Answer:
Step-by-step explanation:
We can use the given formula to set up an equation and solve for x:
V = 20,000(0.8)x
where V is the value of the car after x years.
We want to find x when the value of the car is $8,200, so we set V equal to 8,200 and solve for x:
8,200 = 20,000(0.8)x
Dividing both sides by 20,000:
0.41 = 0.8x
Taking the natural logarithm of both sides:
ln(0.41) = x ln(0.8)
Dividing both sides by ln(0.8):
x = ln(0.41) / ln(0.8)
Using a calculator:
x ≈ 6.11
Therefore, it will take about 6.11 years for the car to be worth $8,200.
2x(x+4) in standard form
Answer:
To write 2x(x+4) in standard form, we need to expand the product and simplify:
2x(x+4) = 2x^2 + 8x
Therefore, the standard form of 2x(x+4) is 2x^2 + 8x.
Step-by-step explanation:
O
The value of "y" varies directly with "x"!
If y = 100, then x = 20.
Solve for y when x = 18.
k = 5
y = [?
Remember: y=kx
Answer:
Step-by-step explanation:
PLEASE HELP !! ASAP :)
Based on the given information, the graph of the function will shift 6 units up from the parent graph, f(x).
What is function?A function is a mathematical rule that relates one input value to one output value. The parent graph of a function is the simplest form of the graph that shows the basic behavior of the function.
In this case, the function is being shifted vertically by 6 units. This means that all points on the graph will be shifted upward by 6 units compared to the parent graph.
The shape of the graph will remain the same, but its position will change. Understanding how functions are transformed is important in mathematics and can be used to model a wide range of real-world phenomena.
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100 POINTS PLEASE HELP
Consider the surface
Find the following partial derivatives
The value of dz/ dt using Chain Rule is (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex].
What is Chain Rule?The chain rule states that the derivative D of a composite function is given by a product, as D(f(g(x))) = Df(g(x)) ∙ Dg(x).
In other words, the first factor on the right, Df(g(x)), indicates that the derivative of f(x) is first found as usual, and then x, wherever it occurs, is replaced by the function g(x).
Given:
By chain rule we can write z= f(x, y) = f( x(t), y(t))
dz/ dt = df/ dx . dx/ dt + df/ dy. dy/dt
So, df/ dx = [tex]e^y[/tex]
df/dy = [tex]e^y[/tex] + (x+ y) [tex]e^y[/tex]
x(t)=5t, while y(t)=1-t², So,
So, dx/dt = 5
and, dy/dt = -2t
Now, dz/ dt = 5 . [tex]e^y[/tex] + -2t ( [tex]e^y[/tex] + (x+ y) [tex]e^y[/tex])
= (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex]
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Select the equation that represents this problem: Anthony read 5 /6 hour each day for 2 days. A. 2 × 5 6 = 10 12 B. 2 × 5 6 = 10 × 1 6 C. 2 + 5 6 = 2 5 6 D. 5 1 + 5 1 + 5 1 + 5 1 + 5 1 + 5 1 = 30 6
you will get brainless
An equation that represents this problem "Anthony read 5/6 hour each day for 2 days." is: A. 2 × 5/6 = 10/12.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we can reasonably infer and logically deduce that Anthony's reading rate is 5/6 hour on a daily basis and for a period of 2 days only:
Total number of hours = 2 × 5/6
Total number of hours = 10/12 hours.
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. Aisha went to the local gas station to get a gallon of milk. She saw that the store had quart containers of milk for $1.19 while a gallon was $4.66. Aisha bought four quarts instead of the gallon because she thought it would be cheaper for the same amount of milk. Did Aisha save money? Explain your reasoning.
Therefore , the solution of the given problem of unitary method comes out to be she actually paid more for the same quantity of milk in the end.
What does unitary method mean?Divide the measures of just this microsecond portion by two variable in order to complete the task using the unitary technique. Briefly stated, the characterised by a group and colour subgroups are both removed from the unit method expression when a wanted item is present. For example, 40 pens with a changeable price would cost Rupees ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this.
Here,
4 gallons of milk make up a gallon of milk. Four pints would cost $1.19 each, or
=> $1.19 x 4 = $4.76.
