If random sample yielded these observed scores: 6 12 5 10 6 9 12 20 5 23 10 20 11 28 13 18. The 99% confidence interval for the mean height of both groups combined is approximately (3.92, 20.58) cm.
To calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution, since the sample size is relatively small (less than 30) and the population standard deviation is unknown.
First, we need to calculate the sample mean and sample standard deviation. The sample mean can be calculated by adding up all the observed scores and dividing by the total number of scores. In this case, the sample mean is (6+12+5+10+6+9+12+20+5+23+10+20+11+28+13+18) / 16 = 12.25 cm.
The sample standard deviation can be calculated using the formula:
s = √((∑(x - x')^2) / (n - 1))
where x is each observed score, x' is the sample mean, and n is the sample size. In this case, the sample standard deviation is approximately 7.05 cm.
Next, we need to calculate the t-value for a 99% confidence level, with 15 degrees of freedom (16 - 1). Using a t-table or a statistical software, we can find that the t-value is approximately 2.947.
Finally, we can calculate the confidence interval using the formula:
Confidence interval = sample mean ± (t-value * (sample standard deviation / √(sample size)))
Plugging in the values, we get:
Confidence interval = 12.25 ± (2.947 * (7.05 / √(16))) = 12.25 ± 8.33
In summary, to calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution and the formula for confidence intervals. We need to calculate the sample mean, sample standard deviation, t-value for the desired confidence level, and then plug these values into the formula to get the confidence interval.
This interval represents the range of values within which we can be 99% confident that the true mean height of both groups combined falls.
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Pls show your work thank you will mark the Brainliest
Answer: A
Step-by-step explanation: There isn't much work to be shown here, however you can look at graphical patterns to get your answer. It says the initial value is $200000 so you can eliminate B and D because they start at $100000. That leaves A and C. C is increasing at a higher rate and is greater than 100% per year. That leaves option A.
what number solves the equation 1/3x = -20
Answer:
x=-60
Step-by-step explanation:
Answer:
-60
Step-by-step explanation:
1/3 x = -20 Multiply both sides by 3
3(1/3) x = 3(-20)
x = -60
Check
1/3(-60) = -20
-20 = -20
there are 14 people in an office with 5 different phone lines. if all the lines begin to ring at once, how many groups of 5 people can answer these lines?
There are 2002 groups of 5 people that can answer the 5 phone lines.
This is a combination problem, because we want to choose groups of 5 people from a group of 14, and the order in which we choose the people does not matter.
The formula for the number of combinations of n objects taken r at a time is:
C(n,r) = n! / (r! * (n-r)!)
In this case, we want to choose 5 people out of a group of 14, so we can plug those values into the formula:
C(14,5) = 14! / (5! * (14-5)!)
Simplifying the factorial terms:
C(14,5) = (1413121110) / (54321)
C(14,5) = 2002
Therefore, there are 2002 groups of 5 people that can answer the 5 phone lines.
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Which function has a simplified base of 4RootIndex 3 StartRoot 4 EndRoot?
f(x) = 2(RootIndex 3 StartRoot 16 EndRoot) Superscript x
f(x) = 2(RootIndex 3 StartRoot 64 EndRoot) Superscript x
f(x) = 4(RootIndex 3 StartRoot 16 EndRoot) Superscript 2 x
f(x) = 4(RootIndex 3 StartRoot 64 EndRoot) Superscript 2 x
The function that has a simplified base of (4∛4) is 4(∛16[tex])^({2x)[/tex].
What is Exponential Function?Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.
From the general formula of an exponential function, we know that;
f(x) = a[tex](b)^x[/tex]
Now, we have;
f(x) = (4∛4[tex])^x[/tex]
4(∛16[tex])^({2x)[/tex], the base is (∛16)²
(∛16)²
= √(16^(⅔))
=256^(⅓)
= 4∛4
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Answer:
C.
Step-by-step explanation:
Took the test. :)
can someone explain as well so i can understand......A savings account with simple annual interest rate of 3.92% and an initial deposit of $5,460.75 yields a final account balance of $6,370.51 after 51 months. Part A: Using the rate and term as the simple interest account, calculate the final account balance if the initial deposit is invested for the same number of months, with interest compounded semiannually. Show all work. (3 points) Part B: Compare that simple interest final account balance with the compound interest final account balance. (2 point)
Answer:
Step-by-step explanation:
To calculate the final account balance for a savings account with an initial deposit of $5,460.75, compounded semiannually with an interest rate of 3.92%, for 51 months, we need to use the formula:
A = P * (1 + r/n)^(nt)
where A is the final account balance, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times the interest is compounded in a year, t is the number of years, and nt is the number of compounding periods.
