The sample space for choosing one card is, S={I, L, L, M, P, T, U, Y}
What is a sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given that,
A set of eight cards were labeled with M, U, L, T, I, P, L, Y.
Here, the sample space is;
{ S, U, B, T, R, A, C, T}
Now, Elements in order is,
⇒ S = {I, L, L, M, P, T, U, Y}
Therefore, the sample space for the given cards is,
S = {I, L, L, M, P, T, U, Y}
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Answer: I think the answer would be C
PQR is a straight line, (m+n)=120° and (n+r)=100°. find (m+r)
Imagine you have a bond with ten years left until maturity, a face value of $1000 and a 4% coupon rate. Interest rates recently rose to 6% and you want to figure out how it might impact the price of your bond. How much would this bond pay you back in principal at the end of the 10 years?
The bond would pay back its face value of $1000 at the end of the 10 years.
How to determine the amount to pay backThe face value of the bond is the amount the bond will be worth when it matures, and it is also known as the "par value" or the "principal amount."
In this case, the face value of the bond is $1000, so at the end of the 10 years, the bond will pay back $1000 in principal to the bondholder.
The coupon rate, which is 4% in this case, determines the amount of the annual interest payment that the bondholder will receive.
Therefore, regardless of the changes in interest rates, the bond will pay back its face value of $1000 at the end of the 10 years.
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17. A rectangle's length is 5 centimeters greater
than its width. The perimeter of the rectangle
is 46 centimeters. Which equation could be
used to find the width?
A. 4w + 5 = 46
B. 4w + 10 = 46
C. 2w + 5 = 46
D. 2w + 10 = 46
Answer:
B. 4w + 10 = 46
Step-by-step explanation:
If we let l be the length of the rectangle and w its width
Fact 1: A rectangle's length is 5 centimeters greater than its width
This translates to l = w + 5 (1)
Fact 2: he perimeter of the rectangle is 46 centimeters
Perimeter is given by 2(l + w)
So fact 2 translates to:
2(l + w) = 45
2l + 2w = 46 (2)
Substitute l = w + 5 from (1) for l in (2):
2(w + 5) + 2w = 46
2w + 10 + 2w = 46
4w + 10 = 46
This is Option B
Answer:
C. 2w + 5 = 46
Reason why is because a rectangle has 4 sides, but you only want to multiply length times the width, to get the perimeter, which is why 2w in the equation is correct.
It also says 5 centimeters greater, the is why it would be + 5 instead of 10.
Step-by-step explanation:
Hope it helps! =D
Meagan gets a third of the money that her family earns selling cookies, and the amount that she gets can be shown with the expression m
3
. What is the meaning of the variable m in the expression?
Answer: the meaning of the variable m is Meagan, M is a shortened version to show that 3 is how much money she has.
Step-by-step explanation:
hope this helps ^^
determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.) an = cos2(n) 5n lim n→[infinity] an =
The sequence diverges.
There is just one possible outcome for a sequence: either it converges or it diverges. This does not imply that we can always detect whether the sequence converges or diverges; in fact, there are occasions when it can be very challenging for us to do so.
The limit of the sequence an = cos(2n) / 5n as n approaches infinity does not exist, so the sequence diverges.
The cosine function oscillates between -1 and 1, so the value of cos(2n) can be arbitrarily large or small as n gets larger. As a result, the ratio of cos(2n) to 5n also becomes arbitrarily large or small, and the limit does not exist.
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HELP FIND X & Y!!! NEED ASAP! (FOR 100 POINTS!)
[tex]\huge\begin{array}{ccc}x=1;&y=\frac{\sqrt3}{2}\end{array}[/tex]
The triangle with angles 30°, 60° and 90°.
Look at the picture.
We have:
[tex]a=\dfrac{1}{2}\\\\2a=x\\\\a\sqrt3=y[/tex]
Therefore:
[tex]x=2\cdot\dfrac{1}{2}\to\boxed{x=1}\\\\y=\dfrac{1}{2}\cdot\sqrt3\to\boxed{y=\dfrac{\sqrt3}{2}}[/tex]
Drag the tiles to the boxes to form correct pairs. Polygon ABCD has sides with these lengths: A B ¯ , 5 units; B C ¯ , 4 units; C D ¯ , 4.5 units; and A D ¯ , 7 units. The slope of A B ¯ is 5, the slope of B C ¯ is 0.25, the slope of C D ¯ is -2, and the slope of A D ¯ is 0. The polygon is dilated from point A by a scale factor of 1.2 to form polygon A′B′C′D′. Match the slopes and lengths of the sides of polygon A′B′C′D′ to their values.
