The limit of the function (cos(12x) - cos(3x))/x^2 as x approaches 0 is approximately -99862.9534, as determined by evaluating the function at various values near x=0.
Let f(x) : (cos(12x) - cos(3x))/x^2
We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2
Step 1: Calculate the value of the function for x=0.2
fx = (cos(12(0.2)) - cos(3(0.2)))/(0.2)^2
fx = (cos(2.4) - cos(0.6))/0.04
fx = (0.92358 - 0.95105)/0.04
fx = -24.987664
Step 2: Calculate the value of the function for x=0.1
fx = (cos(12(0.1)) - cos(3(0.1)))/(0.1)^2
fx = (cos(1.2) - cos(0.3))/0.01
fx = (0.9589 - 0.9511)/0.01
fx = -98.998848
Step 3: Calculate the value of the function for x=0.05
fx = (cos(12(0.05)) - cos(3(0.05)))/(0.05)^2
fx = (cos(0.6) - cos(0.15))/0.0025
fx = (0.9802 - 0.9657)/0.0025
fx = -19.923683
Step 4: Calculate the value of the function for x=0.01
fx = (cos(12(0.01)) - cos(3(0.01)))/(0.01)^2
fx = (cos(0.12) - cos(0.03))/0.0001
fx = (0.9999 - 0.9998)/0.0001
fx = -99.853172
Step 5: Calculate the value of the function for x=0.001
fx = (cos(12(0.001)) - cos(3(0.001)))/(0.001)^2
fx = (cos(0.012) - cos(0.003))/0.000001
fx = (0.999983 - 0.999971)/0.000001
fx = -998.62855
Step 6: Calculate the value of the function for x=0.0001
fx = (cos(12(0.0001)) - cos(3(0.0001)))/(0.0001)^2
fx = (cos(0.0012) - cos(0.0003))/0.00000001
fx = (0.99999983 - 0.99999971)/0.00000001
fx = -9989.29525
Step 7: Calculate the value of the function for x=0.00001
fx = (cos(12(0.00001)) - cos(3(0.00001)))/(0.00001)^2
fx = (cos(0.00012) - cos(0.00003))/0.0000000001
fx = (0.9999999983 - 0.9999999971)/0.0000000001
fx = -99862.9534
Therefore, the limit of the function
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Which equation can be used to find the area in square feet of the piece of glass?
Answer:
Area = length x width (in feet)
Step-by-step explanation:
The area of a 2-dimensional shape can be found by multiplying its length by its width. The equation to find the area of a rectangle is:
Area = length x width
So if you know the length and width of a piece of glass in feet, you can use the above equation to find its area in square feet. For example, if the length of the glass is 10 feet and the width is 5 feet, the area would be:
Area = 10 feet x 5 feet = 50 square feet
So the equation to find the area of a piece of glass in square feet is:
Area = length x width (in feet)
It's worth noting that this equation applies to any 2-dimensional shape that has a length and a width, not just a rectangle.
URGENT PLEASE HELP!!!!!!
Answer:
یه گل یک گل بام میی مه فیلم بام حس بام حس فمس یکم باشگاه هی یک گل یه حس سیم هی فکریه خشک پیل هر یک حس صب زی صب هم گچ نی بلن هر بر قل هم بی دو حس قیین
Step-by-step explanation:
سبک حس بام نی شیک حس
یا کمی سیم حس او
نی یک حس بکشم یک حس بام نی که خیلی تنیام که اما الا دیه انجام نمییم ای موضوع که دعوا خیلی تخفیف خیلی خوعه ای موضوع که اما الا دیمش خوش
۳ خشک هی یک هی بام نی با که اما ۷غ هه بام نی بلن کف بام نی بکر
به نمییم هی بام میی لاک حس بام
بلن هی یک
حالم ای زبونه فراموش که
فخ بیم فک
toss a coin three times, and let x be the number of heads. find the probability mass function of x.
The probability mass function of x is P(0)= 1/8, P(1)= 3/8, P(2)= 3/8, P(3)= 1/8.
Here number of trials = 3
In tossing a coin for once, the outcomes of the trial are either head or tail.
The trials are independent.
probability of getting head(success)=p=1/2
probability of getting tail(failure)=1-p=1-(1/2)=1/2
Number of success=X
Since there are two mutually exclusive outcomes of independent trials, the probability mass function of Binomial = (nx)px(1−p)n−x(nx)px(1 − p)n−x {in this case n=3}
The probability distribution of X is -
= X=0, P(X=0)=1/8
= X=1, P(X=1)=3/8
= X=2, P(X=2)=3/8
= X=3, P(X=3)=1/8
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Please Hurry!
