of a rectangular prism you need to use the formula Base times height or in this case length times-width times height so multiply 5 x 4 x 3 to get your answer
which algebraic expression represents the phrase 14 increased by a number
Answer:
The answer is 14 plus y
Step-by-step explanation:
Number A is correct
If one zero is irrational, the other zero is
Answer:
rational
Step-by-step explanation:
The correct statement is:
c. The other zero can be either rational or irrational.
A quadratic equation with integer coefficients can have two distinct zeros, and if one of the zeros is irrational, the other zero can be either rational or irrational.
The nature of the zeros depends on the specific values of the coefficients in the quadratic equation.
A quadratic equation with integer coefficients can be written in the form: [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are integers.
The solutions to this equation can be found using the quadratic formula:
[tex]\mathrm x = \frac{\mathrm{-b}\pm \sqrt{\mathrm b^2-4\mathrm a \mathrm c} }{2 \mathrm a}[/tex]
If one zero is irrational, it means that one of the solutions obtained from the quadratic formula is an irrational number.
However, the other solution can still be either rational or irrational.
The discriminant, [tex]b^2 - 4ac[/tex], determines the nature of the solutions.
If the discriminant is a perfect square, both solutions will be rational.
If the discriminant is not a perfect square, one solution will be irrational, and the other may be either rational or irrational.
Therefore, it is possible for the other zero to be rational or irrational, depending on the specific values of a, b, and c in the quadratic equation.
Thus, option (c) is the correct answer.
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Complete question =
Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero?
a. The other zero must be rational.
b. The other zero must be irrational.
c. The other zero can be either rational or irrational.
d. The zero must be non-real.
An item costs n dollars. If the price of the item increases by 15%, the new price can be represented by the expression n + 0.15n. Which expression can also represent the new price?
a. 0.15n
b. n + 1.15
c. 15n
d. None
e. 1.15n
Answer:
d. none
Step-by-step explanation:
In Prof. Smith's class, the 11 students had the following scores on the last midterm.
73, 77, 78, 82, 83, 85, 86, 89, 95, 95, 188
Identify all values that are outliers.
If there is more than one outlier, separate them with commas.
If there are no outliers, click on "None".
Answer:
There are no values that are outliers.
in the year 2005 a company made $6.6 million in profit for each consecutive year after that their profit increase by 9% how much would a companies profit be in the year 2009 to the nearest 10th of $1 million
Answer:
$9.3 million
Step-by-step explanation:
Given that the company profit increases by 9% yearly from 2005.
Using the exponential growth formula;
A = P(1+r)^(t) .....1
Where;
A = final amount/value of profit
P = initial amount/value = $6.6 million
r = growth rate yearly = 9% = 0.09
t = time of growth in years = 2009 - 2005 = 4 years
Substituting the values;
A = 6.6(1+0.09)^(4)
A = 6.6(1.09)^(4)
A = 9.3164386 million
A = $9.3 million
The companies profit in the year 2009 to the nearest 10th of $1 million is $9.3 million
I need help on this problem please
Step-by-step explanation:
side ratio = big/small = 28/4 = 7
perimeter ratio = side ratio = 7
-> perimeter ratio = big / small = big/34 = 7
-> big perimeter= 7*34 = 238
Iliana is shopping at a baseball card show. The table shows prices for cards on special. On a coordinate plane, cards are on the x-axis and dollars are on the y-axis. Points (1, 2), (3, 6), and (4, 8) are plotted. A 2-column table with 4 rows titled Baseball Card Prices. Column 1 is labeled Cards (x) with entries 1, blank, 3, 4. Column 2 is labeled Dollars (y) with entries 2, blank, 6, 8. Which ordered pair completes the table and follows the pattern in the graph? (2, 4) (2, 5) (4, 2) (5, 2)
Answer:
the answer is a
Step-by-step explanation:
because the pattern multiplies by 2 for the y axis and for the x axis it just goes up 1
Answer:
answer C is coreect
Step-by-step explanation:
Which ratio is less than StartFraction 15 Over 24 EndFraction?
One-half
StartFraction 7 Over 8 EndFraction
StartFraction 19 Over 24 EndFraction
StartFraction 6 Over 8 EndFraction
Answer:
[tex]\frac{1}{2}[/tex] (one-half)
Step-by-step explanation:
Given: Fraction is [tex]\frac{15}{24}[/tex]
To find: the correct option
Solution:
A fraction represents part of a whole.
An improper fraction is a fraction in which numerator is greater than the denominator and a proper fraction is a fraction in which numerator is less than the denominator.