Instead of purchasing a gallon of milk for $4.66,
Aisha opted to purchase four pints for $4.76.
Thus, by purchasing four pints rather than a gallon, Aisha did not save money.
She actually paid more for the same quantity of milk in the end.
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Find measurement of side A'C' and B'C'?
Answer:
AC = 14.9
BC = 10.5
Step-by-step explanation:
The triangle is a isosceles right triangle with ∠B = 90o, ∠A = ∠C = 45o.
Therefore AB = BC = 10.5
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse, which is AC.
AC^2 = AB^2 + BC^2
AC^2 = 2AB^2
AC^2 = 2(10.5)^2
AC^2 = 220.5
AC = √220.5 = 14.85 or 14.9
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below.
Course grades from A to F
Question content area bottom
Part 1
Choose the correct answer below.
A.
The ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural starting point.
B.
The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.
C.
The nominal level of measurement is most appropriate because the data cannot be ordered.
D.
The interval level of measurement is most appropriate because the data can be ordered, differences obtained by subtraction can be found and are meaningful and there is no natural staring point 
Option (B): The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.
What are the levels of measurement?
You may find out how accurately variables are recorded using levels of measurement, also known as scales of measurement. A variable in scientific research is anything that can have several values depending on the data collection.
Four levels of measuring exist:
Nominal: The information is only classifiable.Ordinal: The information is classifiable and rankableInterval: Data can be categorised, rated, and spaced evenly.Ratio: The data is equally distributed, categorised, ranked, and has a natural zero.You might only be able to perform a limited amount of data analysis depending on the level of measurement of the variable. From low (nominal) to high, there is a hierarchy in the complexity and precision of the level of measurement (ratio).
We have to find the appropriate level of measurement for the data course grades from A to F.
Here there is an order for ranking. This is because A is the highest grade followed by B, C, D, E and F respectively.
So nominal level of measurement is out of the question.
Now, there are no numerical values associated with the grades. We have no means to find the difference between the two grades.
Therefore the most appropriate level of measurement for Course grades from A to F is,
Option (B): The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.
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Every morning before your first class, you line up at Tim Horton's on the BCIT campus.
You notice that it takes between 19 to 35 minutes to get through the lineup, give your
order to the cashier, and receive your coffee, donut, and wrap. The time to get your
order follows a uniform distribution.
(a) What is the probability that it will take at least 23minutes to get your order??
(enter a number between 0 and 1 in 4 decimal places)
(b) You arrive at Tim Horton's at 7:30am. What is the probability that you receive your
order before your friends show up at 8:00am at Tim's?
(enter a number between 0 and 1 in 4 decimal places)
(c) 10% of the time it takes you longer than how many minutes to get your
order?
(answer in 2 decimal places)
min
Answer: (a) Since the time to get the order follows a uniform distribution between 19 to 35 minutes, the probability of getting the order in any interval of time within this range is proportional to the length of that interval. Therefore, the probability of taking at least 23 minutes to get the order is:
P(X ≥ 23) = (35 - 23) / (35 - 19) = 0.4
Rounding to 4 decimal places, the probability is:
P(X ≥ 23) ≈ 0.4000
(b) If you arrive at Tim Horton's at 7:30am and your friends show up at 8:00am, you have 30 minutes to receive your order. Since the time to get the order follows a uniform distribution, the probability of receiving the order before your friends show up is the probability of getting the order in 30 minutes or less, which is:
P(X ≤ 30) = (30 - 19) / (35 - 19) = 0.5789
Rounding to 4 decimal places, the probability is:
P(X ≤ 30) ≈ 0.5789
(c) Let's call the time in minutes to get the order that is longer than 10% of the time as t. Since the distribution is uniform, we know that the probability of taking longer than t minutes is 0.1. Therefore, we can write:
(35 - t) / (35 - 19) = 0.1
Solving for t, we get:
t = 19 + 0.9(35 - 19) = 32.4
Rounding to 2 decimal places, we get:
t ≈ 32.40 minutes
Therefore, 10% of the time it takes longer than 32.40 minutes to get the order.
