Answer:
The probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42 is 0.3115
Step-by-step explanation:
From the question, we can deduce the following;
n = 75
p = 0.35
where q = 1-p = 1-0.35 = 0.65
To compute the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42, we start by calculating the standard deviation of sample proportion.
Mathematically;
Standard deviation of sample proportion = √pq/n
SD = √(0.35)(0.65)/75 = 0.055 which is approximately 0.06
Let’s now compute the z-scores
For 0.36, we have ; (0.36-0.35)/0.06 = 0.01/0.06 = 0.17
For 0.42, we have; (0.42-0.35)/0.06 = 0.07/0.06 = 1.17
So the probability we want to calculate is :
P(0.17<z<1.17) = P(z<1.17) - P(z < 0.17) = 0.8790 - 0.5675 = 0.3115
There is a regular dodecahedron with all the points connected to each other. What is the area if each of the shales formed if the distance between each Point is x?
Answer:
18581.16
Step-by-step explanation:
The area of each of the shale can be calculated as
distance between each point = x
The area of the regular Dodecahedron
A = [tex]\sqrt[3]{25+10\sqrt{5} } a^{2}[/tex]
where a = number of edges = 30
hence the area of the regular dodecaheron = 18581.16
which expression is equivalent to (3x-6)(4x+1)
Answer:
12x^2 -21x -6
Step-by-step explanation:
(3x-6)(4x+1)
FOIL
first 3x*4x= 12x^2
outer 3x*1 = 3x
inner -6*4x = -24x
last -6*1 = -6
Add them together
12x^2 +3x -24x -6
Combine like terms
12x^2 -21x -6
Raj tested hist new flashlight by shining it on his bedroom wall. The beam of light can be described by his equation x^{2}+y^{2}-2x-4y-31=0. How many inches wide is the beam of light on the wall?
Answer:
Diameter=12 inches
Step-by-step explanation:
Given:
x^{2}+y^{2}-2x-4y-31=0
Using completing the square
x^2 - 2x + 1 + y^2 - 4y + 4 = 31+1+4
(x-1)^2 + (y-2)^2 = 36
Rewrite in the form
(x-h)^2+(y-k)^2=r^2
We have,
(x-1)^2+(y-2)^2=6^2
radius = 6
Diameter =radius ×2
=6 × 2
diameter = 12 inches
what number is the opposite of 0.93?
Answer:
- 0.93
Step-by-step explanation:
0.93 has an absolute value of 0.93 and is positive, so its opposite would be negative with the same absolute value.
The opposite number of 0.93 is -0.93.
What is opposite number?The number that produces zero when added to an is known as the additive inverse of a number, or a, in mathematics. This number is also referred to as the opposite number. In another word, oppositely positioned numbers on the number line are called opposite number.
Hence, opposite number of a positive number is a negative number and opposite number of the negative number is a positive number.
For an example, the opposite number of +7 is -7 because +7 + ( -7) = 0.
The opposite number of -0.5 is 0.5 because (-0.5) +0.5 = 0.
In this question, the given number is +0.93.
Let the opposite number of +0.93 is x.
Then it can be written that:
+0.93 + x = 0
⇒ x = 0 -0.93
⇒ x = -0.93
Hence, the opposite number of 0.93 is -0.93.
Learn more about opposite numbers here:
https://brainly.com/question/28492868
#SPJ3
5 and 6? i got 3 for both
Answer:
Hey there!
5. f(4) is 3. f(3) is 2. Thus, f[f(4)]=2
6. g(2) is 3. g(3) is 1. g[g(2)]=1
Hope this helps :)
Tim has an after-school delivery service that he
provides for several small retailers in town. He
uses his bicycle and charges $1.25 for a delivery
made within 1 mi, $1.70 for a delivery of at
least 1 mi but less than 1 mi, $2.15 for a
delivery of at least 1. mi but less than 2 miles,
and so on. If Tim raised his rates by 10%, what
would he be paid to deliver a package 35
miles?
Answer:
Step-by-step explanation:
tim has an after school delivery service that he provides for several small retailers in town. he uses his bicycle and charges $1.25 for a delivery made within 1 1/2 miles, $1.70 for a delivery of at least 1 1/2 miles but less than 1 3/4 miles. $2.15 for a delivery of at least 1 3/4 miles but less than 2 miles, and so on. if tim raised his rates by 10%, what would he be paid to deliver a package 3 1/8 miles.
Answer:
From the question asked the cost of additional 1/4 mile (1 3/4 - 1 1/2) is $0.45 ($1.7 - $1.25). If the rate is increased by 10% (0.1), the new price for an additional 1/4 mile would be 1.1 (1 + 0.1) × 0.45 = $0.495.