[tex]\frac{1}{2}=\frac{1\times 12}{2\times 12}=\frac{12}{24}< \frac{15}{24}\\\frac{7}{8}=\frac{7\times 3}{8\times 3}=\frac{21}{24}> \frac{15}{24}\\\frac{19}{24}> \frac{15}{24}\\\frac{6}{8}=\frac{6\times 3}{8\times 3}=\frac{18}{24}> \frac{15}{24}[/tex]
So, ratio [tex]\frac{1}{2}[/tex] is less than the given fraction [tex]\frac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
Write a division word problem for 31 divided by 4 that requires to round up
Answer:
31/4 is 7.75 so you could round up to 7.8 or 4/31 which is. 0.129... and you could round up to 0.13
Word problem:
Mark has 31 Starburst and wants to give them all to his 4 friends. About how many starburst will each friend have. Be sure to round your answer.
Answer:
This is just going to be a word problem so Imma just give you one you can use.
Step-by-step explanation:
Stacy has 31 cookies that she wants to divide for herself and her three other siblings. About how much cookies did each person get?
A fenced enclosure consists of a rectangle (length L and width 2R) attached to a semicircle with a radius R as pictured below. Note: there is fencing between the rectangular and semi-circular portions. The enclosure is to be built to have a total area (the entire shaded region), A, of 2000 ft2. The cost of the fence is $20/ft for curved sections and $30/ft for straight sections. Analytically (show all of your steps using algebra and calculus in the write up), find the minimum cost to build the fence and the dimensions of the enclosure. Show all equations that you derive and use. This part should be done entirely in the write-up: no coding. It is fine to do this by hand and include a high-resolution picture in the writeup rather than using Equation Editor. Hint: you will need to use two equations in order to find the cost as a function of only R or L. Construct a plot to graphically determine the values of R and L (x-axis) that minimize the total cost (y-axis) of the fence. Using the MIN function, determine the R and L that minimize cost and what that cost is Do your answers in A, B and C all agree? Why or why not?
Answer:
A. $ 6053.44
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
Step-by-step explanation:
A. The area A of the enclosure equals, A = 2RL + πR²/2.
The total cost C = 20 × length of curved section + 30 × length of straight section
C = 20πR + 30[2(L + 2R)]
= 20πR + 60L + 120R
Making L subject of the formula from A,
L = A/2R - πR/4
Substituting L into C, we have
C = 20πR + 60(A/2R - πR/4) + 120R
= 20πR + 30A/R - 15πR + 120R
= 5πR + 30A/R + 120R
We now differentiate C with respect to R to find the value of R for minimum cost
dC/dR = 5π - 60A/R² +120
Equating dC/dR to zero, we have
5π - 60A/R² + 120 = 0
So, R = ±√[60A/(5π + 120)]
substituting A = 2000 ft²
R = ±√[60 × 2000/(5π + 120)] = ±29.74 ft
We take the positive answer, R = 29.74 ft since R cannot be negative.
To determine if this is a minimum point, we differentiate dC/dR with respect to R.
So d²C/dR² = 120A/R³
Since d²C/dR² = 120A/R³ > 0 for positive R, it is a minimum point.
Substituting the value of R into C we have
C = 5πR + 30A/R + 120R
= 5π(29.74) + 30 × 2000/29.74 + 120(29.74)
= 467.155 + 2017.485 + 3568.8
= $ 6053.44
and L = A/2R - πR/4
= 2000/2(29.74) - π(29.74)/4
= 33.625 - 23.356
= 10.269
≅ 10.27 ft
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
Function f is an increasing exponential function that is negative on the interval (-∞, 2) and positive on the interval (2, ∞). Which could be the graph of function f?
Answer:
An exponential function is a function in the form of f(x) = bx or y = bx (if we wish to express the function in terms of y instead of f(x)), where b > 0, b ≠ 1 and x is a ... the interval (-∞, ∞) is because any real number can be put in for x the function f(x) ... zero and negative numbers are not part of the range is because any positive
Step-by-step explanation:
The percent markup on a video game is known to be 108% based on cost. If the seller paid $35 for one, then what would be the corresponding percent markup based on the sale price? (Round to the nearest tenth percent)
Answer: 48.1%
Step-by-step explanation:
The percent markup is defined as:
PM = (gross benefit/cost per unit.)*100%
We know that the cost per unit is $35
then we have:
108% = (gross benefit/$35)*100%
gross benefit = (108%/100%)*$35 = $37.8
This means that a game is selled by $35 + $37.8 = $72.8
Now we have:
Markup percent = (gross benefit/selling price)*100% = ($35/$72.8)*100% = 48.1%
The ages of Rohit and James are in the ratio 2 : 5. In 9 years, the ratio of their ages will be 5 : 8. Find their present ages.
