Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the estimated value of each expression with its position on the number line.
Answers
From the number line √90-√40 match with D, [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C, 2√27 -√48 match with E and [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.
In the given question we have to match the each expession with its position on the number line.
The given first expression is √90-√40.
We firstly simplifying the expression.
√90-√40=√9×10-√4×10
√90-√40=3√10-2√10
Taking common [tex]\sqrt{10}[/tex] on both side
√90-√40=√10(3-2)
√90-√40=√10
√90-√40=3.16
From the number line √90-√40 match with D.
The given second expression is [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex].
We firstly simplifying the expression.
We can write it as
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{5\times7}-\sqrt{6\times7}}{\sqrt{5}-\sqrt{6}}[/tex]
Taking common √7 on both side
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{7}(\sqrt{5}-\sqrt{6})}{\sqrt{5}-\sqrt{6}}[/tex]
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\sqrt{7}[/tex]
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] = 2.65
From the number line [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C.
The given third expression is 2√27 -√48.
We firstly simplifying the expression.
We can write it as
2√27 -√48=2√3×9 -√16×3
2√27 -√48=2×3√3 -4√3
2√27 -√48=6√3 -4√3
Taking √3 common on both side, we get
2√27 -√48=√3(6 -4)
2√27 -√48=2√3
2√27 -√48=2×1.71
2√27 -√48=3.42
From the number line 2√27 -√48 match with E.
The given fourth expression is [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex].
We firstly simplifying the expression.
We can write it as
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{9\times6}-\sqrt{4\times6}}{\sqrt{2\times9}-\sqrt{2\times4}}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{3\sqrt{6}-2\sqrt{6}}{3\sqrt{2}-2\sqrt{2}}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{6}(3-2)}{\sqrt{2}(3-2)}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\sqrt\frac{6}{2}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] =√3
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] = 1.71
From the number line [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.
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Answer: d,c,e,
ur welcomee!
Related Questions
At time t = 0, water begins to drip out of a pipe
nto an empty bucket. After 56 minutes, 8 inches
of water are in the bucket. What linear function
n the form y = mx + b represents the amount of
water in inches, w, in the bucket after t minutes?
Answers
Step-by-step explanation:
w = t/7
at the beginning we 0 inches of water.
after 56 minutes we have 8 inches of water.
that is a ratio of 56 minutes / 8 inches = 7/1 = 1 / 1/7.
so, in 1 minute we get 1/7 inch of water.
in 2 minutes 2×1/7 = 2/7.
in 3 minutes 3×1/7 = 3/7.
...
hence the equation.
Answer:
y = t/7Step-by-step explanation:
GivenStart time t = 0,Start level y = 0,Level of y = 8 in after t = 56 minSolutionFind the value of m and b in the equation y = mx + b.
The value of b = 0, since there is no level in the bucket initially.
Find the value of m, the slope:
8 = 56m,m = 8/56m = 1/7So the equation is:
y = (1/7)t + 0or
y = t/7Please help an 8th grader in needdddddddddddd!!!!!!!!
Answers
Answer:
y = (24/5)x + 24
Step-by-step explanation:
Knowing that the parent equation for linear functions is "y = mx+b", where "m = slope" and "b = y-intercept", we can create an equation for the line of best fit.
We also need to know the formula for using two points to find the slope is "(y2 - y1)/(x2 - x1)", where (x2, y2) is a point on the graph and (x1, y1) is a point on the graph.
Finding the slope:
I will be using points (5, 48) and (0, 24).
(24 - 48)/(0 - 5)
(-24)/(-5)
24/5 is the slope so "m = 24/5"
We can tell from the graph (0, 24) is the y-intercept, so "b = 24"
Final equation:
y = (24/5)x + 24
Jimmy is writing a paper for one of his classes. The paper has to be 3,000 words long, and so far he has written 786 words. If he only has 6 more days to write his paper and wants to write the same number of words each day, then how many words must he write per day to finish the paper?
Answers
Jimmy has to write 369 words per day for the next 6 days to finish the paper.
The total number of words in the paper has to be 3000
Jimmy has already written = 786 words.
3000-786 = 2214
So, Jimmy still has to write 2214 words.
He has 6 days to write the paper and he wants to write the same number of words per day.
With this in mind to find out how many words he has to write per day we can divide 2214 by 6.