Tim new charge rate are as follows:
$1.25 for a delivery made within 1 1/2 miles
$1.745 for a delivery of at least 1 1/2 miles but less than 1 3/4
$2.24 or a delivery of at least 1 3/4 miles but less than 2
$2.735 or a delivery of at least 2 miles but less than 2 1/4
$3.23 or a delivery of at least 2 1/4 miles but less than 2 1/2
$3.725 or a delivery of at least 2 1/2 miles but less than 2 3/4
$4.22 or a delivery of at least 2 3/4 miles but less than 3
$4.715 or a delivery of at least 3 miles but less than 3 1/4
Since 3 1/8 is within 3 miles and 3 1/4 miles, Tim would charge $4.715 to deliver a package 3 1/8 miles.
I beed help nowww hjbiuhkju uhbjknjhiuy
Answer:
answer hoga 3/2 ok.....
Answer: 3/2
Step-by-step explanation:
♡Easy Brainliest♡ Which statement BEST explains why the sine of an acute angle is equal to the cosine of the angle's complement? A Both sinA and cosB are equal to ab. B Both sinA and cosB are equal to ac. C For sinA to equal cosB, a and c must be equal. D For sinA to equal cosB, a and b must be equal.
Answer:
Answer is A
Step-by-step explanation:
Hope it helps
Anyone help me.... BTW I need proper working.
Answer:
that answer i already give in another page...
The sum of three consecutive numbers is greater than 40. The inequality that represents this is x+x+1+x+2>40. Which value of x hold true for the inequality?
Answer:
x can be any integer greater than 12.
Step-by-step explanation:
x + x + 1 + x + 2 > 40
3x + 3 > 40
3x > 37
x > 12 1/3
x can be any integer greater than 12.
Evaluate without actual multiplication 1) 95x96 2)103x107
Answer:
:
"(100 + 3) (100 + 7)
Now, by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = 3 , b = 7
= (100)² + (3+7)*100 + (3*7)
= 10000 + 1000 + 21
= 11021
.
(110 - 7) (110 - 3)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = (-7) , b = (-3)
= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}
= 12100 + (-10)*110 + 21
= 21200 - 1100 + 21
= 11021
.
➖➖➖➖➖➖➖➖➖➖
.
(90 + 5) (90 + 6)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 90 , a = 5 , b = 6
= (90)² + (5+6)*90 + (5*6)
= 8100 + 990 + 30
= 9120
.
(100 - 5) (100 - 4)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = (-5) , b = (-4)
= (100)² + { (-5) + (-4) }*100 + 20
= 10000 + (-9)*100 + 20
= 10000 - 9000 + 20
= 10020 - 900
= 9120
.
➖➖➖➖➖➖➖➖➖➖
.
(100 + 4) (100 - 4)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 100 , a = 4 , b = (-4)
= (100)² + { 4 + (-4) }*100 + 4*(-4)
= 10000 + (4 - 4)*100 - 16
= 10000 + 0*100 - 16
= 10000 - 16
= 9984
.
(90 + 14) (90 + 6)
by using identity
(x + a) (x + b) = x² + (a+b)*x + ab
So,
x = 90 , a = 14 , b = 6
= (90)² + (14 + 6)*90 + (14*6)
= 8100 + 20*90 + 84
= 8100 + 1800 + 84
= 9984"
This answer was in another question
This answer was given by BloomingBud
Step-by-step explanation:
Answer:
1) 9120 2) 11021
Step-by-step explanation:
95 * 96 = (100-5)(100-4) = 10000 - 500 - 400 + 20 = 9120
103 * 107 = (100+3)(100+7) = 10000 + 300 + 700 + 21 = 11021
Please answer quickly!
Answer:
T'(-1, -3)
U'(-8, -3)
V'(-9, -10)
W(1, -10)
Step-by-step explanation:
For each point, draw a segment from it to the line y = -x and perpendicular to the line, and extend it the same distance to the other side of the line.
T'(-1, -3)
U'(-8, -3)
V'(-9, -10)
W(1, -10)
. An image rotated around its centre point appears unchanged after 180° and 360° turns.
This is an example of:
a) line symmetry
b) rotation symmetry
c) tessellation
d) vertex
It's an example of rotation symmetry, if the image appears unchanged. If the rotation symmetry exists there is a one centre point around which an image appears unchanged.
Answer:
It's an example of rotation symmetry, if the image appears unchanged. If the rotation symmetry exists there is a one centre point around which an image appears unchanged.