In this case, n = 2 (since the interest is compounded semiannually), r = 3.92%/100 = 0.0392, t = 51 months / 12 months/year = 4.25 years, and nt = 2 * 4.25 = 8.5.
Substituting the values into the formula, we get:
A = $5,460.75 * (1 + 0.0392/2) ^ (8.5)
A = $5,460.75 * 1.0196^8.5
A = $5,460.75 * 1.2408
A = $6790.32
So, the final account balance if the initial deposit is invested with interest compounded semiannually is $6790.32.
B) Comparing the final account balance of the simple interest account and the compound interest account, we can see that the compound interest account yields a higher balance ($6790.32) than the simple interest account ($6370.51). This is because compounding interest allows for the interest earned in one period to be reinvested, so the interest earns interest in future periods, which increases the overall amount of interest earned over time. In contrast, simple interest is calculated only on the initial deposit, so the amount of interest earned remains constant over time.
The table shows the responses from 103 people when asked if they support a proposal to expand the public library.
What is the probability of a person responded Yes OR Under the Age of 55?
A. 43%
B. 51%
C. 57%
D. 49%
The probability that a person responded Yes or was under the Age of 55 was C. 57 %
How to find the probability ?The probability that a person who responded either said yes or was under the Age of 55 is:
= Probability that a person answers yes + probability that a person is under 55 - Probability that a person was under 55 and answered yes
The probability a person who responded either said yes or was under the Age of 55 is therefore:
= ( 25 / 103 ) + ( 59 / 103 ) - 17 / 103
= 57 %
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There are 5 slices of pepperoni pizza, 1 slice of sausage pizza, and 3 slices of cheese pizza left. Without looking, Douglas took a slice of pizza, ate it, and then took another slice.
What's the probability of Douglas eating two of the same kinds of pizza?
PLEASE GIVE BRAINLIEST!
thank you and have a good day, I hoped this helps :)
Answer:
1/12
Step-by-step explanation:
To calculate the chances of Douglas eating one slice of cheese pizza
3/(5+3+1) = 1/3
To calculate the odds of him eating another cheese pizza slice
2/(5+2+1) = 1/4
To calculate the odds of Douglas eating the same two kinds of pizza
1/4 times 1/3
there you go! :)
help plssssssssssssssssssss
Answer: look at the image for the answer and solution
Step-by-step explanation:
What percent of Jemma's answers did she get incorrect?
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, then the incorrect percent is 10% .
Total number of questions in the Math's quiz is = 20 ;
Number of incorrect questions done by Jemma is = 2 ;
Number of correct questions done by Jemma are = 18 ;
So , to find the percentage she got incorrect, we divide ; (number of incorrect answers) by (total number of questions) and then multiply by 100 ;
that means ⇒ (2/20) × 100 = 10% ;
Therefore, Jemma got 10% of the questions incorrect on her most recent math quiz.
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The given question is incomplete , the complete question is
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, what percent did she get incorrect ?
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students. Ice Cream Candy Cake Pie Cookies 81 9 72 36 27 Which statement is the best prediction about the slices of pie the college will need? The college will have about 480 students who prefer pie. The college will have about 640 students who prefer pie. The college will have about 1,280 students who prefer pie. The college will have about 1,440 students who prefer pie.
Answer:480
Step-by-step explanation
A candy store sells a brand of nuts that costs $2 per pound and a brand of chocolate coated candies that costs $0.95 per pound. Select the equation that solves for x lb of nuts that must be mixed with 32 lb of the chocolate coated candies in order to have a mixture that costs 1.48 per pound.
A. 2x + 0.95(32) = 1.48x
B. 2x + 0.95(32) = 1.48(x + 32)
C. 0.95x + 2(32) = 1.48(x + 32)
D. 0.95x + 2(32) = 1.48x
E. none of these
We know that the store sells nuts for $2 per pound and chocolate for $0.95 per pound. We also know that x represents the total pounds of nuts, and 32 represents the total pounds of chocolate.
In order to write an equation that represents a mixture that costs $1.48 per pound, we first need to find an expression to represent the total pounds in this situation, which would be (x + 32).