2214/6 = 369 words
So, Jimmy has to write 369 words per day for the next 6 days to finish the paper.
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The wholesale cost of a dining room table at a furniture store is $1,115.80. The
markup for the table is 20%. What is the selling price of the dining room table?
Answers
Answer: $1338.96
Step-by-step explanation:
The wholesale cost means the cost that the store buys the table from the supplier. To find the price that the store sells it, it is a 20% markup.
The orginal price is $1,115.80. What is 20% of $1,115.80?
$1,115.80 * .20 = $223.16
Lets add the original price to the markup.
$1,115.80 + $223.16 = $1338.96
Hope this helps <3
X= Y. Y = 3. Which statement below is true?
Answers
Answer:
X=3
Step-by-step explanation:
I'm not sure what statements below you want me to confirm that X=Y, Y=3
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.
Answers
The probability that the person is between 67.1 and 68.3 inches, using the normal distribution, is of:
0.1056 = 10.56%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the heights of UCB students are given as follows:
[tex]\mu = 65, \sigma = 2.4[/tex]
The probability that the person is between 67.1 and 68.3 inches is the p-value of Z when X = 68.3 subtracted by the p-value of Z when X = 67.1, hence:
X = 68.3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (68.3 - 65)/2.4
Z = 1.38.
Z = 1.38 has a p-value of 0.9162.
X = 67.1:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (67.1 - 65)/2.4
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
0.9162 - 0.8106 = 0.1056 = 10.56%.
Missing informationThe problem asks for the probability that the person is between 67.1 and 68.3 inches.
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What is value of x?
Responses
12
12,
10
10,
9
9,
3
Answers
(MAKE BRAINLIEST IF I HELPED)
Answer:
x=10
Step-by-step explanation::
We can use Triangle angle bisector theorem and proportions to solve this problem. We put the small triangle side over the large triangle side
8 x+4
------ = ------------
12 2x+1
Using cross products
8(2x+1) = 12(x+4)
16x+8 =12x+48
Subtract 12x from each side
16x-12x +8 = 12x-12x+48
4x+8 = 48
Subtract 8 from each side
4x+8-8 = 48-8
4x = 40
Divide by 4
4x/4 = 40/4
x = 10
Answer:
x=10
Step-by-step explanation:
Use a table of values to graph the function ƒ(x) = –2 ∛x . Select the correct graph below.
Answers
The table of values for the function ƒ(x) = –2 ∛x is
x y
-8 4
-4 3.175
0 0
4 3.175
8 4
The correct graph option is attached
How to construct the table of values
Using the given expression, the table of values is calculated with the input values as
x = -8, -4, 0, 4, 8
for x = -8
ƒ(x) = –2 ∛-8 = 4
for x = -4
ƒ(x) = –2 ∛-8 = 3.175
for x = 0
ƒ(x) = –2 ∛-8 = 0
for x = 4
ƒ(x) = –2 ∛-8 = -3.175
for x = 8
ƒ(x) = –2 ∛8 = -4
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9,70,499,2488,7469 complete the series
Answers
To complete the given series 9, 70 , 499, 2488, 7469 the next number is given by 7466.
As given in the question,
Given series is equal to :
9, 70 , 499, 2488, 7469
Simplify the given series to get the next sequence number we have:
Pattern of the given series is given by:
9
70 = 9 × 9 -11
= 70
499 = 70 × ( 9 -2 ) + ( 11 - 2 )
= 70 × 7 + 9
= 499
2488 = 499 × ( 7 - 2 ) - ( 9 - 2 )
= 499 × 5 - 7
= 2488
7469 = 2488 × ( 5 - 2 ) + ( 7 -2 )
= 2488 × 3 + 5
= 7469
Next number is :
7469 × ( 3 - 2 ) - ( 5- 2 )
= 7469 × 1 -3
= 7466
Therefore, to complete the given series 9, 70 , 499, 2488, 7469 the next number is given by 7466.
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What is 79 - 75 / 75 * 100 ?
I'm dividing 75 into 79 - 75 then timesing that by 100, I keep getting -21 but that's not right. I need help please
Answers
The required value of the given expression : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100 = 5.3
What is BODMAS rule ?The Bodmas rule is based on the BODMAS acronym, which stands for Brackets, Order of Powers or Roots, Division, and Multiplication. Subtraction is represented by the letter S, while addition is represented by the letters A and S. According to the BODMAS rule, mathematical expressions with multiple operators must be resolved in the order of BODMAS, starting from the left. As with addition and subtraction, division and multiplication are interchangeable and depend on which comes first in the expression.
