Answer:
Step-by-step explanation:
Solve:
a)4 cosx^4 - cos²2x=0
b)sec x tan x =sqrt(2)
Answer:
a) 4 cosx^4 - cos²2x=0
We can start by splitting the equation into two parts:
4 cosx^4 = cos²2x
cosx^4 = (1/4)cos²2x
From here, we can use the identity:
cos²2x = (cos 2x)² = (2cos²x -1)²
So, we have:
cosx^4 = (1/4)(2cos²x -1)²
Now we can square root both sides:
cosx^2 = (1/2) (2cos²x -1)
Now we square both sides again:
cos²x = (1/4) (2cos²x -1)
We can now subtract (1/4) from both sides and add cos²x to both sides:
(3/4)cos²x = (1/4)
We can now divide both sides by (3/4) to find the value of cosx:
cosx = sqrt(1/3)
So the solutions of the equation are x = (2n+1)π/3, where n is an integer.
b) sec x tan x =sqrt(2)
We know that sec x = 1/cosx and tan x = sinx/cosx.
So we can substitute these values into the equation:
1/cosx * sinx/cosx = sqrt(2)
This simplifies to:
sinx = sqrt(2)cosx
We can now divide both sides by cosx:
tan x = sqrt(2)
So the solutions of the equation are x = pi/4 + nπ, where n is an integer.
Note that the solutions are restricted to the domain where cos(x) is not equal to 0.
It is important to note that this solution is only a small part of the full solution set and that there might be more solutions in specific intervals.
Brian’s employer withheld $15,987.76 in federal income tax. After completing his return, Brian has determined that his tax is $18,945.22. Will Brian get a refund, or does he owe the IRS and how much? Tax refund or owed = taxes paid – taxes due
To determine whether he will receive a refund or owe money to the IRS, the result is negative, Brian owes the IRS $2,957.46.
What do you mean by federal income tax?
The federal government levies an income tax known as the federal income tax on income received by people, businesses, and other entities in the United States. The amount of tax due is determined by a progressive tax system, which means that the tax rate rises as income rises. The tax is based on the income received by an individual or company.The national military, social welfare, and infrastructure development are just a few of the government initiatives and services that are funded in part by the federal income tax. An individual's federal income tax liability is determined by their income level, filing status, and any available deductions and credits.
Brian paid $15,987.76 in federal income tax and his actual tax liability is $18,945.22.
To determine whether he will receive a refund or owe money to the IRS, we can use the formula:
Tax refund or owed = taxes paid – taxes due
Tax refund or owed = $15,987.76 - $18,945.22
Tax refund or owed = -$2,957.46
Since the result is negative, Brian owes the IRS $2,957.46.
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Jason made the number line below to represent the number of layups he made during basketball practice.
What fraction of layups did Jason make during basketball practice?
a.3/5
b.3/10
c.3/7
d.7/10
Based on the number line provided, it appears that Jason made 3 out of 7 layups during basketball practice. Therefore, the fraction of layups Jason made during practice is 3/7.
To arrive at this conclusion, we can count the number of dots that represent successful layups (three dots) and divide it by the total number of dots on the number line (seven dots). This gives us a ratio of 3:7, which can be simplified to the fraction 3/7.
It is important to note that although the number line may not be drawn to scale, we can still determine the fraction of successful layups Jason made by counting the number of dots representing successful layups and the total number of dots on the line. Therefore, the correct answer is c. 3/7.
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Please help meee! I will give brainleiest!
Answer:
B) 3.0 ml
Step-by-step explanation:
Find the volume. Show equations used
Answer:
2714.3 or 864 pi
Step-by-step explanation:
Use 3.14 for π Round to the nearest 100th if necessary A ball has a diameter of 20 inches. What is its volume?