Now that we have this, let's just combine everything we know into one equation:
2x + 0.95(32) = 1.48(x + 32)
Therefore, the correct answer choice is option B.
In a group of 62 people 27 like cold tea while 42 like hot tea how many people like neither of the two
What is the area of a right triangle with a height of seven and three fourths yards and a base of 20 yards?
If the height of seven and three fourths yards and a base of 20 yards, then the area of the right triangle is 77.5 square yards.
To calculate the area of a right triangle, we can use the formula:
Area = (base * height) / 2
where the base is one of the sides of the triangle, and the height is the perpendicular distance from that side to the opposite vertex.
In this case, the height of the right triangle is 7 and 3/4 yards, and the base is 20 yards. Plugging these values into the formula, we get:
Area = (20 * 7.75) / 2 = 155 / 2 = 77.5 square yards
In summary, to calculate the area of a right triangle, we can use the formula that relates the base and height to the area. In this case, we needed to use the given values of the height and base of the right triangle to compute the area in square yards.
The resulting area represents the amount of surface inside the triangle and is useful in many applications, such as geometry, physics, and engineering.
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A, B & C form the vertices of a triangle, where ∠CAB = 90°.AB = 10.5 m and AC = 5.2 m.
Evaluate ∠CBA, giving your answer rounded to 3 SF.
Answer: In a right-angled triangle, we can use the Pythagorean Theorem to find the length of the remaining side. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of side BC can be found using the Pythagorean Theorem:
BC^2 = AB^2 + AC^2
BC^2 = 10.5^2 + 5.2^2
BC^2 = 110.25 + 27.04
BC^2 = 137.29
BC = √137.29
BC ≈ 11.68 m
Now that we have the length of side BC, we can use the inverse cosine function (cos^-1) to find the angle ∠CBA:
∠CBA = cos^-1 (BC / AB)
∠CBA = cos^-1 (11.68 / 10.5)
∠CBA ≈ 68.194°
Rounding to 3 significant figures, the answer is ∠CBA = 68.2°.
Step-by-step explanation:
SOLVING EQUATIONS Solve the equation. Check your solution.
50. y+4-1 = 18
52. v-7= 9+12
St 53.5+44=2+r
51. m+ 18+ 23 = 71
54. 22 +15=d-17
The solution of the equation are as follows:
y = 15
v = 28
r = 95.5
m = 30
d = 54
How to solve equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The equation can be solved by finding the value of the variables.
A variable is a number represented with letter in an equation.
Therefore, let's solve the equation.
y + 4 - 1 = 18
y = 18 - 4 + 1
y = 15
v - 7 = 9 + 12
v = 12 + 9 + 7
v = 28
53.5 + 44 = 2 + r
r = 53.5 + 44 - 2
r = 95.5
m + 18 + 23 = 71
m = 71 - 18 - 23
m = 30
22 + 15 = d - 17
d = 22 + 15 + 17
d = 54
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I'LL GIVE BRAINLIEST JUST PLEASE ANSWER
countries represented at each festival 1: 0-5 3:6-11 5:12-17 4:18-23 2:24-29. How many festivals were there?
ANSWER ASAP PLEASE!!!!!
Answer:Twerk
Step-by-step explanation:Twerk
What is the length of the other diagonal, df? 5 cm 16 cm 21 cm 32 cm
Referring to the given kite, the length of the other diagonal. DF, is 21 cm.
A kite is a quadrilateral shape, meaning it has four sides. The two pairs of adjacent sides are of equal length, while the opposite sides are not.
The shape of a kite is typically described as having two pairs of congruent adjacent sides that are connected by two diagonal lines that intersect at a right angle. The diagonal lines of a kite are perpendicular to each other, and the shorter diagonal bisects the longer diagonal.
Let's denote the point of intersection of the two diagonals as O.
Since the two diagonal intersect at a right angle, diagonal DF is perpendicular to diagonal EG.
DG = 13 cm
FG = 20 cm
OG = 1/2 EG = 1/2 x 24 = 12 cm
Using the Pythagorean Theorem:
OD = √(DG² - OG²)
= √(13² - 12²) = 5 cm
OF = √(FG² - OG²)
= √(20² - 12²) = 16 cm
DF = OD + OF
= 5 + 16 = 21 cm
The picture in your question is missing, most likely it was like on the attached picture.
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Answer: c
Step-by-step explanation: I got it right
ANSWER QUICK!! I WILL GIVE BRAINLIEST!!!!!!!!!!!