Given : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100
on calculating it further
we get :
[tex]\frac{4}{75}[/tex] × 100
0.0533 X 100
=> 5.3
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what is the same value as 8.76
Answers
Answer:
B, C
Step-by-step explanation:
A is incorrect, it should be seventy-six hundredths.
D is incorrect, the place value for the third term is wrong - it should be 0.06.
HFHFHFHHFHFHFHHHVHFHVHVHHVHVHHV
Answers
Students from the local high school are selling tickets to the town's annual carnival. Adult admission is $4.00 and child admission is $2.00. Four hours after the carnival opened its first day, 440 tickets had been sold totaling $1380. How many adults and how many children entered the carnival after it was opened?
Answers
The number of adults is 200 and the number of children that entered the carnival after it was opened is 240.
How to find the number tickets sold?Let a represent the number of adult tickets sold
Let c represent the number of children tickets sold
4a + 2c = 1380
Hence,
a + c = 440
Solving for c
4 (440-c) +2c = 1280
1760-4c +2c = 1280
-4c+2c = -480
-2c=-480
Divide both side by -2c
c = -480/-2
c = 240 (children tickets)
Solving for a
a =440-c
a =440 -240
a=200 (Adult tickets)
Therefore 240 and 200 tickets were sold.
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Evaluate the equation:
6w = 180
W = ____
Answers
Answer:
30
Step-by-step explanation:
Divide each term in 6 w = 180 by 6 and simplify. w = 30
Answer:
w = 30
Step-by-step explanation:
Given equation,
→ 6w = 180
Now the value of w will be,
→ 6w = 180
→ w = 180/6
→ [ w = 30 ]
Hence, the value of w is 30.
100 points for this There was a blizzard. Snow was falling at the rate of 3
inches per hour. If the snow keeps acclimating how long will 5 feet of snow to accumulate ?
Answers
Since there are 60 inches in 5 feet (5*12), we know that it will take 20 hours for 5 feet of snow to accumulate (60/3).
Hope this helps!
Wendy solved a problem with her calculator, and she got this answer:
2.35E7
Which expressions are equivalent to the answer she got? Select all that apply.
2.35 7
395.8
23,500,000
16.45
2.357
2.35 x 10²
Answers
Expression is equal to = 2.35 x 10^7.
Given,
In the question:
Wendy solved a problem with her calculator, and she got this answer:
2.35E7
To find the which expressions are equivalent to the answer she got?
Now, According to the question;
The number is given as:
2.35E7
Expression is equal to = 2.35 x 10^7
Hence, Expression is equal to = 2.35 x 10^7.
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Which of the following are characteristics of the graph of the linear parent
function?
Check all that apply.
A. It goes through the origin.
B. It has a slope of 1.
C. It is a parabola.
D. It is a straight line.
Answers
The following are the characteristics of the graph of the linear parent function:
B. It has a slope of 1.
C. It is a parabola.
D. It is a straight line.
Lets explain the meaning of linear parent function
- A linear parent function is the equation y = x or f(x) = x
- A parent function is the simplest equation of a function
- It represented by a straight line passing through the origin point O
- The x-coordinate and the y-coordinate of any points lie on it are equal
- The slope of the line is 1 because the slope is the change of Δy/Δx
and Δy = Δx
The characteristics of the graph of the linear parent function are
∵ Linear parent function is f(x) = x and f(x) = y
∴ x = y
∵ The slope = Δy/Δx
∵ Δx = Δy because x = y
∴ The slope of it is 1
B. It has a slope of 1
∵ y = 0
∵ If x = 0 then y must = 0
∴ It goes through the origin
C. It goes through the origin
∵ It is a linear function
∵ All linear function represented by a straight line
∴ The graph of the linear parent function is a straight line
D. It is a straight line
Hence we get the right answers.
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The function f(x) = 16.4x + 2 is used by a construction company to estimate the amount of fuel necessary for a truck to get to a job site depending on the miles from the office, x. The mathematical domain for the function is the set of real numbers.
How does the reasonable domain differ from the mathematical domain?
The reasonable domain is the set of positive real numbers.
The reasonable domain is the set of positive whole numbers.
The reasonable domain is the set of real numbers greater than 2.