Answer:
4186.67 cubic inches
Step-by-step explanation:
Volume of a sphere = 4/3 π r³
π = 3.14
Diameter = 20 inches
Radius = r = Diameter/2 = 20 inches/2 = 10 inches
Volume of the sphere = 4/3 × 3.14 × (10 inches)³
Volume of the sphere = 12560 ÷ 3
= 4186.6666667 cubic inches
Approximately to the nearest hundredth = 4186.67 cubic inches
Therefore, the volume of the ball is 4186.67 cubic inches.
prove. sin³A-cos³A/sinA-cosA = 1+sinAcosA
Answer:
\( \frac{ \sin {}^{3} A - \cos {}^{3} A }{ \sin A - \cos A} \\ \\ { \sf{ = \frac{ {( \sin A - \cos A)}^{3} + 3 \sin A \cos A( \sin A - \cos A)}{ \sin A - \cos A} }} \\ \\ = { {( \sin A - \cos A)}^{2} + 3 \sin A \cos A} \\ { \sf{ = ( \sin {}^{2} A + \cos {}^{2} A) - 2 \sin A \cos A + 3\sin A \cos A}} \\ = { \sf{1 +\sin A \cos A }} \)
#hence proved
Which of the following does not apply to an X.509 certificate?A) Certificate versionB) The issuer of the certificateC) Public Key InformationD) Owner's symmetric key
X.509 certificates are widely used in public key infrastructure (PKI) systems to verify the authenticity and integrity of digital identities. Therefore, among the given options, D) Owner's symmetric key is the item that does not apply to an X.509 certificate.
X.509 certificates are widely used in public key infrastructure (PKI) systems to verify the authenticity and integrity of digital identities. They contain various information related to the certificate itself and the entity it represents. Let's examine the options to determine which one does not apply to an X.509 certificate:
A) Certificate version: X.509 certificates include a version number to indicate the format and features of the certificate.
B) The issuer of the certificate: X.509 certificates specify the entity or authority that issued the certificate, which is crucial for validating the certificate's trustworthiness.
C) Public Key Information: X.509 certificates contain public key information, such as the public key itself and related parameters, to facilitate secure communication and cryptographic operations.
D) Owner's symmetric key: X.509 certificates do not typically include the owner's symmetric key. They primarily focus on the public key infrastructure and asymmetric key cryptography.
Therefore, among the given options, D) Owner's symmetric key is the item that does not apply to an X.509 certificate.
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Solve -7 < 3x + 2 < 14
Answer:
\( - 7 < (3x + 2) < 14 \\ \\ = \: \: - 7 - 2 < 3x < 14 - 2 \\ \\ = \: \: - 9 < 3x < 12 \\ \\ = \: \: \frac{ - 9}{3} < \frac{3x}{3} < \frac{12}{3} \\ \\ = { \boxed{ \boxed{ - 3 < x < 4}}}\)
Answer:
-3<x<4
Step-by-step explanation:
Hi there!
We are given the double inequality -7<3x+2<14 and we want to solve it.
If we have a double inequality and we want to do something (like subtract 3), then we must subtract 3 from the left side, middle, and right side.
An example would be with the inequality 1<x+3<5
In order to isolate x, we'll subtract 3 from the center. However, we'll also be needing to subtract 3 from the left (1-3) and the right (5-3)
Hence,
1<x+3<5
-3 -3 -3
___________
-2<x<2
In our problem then, we'll be subtracting 2 from EVERY side.
-7<3x+2<14
-2 -2 -2
________________
-9 < 3x < 12
Now in order to isolate x, we'll divide by 3, which once again, we divide on EVERY side
-3<x<4
Hope this helps!
use dimension analysis, construct a quantity using g, c, and h, that has the dimension of time.
Let Q=k\(g^{x} h^{y} c^{z}\) where x,y,z are the dimensions and k is dimensionless constant. It will give the Planck's length.