The required match for the dilation of the polygon from ABCD to A'B'C'D',
The slope of A'B' = 5
Length of C'D' = 5.4
Length of A'D' = 8.4
The Slope B'C' = 0.25
The scale factor is defined as the ratio of the modified change in length to the original length.
here,
After the dilation of the polygon from ABCD to A'B'C'D',
The slope of A'B' = 5
[scale dilation does not affect the orientation of geometry.]
Length of C'D' = 5.4 [length of C'D' = 1.2 × CD]
Length of A'D' = 8.4 [length of A'D' = 1.2 × AD]
The Slope B'C' = 0.25
[scale dilation does not affect the orientation of geometry.]
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Shirley is building a shed. The length is 2x + 3 feet long and the width is x + 1 feet long
1) what is the perimeter of the shed
2) what is the area of the shed
Please help I really want to go to sleep please
The perimeter is 6x + 8 feet and the area is (2x^2 + 5x + 3) square feet
How to determine the perimeter and the areaThe perimeter of a rectangle is equal to the sum of the lengths of all four sides.
The length of the shed is 2x + 3 feet, and the width is x + 1 feet, so the perimeter of the shed is:
2 * (2x + 3) + 2 * (x + 1) = 4x + 6 + 2x + 2 = 6x + 8 feet
The area of a rectangle is equal to the product of its length and width.
So, the area of Shirley's shed is:
(2x + 3) * (x + 1) = (2x^2 + 5x + 3) square feet
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Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [1 h 2 -5 20 - 12] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix is the augmented matrix of a consistent linear system if ht -9 (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. The matrix is the augmented matrix of a consistent linear system if h = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) C. The matrix is the augmented matrix of a consistent linear system for every value of h. D. The matrix is not the augmented matrix of a consistent linear system for any value of h.
C. The matrix is the augmented matrix of a consistent linear system for every value of h.
What is augmented matrix ?
An augmented matrix is one that is created by joining the columns of two matrices.
The augmented matrix of a consistent linear system can have any value in the last column, as long as it corresponds to a valid solution of the system of linear equations.
The presence of a non-zero value in the last column simply indicates that the system has a unique solution, while a zero value in the last column indicates that the system is either inconsistent or has infinitely many solutions.
In this case, the value of h does not affect the consistency of the system.
Hence, The matrix is the augmented matrix of a consistent linear system for every value of h.
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Keith has 16 cups of dough to make dumplings. If he uses 4/5 cup of dough for each dumpling, how many dumplings can he make?
Answer:
20 dumplings.
Step-by-step explanation:
Keith can make 16 / (4/5) = 16 * 5/4 = 20 dumplings.
What is the mean for the answers
A: Range is 4
Range is from the smallest to the greatest so 10 - 6 = 4.
B: There are 5 students in the groups.
Five marks, five students.
C: Mean is 8.
The mean is to add all the marks 6 + 7 + 8 + 9 + 10 = 40. Then, divide by the numbers. There are 5 numbers so, 40 ÷ 5 = 8.
Mark me Brainliest. :D
subtract (2x^2-3x+5)-(3x^2-4x+7)
Answer:
−x^2+x−2
Step-by-step explanation:
Define response variable. Choose the correct answer below.
A.The effect of two factors (explanatory variables on the response variable) cannot be distinguished.
B.The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable
C.An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
D.The variable whose effect on the response variable is to be assessed by the experimenter
Response variable defined with:
B. The number or quality of the variable for whom the value the experimenter wants to figure out how the explanatory variable affects.
Define Response VariableOption B describes the response variable as the variable of interest that the experimenter is trying to study and understand how it is affected by other variables, known as explanatory variables. The response variable is often the dependent variable in a study and the focus of the analysis.
On the other hand, option A describes a situation in which the effect of two factors on the response variable cannot be distinguished, which is not a definition of the response variable itself. Option C describes a placebo, which is a different concept in experimental design.