A box of apples sells for $17. At this rate, which expression represents the cost, in dollars, of 100 apples?
A) 5/17•20
B) 5/20•17
C) 100/17•20
D) 100/20•17
E) 17•5•20
Answer: D
Step-by-step explanation:
20 apples cost $17
100 apples = 100/20 * 17 = D
What is 26,430,000 in expanded form
Answer: 20,000,000 + 6,000,000 + 400,000 + 30,000
Step-by-step explanation:
A person borrowed $2100 from his home equity line of credit to pay off his car loan. He then borrowed another $1200 to have his kitchen repainted. Represent how much
he owed on his home equity line of credit as a real number.
What is the real number that represents the amount he owed on his home equity line of credit?
The real number that represents the amount he owed on his home equity line of credit would be = $3,300
What is a real number?A real number is defined as the type of number that can be used to represent a one directional measurement which can be rational or irrational.
The first amount of money borrowed by a person from his home equity line of credit = $2100
The second amount of money borrowed by a person from his home equity line of credit = $1200
Therefore, the total amount that was borrowed= 2100+1200 = $3,300.
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What is the value of the 6 in 62.75 compared to the 6 in 6,275?
Answer:
6 in 6,275 is 100 times greater than 6 in 62.75
What is place value?
Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
as, 6 in 6,275 have a place value 6000.
and in 62.75, 6 have place value 60.
So, the difference is
6000/60
=100
Hence, 6 in 6,275 is 100 times greater than 6 in 62.75
Step-by-step explanation:
The value of the 6 in 62.75 is 60, while it is 6000 in the number 6275. This is due to the concept of place value in the decimal number system.
Explanation:In terms of place value, the value of the 6 in 62.75 is 60, because it is in the tens place. However, the value of the 6 in 6,275 is 6,000 because it is in the thousands place. This is based on the concept of place value in the decimal number system where each digit has a value depending on where it is located within the number. The further to the left a digit is, the larger its value.
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Why is f not a function from R to R if
a) f (x) = 1/x?
The domain of the function is not the set of all real numbers, that is why it is not from R to R
Why is f not a function from R to R?Here we want to see why the function f is not a function from R to R, where R is the set of the real numbers.
The function here is:
f(x) = 1/x
Notice that x is on the denominator, so we can't evaluate that function on x = 0.
So there is a real number that we can't use on that function, then the domain is not R, is R minus the element {0}
That is why f(x) is not a function from R to R, because the domain is not the set of the real numbers.
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A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2- hour reserve, and the second book can be checked out overnight. a. Construct a tree diagram to display the 12 outcomes in the sample space. b. Let A denote the event that at least one of the books selected is an even-numbered copy. What outcomes are in A? c. Suppose that copies 1 and 2 are first printings, whereas copies 3 and 4 are second printings. Let B denote the event that exactly one of the copies selected is a first printing. What outcomes are contained in B?
The event A is that at least one of the books selected is an even-numbered copy. The event B is that exactly one of the copies selected is a first printing.
A tree diagram to display the 12 outcomes in the sample space would look like this:
1st Selection | 2nd Selection
----------------------------
1 | 2
1 | 3
1 | 4
2 | 1
2 | 3
2 | 4
3 | 1
3 | 2
3 | 4
4 | 1
4 | 2
4 | 3
The event A is that at least one of the books selected is an even-numbered copy. This would include outcomes 1-2, 1-4, 2-1, 2-3, 2-4, 4-1, 4-2, and 4-3.
The event B is that exactly one of the copies selected is a first printing. This would include outcomes 1-3, 1-4, 3-1, 3-2, 3-4, 4-1, 4-2, and 4-3.
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5 divided by 4/5???????????????????????????????????????????????????????
Answer:
6.94??????‽??????????????
Step-by-step explanation:
5÷4/5?????????
5×5?????????‽?/4
2.777777778/4
=69.4????????????????????
Given f(x) = 3x^3+kx-13, and x-1 is a factor of f(x), then what is the value of k?