Step-by-step explanation:
learner sell 300 vetkoet every week for 12 they charge 10 for each vetkoet calculate the profit they will if the cost for each vetkoet is 3.80
The profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To calculate the profit for selling 300 vetkoek every week, we need to first calculate the total revenue generated and the total cost of producing the vetkoek.
Total revenue = Price per vetkoek x Number of vetkoek sold
Total revenue = 10 x 300 = 3000
Total cost = Cost per vetkoek x Number of vetkoek sold
Total cost = 3.80 x 300 = 1140
Profit = Total revenue - Total cost
Profit = 3000 - 1140 = 1860
Therefore, the profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.
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The population of Mexico between 1921 and 2010 can be modeled as
p(t) = 8.028e^0.025t million people, where t is the number of years since 1900.†
(a) What was the population of Mexico in 2006? (Round your answer to three decimal places.)
____________ million people
How rapidly was the population of Mexico growing in 2006? (Round your answer to three decimal places.)
____________ million people per year
(b) Write a linearization of p in 2006. (Round all numerical values to three decimal places.)
pL(t) = ______________
(c) Use linearization to estimate the population of Mexico in 2011. (Round your answer to three decimal places.)
_______________ million people
By answering the above question, we may state that As a result, in 2006, equation Mexico's population was expanding at a pace of around 2.708 million people each year.
What is equation?When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.
We must enter t = 2006 - 1900 = 106 into the population model and do the following calculations to get the population of Mexico in 2006:
p(106) = 8.028e (0.025 * 106) million individuals
108.191 million individuals, or p(106) (rounded to three decimal places)
Finding the derivative of the population model with respect to time t will allow us to determine how quickly Mexico's population was rising in 2006:
Each year, p'(t) = 0.025 * 8.028e(0.025t) million individuals.
We may then calculate the derivative at time t = 106 as follows:
P'(106) = 0.025 * 8.028e(0.025*106) million individuals annually P'(106) 2.708 million individuals annually (rounded to three decimal places)
As a result, in 2006, Mexico's population was expanding at a pace of around 2.708 million people each year.
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1.1 Measure the diameter of the tin in mm and write down the real diameter in mm 1.2 Hence, determine the circumference of the base of the tin in mm. You may us the formula: C = 2лr π = 3,142 Hint: radius = half of diameter 1.3 Measure the height of the tin in mm and write down the real height in mm. MATHEMATICAL LITERACY GRADE 11, 2023 SBA GUIDELINE
We can write the diameter and circumference of the base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
Mathematically, we can write,
y = f(x) = ax + b.
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumference as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumference of the base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
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7(x+8)=49
i know the answer but tell me how did you solve it only with numbers and mathematical letters nothing else
What is the quotient of 16sup(x,-2)-8sup(x,-2)-2sup(x,-9) and 2x?
The required quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.
What is arithmetic?Arithmetic involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Here,
To simplify the given expression, we can start by factoring out the common factor of 2x from the numerator. This gives:
(16x⁻² - 8x⁻² - 2x⁻⁹) / 2x
Next, we can simplify the terms in the numerator by combining the like terms:
= (4x⁻² - x⁻⁹) / x
= 4x⁻²⁻¹ - x⁻⁹⁻¹
= 4x⁻³ - x⁻¹⁰
= 4x⁻³ - x⁻¹⁰
Therefore, the quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.
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help me pls i will give brainless
find the area of this semi circle with radius r=19cm give your answer rounded to 1 dp
the answer is 283.4
I can't write a formula
what's the end behavior of: y= 2 + log2(x - 1)
We can infer that the function y = 2 + log2(x - 1) has the following final behaviour:
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.what is a function?A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input. Y = f is a common way to represent a function (x).
A function in mathematics is a certain configuration of the inputs (also known as the domain) and their outputs (also known as the codomain), where each input has precisely one output and the output can be connected to its input.
from the question;
We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behaviour of the function
y = 2 + log2(x - 1).