Option D is similar to option B but does not describe the response variable as being the focus of the experimenter's study.
The response variable, also known as the dependent variable, is a variable in a statistical model or experiment that is being measured or studied. It is the outcome of interest that the experimenter wants to understand and explain by considering the effects of one or more independent variables, also known as explanatory variables.
The goal of the experiment is to determine how changes in the explanatory variables affect the response variable. In a sense, the response variable is the dependent variable because its value depends on the values of the independent variables.
Understanding the relationship between the response and explanatory variables is important in fields such as science, medicine, and engineering, where researchers are often interested in predicting or controlling outcomes based on various inputs.
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Evaluate the integral. (Use C for the constant of integration.) ∫15sin3(x)cos2(x)dx∫15sin3(x)cos2(x)dx
The result of the original integral is:
∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C
What is the integration?
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.
The integral of the product of sine and cosine functions can be evaluated using the identity:
sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))
Therefore, we can rewrite the integrand as:
15sin3(x)cos2(x) = (15/2)sin(3x + 2x) + (15/2)sin(3x - 2x)
Now, we can integrate each of the two terms separately:
∫(15/2)sin(3x + 2x)dx = (15/2)cos(3x + 2x) + C
∫(15/2)sin(3x - 2x)dx = (15/2)cos(3x - 2x) + C
Therefore, the result of the original integral is:
∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C
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Serenity wants to ride her bicycle 35. 8 miles this week. She has already ridden 17
miles. If she rides for 4 more days, what is the average number of miles she would
have to ride each day to meet her goal?
Answer:
4.7 miles per day
Step-by-step explanation:
35.8 - 17 = 18.8 miles
So, she needs to ride 18.8 miles in 4days
18.8 divided by 4 = 4.7 miles per day
So, she needs to ride 4.7 miles each day to meet her goal.
if f (x) = startfraction x over x squared minus 9 endfraction, which table identifies the increasing and decreasing behavior of the function on the intervals (−[infinity], −3), (–3, 3), and (3, [infinity])?
The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:
On the interval (-∞, -3), f(x) is increasing.
On the interval (-3, 0), f(x) is decreasing.
On the interval (0, 3), f(x) is increasing.
On the interval (3, ∞), f(x) is decreasing.
We have,
To determine the increasing and decreasing behavior of the function f(x) = x / (x² - 9) on the given intervals, we can evaluate the sign of the derivative of the function.
Taking the derivative of f(x) with respect to x and simplifying, we have:
[tex]f'(x) = (-x^2 + 9 - x(2x)) / (x^2 - 9)^2\\= (-x^2 + 9 - 2x^2) / (x^2 - 9)^2\\= (-3x^2 + 9) / (x^2 - 9)^2[/tex]
To identify the increasing and decreasing behavior, we need to examine the sign of f'(x) on each interval.
For the interval (-∞, -3):
Plugging in a value less than -3, such as -4, into f'(x) yields a positive result.
Plugging in a value between -3 and 0, such as -2, into f'(x) gives a negative result.
Therefore, f'(x) is positive for x < -3 and negative for -3 < x < 0, indicating that f(x) is increasing on the interval (-∞, -3) and decreasing on the interval (-3, 0).
For the interval (-3, 3):
Plugging in a value between -3 and 0, such as -2, into f'(x) yields a negative result.
Plugging in a value between 0 and 3, such as 1, into f'(x) gives a positive result.
Therefore, f'(x) is negative for -3 < x < 0 and positive for 0 < x < 3, indicating that f(x) is decreasing on the interval (-3, 0) and increasing on the interval (0, 3).
For the interval (3, ∞):
Plugging in a value between 3 and 4, such as 3.5, into f'(x) yields a positive result.
Plugging in a value greater than 4, such as 5, into f'(x) gives a negative result.
Therefore, f'(x) is positive for 3 < x < 4 and negative for x > 4, indicating that f(x) is increasing on the interval (3, 4) and decreasing on the interval (4, ∞).
Thus,
The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:
On the interval (-∞, -3), f(x) is increasing.
On the interval (-3, 0), f(x) is decreasing.
On the interval (0, 3), f(x) is increasing.
On the interval (3, ∞), f(x) is decreasing.