Answer: k=10
Step-by-step explanation:
what is the slope through the line of (9, 10) and (7, 2)
Answer:4
Step-by-step explanation:
Which is the common difference for this arithmetic series? 8, 30, 52, 74, 96, 118 a. d = 8 b. d = 22 c. d = 32 d. d = 38
Answer:
d = 22
Step-by-step explanation:
you add 22 to a number in the sequence to get the next number
8 + 22 = 30
30 + 22 = 52 and so on...
describe your sketch. the solid has no negative x-values. the solid has both positive and negative y-values. the solid has no negative z-values. the solid has a straight side and a curved side in the x y-plane. the solid has ---select--- in the x z-plane. the solid has ---select--- in the y z-plane.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
The solid has no negative x-values, meaning all x-values are positive. It has both positive and negative y-values, indicating that it is symmetrical around the x-axis. The solid has no negative z-values, meaning all z-values are positive. In the x y-plane, the solid has a straight side and a curved side. In the x z-plane, the solid has a curved side and in the y z-plane, the solid has a straight side.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
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pls help me
Josh is the owner of CranBog, a Cranberry Bog in Massachusetts. Cranberry production at CranBod can be represented by the inequality y ≤ 150x - 3100
under normal climate conditions, where y
is the annual production of cranberries at CranBog, in thousands of pounds, and x
is the number of acres of land that produce cranberries.
The TRUE statements about the inequality y ≤ 150x - 3100 are:
A) For a solution to be viable, both x and y must be integers.E) The ordered pair (40, 2900) is a solution to the inequality and means that with 40 acres of land, CranBog can produce 2,900 (in thousands of) pounds of cranberries.What is inequality?Inequality is a mathematical statement showing that two or more mathematical expressions are unequal or not equivalent.
Inequalities are represented by the following types and inequality symbols:
Less than (<)Greater than (>)Not equal to (≠)Less than or equal to (≤)Greater than or equal to (≥).Check:
Ordered pairs (40, 2900)
y ≤ 150x - 3100
y ≤ 150(40) - 3100
y ≤ 6,000 - 3100
y ≤ 2900
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. The following list of monthly expenses for a first-year student at a post-secondary
institution are presented. The student has a monthly income of $1,450. Is the student
following the recommended rule of allocating 50% of monthly income to needs, 30% to
wants and 20% to savings or debt?
Income: $1,450
Based on the information provided, it can be concluded the student is not following the rule of allocating 50% to needs, 30% to wants, and 20% to savings.
What percentage is the student allocating for each category?Needs: 300 +10 + 50 +150 + 100 + 100= $710
Now, let's calculate the percentage this represents:
710 x 100 / 1450 = 48%
Wants: 9.99 + 9.95 +9.99 + 19.99 + 25 + 500 + 65= $639.92
Now, let's calculate the percentage this represents:
639 x 100/ 1450 = 44%
Savings: 48 + 44 = 92 which means he can save 8%
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find each measure m < 5
The measure of all the angles are estimated.
∠1 = 104 ; ∠4 = 45 ; ∠3 = 65 ; ∠2 = 79.Explain the term linear pair?When two lines cross at one point, a linear pair with angles is created. If the angles follow the intersection of both the two lines in a straight line, they are classified as linear. A linear pair's total angles are indeed equal to 180°.For the stated question:
For ∠1
∠1 = 68 + 36 (sum of opposite interior angle equals exterior angle).
∠1 = 104
For ∠4.
∠4 = 180 - 70 - 65 (linear pair)
∠4 = 45
For ∠3.
∠3 = 65 (vertically opposite angle)
For ∠2.
∠2 = 180 - 65 - 36 (sum of angles of triangle are 180)
∠2 = 79
Thus, the measure of all the angles are estimated.
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Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.
16o sin(x) dx, n = 4
the value of integration [tex]\int\limits^{64}_0 {sinx} \, dx =5[/tex] by the midpoint rule of approximate.
we want to approximate the integral
[tex]\int\limits^{64}_0 {sinx} \, dx \\using n=4[/tex]
the midpoint rule is given by.
[tex]\int^b_af(x)dx=\triangle x(f(\frac{x_{0} +x_1)}{2})+f(\frac{x_1+x_2}{2} )+....+f(\frac{x_{n-1}+x_n}{2}))[/tex]
where Δx=(b-a)/n
we know that a=0,b=64 and n=4
Δx=64/4=16
we need to divide the interval [0,64] into four subinterval of length Δx=16: 0,16,32,48,64.
now, we just evaluate the function at these endpoints.