This length is the Planck length, and it is 1.6 x 10-35 meters. Writing the dimensions in Q, we will get the following expression :
[M0L1T0]=(M−1L3T−2)x(ML2T−1)y(LT−1)z = M−x+yL3x+2y+zT−2x−y−z
Applying the principle of homogeneity of dimensions, we get
−x+y=0∴y=x. iii
3x+2y+z=1 iv
−2x−y−z=0
Add (iii) & (iv) x+y=1 or x+x ,x=1/2
From Q, y=x=12
From (iv) z=−2x−y=−2(12)−12=−32
Put in (i) Q=kG1/2h1/2c−3/20
Q=kGhc^3
Taking k=1 and putting the standard values : G=6.67×10^−11 SI units.
h=6.63×10^−34-sec
c=3×10^8m/s , we get
Q≅ \(10^{-35}\) m
This length is called Planck's length.
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however, you recently selected a file at random and found that the paper work was not in order. who is the most likely culprit?
The most likely culprit is whoever was responsible for filing the paper work. They likely failed to properly organize and file the documents.
The most likely culprit for the paper work not being in order is whoever was responsible for filing it. To determine who this is, it is helpful to look at who had access to the documents. This could include the person who initially created the paperwork, anyone who has handled the paperwork since then, and anyone with access to the file where the paperwork is stored. Once the list of possible suspects has been narrowed down, it is important to check if any of them have a history of filing incorrectly or not following proper procedure. It is also helpful to look at any recent changes to the filing system or personnel which may have caused an inadvertent disruption in the filing process. Taking all of these factors into account can help to identify the most likely culprit.
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determine whether the given lines are parallel, perpendicular or neither 2x+3y=1, 3x-2=1
Answer:
Neither
Step-by-step explanation:
Perpendicular: Slope = -1/x
Parallel: Slope = x
Perpendicular slope is negative reciprocal of original slope. Parallel slope is equal to original slope.
Make these lines into slope-intercept form.
1)
2x+3y=1
3y=-2x+1
y=-2/3x+1/3
Slope: -2/3
2)
3x=3
x=1
Slope = undefined
Undefined ≠ -2/3
what is (6x-4)+(5z+8)
Combine like terms.
6x + 5z + 4
Pls help me it’s so hard imo thank you sm
Answer: 7e-5 millimeters, and the nanometer scale is more appropriate
Step-by-step explanation: PLEASE MARK ME BRAINLIEST!!!!!!
-divide the length value by 1e+6
-The millimeter scale and the centimeter scale are two huge, while the nanometer scale is too small. The nanometer scale is often used to measure atoms and viruses.
Answer:
a) The length of the virus in millimetres is 0.000 07 mm.
b) Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.
Step-by-step explanation:
SI is the abbreviation for The International System of Units.
The SI base unit for length is metres (m).
Milli and nano are SI prefixes used to form decimal multiples or submultiples of SI units.
1 millimetre (mm) = 1 × 10⁻³ metres = 0.001 m1 nanometre (nm) = 1 × 10⁻⁹ metres = 0.000 000 001 mTherefore, to convert nanometres to millimetres, multiply the nanometres by 10⁻⁶:
1 nm = 1 × 10⁻⁶ mmSo 70 nanometres is:
70 × 10⁻⁶ mm = 0.000 07 mmViruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.
What are the coordinates of the point (-1,0) after a translation 5 units to the right?
The coordinates of the given point; (-1, 0) after a translation of 5 units to the right are; (4, 0).
What are the coordinates of the point (-1,0) after a translation 5 units to the right?It follows from the task content that the coordinates of the point (-1, 0) after a translation of 5 units to the right is to be determined.
It is noteworthy to know that a translation of a point (x, y) k units to the right transforms the point to; (x+k, y).
Therefore, the required coordinates of the point (-1, 0) 5 units to the right is; (-1+5, 0) = (4, 0).
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on an algebra quiz, 10\% of the students scored 7070 points, 35\5% scored 8080 points, 30\0% scored 9090 points, and the rest scored 100100 points. what is the difference between the mean and median score of the students' scores on this quiz?
Using the Mean and median formulae ,
The difference between the mean and median score of the students' scores on this quiz is 3.
Mean : The mean is the number which we get by dividing the sum of a set of values by the number of values in the set.
