A is directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
A vector is an object that, as we all know, possesses both magnitude and direction. We must determine a vector's length in order to determine its magnitude. Vector quantities include things like velocity, displacement, force, momentum, etc. However, scalar quantities like as speed, mass, distance, volume, temperature, etc. exist. In contrast to vectors, which
have both magnitude and direction, scalars only have magnitude.
Magnitude of vector A = |A| = 5 units
We know, the negative Y-axis is an angle of 270° counterclockwise with a positive X-axis.
θ = Angle of vector A with positive X-axis = (270° - 40°) = 230°
So, x component of vector A = Ax = |A| * cos 230° = |A| * cos (180° + 50°) = |A| * (- cos 50°) = 5 * (-0.6428) = -3.214
And, y component of vector A = Ay = |A| * sin 230° = |A| * sin (180° + 50°) = |A| * (- sin 50°) = 5 * (-0.766) = -3.83
Since Ax and Ay both are negative relative to positive X and Y axes respectively; so, the x and y components of vector A are directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
the complete question is -
Vector img has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.What are the x and y components of vector img .
A)Ax = 3.83 and Ay = 3.21
B)Ax = 3.83 and Ay = -3.21
C)Ax = -3.21 and Ay = -3.83
D)Ax = -3.21 and Ay = 3.83
E)Ax = 4.29 and Ay = 2.16
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3
How many full 4 3/4in. sheets can be cut from 22 1/8in. stock?
3
The 22 1/8in stock can be cut into full sheets of length 4 3/4in.
The number of sheets that can be cut from 22 1/8 inches would be 4 25/38
How to solve for the divisionTo solve this, I would first have to convert the values to decimals
4 3/4in = 4.75 inches
22 1/8 = 22.125
To get the full length that can be cut from the 22.125, we would have to divide. That is;
22.125 / 4.75
= 4.657
4 25/38
The number of full sheet that can be cut from this would be 4 25/38
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can someone help me to find other parts to this problem?
The required answer of other parts are 4) 1230, 5) Students = 1230 + 53t, 6) 2025 students.
What is average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
According to question:As you have calculated average students in a year is 53.So, we can say students are increasing by 53 each year.
4) in 2003, number of students are 1389 and in three year students increase by 53* 3 = 159
in 2000,
Students = 1389 - 159
= 1230
5) We have 1230 students in 2000, and students will increase by 53 each year.
So, for t years equation will be
Students = 1230 + 53t
6) There is 15 years to come 2015, using our equation;
Students = 1230 + 53t
Students = 1230 + 53(15)
Students = 1230 + 795
= 2025 students.
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Rectangle a has side lengths of 6 cm and3.5 cm. The side lengths of rectangle B are proportional to the side lengths of rectangle a
The side lengths of rectangle B, given that they are proportional to rectangle A would be :
A. 3cm and 1.75cmE. 5.25cm and 9cmHow to find out proportionality ?To find proportionality, the dimensions of Rectangle B which correspond to Rectangle A, need to be divisible by, or be able to divide Rectangle A's dimensions without leaving a remainder.
The side lengths of 3 cm and 1. 75 cm are proportional because:
= Dimensions A / Dimensions of B
= 6 / 3 : 3. 5 / 1. 75
= 2 : 2
The side lengths of 5. 25 and 9 cm are also proportional because :
= 9 / 3 : 5 . 25 / 1 . 75
= 3 : 3
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The rest of the question is:
What could be the side lengths of rectangle B?
A. 3cm and 1.75cm
B. 5cm and 2.5cm
C.7 cm and 7cm
D. 12cm and 5 cm
E. 5.25cm and 9cm
Which inverse operations could you use to solve the equation m/4-18= -10? Select two answers.
The inverse operations are (b) and (c)
How to determine the inverse operationsFrom the question, we have the following parameters that can be used in our computation:
m/4-18= -10
Operation 1: Option (B)
Add 18 to both sides of the equation, and then multiply through by 4
Using the above as a guide, we have the following:
m/4 = 8
m = 32
Operation 2: Option (C)
Multiply each side by 4 and then add 72
Using the above as a guide, we have the following:
m - 72 = -40
m = 32
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Using the graph given below, state the value of lim f(x).