The reasonable domain is the set of whole numbers greater than 2.
Answers
The domain of the function f(x) = 16.4·x + 2, where x is the distance from the office, which is (always) a positive number is the set of all real numbers but the reasonable domain differs from the mathematical domain in that; The reasonable domain is the set of positive real numbers
What is the domain and range of a function?The domain is the set of the possible inputs while the range is the set of the possible outputs of the function.
The mathematical domain is the set of the inputs that the function accepts
The function, f(x) = 16.4·x + 2, mathematically, is continuous for all real number value of x. that is the function has an output when the input, x, is a member of the set of real numbers which includes negative number.
The number of miles from the office, which is the distance from the office is (always) a positive number, because it is the distance between two places, and therefore is not a negative number.
The values of x are therefore positive numbers and the reasonable values of the variable, x, which is the distance from the office is the set of positive real numbers.
The option that indicates how the reasonable domain differ from the mathematical domain is therefore;
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A house on the market was valued at $447,000. After several years, the value decreased by 17%. By how much did the house's value decrease in dollars? What is the current value of the house?
Decrease in value:
Current house value:
Answers
The rate that the house's value decrease in dollars, that is the current value of the house in terms of:
Decrease in value: $75,990Current house value: $371,010What causes a decline in market value?A stock's price rises if there is a greater demand (buyers) than supply (sellers) for it. On the other hand, if there was a bigger supply than there was a demand for a stock, the price would drop. It's simple to comprehend supply and demand.
The price decreases by:
= $447, 000 * (0.17)
=$75,990.
The current value is:
= 447, 000 - 75,990
= $371,010.
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I need some help please
Answers
Check the picture below.
(b) The graph of y=g(x) is shown. Draw the graph of y=g(1/2x)
Answers
The graph of the piece-wise function g(0.5x) is given by the second image at the end of the answer.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the function given by the first graph has two definitions, as follows:
To the left of x = 0.To the right of x = 0.The two functions are linear with intercept 0, hence the definitions are given as follows:
x < 0: y = 2x, as when x increases by 1, y increases by 2, hence slope of 2.x > 0: y = -0.5x, as when x increases by 2, y decreases by 1, hence slope of -0.5.After the transformation x -> 0.5x, the definitions are given as follows:
g(0.5x) = 2(0.5x) = x, x < 0.g(0.5x) = -0.5(0.5x) = -0.25x, x > 0.Missing InformationThe graph of g(x) is given by the first image at the end of the answer.
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Finding a percentage of a total amount
Answers
0.124 x 173 = 21.452
Answer 21.5 (rounded to the nearest tenth)
h(t)= t+ 1/t^2+2t+2.
Find derivative.
Answers
The derivative of given function is H’(t) = 3 – 2/t3
A derivative is a two-party contract whose value/price is derived from an underlying asset. Futures, options, forwards, and swaps are the most prevalent types
Given that H(t)= t+ 1/t^2+2t+2
We must calculate the derivative
H(t)= t+ 1/t^2+2t+2
H(t) = 3t + 1/t^2 + 2
H’(t) = d/dt(3t + 1/t^2 + 2)
H’(t) = d/dt(3t) + d/dt (1/t^2) + d/dt ( 2)
H’(t) = 3xd/dt(t) + d/dt (1/t^2) + d/dt ( 2)
H’(t) = 3xd/dt(t) + d/dt (t-2) + d/dt ( 2)
H’(t) = 3 – 2t-3
H’(t) = 3 – 2/t3
Therefore the derivative of the given function is H’(t) = 3 – 2/t3
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At the store where you work, the prices on a clearance rack of merchandise are 0.62 of the original price. The sign on the clearance rack states that an additional 23% of the original price will be taken off at checkout. In total, what portion of the original price has been deducted to get the clearance price?
0.29
0.49
0.65
0.85
0.95
Answers
The portion of the original price that has been deducted to get the clearance price is D. 0.85
How to calculate the value?Given that the the prices on a clearance rack of merchandise are 0.62 of the original price and that the sign on the clearance rack states that an additional 23% of the original price will be taken off at checkout.
Therefore, the prices deducted will be:
= 0.62 + 23%
= 0.62 + 0.23
= 0.85
In conclusion, the correct option is D.
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In 1/6 of a day Bart read 4/7 of comic book .what rate can he read in a day
Answers
The rate at which Bart read is 24/7 book/day.
