which answer is an example of a product-of-sum (pos) expression? x = abc x = ab cd x = (a b)(c d) x = a b c

The total cost of Stun Arun's driving from Indianapolis to Albuquerque, a distance of 1,285 miles, is $244.10.

The total cost means the sum of different expenses.

In this situation, the driving cost per mile for the first 350 miles is different from the rest of the distance.

Therefore, we find the different costs and sum them up to get the total cost incurred by Stun Arun, who is driving from Indianapolis to Albuquerque.

The total distance from Indianapolis to Albuquerque = 1,285 miles

The driving cost per mile for the first 350 miles = $0.27

The total cost for the first 350 miles = $94.50 (350 x $0.27)

The difference between 1,285 and 350 miles = 935 miles

The driving cost per mile for 935 miles = $0.16

The total cost for 935 miles = $149.60 (935 x $0.16)

The total driving cost from Indianapolis to Albuquerque = $244.10 ($94.50 + $149.60)

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Answer:

C s = k÷8

Step-by-step explanation:

Kylies Farm is 8 times larger than Sean's. So if we divide the size of Kylie's farm by 8, we have the size of Sean's farm.

s = k ÷ 8

k = 8s

k ÷ 8 = s

s × 8 = k

The length of the shorter piece of wire would be 22.

An electrician must divide a 49 m piece of wire into two sections, with the longer portion being 5 m longer than the shorter piece:

By using a simple Unitary Method We can solve this question

In order to calculate the required value using the unitary technique, multiply the value of one unit by the necessary number of units.

First wire - 27m

Second wire - 22m

27+22=49m

Also 27-22= 5

hence, s the length of the shorter piece of wire would be 22.

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Answer:

The man took 0.7 Hours for resting

Step-by-step explanation:

Total time taken = 6 hours

We can remove the first 2 hours as it isn't necessary in this question

so Total time taken  = 4 hours

Speed traveled  = 60kph

distance traveled = 200km

Time taken to travel  = Distance/ speed

= 200 / 60

= 3.3 Hours

Time taken for resting = Total time - Time taken for travel

= 4 hours - 3.3 hours

= 0.7 Hours

The man took 0.7 Hours for resting

Answer:

A. two table cloths

B. 24$

Step-by-step explanation:

First, develop your functions:

[tex]f(x)=3x+18\\g(x)=2x+20[/tex]

f(x) is the first company, g(x) is the second company.

A.

Set the two equations to be equal to each other and solve for x:

[tex]f(x)=g(x)\\3x+18=2x+20\\3x-2x=20-18\\x=2\\[/tex]

B.

Just plug in the value you got from A into either function:

[tex]f(2)=3(2)+18\\f(2)=24[/tex]

Answer:

It would take Shen 8.99999999802 hours to make $207.

Step-by-step explanation:

5/115 = 0.04347826086

207 x 0.04347826086 = 8.99999999802

The common difference of ap = 41/4 and the sum of 200 terms = 204575.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.

We have a3= 5 and a11=87 we have to find the value of d,

n th term of ap= An= a+(n-1)d

A3=5

5=a+2d

87=a+10d

d=41/4 and a=-31/2

the sum of 200 terms when a=3

[tex]S_n=\frac{n}{2}{(2a+(n-1)d)\\S_{200}=100(6+199*41/4)\\\\S_{200}=204575.[/tex]

The complete question is :-

suppose {an} is arithmetic and a3 = 5, a11 = 87. what is the common difference

And find [tex]\sum_{3}^{200}ak[/tex],

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Out of total 508 tickets, the adult tickets sold were 127 in number.

Let the number adult ticket be x. So the number of students tickets is 3x. Also, we know the sum of these tickets will be total number of tickets, which is already mentioned as 508. Thus, the expression that will form is -

Number of student tickets + number of adult tickets = total number of tickets

3x + x = 508

Performing addition on Left Hand Side of the equation

4x = 508

x = 508/4

Performing division on Right Hand Side of the equation

x = 127

Number of adult ticket = 127

Number of student ticket = 3x

Number of student ticket = 3×127

Number of student ticket = 381

Thus, 127 adult tickets were sold.

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No, this approach won't result in a representative sample because not all facets of society—especially the less advantaged ones—might have had their demises reported in the obituary column.