Which system of equations represents the matrix shown below?
Answer:
D
Step-by-step explanation:
just compare the augmented matrix to the possible answers and you will see it the option D
Solve for y
8+3y=-17
Simplify your answer as much as possible.
Write two different polynomials with a difference of
- 3x² + 5x - 7
Answer:
(-5 +/- i√59)/-6
Step-by-step explanation:
(-5 +/- √25-84)/2(-3)
(-5 +/- i√59)/-6
Simplify to create an equivalent expression. -3(2+4k)+7(2k-)
Answer:
[tex]-3(2 + 4k) + 7(2k)[/tex] = [tex]2k - 6[/tex] or [tex]2(k - 3)[/tex]
Step-by-step explanation:
The question seem incomplete; however, the given parameter is assumed as
[tex]-3(2 + 4k) + 7(2k)[/tex]
Required
Simplify
[tex]-3(2 + 4k) + 7(2k)[/tex]
Start by opening the brackets
[tex]-3*2 -3* 4k + 7*2k[/tex]
[tex]-6 -12k +14k[/tex]
Collect Like Terms
[tex]-6 -12k +14k[/tex]
[tex]-6 + 2k[/tex]
Reorder the above expression
[tex]2k - 6[/tex]
The answer can be further simplified as
[tex]2(k - 3)[/tex]
Hence;
[tex]-3(2 + 4k) + 7(2k)[/tex] = [tex]2k - 6[/tex] or [tex]2(k - 3)[/tex]
Two students use different methods to solve this multiplication problem:
3/4*-4 2/9
Read each of their methods below and then enter numbers to correctly complete their
work.
Answer/Step-by-step Explanation:
Given, [tex]\frac{3}{4}*-4\frac{2}{9}[/tex]
Ivy solves this problem by writing each number as a fraction and then multiplies as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}* -\frac{38}{9} [/tex]
[tex] = \frac{3}{4}*-\frac{38}{9} = -\frac{3*38}{4*9} = -\frac{1*19}{2*3}[/tex]
[tex]= -\frac{19}{6}[/tex]
Fabian solves this problem by writing the mixed number as a sum and applies the distributive method of multiplication as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}(-4 + -\frac{2}{9}) [/tex]
[tex] = \frac{3}{4}*-4 + \frac{3}{4}*-\frac{2}{9} [/tex]
[tex] = -\frac{3}{1} + \frac{1}{2}*-\frac{1}{3} [/tex]
[tex] = -3 + (-\frac{1}{6}) [/tex]
[tex] = -3 - \frac{1}{6} = -3\frac{1}{6} [/tex]
PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
140°
Step-by-step explanation:
[tex] \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\
\therefore m\widehat{BG} = 360\degree - 300\degree \\
\therefore m\widehat{BG} = 60\degree \\
\because m\widehat{BGD} = m\widehat{BG}
+m\widehat{GD}\\
\therefore m\widehat{BGD} = 80\degree+60\degree\\
\therefore m\widehat{BGD} = 140\degree\\
\because m\angle BAD = m\widehat{BGD} \\
\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} [/tex]
In a triangle ABC with |AB|=9m,|AC| =6m ,the sides AB and AC are produced to points X and Y respectively such that angleBXY=62°,and angle AYX=51°, calculate |BC| ..please help Mee♀️♀️
Answer:
|BC| = 9.4 m
Step-by-step explanation:
Angle bxy = angle abc (reason, corresponding angles)
Angle ayx = angle acb ( reason , corresponding angles)
So angle abc= 62°
Angle acb = 51°
Angle acb + and + bac = 180 (reason, sum of angles in a triangle)
Anlge bac = 180-62-51
Angle bac= 180-113
Angle back = 67°
Using sine formula
|BC| /sin 67 = 9/sin 62
|BC| = sin 67 *9/sin62
|BC| = 9.4 m
Solve the triangle. A = 51°, b = 14, c = 6
Answer: a = 11.24 B = 75.5° C = 53.5°
Step-by-step explanation:
Use Law of Cosines to find a: a² = b² + c² - 2bc · cos A
Given: b = 14, c = 6, A = 51°
a² = (14)² + (6)² - 2(14)(6) · cos 51°
a² = 196 + 36 - 168 · cos 51°
a² = 232 - 105.72
a² = 126.27
a = 11.24
Use Law of Sines to find B: [tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]
Given: A = 51°, a = 11.24, b = 14
[tex]\dfrac{\sin 51^o}{11.24}=\dfrac{\sin B}{14}\\\\\\\dfrac{14\sin51^o}{11.24}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{14\sin51^o}{11.24}\bigg)=B\\\\\\75.5^0=B[/tex]
Use Triangle Sum Theorem to find C: A + B + C = 180°
Given: A = 51°, B = 75.5°
51° + 75.5° + C = 180°
126.5° + C = 180°
C = 53.5°
Please answer this question now
Answer:
82 degrees
Step-by-step explanation:
Measure of arc ABC = 86*2 = 172 degrees.