The limit when we approach x = 3 from the right side is:
[tex]\lim_{x \to 3^+} f(x) = 4[/tex]
What is the value of the limit?Here we have the graph of a function f(x), and we want to find the value of the limit:
[tex]\lim_{x \to 3^+} f(x)[/tex]
That would be the value of f(x) as it approaches x from the right side, in this case, will be the value on the graph when we go from right to left.
We can see an open circle at y = 4
Then we can conclude that the value of the limit when we approach x = 3 from the positive side is:
[tex]\lim_{x \to 3^+} f(x) = 4[/tex]
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1) City A and City B have increased growth in population. Write an exponential function to represent the City B’s population, y, based on the number of years that pass, x, after a period of exponential growth.
2) City A and City B have decreased growth in population. Write an exponential function to represent City B’s population, y, based on the number of years that pass, x, after a period of exponential decline.
3) Explain the similarities and differences between your GROWTH equations and your DECAY equations.
If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is farther than 2. 5 standard deviations from its mean value.
The probability that the thread length of a randomly selected bolt is farther than 2. 5 standard deviations from its mean value is 0.62%.
If the thread length of bolts is normally distributed, then we can use the concept of probability to determine the probability that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value.
This can be calculated using the area under the normal curve.
Specifically, the area to the right of 2.5 standard deviations is 0.0062, meaning that there is only a 0.0062 probability (or 0.62%) that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value
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If you add Natalie's age and Fred's age, the result is 41. If you add Fred's age to 4 times Natalie's age, the result is 80. Write and solve a system of equations to find how old Fred and Natalie are
Mr. Green gave his students a biology test last week. Here are the test scores for each of the eleven students. Complete the grouped frequency distribution for the data. In the distribution, the frequency of a class is the number of test scores in that class. (Note that we are using a class width of 6.)
The grouped frequency distribution for the data is shown below.
What is grouped frequency distribution ?A grouped frequency distribution is a way of summarizing and organizing raw data into a more manageable and meaningful form. The data is divided into intervals or "classes", and the number of data points that fall into each class is counted and recorded as the frequency of that class. This allows for easier interpretation and comparison of the data, as well as identifying patterns or trends. The grouped frequency distribution is commonly displayed in a table or a histogram.
Given that,
79, 85, 71, 83, 78, 67, 70, 87, 81, 86, 74, 67, 68, 76, 66, 72, 76, 80
Now, arranging the given data in ascending order,
66, 67, 67, 68, 70, 71, 72, 74, 76, 76, 78, 79, 80, 81, 83, 85, 86, 87
The grouped frequency distribution for the data:
Test Scores Frequency
65.5 - 71.5 6
71.5 - 77.5 4
77.5 - 83.5 5
83.5 - 89.5 3
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b) Write the number in scientific notation:
2,150,000 =
Answer:
2.15 * 10⁶
Step-by-step explanation:
1,000,000= 1 * 10⁶
2,150,000= 2.15 * 10⁶
Answer:
The answer is 2.15×10 power 6NEED HELP ASAP!!!!
The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 21 salespeople using Hamiltons method given the information below
Using Hamilton's method of apportioning, 21 salespeople can be assigned in the table in the following order:
2, 5, 6, 8.
What do you mean by Hamilton's method of apportioning?The approach that now bears his name was first proposed by Alexander Hamilton. Congress endorsed his approach in 1791, but President Washington rejected it. Later, in 1852, it became widely used until 1911. He starts by calculating the precise number of items that each group needs.
Since in the interested question it's about salesperson assigned, we’ll use the language of shift and hours, so we can determine how many salespersons each shift should get.
Now total no. of customers given = 125 + 305 + 439 + 515
= 1375
Now total no of salesperson available = 21.
So, the divisor = 1375/21
= 65.47
Now using Hamilton's method when we divide the average customers per shift by the divisor, we get the no. of salesperson assigned.
So, the salesperson assigned are:
Morning = 125/65.47
= 2
Midday = 305/65.47
= 5
Afternoon = 430/65.47
= 6
Evening = 515/65.47
= 8 (Decimals rounded according to Hamilton's principle)
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Which set of ordered pairs (x, y) could represent a linear function?
A = {(-8,8), (-4,5), (0, 2), (5, -1)}
B = {(-1, -2), (2,1), (5,4), (8,7)}
C = {(-2,8), (1,5), (4,2), (6, -1)}
D = {(-1,0), (1, 1), (7,5), (9,6)}
The ordered pairs that represent the linear function is Option A, B and C.
What is linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function.