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There are currently 54 million cars in a certain country, decreasing exponentially by 6.8 % annually. How many years will it take for this country to have 46 million cars? Round to the nearest year.
Answer:
16.7 years (not sure)
Step-by-step explanation:
To solve this problem, we can use the formula for exponential decay:
y = y0 * (1 - r)^t
Where y is the number of cars after t years, y0 is the initial number of cars (54 million), r is the annual decrease rate as a decimal (6.8% = 0.068), and t is the number of years.
We want to find t when y = 46 million:
46 million = 54 million * (1 - 0.068)^t
Dividing both sides by 54 million:
46 million / 54 million = (1 - 0.068)^t
Taking the natural logarithm of both sides:
ln(46 million / 54 million) = ln((1 - 0.068)^t)
Using the logarithmic identity:
ln(46 million / 54 million) = t * ln(1 - 0.068)
Dividing both sides by ln(1 - 0.068):
t = ln(46 million / 54 million) / ln(1 - 0.068)
Using a calculator, t = approximately 16.7 years. Rounding to the nearest year, it will take 17 years for this country to have 46 million cars.
A set of scores ranges from a high of X = 75 to a low of X = 23. If the bottom interval in a frequency table is 18-23, what is the top interval?
The top interval in a frequency table for a set of scores ranging from a high of X = 75 to a low of X = 23 would be 73-75.
This is because the bottom interval is 18-23, and the intervals in a frequency table are generally of equal size. This means that the highest interval must be of a similar size, and would thus be 73-75. The purpose of a frequency table is to show how often values from a numerical data set occur.
The data is usually divided into intervals of equal size, such as the 18-23 interval mentioned in this scenario. The intervals are usually calculated by subtracting the lowest value from the highest value, and then dividing the result by the number of intervals desired. In this case, the highest interval must be of equal size to the 18-23 interval, resulting in a range of 73-75.
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Can someone please answer this
The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
Let the angle be 'x'. Then the equation is given as,
x + 13° = 71°
x = 71° - 13°
x = 58°
The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.
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y=3x+4
-12x+4y= 16
A. one solution
B. no solution
C. infinitely many solutions
There is only one solution to the equation y=3x+4 and -12x+4y=16 since there are neither no solutions nor an unlimited number of them.
what is solution ?curing a problem by a method but rather action; explaining the answer. a range of values for a variable that fulfill an equation, specifically The solution of an equations is any value of both a variable that gets the Left Hand Side (LHS) and thus the Nondominant Hand Side (RHS) of the equations equal. To solve an equation is to identify its answer or solutions. One approach to express the concentration of a solvent is as a percentage of the solute in the solvent. The ratio of the mass of something like the solute here to mass of the solution, or the fraction of the mass of something like the solute here to mass of the solution, is one of two supplementary techniques for computing the percentage.
given
When we multiply equation 1 by 4 we get:
-3x + y = 4
-12x + 4y = 16
Due to the fact that there is no solution for x, -12x + 4y = 16
There is only one solution to the equation y=3x+4 and -12x+4y=16 since there are neither no solutions nor an unlimited number of them.
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What is the result of 1.58/3.793 written with the correct number of significant figures?
A.) 0.41656
B.) 0.4166
C.) 0.417
D.) 0.42
E.) 0.4
Answer:C
Step-by-step explanation:
Which boundary marker did the organizers of New York City's annual India Day Parade use to exclude a particular group from participating
Sexuality is boundary marker that organizers of New York City's annual India Day Parade use to exclude a particular group from participating.
What exactly do you mean by groupism?The proclivity to think and act as members of a group: the proclivity to conform to a group’s cultural pattern at the price of individualism and cultural variety. Groupism… is founded not on evident group emergencies, but on the nebulous unease of lonely individuals. Mr. David Riesman.
Tangible culture (such as buildings, monuments, landscapes, literature, works of art, and artifacts), intangible culture (such as folklore, traditions, language, and knowledge), and natural heritage are all examples of cultural heritage (including culturally significant landscapes, and biodiversity).Sexuality, gender, religion, race, socioeconomic status, and area are examples of cultural identities.
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math ridle a 12 hour clock loses 1 minute every hour suppose it shows the correct time now what is the least number of hours from now when it will again show the correct time?