Median: the median is the middle number in a set of values when those values are arranged in either ascending or descending order.
let us consider there are a total 100 students.
and X denotes the marks obtained by students.
We have given that,
10% of student scored 70 points i.e.,
P(X=70) = 10% of 100 = 10
35% of students scored 80 points i.e., number of students whose obtained 80 points
= 35% of 100 = 35
30% of students scored 90 points , number of students whose obtained 90 points
= 30% of 100 = 30
remained ( 25%) of students scored 100 points
= 100 - 10 - 35 - 30 = 25
total marks obtained by students
= 80+70+90+100
= 340
Mean of score of students'scores on the quiz
= (70×10+ 80×35 + 90×30 + 100×25)/100 = 87
when we arranged the in ascending students in order , the 50th and 51th student lies in middle and marks obtained by both (50th and 51th) is 90 points .
So, Median score of the students' scores on this quiz = 90
Now, we shall calculate the difference between mean and median of score of the students' scores on this quiz which is equal to( 90 -87)
= 3
Hence, difference between the mean and median score of the students' scores on this quiz = 3
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select whether the following statement is always true, sometimes true, or never true. a proof should have more steps in the reason column than steps in the statement column. sometimes always never
The statement is sometimes true. The number of steps in the reason column can vary depending on the complexity of the proof and the level of detail required to explain each step
The statement that a proof should have more steps in the reason column than steps in the statement column is sometimes true. This is because the number of steps in the reason column depends on the complexity of the proof and the level of detail required to fully explain each step.
Sometimes a proof may have many steps in the statement column but only a few in the reason column if the steps are straightforward and do not require much explanation. On the other hand, some proofs may have fewer steps in the statement column but more in the reason column if the proof involves complex calculations or requires a detailed explanation of each step to fully understand.
Therefore, the number of steps in the reason column cannot always be predicted based on the number of steps in the statement column and can vary depending on the nature of the proof being presented.
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Chastity ran a hypothesis test with an alpha level of .01 and her test statistic fell outside of the critical region. what should she do?
The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.
If Chastity ran a hypothesis test with an alpha level of .01 and her test statistic fell outside of the critical region, it means that the test statistic does not provide enough evidence to reject the null hypothesis.
In this case, Chastity should fail to reject the null hypothesis and accept it as the plausible explanation. This implies that there is not enough evidence to support the alternative hypothesis.
When a test statistic falls outside of the critical region, it indicates that the observed data is not extreme enough to reject the null hypothesis. The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.
In summary, when Chastity's test statistic falls outside of the critical region, she should fail to reject the null hypothesis and accept it as the plausible explanation. This means that there is not enough evidence to support the alternative hypothesis at the given alpha level of .01.
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A square garden has area 1764meter find it's length and perimeter
Answer:
\(area \: of \: a \: squre = {a}^{2} \\ {a}^{2} = 176 \\ a = 13.26m \\ perimeter = 4a = 4 \times 13.26 = 53.04m^2 \\ thank \: you\)
Answer:
Length = 42 mPerimeter = 168 mConcept:
Here, we need to know how to find the area and perimeter of the square.
Area (square) = s²
s = side lengthPerimeter (square) = 4s
s = side lengthSolve:
PART I: Find the lengthGiven information
Area = 1764 m²
Given formula
A = s²
Substitute values into the formula
1764 = s²
Square root both sides
√s² = √1764
\(\boxed{s=42m}\)
--------------------------------------------------------------------------------------------------------
PART II: Find the perimeterGiven information
s = 42 m
Given formula
P = 4s
Substitute values into the formula
P = 4 (42)
Simplify by multiplication
\(\boxed{P=168m}\)
Hope this helps!! :)
Please let me know if you have any questions
what is the oppistite of 63
Answer:
-63
Step-by-step explanation:
The opposite, or additive inverse of a number is found by changing the sign of the number. With the exception of zero, a number and its opposite (additive inverse) sum to zero.
Hello there! :)
The opposite of 63 is -63.