[tex]f(\frac{x_1+x_0}{2} ) =f(\frac{0+64}{2} )\\f(8)=sin8=0.9894\\\\f(\frac{x_1+x_2}{2}) =f(\frac{16+32}{2} )\\\\f(24)=sin24=-0.9056\\\\similarly\\\\f(40)=sin(40)=0.7451\\\\f(56)=sin56=-0.5216[/tex]
finally, just sum up above values and multiply by Δx=16.
[tex]\int\limits^{64}_0 {sinx} \, dx=4.9168= 5[/tex]
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Dr. Chandler wants to print copies of
his thesis in hardcover book format. He
could use Washington Printing, paying a
setup fee of $41 and $6 for every book
printed. Or, he could go through Fairfax
University, paying an up-front fee of
$32 and $9 per book. For how many
books will the costs be the same? How
much is that?
Answer:
For 3 books, costs are the same
$59
Step-by-step explanation:
x = number of books
$41 + ($6/book)(x) = $32 + ($9/book)(x)
41 - 32 = 9x - 6x
9 = 3x
x = 9/3 = 3
41 + 6(3) = 32 + 9(3) = $59
What inverse operation is used to solve the equation?
x + 2 = 5
Responses
A multiply by 2 on both sidesmultiply by 2 on both sides
B divide by 2 on both sidesdivide by 2 on both sides
C add 2 to both sidesadd 2 to both sides
D subtract 2 from both sides
Answer:
D subtract 2 from both sides
Step-by-step explanation:
x + 2 - 2 = 5- 2
==> x = 3
The solution of the equation is x = 3.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation,
x + 2 = 5.
To solve the equation:
Subtract 2 from both sides,
x +2 -2 = 5 -2
x = 3
Therefore, the solution is x = 3.
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Distributive property c3/c when c=3
Answer: The answer is 9
Step-by-step explanation: 3^3/3=9
Could you help me find the inverse of the function F(n)=n+1
Answer: [tex]F^{-1} (n)=n-1[/tex]
Step-by-step explanation:
[tex]F(n)=n+1[/tex]
[tex]F(n)-1=n[/tex] Subtract 1 from both sides
Done!
We can rewrite as: [tex]F^{-1} (n)=n-1[/tex]
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
A. Equally likely and unlikely
B. Likely
C. Unlikely
D. This value is not possible to represent probability of a chance event.
The baker made a batch of chocolate chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is B. Likely.
What is probability?Generally, Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
A probability of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform decision-making in a wide range of fields, including statistics, finance, and engineering.
A probability of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.
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the range (in miles) of a broadcast signal from a radio tower is bounded by a circle given by the equation
The cars receive the broadcast signal for length of about 36 miles.
What is meant by equations?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution or root of the equation is the quantity at which the variable's value satisfies the equation. If you swap the LHS and RHS, an equation still makes sense.
Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.
Simultaneous equations are obtained:
[tex]$$x^2+y^2=1620 \\y=-\frac{1}{3} x+30\end{array}\right.$$[/tex]
[tex]$x^2+\left(-\frac{1}{3} x+30\right)^2=1620$[/tex]
simplifying the above equation, we get
[tex]$x^2-18 x-648=0$[/tex]
(x - 36)(x + 18) = 0
x = -18 and x = 36
Therefore, the cars receive the broadcast signal for length of about 36 miles
The complete question is:
The range (in miles) of a broadcast signal from a radio tower is bounded by a circle given by the equation [tex]$x^2+y^2=1620$[/tex]. A straight highway can be modeled by the equation [tex]$y=-\frac{1}{3} x+30$[/tex]. For what length of the highway are cars able to receive the broadcast signal? Round your answer to the nearest tenth.
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please help solve it
Note that if the family is to spend less than $60 dollars without further expenses, then they will have to spend nothing more than 6 hours. The inequality expression is given as: 36+4h < 60
What is the justification for the above result?First, the inequality expression is given as:
36+4h < 60
Where h is the number of hours they could spend.
We arrive at the above because we were given the following:
Cost of Movie = $36
Cost of parking Per Hour= $4
The maximum amount to be spent = $60
Thus, to find the number of hours the can spend without overshooting $60, we must find h. To do this, we must make h the subject of the formula by first removing 36 from both sides:
36+4h-36 < 60-36
4h < 24
h < 24/4
h < 6
What the above result show is that the number of hours that must be spent must be less than 6.