Answer:
Step-by-step explanation:
I don't say you have to mark my ans as brainliest but if you think it has really helped you then plz don't forget to thank me...
Answer:
Rohit is 6 years old
James is 15 years old
Step-by-step explanation:
Rohit : James 2 : 5
the difference between their units is 3
Now we add the 9 years
5 : 8the difference between their units should be 3 because they both age every year. the question was nice enough to give to same amount of units
Now we subtract James's original 'unit age' from his new one
8u - 5u = 3 uWe also need to make sure the difference between Rohit's original 'unit age' is 3
5u - 2u = 3uthis 3 units represent the 9 years that have passed
3 units = 9 yearsTo find James's age all we ahve to find is their original unit number
James (5 units) -> 3 × 5 = 15same for Rohit
Rohit (3 units) -> 3×3 = 9hence, Rohit's and James's ages are 9 and 15 respectivelyPLEASE ANSWER ASAP!!!!!!!!! WILL GIVE BRAINLIEST ANSWER!
Rewrite the expression in the form 9^n.
9 . 9^2 =
Answer:
9^3
Step-by-step explanation:
9* 9^2
9*9(9) = 9^3
We could also look at it as
9^1 * 9^2
We know that a^b * a^c = a^(b+c)
9^(1+2) = 9^3
A television is 28.5 inches wide and 16 inches long.
Using the Pythagorean Theorem, what is the length of the diagonal of the television, rounded to the nearest inch?
Answer:
33 in
Step-by-step explanation:
The Pythagorean theorem tells you ...
diagonal² = length² +width²
diagonal² = (16 in)² +(28.5 in)² = 1068.25 in²
diagonal = √(1068.25 in²) ≈ 32.684 in
The diagonal of the television is about 33 inches.
Find the equation of a circle with the Endpoints of a diameter: (11, −5), (3, 15)
Answer:
(x - 7)² + (y - 5)² = 116
Step-by-step explanation:
equation of a circle:
(x - h)² + (y - k)² = r²
where (h,k) is the centre and r is the radius
centre is the midpoint of the diameter:
(h,k) = (11+3)/2 , (-5+15)/2
(h,k) = (7,5)
diameter = sqrt[(15--5)² + (3-11)²]
diameter = sqrt(464) = 4sqrt(29)
radius = ½ diameter
radius = 2sqrt(29)
r² = 116
equation:
(x - 7)² + (y - 5)² = 116
Answer:
[x-7]^2 + [y-5]^2= 116
Step-by-step explanation:
General equation of a circle is
[x2 - xo]^2 + [y2- yo]^2 = r^2
Where xo and yo are coordinates of the circle at the origin.
But xo = [x2 + x1]/2
= 11 + 3 / 2 = 7
yo = [y2 + y1] / 2 = [-5 + 15] /2 = 5
x2= 11, x2= 3; y1= -5, y2= 15
[11-7]^2 + [15-5]^2 =
16+ 100=116 = r^2
From the expression below;
[x2-xo]^2 + [y2-yo] ^2 = r^2
[x1-xo]^2 + [y1-yo] ^2 = r^2
[x-7]^2 + [y-5]^2= 116
Find the missing factor (6 + 3) + 5 = (3 × _?_ ) + 5
Answer:
(6+3)+5=(3x?)+5
9+5=(3×3)+5
14=9+5
14=14
so,the missing factor is 3.
(2x-23) value of angle x
Answer
65 degrees
Step-by-step explanation:
The value of x for which Angle B is supplementary to Angle A would be x = 26.17.
Used the definition of supplementary angle that states,
The sum of supplementary angles in any figure gives 180 degrees always.
Given that,
Angle A measures (2x - 23)°.
And, Angle B is supplementary to Angle A and measures (4x + 46)°.
Since Angle A and B are supplementary.
Hence the sum of both Angles is 180 degrees.
This gives,
∠A + ∠B = 180°
Substitute the given values,
(2x - 23)° + (4x + 46)° = 180°
Combine like terms,
6x + 23 = 180
Subtract 23 on both sides,
6x = 180 - 23
6x = 157
Divide 6 on both sides,
x = 26.17
Therefore, the value of x = 26.17
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The complete question is,
Angle A measures (2x - 23)°. Angle B is supplementary to angle A and measures (4x + 46)°. Write and solve an equation to find the value of x.