The opposite of a positive number is a negative number.
Hope it helps!
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For the x-values 1,2,3, and so on, the y-values of a function form an arithmetic sequence that decreases in value. What type of function is it? A. Exponential growth
B. Increasing linear
C. Exponential decay
D. Decreasing linear
Answer:
Decreasing linear
Step-by-step explanation:
its c
Answer:
decreasing linear
Step-by-step explanation: I took the test
Need help this is my last one i need can anybody help i don't get it thanks if you do help
Answer:
its c
Step-by-step explanation:
Hope this Helps!!!
What is the value of the expression below? (4^2)^1/4
Answer:
the value for the expression for below is (4^2) ^1/4 is 2
Answer:
2
Step-by-step explanation:
Exponent law\(\sf \boxed{(a^m)^{n}=a^{m*n}}\)
\(\sf (4^2)^\frac{1}{4}=4^{2*\frac{1}{4}}\)
\(\sf = 4^{\frac{1}{2}}\\\\ = \sqrt{4}\\\\=2\)Write an
expression that is equivalent to -0.5(20f – 16).
Answer:
- 10f + 8Step-by-step explanation:
Given expression:
- 0.5(20f - 16)Distribute and simplify:
-0.5(20f) - 0.5(- 16) = - 10f + 8Apply distributive law
a(b-c)=ab-ac\(\\ \tt\longmapsto -0.5(20f-16)\)
\(\\ \tt\longmapsto -0.5(20f)-0.5(-16)\)
\(\\ \tt\longmapsto -10f+8\)
Please help me with this I’m really confused
Answer:
13.5 minutes
Step-by-step explanation:
We can divide the final temperature to the rate of change to find the time it will take.
-10.8 ÷ -0.8 = 13.5
Check if needed.
13.5 * -0.8 = -10.8
Best of Luck!
Answer: 13.5 minutes
Step-by-step explanation:
We have to divide the temperature you need to reach by the temperature than rate changes at every minute.
-10.8 ÷ -0.8 = 13.5
The answer is 13.5 minutes. Hope this helps!
solving multistep equations(with work shown, please)
116= -4 + 5(-6 - 5a)
8m + 4(4m -5) = -92
-3(8 - 6x) = -96
-126 = -3 (6+6x)
-8 -8(5a + 7)=-224
-2(-5x -1) = 82
-7(4x + 6) = -182
Answer:
#1) 116= -4 + 5(-6 - 5a) : a = -6
#2) 8m + 4(4m -5) = -92 : m = -3
#3) -3(8 - 6x) = -96 : x = -4
#4) -126 = -3 (6+6x) : x = 6
#5) -8 -8(5a + 7)=-224 : a = 4
#6) -2(-5x -1) = 82 : x = 8
#7) -7(4x + 6) = -182 :x = 5
Step-by-step explanation:
Remember: An equation must be equal at all times. This means if something is added to one side, it must also be added to the other. This holds true for addition, subtraction, division, and multiplication.