The formulas (x - 1) and log2(x - 1) also approach infinity as x gets closer to positive infinity. As a result, y increases as x moves closer to positive infinity. The following can be written:
lim x→∞ 2 + log2(x - 1) = ∞
Expression (x - 1) moves closer to zero and log2(x - 1) moves closer to negative infinity as x moves towards 1 from the right. So, as x moves closer to 1 from the right, y moves closer to negative infinity. The following can be written:
lim x→1+ 2 + log2(x - 1) = -∞
This leads us to the following conclusion about the final behaviour of the function y = 2 + log2(x - 1):
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.to know more about the function visit:
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Question
Let C be the event that a randomly chosen cancer patient has received chemotherapy. Let E be the event that a randomly
chosen cancer patient has received elective surgery. Identify the answer which expresses the following with correct
notation: Of all the cancer patients that have received chemotherapy, the probability that a randomly chosen cancer patient
has had elective surgery.
Answer:
The probability that a randomly chosen cancer patient who has received chemotherapy has also had elective surgery can be expressed as P(E|C), where "P" represents probability and the vertical bar "|" indicates "given." So, P(E|C) represents the probability of event E given that event C has occurred.
Step-by-step explanation:
What is the output?
listC=[3, 2.5, 10]
listC.pop()
print(listC)
O There is no output because there is an error in the program.
O [2.5, 3, 10]
OI
O [3, 2.5]
Answer: [3, 2.5]
Step-by-step explanation:
Describe the sampling distribution of p^ Assume the size of the population is 15,000 n = 700, P = 0.172 determine the standard deviation of the sampling distribution of p^
Answer
The shape of sampling distribution of ^p is approximately normal because n < greater than 0.05N and np (1-p) > less than 10.
Step-by-step explanation:
The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
What is defined by the Central Limit Theorem?The distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n is defined by the central limit theorem, where:
The mean is [tex]\mu[/tex] = 9.The standard deviation is √p (1-p)/ n The shape is approximately normal.As long as these two conditions are respected:
n≤ N
np(1-p) > 10.
Here, we have the parameters
n= 700, p = 0.172, N= 15, 000
So, n/N = 0.0466 < 0.05
and, np(1-p)
= 700 x 0.172 ( 1- 0.172)
= 99.69 >10
Then the shape is approximately normal.
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squared root of x-45 equals squared root of x minus 3
Answer:
No solution
Step-by-step explanation:
[tex]\sqrt{x-45} =\sqrt{x-3} \\(\sqrt{x-45} )^2=(\sqrt{x-3} )^2\\x-45 = x-3\\x-x = 45-3\\0 = 42\\[/tex]
what is the value of p
Answer:
52 - 13 = 39 so p = 39
Step-by-step explanation:
Answer:
P=25
Step-by-step explanation:
180=52+90+p+30
180=155+P
180-155=p
p=25
The Zyco corporation pays an annual dividend of $2.10 per share. on Tuesdays it closed at $72 per share with a net change of +0.95. The dividend remained at $2.10 for several months. What was the yield on Tuesday? Round to the nearest tenth of a percent. At what price did Zyco close on Monday? nWhat was thenyield at Monday's Close? Round to the nearest tent of a percent?
In response to the given question, we have that Therefore, on Tuesday, equation the yield was 2.92%, and on Monday, it was 2.96%.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.
Divide the yearly dividend by the share price to determine the yield, then multiply the result by 100 to get the percentage:
Tuesday's yield is calculated as (Annual dividend / Share Price) times 100.
Tuesday's yield is calculated as ($2.10 / $72) times 100, which is 2.92%.
Tuesday's closing price minus Monday's closing price is the difference.
The price on Monday was $72 minus $0.95.
$71.05 was the final price on Monday.
We apply the same procedure as previously to determine the yield as of Monday's close:
Monday's yield is calculated as (annual dividend / share price) x 100.
Yield on Monday is equal to ($2.10 / $71.05) times 100, or 2.96%.
Therefore, on Tuesday, the yield was 2.92%, and on Monday, it was 2.96%.
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What are the values of x when x²+x-6 = -4?
OA. x = -4 and x = 6
OB. x = -2 and x = 1
OC. x = -3 and x = 2
OD. x = -5 and x = -6
edu
play
Answer:
0
Step-by-step explanation:
for x x^2+x-6=-4. x2+x−6=−4 x 2 + x - 6 = - 4. Step 1. Add 4 4 to both sides of the equation. x2+x−6+4=0 x 2 + x - 6 + 4 = 0.