To determine which ordered pairs represent a linear function we use the equation of slope.
The slope is given as:
m = (y2 - y1) / (x2 - x1)
Option A:
m = (5 - 8) / (-4 + 8) = -3 / 4
m = (2 - 5) / (0 + 4) = -3/ 4
The slopes between the consecutive points are same hence option A represents a linear equation.
Similarly, for option B:
m = (1 + 2) / (2 + 1) = 1
m = (4 - 1) / (5 - 2) = 1
Option B is correct.
Option C:
m = (5 - 8) / (1 + 2) = -3 / 3 = -1
m = (2 - 5)/ (4 - 1) = -1
Option C is correct.
Option D:
m = (1- 0)/ (1 + 1) = 1/2
m = (5 - 1) / (7 - 1) = 4 / 6 = 2/3
Option D is incorrect.
Hence, the ordered pairs that represent the linear function is Option A, B and C.
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Find the volume of the figure. Express answers in terms of pi then round to the nearest whole number.
Answer:
Below
Step-by-step explanation:
Volume of a cylinder = area of end X height = pi r^2 * h
r = 4 in h = 10 in
volume = pi (4)^2 * 10 = 160 pi in^3 or ~ 503 in^3
Answer:
160π in.³
Step-by-step explanation:
Get the circle area then multiply for the height. In the end, devide the result by 3,14 (π).
π* . r² 50,24 . 10*
π* . 4² 502,40 in.³ (cylinder volume)
50,24 (circle area)
obs: 502,4 leads you to a non-comma π result, considering π as 3,14. If you round, the correct way will be transforming into 502. But 502/3,14 is equal to 159,87..., infinite non-repetitive numbers.
Result in π = 160π* in.³
r - circle radius
10* - height
π* - 3,14 (Used that way)
Use the distributive property to write an equivalent expression. 6a + 9 =
Answer: 15a
Step-by-step explanation: 6 + 9 = 15, 6a + 9 = 15a
Two points on a line are (10,55) and (15,82.5). what is the slope of the line
Find a linear equation who’s graph is the straight line with given properties
(1,-8) and (-1,-1)
Answer:
y=-7/2x-9/2
Step-by-step explanation:
Topford supplies X-Data DVDs in lots of 50, and they have a reported defect rate of 0.5% so the probability of a disk being defective is 0.005. It follows that the probability of a disk being good is 0.995. What is the probability of getting at least one defective disk in a lot of 50?
The probability of getting at least one defective disk in a lot of 50 is 0.2217.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Given that,
P (defective disc) = 0.005
P (non-defective) = 1 - 0.005 = 0.995
Now,
P(Getting one defective) = 1 - P(getting 50 non -defective)
= 1 - (0.995)^(50)
= 1- 0.7783
= 0.2217
Hence, the probability of getting at least one defective disk in a lot of 50 is 0.2217.
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Adam can run 10 laps in 5 minutes. How many laps can he run per minute?
You owe $488.32 on your credit card. Because you have not paid your bill on time, you have to add a past due charge of $29, an over limit fee of $50, and a service charge of 11% of the amount owed on the credit card (without the past due charge and over limit fees). If you wish to send a check for the full amount immediately, how much should you write the check for? Round your answer to the nearest cent, if necessary.
QUESTION 7 A family moved to Orlando, FL and bought a home. They paid $350,000 for their house. In their neighborhood the mean price of a home is $375,000 with a standard deviation of $7,500. Calculate the z-score for the price of their home and indicate if the price they paid for their home usual or unusual. Choose one • 10 points The z-score is 3.333 and it is usual The z-score is -3.333 and it is usual The z-score is 3.333 and it is unusual The z-score is -3.333 and it is unusual
Step-by-step explanation:
The z-score for the price of the family's home can be calculated as follows:
z = (350,000 - 375,000) / 7,500 = -3.333
A negative z-score indicates that the value is below the mean. Therefore, the price the family paid for their home is lower than the average price of homes in their neighborhood, so it can be considered unusual.
So, the answer is: The z-score is -3.333 and it is unusual.
Dana read this statement in a book about softball.
The diameter of a softball is 0.304 meter.
Which completes the statement as it would be heard?
The diameter of a softball is ______.
Answer:
Step-by-step explanation:
14
Rectangle MNOP is similar to rectangle WYXZ.
The scale factor of rectangle MNOP to rectangle WYXZ is 2:3.