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Use the following statements to write a compound statement for each conjunction or disjunction. Then find its truth value.
p: 60 seconds = 1 minute
q: Congruent supplementary angles each have a measure of 90.
r: –12 + 11 < –1
answer choices
O Congruent supplementary angles each have a measure of 90 and –12 + 11 < –1; true.
O Congruent supplementary angles each have a measure of 90 and –12 + 11 < –1; false.
O Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1; true.
O Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1; false.
The answer is O Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1; true.
This can be proven by using the following formula:
p: 60 seconds = 1 minute
q: Congruent supplementary angles each have a measure of 90.
r: –12 + 11 < –1
For p, we can use the formula to calculate the number of minutes:
60 seconds * 1 minute = 60 minutes.
Therefore, 60 seconds = 1 minute.
For q, we can use the formula to calculate the measure of each angle:
2x = 90
Therefore, each angle has a measure of 45°.
For r, we can use the formula to calculate the result of the operation:
–12 + 11 = –1
Therefore, –12 + 11 < –1 is true.
In conclusion, the compound statement “Congruent supplementary angles each have a measure of 90 or –12 + 11 < –1” is true.
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Nancy and Martin are making kites. The kites are similar figures. The side lengths of Nancy's kite are 16 inches, 16 inches, 24 inches, and 24 inches. The side lengths of Martin's kite are (5x + 5) inches, (5x + 5) inches, 10x inches, and 10x inches. Assume that 10x > 5x + 5. Find the perimeter of Martin's kite.
Answer: 100 inches
Step-by-step explanation:
Corresponding sides of similar figures have proportional side lengths, so:
[tex]\frac{10x}{24}=\frac{5x+5}{16} \\\\\frac{2x}{24}=\frac{x+1}{16}\\\\\frac{x}{12}=\frac{x+1}{16}\\\\16x=12x+12\\\\4x=12\\\\x=3\\\\[/tex]
So, the perimeter is [tex]5x+5+5x+5+10x+10x=100[/tex].
15. For the graph below, which of the following is a possible function for g?
The graph demonstrates that the function g's line goes through the locations (0,2) and (2,8). The slope of the line is 3, implying that its equation is g(x) = 3x + 2.
What is a slope?The steepness or inclination of a line, route, or surface is measured by slope. It is the vertical distance divided by the horizontal distance between two locations on a line, route, or surface.
According to the graph, the function g is a line with a slope of 3 and a y-intercept of 2. This suggests that the line's equation is g(x) = 3x + 2. According to this equation, increasing the y-coordinate by one increases the x-coordinate by three. The line connects the points (0, 2) and (2, 8), which means that when x = 0, y = 2 and when x = 2, y = 8. This may be demonstrated by plugging the x-values into the equation, which will produce the matching y-values.
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I have a candy mix composed of Jolly Ranches, Starburst, and Twizzlers in a ratio of
7:5:3. I have 35 Jolly Ranchers. How many Starburst and Twizzlers do I have?
Answer:
25 Starburst
15 Twizzlers
========================================================
Explanation:
The ratio of Jolly Ranchers to Starburst to Twizzlers is 7:5:3
It means that you could have 7 Jolly Ranchers, 5 Starburst, and 3 Twizzlers.
In reality you actually have 35 Jolly Ranchers. So we'll multiply that "7" by 5. Do the same thing to all parts of the ratio to keep things balanced.
7*5 = 355*5 = 253*5 = 15The ratio 7:5:3 scales up to its equivalent form 35:25:15
35 Jolly Ranchers25 Starburst15 Twizzlers(07.01 mc) select the general solution to x squared dy over dx equals 3 plus 2y period one half ln absolute value of quantity 3 plus 2y close absolute value equals ln absolute value of x squared close absolute value plus c one half ln absolute value of quantity 3 plus 2y close absolute value equals negative 1 over x plus c
The general solution to x squared dy over dx equals 3 plus 2y is given by 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant.
To calculate this, we begin by taking the derivative of both sides of the equation with respect to x. We then rearrange the equation to yield 2y + x^2 dy/dx = 3. We divide both sides by x^2 so that dy/dx is isolated on one side of the equation, yielding dy/dx = (3 - 2y) / x^2. We can then integrate both sides of the equation, with respect to x, to yield 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant. This equation is the general solution to x squared dy over dx equals 3 plus 2y.
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