Measure of arc DC = 360 - (145+172) = 360-317 = 43 degrees.
Measure of arc BCD = 121+43 = 164 degrees.
Measure of angle A = 164/2 = 82 degrees
please do the steps Solve for d: 1/6d-8=5/8 2. Solve for x: 3x-4+5x=10-2z 3. Solve for c: 7(c-3)=14 4. Solve for m: 11(m/22+3/44)=87m+m 5. Solve for k: ck+5k=a
Answer:
d = 55.5
x = 1
c = 11
m = [tex]\frac{1}{122}[/tex]
k = [tex]\frac{a}{(c + 5)}[/tex]
Step-by-step explanation:
Sorry, the formatting is slightly hard to understand, but I think this is what you meant.
Q1.
[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{5}{8}[/tex] x 2
Step 1. Simplify.
[tex]\frac{5}{8}[/tex] x 2 = [tex]\frac{5}{8}[/tex] x [tex]\frac{2}{1}[/tex] = [tex]\frac{10}{8}[/tex]
Step 2. Cancel out the negative 8.
[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{10}{8}[/tex]
+ 8 to both sides (do the opposite: [tex]\frac{1}{6}[/tex]d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)
[tex]\frac{1}{6}[/tex]d = [tex]\frac{10}{8}[/tex] + 8
Step 3. Simplify.
[tex]\frac{10}{8}[/tex] + 8 = [tex]\frac{10}{8}[/tex] + [tex]\frac{8}{1}[/tex] = [tex]\frac{10}{8}[/tex] + [tex]\frac{64}{8}[/tex] = [tex]\frac{74}{8}[/tex] = [tex]\frac{37}{4}[/tex]
Step 4. Cancel out the [tex]\frac{1}{6}[/tex].
[tex]\frac{1}{6}[/tex]d = [tex]\frac{37}{4}[/tex]
÷ [tex]\frac{1}{6}[/tex] from both sides (do the opposite: d is multiplied by [tex]\frac{1}{6}[/tex] right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)
÷ [tex]\frac{1}{6}[/tex] = x 6
So....
x 6 to both sides
d = [tex]\frac{37}{4}[/tex] x 6 = [tex]\frac{37}{4}[/tex] x [tex]\frac{6}{1}[/tex] = [tex]\frac{222}{4}[/tex] = [tex]\frac{111}{2}[/tex] = 55.5
Step 5. Write down your answer.
d = 55.5
Q2.
3x - 4 + 5x = 10 - 2x × 3
Step 1. Simplify
3x - 4 + 5x = 3x + 5x - 4 = 8x - 4
10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x
Step 2. Cancel out the negative 6x
8x - 4 = 10 - 6x
+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)
14x - 4 = 10
Step 3. Cancel out the negative 4
14x - 4 = 10
+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)
14x = 14
Step 4. Divide by 14
14x = 14
÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])
x = 1
Step 5. Write down your answer.
x = 1
Q3.
7(c - 3) = 14 × 4
Step 1. Expand the brackets
7(c - 3) = (7 x c) - (7 x 3) = 7c - 21
Step 2. Simplify
14 x 4 = 56
Step 3. Cancel out the negative 21
7c - 21 = 56
+ 21
7c = 56 + 21
7c = 77
Step 4. Cancel out the ×7
7c = 77
÷ 7
c = 77 ÷ 7
c = 11
Step 5. Write down your answer.
c = 11
Q4.
11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = 87m + m × 5
Step 1. Expand the brackets
11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = (11 x [tex]\frac{m}{22}[/tex]) + (11 x [tex]\frac{3}{44}[/tex]) = ([tex]\frac{11}{1}[/tex] x [tex]\frac{m}{22}[/tex]) + ([tex]\frac{11}{1}[/tex] x [tex]\frac{3}{44}[/tex]) = [tex]\frac{11m}{22}[/tex] + [tex]\frac{33}{44}[/tex] = [tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex]
Step 2. Simplify.