(hope it helps!)
What is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x) +
9?
shifted up
shifted left
shifted down
shifted right
Answer would be shifted up
Step-by-step explanation:
hence the +9 you would be going up 9 units :)
If you spin the spinner 88 times,
what is the best prediction possible
for the number of times it will land on
green?
The answer is 6
but specifically, it can land on green 6.8181%
For a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. For every 4 minutes of play, one half the game awards 1/2 point, and for every 12 minutes of play, one and one half the game awards 1 1/2 points. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many points are awarded for 20 minutes of play? (2 points)
Answer:
Step-by-step explanation:
Therefore, 12 minutes of play awards 4.5 points.
The constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that for every 4 minutes of play, 1/2 point is awarded.
For every 12 minutes of play, 1 1/2 points are awarded.
We can set up a proportion to find the constant of proportionality:
(1/2 point) / (4 minutes) = (3/2 points) / (12 minutes)
Simplifying the left side, we get:
1/8 = (3/2 points) / (12 minutes)
Multiplying both sides by 12, we get:
1.5 = (3/2)P
P = (1.5) x (2/3) = 1
Therefore, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded.
By constant of proportionality, the equation that represents the relationship between the number of points awarded and the amount of time played:
P = (1/4)t
To find the number of points awarded for 20 minutes of play, we can use the equation P = (1/4)t:
P = (1/4)(20)
= 5
Hence, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.
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The distribution of heights of young women is approximately Normal with mean 64 inches and standard deviation 2.7 Use the 68-95-99.7 rule to answer the questions.
Therefore, the height range that encompasses 99.7% of adolescent women is roughly between 55.9 and 68.1 inches.
What can you infer from standard deviation?It reveals the average deviation of each number from the norm. When it comes to normally distributed, a large standard deviation denotes that values are typically out of the mean, whereas a smaller standard deviation denotes that values are grouped closely around the mean.
The 68-95-99.7 rule is a way to remember the percentage of data that falls within certain numbers of standard deviations from the mean in a normal distribution. Specifically:
About 68% of the data falls within 1 standard deviation of the meanAbout 95% of the data falls within 2 standard deviations of the meanAbout 99.7% of the data falls within 3 standard deviations of the meanUsing this rule, we can answer the following questions:
What is the range of heights that includes about 68% of young women?About 68% of young women have heights within 1 standard deviation of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 1 standard deviation from the mean:
64 inches ± 2.7 inches
So the range of heights that includes about 68% of young women is approximately 61.3 inches to 66.7 inches.
2. What is the range of heights that includes about 95% of young women?
About 95% of young women have heights within 2 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 2 standard deviations from the mean:
64 inches ± 2(2.7 inches)
So the range of heights that includes about 95% of young women is approximately 58.6 inches to 69.4 inches.
3. What is the range of heights that includes about 99.7% of young women?
About 99.7% of young women have heights within 3 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 3 standard deviations from the mean:
64 inches ± 3(2.7 inches)
So the range of heights that includes about 99.7% of young women is approximately 55.9 inches to 68.1 inches.
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Mrs. Smith has gallon of orange juice. She divides it equally
among her 8 grandchildren. How much orange juice does each
grandchild get?
Which equation models the situation?
The volume of the right cone below is 1152\piπ units^3
3
. Find the value of x.
x
12
The volume of the right cone below is 1152π/3 cubic units then the value of x is 24.
What is the volume of a right circular cone?The volume of a right circular cone is given by the formula:
V = (1/3)πr²h
where π is pi (approximately equal to 3.14), r is the radius of the circular base, and h is the height of the cone.
In this problem, we are given that the volume of the cone is 1152π/3 cubic units and that the value of x is related to the radius and height of the cone.
Let's first write the formula for the volume of the cone in terms of x:
V = (1/3)π(x/3)²(x/3)
Simplifying this expression, we get:
V = (1/27)πx²
We are given that V = 1152π/3, so we can substitute this into the formula above and solve for x:
1152π/3 = (1/27)πx³
Multiplying both sides by 27/π, we get:
x³ = 1152*27/3
x³ = 27648
Taking the cube root of both sides, we get:
x = 24
Therefore, the value of x is 24.
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