The least number of hours from now when the clock will again show the correct time is 720 minutes
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
The clock will show the correct time again when it lost 12 hours
As every hour it loses 1 minute, the clock have to lose 12 hours in minutes, so we get:
12 hour * (60 minutes / 1 hour) = 720 minutes
Therefore, the least number of hours from now when the clock will again show the correct time is 720 minutes.
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a, P(A B) ≥ P(A). True/False
False, P(A and B) is not always greater than or equal to P(A).
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
P(A B) ≥ P(A)
This means that
Is P(A and B) always greater than or equal to P(A)?
The value of the probability is calculated a
P(A and B) = P(A) * P(B)
This means that there is a direct variation between P(AB) and P(A)
Since P(B) is less than 1, then P(A B) ≥ P(A) is false
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The amounts of time Chauni spent writing a certain number of songs are graphed below.
If Chauni continues to write songs at the same rate, how many songs will she have written in 60 days?
Worth 10 points
Responses
18 songs
18 songs
20 songs
20 songs
24 songs
24 songs
30 songs
30 songs
Answer:
Step-by-step explanation:
18
As many as 49 million Bison used to roam the Great Plains of the United States. When the
American settlers started hunting them for fur, meat and political purposes their survival rate
dropped to 0.81. How many million would have remained after 9 years of hunting?
Answer:
7.35 million
Step-by-step explanation:
49*0.81^9 =7.35 million
A copy machine makes 32 copies per minutes. How long does it take to make 120 copies (with minutes and seconds)
Answer: 3 min 45 sec
Step-by-step explanation:
[tex]\begin{array}{ccll} copies&minutes\\ \cline{1-2} 32 & 1\\ 120& x \end{array} \implies \cfrac{32}{120}~~=~~\cfrac{1}{x} \\\\\\ \cfrac{ 4 }{ 15 } ~~=~~ \cfrac{ 1 }{ x }\implies 4x=15\implies x=\cfrac{15}{4}\implies \stackrel{\textit{3 minutes and 45 seconds}}{x=3\frac{3}{4}}[/tex]
An engineer is designing a fuel tank in the shape of a cylinder. The tank must have a volume of 3,500 cubic inches. The height of the cylinder must be twice the radius. What is the approximate radius of the cylinder?.
An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.
Volume:
V = πr²h
Height:
h = 2r
V = πr²h
V= πr²(2r)
V= 2πr³
And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:
V= πr²h
3500 = 3.14 x 2 x (r)³
r = 8.2 inch
The cylinder's approximate radius must be 8.2 inches.
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.
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For f(x) = 2x³ - 10x + 3, h(x) = x - 5 and g(x)=2x, find the
following:
a) (f + h)(x)
b) (f - h)(x)
c) (fg)(x)
d) (fh)(x)
e) (f/g)(x)
The values of the composite functions are
a) (f + h)(x) = 2x³ - 9x - 2b) (f - h)(x) = 2x³ - 11x + 8c) (fg)(x) = 16x³ - 20x + 3d) (fh)(x) = 2(x - 5)³ - 10(x - 5) + 3 e) (f/g)(x) = (2x³ - 10x + 3)/(2x)How to evaluate the composite functionsFrom the question, we have the following functions that can be used in our computation:
f(x) = 2x³ - 10x + 3, h(x) = x - 5 and g(x)=2x
Using the above as a guide, we have the following:
a) (f + h)(x) = 2x³ - 10x + 3 + x - 5 = 2x³ - 9x - 2
b) (f - h)(x) = 2x³ - 10x + 3 - x + 5 = 2x³ - 11x + 8
c) (fg)(x) = f(g(x)) = f(2x) = 2(2x)³ - 10(2x) + 3 = 16x³ - 20x + 3
d) (fh)(x) = f(h(x)) = f(x - 5) = 2(x - 5)³ - 10(x - 5) + 3
e) (f/g)(x) = f(x)/g(x) = (2x³ - 10x + 3)/(2x)
The above are the values of the composite functions
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation of the circle,
x² + (y – 3)² = 36.
The correct option is A.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Given:
A circle that has a diameter of 12 units and a center that lies on the y-axis.
That means, radius = 6.
And h = 0.
From the given choices:
Now, the equation of the circle,
x² + (y – 3)² = 36.
Therefore, x² + (y – 3)² = 36 is the equation.
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