Given, Bart read 4/7 of comic book in 1/6 of a day.
We have to find the rate at which he read the book in a day.
Now, Bart read 4/7th of a comic book = 1/6th of a day
4/7 comic book = 1/6 day
1 day = (4 × 6)/7 comic book
1 day = 24/7 comic book
So, the rate at which Bart read is 24/7 book/day.
Hence, the rate at which Bart read is 24/7 book/day.
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Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
x - 4 = 0
Answers
There is only one solution for the equation x - 4 = 0 and the solution is 4.
Equation
An equation also known as the expression consists of variables, number and the mathematical operator that are combined using the equal sign.
Given,
Here we have the equation x - 4 = 0
Now, we need to Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
In order to find the solution of the equation, we have to equate the equation with zero and solve it accordingly,
So, the given equation is rewritten as,
x - 4 = 0
Now, we have to move the number to the other side to get the value x, then we get,
x = 4.
Therefore, the equation has only one solution that is 4.
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What is the solution to the following system?
[3x+10y-12z = 40
X-5y = 0
X-4z = 0
(8, 40, 32)
(10, 2, 3)
(20, 4, 5)
(40, 8, 10)
Answers
The solution of the system of equations is (2, 4, 5)
The given equations are :
3x+10y-12z = 40 equation(1)
x-5y = 0 equation (2)
x-4z = 0 equation(3)
From 2nd equation, x -5y = 0, 5y = x, y = x/5
From 3rd equation, x -4z = 0, 4z = x, z = x/4
Putting the values of y and z in equation (1), we get :
[tex]3x +10y -12z = 40\\\\3x +10*\frac{x}{5} -12*\frac{x}{4} = 40\\\\3x +2x -3x =40\\\\2x = 40\\\\x = \frac{40}{2} = 20[/tex]
Now, putting the value of x = 20 to evaluate y and z, we have,
y = 20/5 = 4
and z = 20/4 = 5
Hence, the solution of the system of equations is (2, 4, 5)
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guys please help!! tyyy
Answers
William opened two investment accounts. The first year, these investments, which totaled $2600, yielded $175 in simple interest. Part of the money was invested at 7.5% and the rest at 5%. How much was invested at each rate?
Answers
An amount of $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, one part of $2600 was invested at a rate of 7.5% and the other part was invested at a rate of 5%, and the total yield was $175 simple interest.
Let $x was invested at 7.5%, then $(2600-x) was invested at 5%.
Since the yield is $175, it follows,
7.5% of x + 5% of (2600-x) = 175
7.5x/100 + 5(2600-x)/100 = 175
7.5x + 13000 - 5x = 17500
2.5x = 17500-13000
2.5x = 4500
x = 1800
Now, the value of (2600-x) is,
2600-1800
=800
Hence, $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.
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William invested $1800 at 7.5% and $800 at 5% on his both accounts.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, William opened two investment accounts. In the first year, these investments, which totaled $2600,
Assuming he invested $x at 7.5% on the first account and $(2600 - x) at 5% in the second account and yielded $175 in simple interest.
∴ (x×7.5×1)/100 + {(2600 - x)×5×1}/100 = 175.
7.5x/100 + (13000 - 5x)/100 = 175.
7.5x + 13000 - 5x = 17500.
2.5x = 4500.
x = 1800. And (2600 - x) = (2600 - 1800) = 800.
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Let P be the set of integers that are multiples of 3 between 1 and 10 and Q be the set of positive integers that are multiples of 4 and are less than 15. Which of the following list of elements does not belong to the union of P and Q?
A. 5
B. 3
C. 6
D. 4
Answers
The union of the sets P and Q does not have the integer 5 since it is neither a multiple of 3 or a multiple of 4.
P is the set of integers between 1 and 10 and multiple of 3.
∴P = {3,6,9}
Q is the set of positive integers less than 15 and multiple of 4.
∴Q = {4,8,12}
Now the union of the sets P and Q is given by :
P∪Q = {3,4,6,8,9,12}
Now the union of the sets does not contain the integer 5.
Any collection of items, including a set of raw materials, the seven days of the week, several car types, etc., can be categorized as a set.
Any set component counts as an element of the set. Curly brackets are used to write a set. A very basic set would resemble something like this:
Q = {4,8,12}.
Therefore the integer 5 does not belong to the union of P and Q .
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