The barber cuts 61 haircuts in 4 days. Determine the rate for a ratio of the two different quantities.
61 over 65 haircuts per day
4 over 65 haircuts per day
4 over 61 haircuts per day
61 over 4 haircuts per day
Answer:
61 over 4 haircuts per day
What is a ratio?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
A way to solve for the number of haircuts per day is to use this equation:
total number of haircuts ÷ number of days = haircuts per dayYou could also use this fraction:
[tex]\frac{total-number-of-haircuts}{number-of-days}[/tex]Inserting the numbers into the fraction::
[tex]\frac{61}{4}[/tex]Therefore, the rate for a ratio using the two different quantities is 61 over 4 haircuts per day.
helpppppppppppppppppppppp
Answer:
X Y
2 1
4 7
5 10
Step-by-step explanation:
10. If the opposite angle of the parallelogram is 22 less, than thrice the other angle. Find the other angle (a) 24° (c) 22° (d) 32° (b) 34°
The measure of the other angle of the parallelogram is 22 degrees.
What is the other angle of the parallelogram?Opposite angles of a parallelogram are equal (or congruent).
Let the missing angle be represented by x.
First angle = xOpposite angle = 2x - 22Since the opposite angles of a parallelogram are equal (or congruent).
x = 2x - 22
Solve for x
2x - 22 = x
2x = 22 + x
2x - x = 22
x = 22°
Therefore, 22 degrees is the measure of the other angle.
Option C) 22° is the correct answer.
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Solve for n: 4^n+3 x 16^n - 8^3n
The expression 4^n+3 x 16^n - 8^3n cannot be solved for n
How to determine the solution of nfrom the question, we have the following parameters that can be used in our computation:
4^n+3 x 16^n - 8^3n
The question implies that we solve for n
This in other words mean that we determine the solution for n
The given parameter is an expression (not an equation or an inequality)
To solve for a variable, the given parameter must be an equation or an inequality
Hence, the value of n cannot be determined or it has infinite many solutions
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h(x)=−(x−2)
2
+16h, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 2, right parenthesis, squared, plus, 16
What is the height of the ball at the time it is thrown?
Answer:
speak Spanish
Step-by-step explanation:
I"m sorry
to help
how many slices of pizza did he eat
Answer: The answer is 3 slices
Step-by-step explanation:
if you cut a pizza into 12 peices and devide it by 4 people each person gets 3
Complete the table below treat each row has a different problem.
Important : the last row is sector area (a)
The different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
What is sector?The sector is essentially a section of a circle, and it may be described using the following three criteria:
The area of a disc that is surrounded by two radii and an arc is known as a circular sector.
The circle is divided into the Major Sector and the Minor Sector by a sector.
The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.
Given that,
Central angle = [tex]\frac{\pi}{6}[/tex].
The arc length is given as:
l = α/360 (2πr)
Where, α is the central angle.
Substitute the value of central angle we have:
l = (π/6)/360 2πr
l = 2π²r/ 2160
The sector area is given as:
A = α/360 πr²
A = (π/6)/360 πr²
A = π²r²/ 2160
Similarly, the arc length is given as:
l = π/3
Substituting the value of l in arc length we have:
π/3 = α/360 (2πr)
α = 360(π)/ 6πr
α = 60/r
The sector area is given as:
A = α/360 πr²
A = (60/r) 360 πr²
A = πr/60
Hence, the different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
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Adding and subtracting rational expressions, What is the difference? 2x+5/x^2-3x - 3x+5/x^3-9x - x+1/x^2-9?
After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9 .
We first simplify each expression inside the parentheses :
that means :
⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;
⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³) ;
⇒ (x + 1/x² - 9) = (-9 + x + 1/x²) ;
Now we substitute these expressions into original equation/expression :
we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)
Simplifying further ,
we get ;
⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x² ;
On Combining the like terms, we get ;
⇒ 4x - 4/x² - 5/x³ + 9
Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.
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The given question is incomplete , the complete question is
Adding and subtracting rational expressions, Simplify the rational expression (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9) .
Write the expression as a square monomial
0.16x^2y^2
Answer: (____)^2
Answer:
0.0256x^4y^4
Step-by-step explanation:
consider a variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college. explain how you would use this variable to describe something about the states.
Option b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.
The variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college can provide insights into students' preferences for attending college in their home state. A large proportion of students who attend college in their home state indicates that students prefer to stay close to home for higher education, while a small proportion suggests that they are more likely to attend college in a different state. This information can be useful for policymakers and educators to better understand the higher education preferences of their state's students and to develop policies and programs to encourage more students to attend college within their home state.
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Complete question:
The U.S. Census Bureau collects a large amount of information concerning higher education. For example, the bureau provides a table that includes the following variables: state, number of students from the state who attend college, number of students who attend college in their home state.
Consider a variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college. Explain how you would use this variable to describe something about the states.
a. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that less of the state’s population attend college while a small proportion means that more of the state’s population attend college.
b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.
c. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college outside their home state and a small proportion means that students prefer to attend college in their home state.
d. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that more of the state’s population attend college while a small proportion means that less of the state’s population attend college.
2) The area of Norway's is 24% more than the area of Colorado. So Norway's area if
Colorado's area?
The area of Norway's is 24% more than the area of Colorado.So, the area of Colorado is approximately 260,449 square kilometers.
What is Area?
Area is a measurement of the amount of two-dimensional space occupied by a surface or an object. In mathematics, area is a scalar quantity that describes the size of a region in a plane. The units of area are typically square units, such as square meters, square centimeters, square inches, etc.
The formula for the area of a shape depends on the shape itself. For example, the area of a rectangle is equal to its length multiplied by its width, while the area of a circle is equal to π times the square of its radius. Other common shapes and their area formulas include triangles, parallelograms, and trapezoids.
Let's call the area of Colorado "x". If Norway's area is 24% more than Colorado, then Norway's area can be represented as x + 0.24x = 1.24x.
To find the area of Colorado, we can set up an equation:
1.24x = area of Norway
x = area of Norway / 1.24
The area of Norway is 323,802 square kilometers. Therefore, the area of Colorado can be calculated as:
x = 323,802 / 1.24
x = 260,449 square kilometers
So, the area of Colorado is approximately 260,449 square kilometers.
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Ticket lines are huge around the Colossal Arena. The Boulders, one of the most popular rock groups ever, are giving a concert on Saturday. When the tickets went on sale Monday, 500 were sold in the first hour, 560 tickets were sold in the second hour, and 640 tickets were sold in the third hour. After the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour. If sales continue at that rate, in what hour will 10,000 tickets be sold for the Boulders concert?Explain your answer in detail
If after the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour, it will take 12 hours to sell 10,000 tickets for the Boulders concert.
To solve this problem, we need to find the number of hours it will take to sell 10,000 tickets for the concert. We are given the number of tickets sold in the first three hours and the rate at which ticket sales increase each hour after the second hour.
Let's denote the number of tickets sold in the fourth hour by "x". Then, the number of tickets sold in the fifth hour will be "x + 20", and the number of tickets sold in the sixth hour will be "x + 40", and so on.
Using this information, we can set up an equation to find "x":
500 + 560 + x + (x + 20) + (x + 40) + ... = 10,000
Simplifying the equation, we get:
3x + 1020 + 20n = 9500
where "n" is the number of hours after the third hour.
Solving for "n", we get:
n = (10,000 - 1020 - 3x) / 20
Now, we need to find the value of "x" that satisfies this equation. We can do this by testing different values of "x" until we find the one that gives an integer value for "n".
Let's start by trying "x = 640 + 20 = 660". Plugging this value into the equation, we get:
n = (10,000 - 1020 - 3(660)) / 20 = 9
We arrived at this solution by using the given information about the rate of increase in ticket sales and setting up an equation to solve for the number of hours it will take to sell 10,000 tickets. We then tested different values of "x" until we found the one that satisfied the equation and gave an integer value for "n".
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Explain why you agree or disagree with Bard.
No, I do not agree with Bard. The area of the given circle is 12.56 unit²and, not 3.5 unit² which Bard claims to be.
What is a circle?
A circle is a shape made up of all points in a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to move around a curve while maintaining a constant distance from another point.
From the figure, we can see that the radius of the circle, the distance from the centre of the circle to the boundary is 2 units.
The area of the circle = πr²
where π is a constant with an approximate value of 3.14 and r is the radius of the circle.
Now substituting the value of r of the given circle in the area equation, we get,
the area of given circle = π * 2² = 3.14 * 4 = 12.56 unit²
Therefore the area of the given circle is 12.56 unit²and, not 3.5 unit² which Bard claims to be.
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