87m + m x 5 = 87m + 5m = 92m
Step 3. Cancel out the add [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 92m
- [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = 92m - [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = [tex]\frac{92m}{1}[/tex] - [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = [tex]\frac{368m}{4}[/tex] - [tex]\frac{3}{4}[/tex]
[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]
Step 4. Cancel out the ÷ 4
[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]
x 4
2m = 368m - 3
Step 5. Cancel out the 368m
2m = 368m - 3
- 368m
-366m = - 3
Step 6. Cancel out the × -366
-366m = -3
÷ -366
m = [tex]\frac{-3}{-366}[/tex]
m = [tex]\frac{1}{122}[/tex]
Step 7. Write down your answer.
m = [tex]\frac{1}{122}[/tex]
Q5.
ck + 5k = a
Step 1. Factorise
ck + 5k = (c × k) + (5 × k) = (c + 5) x k = k(c + 5)
Step 2. Cancel out the × (c + 5)
k(c + 5) = a
÷ (c + 5)
k = a ÷ (c + 5)
k = [tex]\frac{a}{(c + 5)}[/tex]
Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.
21.0 m^2
9.8 m^2
19.6 m^2
10.5 m^2
Answer:
10.5 m²
Step-by-step explanation:
Given:
∆ with 2 side lengths, 4.7m, 6.1m, and an included angle, 47°.
Required:
Area of the triangle
SOLUTION:
Area of such triangle that has 2 known sides and an included angle between them is given as ½*a*b*sin(θ).
Where,
a = 4.7 m
b = 6.1 m
θ = 47°
Area = ½*4.7*6.1*sin(47)
Area = 10.5 m² (to the nearest tenth)
The cost of a pizza at the local pizza shop has a base price of $12 for a cheese pizza, plus $2 for each additional topping? What is the value of the slope?
Answer:
$2.
Step-by-step explanation:
This is because the base price is $12, which means the constant is 12. The toppings are the only things you can add to the pizza, so the price of each additional topping is the slope of the pizza's cost. The slope is 2 dollars.
Hope this helps!
Answer:
2
Step-by-step explanation:
If we were to write a linear equation in slope-intercept form (y = mx + b where m = slope and b = y-intercept) of this situation, it would be y = 2x + 12 where y is the price and x is the number of toppings. This is because the price for every topping is 2x but the base price doesn't change, therefore it's a constant so it would be + 12. In this case, since m = slope, the slope is 2.
Please answer this question now
Answer:
200 cubic centimeters is the answer :)
Step-by-step explanation:
1. An average orange has a mass of 270 grams. What is the mass of 8 oranges in kg?
.
.
2. 1 milliliter of ink can print 50 pages of text. If you had 100 gallons of ink then how many pages could you print? 1 gallon = 3.79L
.
.
3. If you are driving 55 miles per hour, how many feet per second are you traveling?
Convert hours to minutes:
Convert minutes to seconds: Convert miles to feet:
.
.
4. Ivan’s car has 40 L gas tank. If gas costs $3.67 per gallon how much does it cost to fill her tank?
1 L = .264 gallons
Convert liters to gallons: Calculate the cost of gasoline:
.
.
5. A child requires a 5 mL dose of medicine each day. How many days would a liter of this medicine last?
Answer:2.the answer is 189,250pages
Step-by-step explanation:
1L=1000ml
3.785=?3785
1ml=50pages
3785ml=?
The answer is 189,250
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x? The graph is not a function of x because the line x = 0 intersects the graph at two points. The graph is a function of x because the line x = 5 does not intersect the graph. The graph is not a function of x because the line y = 0 intersects the graph at two points. The graph is a function of x because the line y = 5 does not intersect the graph.
Answer:
The graph is not a function of x because the line x = 0 intersects the graph at two points.
Step-by-step explanation:
This graph is not a function because it fails the vertical line test, since several vertical lines would intersect the graph at 2 points.
This answer choice is correct, as the line x = 0 intersects the graph at 2 points, (0, 2) and (0, -2).
Answer:
A
Step-by-step explanation:
Eddies saving account has a balance of $140. He deposits $17 for each of the next five weeks. He withdraws $11 in the final week. He wants to use his savings to buy a game system for $210. Do he have enough money to buy the game system?
Answer:
No. he need 64 more
Step-by-step explanation:
17
A pipe can fill a tankin h hours. What part of the tank is
filled in x hours.
a) hx
b)h/x
c) x/h
d) h + x
Answer:
c) x/h
Step-by-step explanation:
The rate of filling is 1 tank per h hours, or 1/h tanks per hour. Then in x hours, the amount of filling will be ...
(x hours)(1/h tanks/hour) = x/h tanks
The part of the tank filled in x hours is x/h.