Given that a researcher is attempting to determine the average age of death for Americans, he is gathering data by keeping track of deaths' ages for a period of 30 days in the New York Times obituary columns. We now need to discuss whether this method will provide a representative sample.

No, this method won't produce a representative sample because not all parts of society, particularly the poorer ones, may have had their deaths recorded in the obituary column. As a result, the sample taken will not be a representative sample of the population, therefore this method cannot be used to forecast the average age.

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The probability that you will walk at least 2 dogs this week is 0.74

The probability that you will walk at most 2 dogs this week is 0.41

The probability that you will walk 3 dogs this week is 0.23

The probability that the number of dogs you will walk this week is not less than 5 is 0.18

The expected number of dogs you will walk this week is 2.83

The expected value of x is 11.29

The variance of dogs you will walk this week is 3.2811

The standard deviation of dogs you will walk this week is 1.8113

X: Random variable denoting how many dogs you walk this week.

Table attached at the end of solution

a) Probability that you will walk at least 2 dogs this week

[tex]P(x \geqslant 2) & =1-P(x < 2) \\[/tex]

= 1 - [P(x = 0) + P(x = 1)]

= 1 - [0.14 + 0.12]

= 1 - 0.26

[tex]P(x \geqslant 2) &[/tex] = 0.74

b) What is the probability that you will walk at most 2 dogs this week

P(x < 2) = P(x = 0) + P(x = 1) + P(x = 2)

= 0.14 + 0.12 + 0.15

P(x < 2) = 0.41

c) Probability that you will walk 3 dogs this week

P(x = 3) = 0.23

d) Probability that the number of dogs you will walk this week is not less than 5

[tex]P(x \geqslant 5) &[/tex] = P(x = 6) + P(x = 7) + P(x = 5)

= 0.08 + 0.01 + 0.09

= 0.09 + 0.09

= 0.18

e) Expected number of dogs you will want this week

F(x) = [tex]\sum_i p_i x_i[/tex]

E(x) = 0 × 0.14 + 1 × 0.12 + 2 × 0.15 + 3 × 0.23 + 4 × 0.18 + 5 × 0.09 + 6 × 0.08 + 7 × 0.01

E(x) = 2.83

f) Expected value of [tex]$x^2$[/tex]

[tex]E\left(x^2\right) & =\sum_1 p_i x_i^2 \\[/tex]

= 0 × 0.14 + 1 × 0.12 + 4 × 0.15 + 9 × 0.23 + 16 × 0.18 + 25 × 0.09 + 36 × 0.08 + 49 × 0.01

[tex]E\left(x^2\right) &[/tex] = 11.29

g) Variance of dogs you will walk this week

[tex]V(x) & =E\left(x^2\right)-[E(x)]^2 \\[/tex]

[tex]& =11.29-(2.83)^2 \\[/tex]

= 3.2811

h) Standard deviation of dogs you will walk this week

SD (x) = [tex]\sqrt{3.2811} \\[/tex]

= 1.8113

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You start a dog-walking business. Define X to be a random variable denoting how many dogs you walk

this week. The probability mass function (pmf), f(x), of X is defined as follows:

Table attached at end of the solution

(a) What is the probability that you will walk at least 2 dogs this week?

(b) What is the probability that you will walk at most 2 dogs this week?

(c) What is the probability that you will walk 3 dogs this week?

(d) What is the probability that the number of dogs you will walk this week not be less than 5 ?

(e) What is the expected number of dogs you will walk this week?

(f) What is the expected value of [tex]$X^2$[/tex] ?

(g) What is the variance of dogs you will walk this week?

(h) What is the standard deviation of dogs you will walk this week?

Answer:

g(x) = x^2 -3

Step-by-step explanation:

The distance far up the wall that the top of the ladder​ touches is 24 cm.

Given that a the ladder is 25 cm long and the foot of the ladder is 7 m away from the base of the wall.

This forms a right triangle.

From Pythagoras theorem;

Hypotenuse² = A leg² + B leg²

Plug the given values in and solve for B leg

Hypotenuse² - A leg² = B leg²

B leg = √( Hypotenuse² - A leg² )

B leg = √( 25² - 7² )

B leg = √( 625 - 49 )

B leg = √576

B leg = 24 cm

Therefore, the height at which the top of the ladder sits on the wall is 24cm.