Problem 1:
116= -4 + 5(-6 - 5a)
move the -4 to the left side by adding 4 to both sides:
116 + 4 = -4 + 5(-6 - 5a) + 4
now 120 = 5(-6 - 5a)
divide both sides by 5:
120/5 = (5(-6 - 5a))/5
now 24 = -6 - 5a
move the -6 to the left side by adding 6 to both sides:
24 + 6 = -6 - 5a + 6
now 30 = - 5a
divide each side by -5:
(30)/-5 = (- 5a)/ -5
now -6 = a or a = -6
___________________________
Problem 2:
8m + 4(4m -5) = -92
begin by diving both sides by 4:
(8m + 4(4m -5))/4 = (-92)/4
now 2m + 4m - 5 = -23
move the -5 to the right side by adding 5 to both sides:
2m + 4m - 5 + 5 = -23 + 5
now 2m + 4m = -18
restate the left side and combine:
now 6m = -18
divide both sides by 6:
6m/6 = -18/6
so m = -3
___________________________
Problem 3:
-3(8 - 6x) = -96
divide both sides by - 3:
(-3(8 - 6x)) / -3 = -96/-3
now 8 - 6x = 32
move 8 to right side by subtracting 8 from both sides:
8 - 6x - 8 = 32 - 8
now -6x = 24
divide both sides by -6:
-6x/ -6 = 24/-6
x = -4
___________________________
Problem 4:
-126 = -3 (6+6x)
divide both sides by - 3:
-126/-3 = (-3 (6+6x)) /-3
now 42 = 6 + 6x
move 6 to left side by subtracting 6 from both sidesL
42 - 6 = 6 + 6x - 6
now 36 = 6x
divide both sides by 6:
36/6 = 6x/6
x = 6
___________________________
Problem 5:
-8 - 8(5a + 7)= -224
add 8 to both sides:
-8 - 8(5a + 7) + 8 = -224 + 8
now -8(5a + 7) = - 216
divide both sides by -8:
(- 8(5a + 7))/-8 = - 216 /-8
now 5a + 7 = 27
move 7 to right side by subtracting 7 from both sides:
5a + 7 - 7 = 27 - 7
now 5a = 20
divide both sides by 5:
5a/5 = 20/5
a = 4
___________________________
Problem 6:
-2(-5x -1) = 82
divide both sides by -2:
(-2(-5x -1))/-2 = 82/-2
now -5x -1 = -41
move -1 to right side by adding 1 to both sides:
-5x - 1 + 1= -41 + 1
now -5x = -40
divide both sides by -5:
-5x/-5 = -40/-5
x = 8
___________________________
Problem 7:
-7(4x + 6) = -182
divide both sides by -7:
(-7(4x + 6))/-7 = -182/-7
now 4x + 6 = 26
move 6 to right side by subtracting 6 from both sides:
4x + 6 - 6 = 26 - 6
now 4x = 20
divide both sides by 4:
4x/4 = 20/4
x = 5
What is the fraction 1/5 as a percent?
The fraction 1/5 as a percentage is 20 %.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Start by changing the fraction to a decimal by diving the numerator by the denominator 1 divided by 5 Which equals 0.2
Change the decimal to a percent by multiplying it by 100%, or moving the decimal to two places. That gives you 20%.
Another way of thinking about it is multiplying the numerator by 100%, then dividing that by the denominator 100%, 1 divided by 5
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Cory makes a map of his favorite park, using a coordinate system with units of yards. The old oak tree is at position (3, 7) and the granite boulder is at position (-2, 6). How far apart are the old oak tree and the granite boulder? Round to the nearest tenth if necessary
Answer:
7.1 yd
Step-by-step explanation:
Help me fast please 50 POINTS giving 50 points and brainliest its only 5 questions
Answer:
2x^2+1=5-2x
2x^2+1-5+2x
2x^2-4+2x=0
x^2-2+x=0
x^2+x-2=0
(x+2)(x-1)
x1= -2
x2= 1
Answer:
\(2x^2+1=5-2x2x^2+1-5+2x2x^2-4+2x=0x^2-2+x=0x^2+x-2=0(x+2)(x-1)x1= -2x2= 1\)
Step-by-step explanation:
I hope this helps and have a good day!
evaluate 2ps for p=3 and s=5
A)30
B)23
C)6
D)10
Answer: the real answer for this will be p=3/2 and s=5
Step-by-step explanation: here
2p=3
2p/2=3b/2 divide both sides by 2
P=3/2
3/2 for p in s=5
S=5
S=5
Answer P=3/2 and s= 5
Got it
Hey there!
“Evaluate 2ps for p=3 and s=5”
• Side note: If p = 3 then SUBSTITUTE where “p” is at in the equation; if s = 5 then SUBSTITUTE where “s” is at in the equation!
• New equation: 2(3)(5)
2(3)(5)
2(3) = 6
6(5) = 30
Answer: A. 30 ☑️
Good luck on your assignment and enjoy your day!
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