"Eat For 10 Hours. Fast For 14. This Daily Habit Prompts Weight Loss, Study Finds"
This is the title of an NPR article about a 2019 study that recruited 19 overweight adults diagnosed with metabolic syndrome (elevated blood sugar, elevated cholesterol levels, high blood pressure). Participants were asked to restrict any eating to a period of just 10 hours each day. The study found a statistically significant reduction in body weight after 12 weeks of this eating pattern.
1. To be able to conclude that a time-restricted eating pattern causes a weight loss in this population on average, we would need to ___________.
O use a much larger sample than what this study used
O collect weight-loss data on all adults, not just adults with metabolic syndrome
O find a significant weight-loss difference for participants that would be randomly assigned to time-restricted eating or regular eating
O collect weight-loss data on the entire population of adults with metabolic syndrome
O make sure that the study found a very small P-value and check that the conditions for inference were all met
Answer:
Option A
Step-by-step explanation:
To conclude that a time-restricted eating pattern causes a weight loss in this population on average, we would need to use a much larger sample than the 19 actually used in the study to get an unbiased conclusion and to also ensure that the sample itself and whatever result produced is a true representation of this particular population itself.
1) Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 43 and standard deviation σ = 9. Find the following probabilities.
a) x is less than 60
b) x is greater than 16
c) x is between 16 and 60
d) x is more than 60
2)Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.5 millimeters (mm) and a standard deviation of 1.0 mm. For a randomly found shard, find the following probabilities. a) the thickness is less than 3.0 mm
b) the thickness is more than 7.0 mm
c) the thickness is between 3.0 mm and 7.0 mm.
Answer:
1)
a) 0.9706 = 97.06% probability that x is less than 60.
b) 0.9987 = 99.87% probability that x is greater than 16.
c) 0.9693 = 96.93% probability that x is between 16 and 60.
d) 0.0294 = 2.94% probability that x is more than 60.
2)
a) 0.0668 = 6.68% probability that the thickness is less than 3.0 mm.
b) 0.0062 = 0.62% probability that the thickness is more than 7.0 mm
c) 0.9270 = 92.70% probability that the thickness is between 3.0 mm and 7.0 mm.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
1)
We have that [tex]\mu = 43, \sigma = 9[/tex]
a) x is less than 60
This is the pvalue of Z when X = 60.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 43}{9}[/tex]
[tex]Z = 1.89[/tex]
[tex]Z = 1.89[/tex] has a pvalue of 0.9706
0.9706 = 97.06% probability that x is less than 60.
b) x is greater than 16
This is 1 subtracted by the pvalue of Z when X = 16.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 43}{9}[/tex]
[tex]Z = -3[/tex]
[tex]Z = -3[/tex] has a pvalue of 0.0013.
1 - 0.0013 = 0.9987
0.9987 = 99.87% probability that x is greater than 16.
c) x is between 16 and 60
This is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 16.
From a), Z when X = 60 has a pvalue of 0.9706.
From b), Z when X = 16 has a pvalue of 0.0013
0.9706 - 0.0013 = 0.9693
0.9693 = 96.93% probability that x is between 16 and 60.
d) x is more than 60
This is 1 subtracted by the pvalue of Z when X = 60.
From a), Z when X = 60 has a pvalue of 0.9706.
1 - 0.9706 = 0.0294
0.0294 = 2.94% probability that x is more than 60.
2)
Now [tex]\mu = 4.5, \sigma = 1[/tex]
a) the thickness is less than 3.0 mm
This is the pvalue of Z when X = 3.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 4.5}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.0668 = 6.68% probability that the thickness is less than 3.0 mm.
b) the thickness is more than 7.0 mm
This is 1 subtracted by the pvalue of Z when X = 7.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7 - 4.5}{1}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938.
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability that the thickness is more than 7.0 mm
c) the thickness is between 3.0 mm and 7.0 mm.
This is the pvalue of Z when X = 7 subtracted by the pvalue of Z when X = 3.
From b), Z when X = 7 has a pvalue of 0.9938.
From a), Z when X = 3 has a pvalue of 0.0668
0.9938 - 0.0668 = 0.9270
0.9270 = 92.70% probability that the thickness is between 3.0 mm and 7.0 mm.
What do you think the message is from the "1936 Nazi Poster" poster?
Answer:
Become the leader of our nation.
Step-by-step explanation:
Like all Nazi propaganda, the 1936 poster suggests that young Germans are highly capable of becoming leaders of the nation. A young man who must be blond, with teeth and a perfect body. It was unconditional for Nazi propagandists to convince young people to support the goals and policies of the political party.
On the other hand, the leaders of the Nazi youths sought to integrate the children into the national Nazi community and prepare them to serve as soldiers in the armed forces or, later, in the SS.