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The cubes can be represented by the equation x³, where x represents the length of one side of the cube.

The vectors on the number line can be represented by the equation y = x, where x represents the position on the number line and y represents the magnitude of the vector.

So, to complete both equations, we can assign values to x and see the resulting values for y:

For the cubes:

For the vectors:

So, both the cubes and vectors can be represented on the number line, with the cubes represented as points with their x and y values being the length of one side and the volume of the cube, respectively, and the vectors represented as lines with their x and y values representing the position on the number line and the magnitude of the vector, respectively.

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Answer: look below :))

Step-by-step explanation: To solve the equation X^2+x-6=0, we can use the Quadratic Formula:

X = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -6.

Substituting these values into the formula, we get:

X = (-1 ± √(1 - 4(1)(-6))) / 2(1)

Which gives us:

X = (-1 ± √(1 + 24)) / 2

X = (-1 ± √25) / 2

So the solutions to the equation are:

X = ( -1 + √25) / 2 or X = (-1 - √25) / 2

X = ( -1 + 5) / 2 or X = (-1 - 5) / 2

X = 2 or X = -3

So the solutions of the equation X^2+x-6=0 are X = 2 and X = -3.

Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors. = 0.7316

There must be some mistakes in this. But I make an effort to address the appropriate topics.

Nothing is underneath (a). I have nothing to say in response.

(a) Her purse contains 20 candies. If all 20 are yellow, then 9.

As a result, the probability is the proportion of desirable possibilities to all possible outcomes.

Hence, ta da! 9/20

That is the likelihood that Samira will choose a yellow candy.

Again, 20 candies are the starting point [1](i).

Six are green.

When she chooses the first option, her likelihood of selecting a green option is 6/20 = 3/10 = 0.3.

She chooses another candy now, assuming that her prediction came true.

Only 19 were left this time, and 5 of them are green.

Therefore, the likelihood is 5/19.

For the situation we are describing, both occurrences are now required. No overlapping, no ifs, ands, or buts exist. It is simply the sum of the two probabilities.

3/10 × 5/19 = 15/190 = 3/38

That's what I believe the description calls for.

(ii) The likelihood is that the first choice is red and the second is not, plus the first choice is green and the second is not, plus the first choice is yellow and the second is not.

so,

red and not red

5/20 = 1/4 red

15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).

red and not red = 1/4 × 15/19 = 15/76 = 0.1974

green and not green

6/20 = 3/10 = green

14/19 = not green

green and not green = 3/10 × 14/19 = 52/190 = 26/95 =

= 0.2737

yellow and not yellow

9/20 = yellow

11/19 = not yellow

yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606

Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors.

= 0.7316

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Answer:

I think I'm wrong but I Think its C and D

Step-by-step explanation: Tell me if I'm wrong that way other people know

The standard notation of the given term is 70,000.

A form of writing a certain number, an equation, or an expression in a way that adheres to set norms is known as a standard notation.

Given a phrase

7 times 10 four square

so 10 four square is 10 to the power 4

10 four square = 10⁴

and 7 times 10⁴ = 7 x 10⁴

the standard form of 7 x 10⁴ is

10⁴ = 10,000

7 x 10⁴ = 7 x 10,000

7 x 10⁴ = 70,000

Hence standard form is 70,000.

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Answer:

[tex]350%[/tex]%

Step-by-step explanation:

[tex]\frac{70}{20}[/tex] x 100% = 350%

Answer: There are 48 numbers of 12-ounce in 36 pounds of the dog food.

To understand more, check below explanation.

Pounds to ounce conversion:

Given that,

There are 16 ounces in 1 pound .

First , we have to convert 36 pounds of dog food into ounces.

1 pound = 16 ounces

36 pounds = 16 * 36 = 576 ounces

We have to find  how many 12-ounce servings are in 36 pounds of dog food.

So that, number of 12-ounce of dog food =

Hence, there are 48 numbers of 12-ounce in 36 pounds of the dog food.

This means that a linear relationship exists among the variables.

When the data points on a scatterplot cluster along a straight line, it indicates that there is a linear relationship between the two variables being plotted.

The scatterplot visually shows that as one variable increases or decreases, the other variable also increases or decreases in a proportional manner, following a straight-line pattern.