What is the length of side WY?
A. 12 inches
B. 9 inches
C. 15 inches
D. 18 inches
Answer:
Option B. 9 inches
Step-by-step explanation:
Given
Rectangle MNOP and Rectangle WYXZ are similar
Scale factor of the two Rectangles = 2:3 or 2/3
MN=6 in
So
MN/WY = 2/3
6/WY = 2/3
WY = 6×3/2
WY = 18/2
WY=9
Therefore length of side WY is 9 inches
Three classes ordered lunch from a restaurant. In one class 5/6 of the children ordered hamburger. In the other class 2/4 ordered hot dogs. 1/2 of the other class ordered chicken wings. What is the total number of children that ordered sandwiches?
The number of children who ordered hamburgers from class A = ( 5/6 )A , where A is the total number of students in the class A
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of students in class A = A
Let the number of students in class B = B
Let the number of students in class C = C
Now , the equation will be
The number of students who ordered hamburgers is = ( 5/6 )A
The number of students who ordered hot dogs is = ( 2/4 )B
The number of students who ordered hot dogs is = ( 1/2 )B
The number of students who ordered chicken wings is = ( 1/2 )C
Hence , the number of students who ordered hamburgers , hot dogs and chicken wings are ( 5/6 )A , ( 1/2 )B and ( 1/2 )C respectively
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Pls help Im so confused
The height of the building is 92.52 ft
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Using law of sines:
first angle A:
sum of all angles in a triangle = 180 degree
A+B+C = 180
A+90+55 = 180
=> A+145 =180
=> A= 180 - 145 = 35 degrees
Use:
AB= c, BC=a
(sin A)/a = (sin C)/c
=> (sin 35)/40= (sin 55)/c
=> -0.4281/40= -0.99/c
=> 0.0107 = 0.99/c
=> c= 0.99/0.0107 = 92.52 ft
The height of the building is 92.52 ft
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the height of a doorway is 2 yds what is the height of the doorway inches
Answer:
72 inches
Step-by-step explanation:
What we know:
1 yard = 3 feet
3 feet = 36 inches
If 1 yard equals 3 feet, which equals 36 inches, then we can multiply 1 yard, 3 feet, and 36 inches by 2.
1 yard * 2 = 2 yards
3 feet * 2 = 6 feet
36 inches * 2 = 72 inches.
So, the answer is 72 inches.
Linear Programming Examples
A Diet Example
Breathtakers, a health and fitness center, operates a morning fitness program for senior citizens. The program includes aerobic exercise, either swimming or step exercise, followed by a healthy breakfast in the dining room. Breathtakers’ dietitian wants to develop a breakfast that will be high in calories, calcium, protein, and fiber, which are especially important to senior citizens, but low in fat and cholesterol. She also wants to minimize cost. She has selected the following possible food items, whose individual nutrient contributions and cost from which to develop a standard breakfast menu are shown in the following table:
The dietitian wants the breakfast to include at least 420 calories, 5 milligrams of iron, 400 milligrams of calcium, 20 grams of protein, and 12 grams of fiber. Furthermore, she wants to limit fat to no more than 20 grams and cholesterol to 30 milligrams.
Therefore , the solution of the given problem of linear equation comes out to be the decision variables x1, x2, x3, and x4 must be non-negative.
What exactly is a linear equation?The formula y=mx+b is used to draw a simple regression graph. The inclination is B, and the y-intercept is m. It is frequently referred to as a "simple algorithm incorporating many factors" even though the section before it includes independent parts. Bivariate linear equations only contain two variables. Application problems with linear equations have no known answers. Y=mx+b, also known as mx+b, provides a number of straightforward equations.
Here,
To solve this linear programming problem, we can use the following decision variables:
Let x1 = number of pancakes
Let x2 = number of eggs
Let x3 = number of sausage patties
Let x4 = number of slices of toast
The objective function is to minimize cost:
Minimize Z = 0.5x1 + 0.2x2 + 0.3x3 + 0.1x4
Subject to the following constraints:
Calories: 120x1 + 90x2 + 280x3 + 70x4 >= 420
Iron: 1.2x1 + 1.8x2 + 2.4x3 + 0.8x4 >= 5
Calcium: 10x1 + 20x2 + 90x3 + 20x4 >= 400
Protein: 3x1 + 6x2 + 9x3 + 3x4 >= 20
Fiber: 2x1 + 0.5x2 + 1x3 + 1x4 >= 12
Fat: 2x1 + 6x2 + 20x3 + 1.5x4 <= 20
Cholesterol: 50x1 + 190x2 + 60x3 + 0x4 <= 30
The decision variables x1, x2, x3, and x4 must be non-negative.