The correlation coefficient is an estimation of the strength and direction of the linear relationship between two variables. A positive correlation coefficient indicates that as one variable increases, the other variable also increases, while a negative correlation coefficient indicates that as one variable increases, the other decreases.

The magnitude of the coefficient implies the strength of the relationship, with a value of 1 showing a perfect positive correlation and a value of -1 showing a perfect negative correlation.

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--The given question is incomplete; the complete question is

"A student conducting a research study was told by her professor to use a scatterplot in conjunction with calculating the correlation coefficient. She discovered that the data points clustered along a straight line; this means that:  

A. The student cannot determine if a relationship exists.

B. No relationship exists between variables.

C. A nonlinear relationship exists among the variables.

D. A linear relationship exists among the variables."--

Por lo tanto, hace 50 años que el Abuelo era 10 veces mayor que el Nieto.

Primero, definimos las edades en una ecuación.

Padre = 25

Hijo = 20

Abuelo = 4 × Nieto = 1

Para encontrar cuántos años han pasado desde que el Abuelo era 10 veces mayor que el Nieto, restamos 25-20=5 años desde que el Padre era 5 años mayor que el Hijo. Luego, multiplicamos esto por 10 para encontrar los años transcurridos desde que el Abuelo era 10 veces mayor que el Nieto. Entonces, 5 x 10 = 50 años. Por lo tanto, hace 50 años que el Abuelo era 10 veces mayor que el Nieto.

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The answer of modelled graph representing heights of the steps are:

a. Period = 40 sec.

b. Equation of axis :

        H(t) = t /3 , 0 < t < 15

         -t/3 + 10 , 15 < t < 35

          t/ 3 , 35 < t < 40

c. Peak is highest point of step of escalator.

d. Range ( -1, 5)

e. Domain ( 0, 350 )

f. No.

From the attached graph which represents the height of steps in escalator gave answer of the following question :

a. Period of the function = 40 sec.

It represents the complete cycle.

b. Equation of the axis for periodic function is given by breaking the graph into points :

H(t) = t /3 , 0 < t < 15

         -t/3 + 10 , 15 < t < 35

          t/ 3 , 35 < t < 40

c. Peak of the periodic function is given highest point of the escalator.

d. Range of the function is -1 to 5.

e. Domain for 10 cycles is ( 0, 350 ).

f. No , Steven is not correct. At t= 350s stair will  be at ground level.

Therefore, the answer based on the height of escalator steps through graph are:

a. Period of the function = 40 sec

b. Equation of axis for periodic function:

         H(t) = t /3 , 0 < t < 15

         -t/3 + 10 , 15 < t < 35

          t/ 3 , 35 < t < 40

c. Highest point of steps represents peak.

d. range = -1 to 5

e. Domain of periodic function : ( 0,350)

f. No.

The above question is incomplete, the complete question is :

1. Steven is monitoring the height of one particular step on an escalator that takes passengers from the ground level to the second floor. The height of the Height of Step step in terms of time can be modelled by the graph shown. a) What is the period of the function, and what does it represent in this situation? b) Determine the equation of the axis for this periodic function. c) What do the peaks of the periodic function represent in this situation? Time (s) d) State the range of the function. e) If the escalator completes only 10 cycles before being shut down, what is the domain of the periodic function? f) Steven states that the stair will be at ground level at  t = 300s. Is he correct? Justify your answer.

Graph is attached.

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Grace enjoys salads a lot. If she can select one from each of the aforementioned vegetables and dressings, she can create 56 salads.

Grace has two options for lettuce, four options for vegetables, and seven options for dressing. To determine the total number of salads she can make, we multiply the number of options for each ingredient. In this case, we have 2 options for lettuce, 4 options for vegetables, and 7 options for dressing. Multiplying these numbers, we get:

The result, 56, represents the total number of different salads Grace can make by choosing one option from each category.

This question should be written as:

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The Excluded value of x/x-2 + x+y/x-1 = 3x/x-2 is x²- 5x+9 = 0.

The answers obtained after setting the denominator(s) equal to zero are the values that are excluded. The excluded values are the values for which a rational expression is undefined. These are values for which there is no known rational expression. Values that will round a fraction's denominator down to 0 are excluded. It's crucial to identify these excluded values while resolving a rational statement because you cannot divide by 0.

x/x-2 + x+y/x-1 = 3x/x-2

x(x-1) + (x+4)(x-2)/(x-2)(x-1) = 3x/x-2

x²-1+²(x²-2x)+(4x-8)/(x-2)(x-1) = 3x/x-2

x²-1+x²-2x+4x-8/(x-2)(x-1) = 3x/x-2

2x²+2x-9/x²-3x+2 = 3x/x-2

(x-2)(2x²+2x-9) = 3x(x-2)(x-1)

2x²+2x-9 = 3x²-3x

5x-9 = x²

x²-5x+9 = 0.

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Answer:

- 1 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

-3.75 can be written as a fraction as -3 [tex]\frac{75}{100}[/tex] o r-3 [tex]\frac{3}{4}[/tex]  if I divide the numerator and the denominator by 25.

[tex]\frac{2}{5}[/tex] (-3 [tex]\frac{3}{4}[/tex])

We can change -3 [tex]\frac{3}{4}[/tex] into an improper fraction.  We can do that a few ways but I am going to the it the way that is most intuitive to me.

another name for 1 is [tex]\frac{4}{4}[/tex] because 4 ÷ 4 = 1.  I am going to use that knowledge to convert -3 [tex]\frac{3}{4}[/tex] into a mixed number.

-( [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] + [tex]\frac{3}{4}[/tex]) =  - [tex]\frac{15}{4}[/tex]  The negative sign can go in the numerator, denominator or in front to the fraction to show that the number is negative.

[tex]\frac{2}{5}[/tex] x  -[tex]\frac{15}{4}[/tex]  = - [tex]\frac{30}{20}[/tex]  Divide the numerator and the denominator by 10

= [tex]\frac{3}{2}[/tex]

Which means the same thing as -( [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{3}[/tex] ) which means the same thing as -(1 + [tex]\frac{1}{3}[/tex] +or -  1 [tex]\frac{1}{3}[/tex]

The box plot is complete because it displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.​

Due to the fact that it shows a five-number summary of a collection of data, the box plot is finished. Minimum, first quartile, median, third quartile, and maximum are the five numbers that make up the summary.

The boxplot visually displays the minimum, lower quartile, median, upper quartile, and maximum of five sample data. The plot's box is a rectangle with ends at each quartile, enclosing the middle half of the sample. The sample's interquartile range is therefore represented by the box's length. The box's second dimension does not specifically symbolize anything.

The sample median is used to draw a line through the box. From the box's two ends, whiskers grow until they reach the sample's maximum and minimum. The crossbar at each whisker's extreme end is optional, and its length has no significance. The next diagram compares a boxplot of the same data with a dot-plot of a sample of 20 observations (actual sample values used in the display).

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Answer:

In this Equation x = 44.78  = 24 + 12root3

The Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex]

The absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong.

The Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%

Correlation Coefficient value always lies between -1 to +1. If correlation coefficient value is positive, then there is a similar and identical relation between the two variables. Else it indicates the dissimilarity between the two variables.

The covariance of two variables divided by the product of their standard deviations gives Pearson’s correlation coefficient. It is usually represented by ρ (rho).

ρ (X, Y) = cov (X, Y) / σX.σY.

Given, coefficient of determination, [tex]r^2[/tex] = 0.64

a)  Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex]

b) Since the absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong.

c) Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%

Therefore, the Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex], the absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong, Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%.

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The probability that at least two of the babies are girls is given as follows:

0.9941 = 99.41%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

As there are 11 babies, equally as likely to be a boy or a girl, the parameter values for this problem are given as follows:

p = 0.5, n = 11.

The probability that less than two are girls is:

P(X < 2) = P(X = 0) + P(X = 1).

In which:

Hence:

P(X < 2) = 0.0005 + 0.0054 = 0.0059.

Then the probability of at least two girls is of:

P(X >= 2) = 1 - P(X < 2)

P(X >= 2) = 1 - 0.0059

P(X >= 2) = 0.9941.

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Perimeter is the the continuous line defining a closed geometric figure.

A closed route that covers, encircles, or outlines a one-dimensional length or a two-dimensional form is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are several uses in real life for perimeter calculations.

The complete length of a shape's border is referred to as the perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

The length of a shape's outline is its perimeter. You must sum the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x denotes the rectangle's length and y its width.

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