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An object was launched off the top of a building. The function
f(x) = -16x² + 16x + 192 represents the height of the object above the ground,
in feet, a seconds after being launched. Find and interpret the given function values
and determine an appropriate domain for the function.
Check the picture below.
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16~\frac{ft}{s}\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&192~ft\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+16t+192\hspace{5em}f(x)=-16x^2+16x+192[/tex]
now, keeping in mind that x-axis is the seconds, however a parabola could go into the 2nd, 3rd and 4th Quadrants, but for this case, we only need it in the 1st Quadrant, because the seconds are positive, it begins at 0 seconds and goes up, then down and hits the ground later on when f(x) = 0, hmmm when is that?
[tex]\stackrel{f(x)}{0}=\stackrel{ \textit{hits the ground} }{-16x^2+16x+192}\implies 0=-16() \\\\\\ 0=x^2-x-12\implies 0=(x+3)(x-4)\implies x= \begin{cases} -3 ~~ \bigotimes\\\\ ~~ 4 ~~ \checkmark \end{cases}[/tex]
now, both values are valid for "x", however for this specific case, we can't have negative seconds, so the negative value won't work. So the appropriate domain or values for "x" are from 0 to 4, the object went up and down in 4 seconds flat.
To prove that there is a unique element x such that P(x) is true is the same as showing which of these statements is true?a) 3xAy(P (y) ↔ x = y)b) 3x(P(x) & Ay( y =/ x --> notP(y)))c) 3x(P(x) & Ay(P(y) --> x = y))
The statement that proves that there is a unique element x such that P(x) is true is: c) 3x(P(x) & Ay(P(y) --> x = y)).
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.
Here,
In this statement, the quantifier "3x" says that for every element x, and the condition "P(x)" says that x satisfies a certain property. The statement "Ay(P(y) --> x = y)" says that for every other element y, if y also satisfies the property, then it must be equal to x. Hence, if there is a unique element x such that P(x) is true, then this statement is true.
Option (a) says that for every element y, P(y) is equivalent to y = x, but this statement alone does not imply that there is only one element that satisfies P(x).
Option (b) says that for every element x, if P(x) is true, then there is no other element y that also satisfies P(y) and is not equal to x. However, this statement alone does not imply that there exists an element x that satisfies P(x).
The following assertion establishes that there is a unique element x such that P(x) is true: c) 3x(P(x) & Ay(P(y) --> x = y)).
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a blueprint of a house has a scale of 2.5 in:5 feet. would a pool table that is 8 by 6 feet fit in a space that has drawing dimensions of 4 inches and 5.2 inches? if so, how much space will remain after the table is put in the room?
Answer:
yes it will fit; there would be 35.2 sf remaining
Step-by-step explanation:
Find the dimensions of the table in inches:
2.5/5 = x/6
x = 3 in
2.5/5 = x/8
x = 4 in
Scaled table area = (3 in)(4 in) = 12 in²
Scaled room area = (4 in)(5.2 in) = 20.8 in²
12 < 20.8, Therefore, the table would fit.
How much room is left over:
Find the room dimensions in feet.
2.5/5 = 4/x
x = 8 ft
2.5/5 = 5.2/x
x = 10.4 ft
Room area = (8)(10.4) = 83.2 sf
Table area = (8)(6) = 48 sf
83.2 - 48 = 35.2 sf space would remain
Aniya has just become the world champion of cartwheels. She is able to travel at 0.5 mph doing cartwheels. She went a distance of 0.1 miles. How long did Aniya do cartwheels?
The time it took Aniya to do cartwheels, which can travel at 0.5 mph for a total distance of 0.1 miles, is 12 minutes.
What are the distance, time, and speed formulas?The distance, time, and average speed formulas are based on distance equals to time multiplied by the average speed.
Conversely, the total time taken to cover a certain distance is equal to distance divided by the average speed.
Total distance traveled doing cartwheels = 0.1 miles
Average speed = 0.5 mph
Time = Distance/Average speed
= 0.1/0.5
= 0.2 hours
1 hour = 60 minutes
= 12 minutes (0.2 x 60)
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