Answer:
(i) To compute the value of the fund based on the withdrawals required, we can use the formula for the future value of an annuity due:
FV = P * ((1 + r)^n - 1) / r) * (1 + r)
where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, n is the total number of periods, and the extra (1 + r) factor is because the payments are made at the beginning of each period.
In this case, P = €25,000, r = 0.065, n = 20. We want to find the future value at the end of the 20-year period:
FV = 25000 * ((1 + 0.065)^20 - 1) / 0.065) * (1 + 0.065)
FV ≈ €743,704.96
Therefore, the value of the fund based on the withdrawals required is approximately €743,704.96.
(ii) To compute the amount of each deposit needed in order to maintain the fund, we can use the formula for the present value of an ordinary annuity:
PV = P * ((1 - (1 + r)^(-n)) / r)
where PV is the present value of the annuity, P is the annual payment, r is the interest rate per period, and n is the total number of periods.
In this case, PV = €743,704.96, r = 0.065, n = 20. We want to find the annual payment:
PV = P * ((1 - (1 + 0.065)^(-20)) / 0.065)
P ≈ €22,630.53
Therefore, the amount of each deposit needed in order to maintain the fund is approximately €22,630.53.
(iii) To compute the total interest earned over the entire 50 years, we can subtract the total deposits from the total withdrawals, and then subtract the initial balance. The total deposits are the annual deposit amount times the number of years (30), and the total withdrawals are the annual withdrawal amount times the number of years (20). The initial balance is the present value of the annuity that we calculated in part (ii).
Total deposits = €22,630.53 * 30 = €678,915.90
Total withdrawals = €25,000 * 20 = €500,000
Initial balance = €743,704.96
Total interest earned = Total withdrawals - Total deposits - Initial balance
Total interest earned = €500,000 - €678,915.90 - €743,704.96
Total interest earned ≈ -€922,620.86
Note that the negative sign indicates that the insurance company actually earned interest on this annuity, rather than the couple earning interest on their investment. This is because the withdrawals are greater than the deposits, and the interest rate earned by the insurance company is greater than the interest rate paid to the couple.
Step-by-step explanation:
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE (Do the one thats C and highlighted, ignore the others) :)
Step-by-step explanation:
3.3% = .033 in decimal
Use the compounding formula
a) P(t) = 18000 (1 + .033)^t
b) for t =2 this computes to 19207.6 bacteria
Is anyone good with Math or History
The probability of passing at least one will be 0.70.
We know that,
Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
here, we have,
Probability of passing history course = 0.59
Probability of passing math course = 0.60
Probability of passing both courses = 0.49
so, we get,
Probability of passing at least one will be
⇒ 0.59 + 0.60 – 0.49
⇒ 0.70
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complete question:
A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?
What is the distance of X?
11/16"
3/4"
7/8"
23/32"
Answer:
C) 23/32
Step-by-step explanation:
count how many lines there are in all
32
Then count from beginning to X
23
The distance of X is 23/32
27 divided by 187 ( so the work please
Answer:
Answer:
= 6 R 25
= 6 25/27
187 divided by 27 equals
6 with a remainder of 25
Step-by-step explanation:
A school is constructing a rectangular play area against an exterior wall of the school building. It uses 120 feet of fencing material to enclose three sides of the play area.
Write an equation to represent l, the length of the play area in feet, as a function of w, the width in feet.
An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²
Here, we have,
According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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Select all of the values of x that make the inequality 100 - 3x ≥ -50 true.
A: 50
B: -50
C: 49.9
D: 50.1
E: 0
Use the equation to find the number of correct answers Gilberto needs to buy a new shirt that costs 25$. Show your work
a) An equation that represents the amount of money that Gilberto
receives during a school year: y = 5 + (0.5) x
b) The number of correct answers Gilberto needs to buy a new shirt that costs $25 = 40
Let us assume that y represents the amount of money and x represents the number of correct answers.
We know that One dollar = 100 cents.
so, 50¢ = 0.5 dollars
From the described informtaion, we can write the equation that represents the amount of money that Gilberto receives during a school year as: y = 5 + (0.5) x
Now we need to find the number of correct answers Gilberto needs to buy a new shirt that costs $25
i.e., for y = 25, we need to find the value of x.
Substitute y = 25 in above equation.
25 = 5 + (0.5) x
We solve this equation for x
(0.5) x = 20
x = 20 / (0.5)
x = 40
This means that he needs to give 40 correct answers.
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The complete question is:
Gilberto's grandfather gives Gilberto $5 and then 50¢ for each math question he answers correctly on his math exams for the year.
a. Write an equation that represents the amount of money that Gilberto
receives during a school year. Explain what the variables and numbers mean.
b. Use the equation to find the number of correct answers Gilberto needs to buy a new shirt that costs $25. Show your work.
Hannah conducted a scientific experiment. For a certain time, the temperature of a compound rose 3 1/2 degrees every 2/3 of an hour. What was the rate, in degrees per hour, that the temperature of the compound rose? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
The rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.
To find the rate at which the temperature of the compound rose, we need to divide the change in temperature by the time interval during which the change occurred.
The temperature rose 3¹/₂ degrees every 2/3 of an hour. To write this as a fraction, we can first convert 3¹/₂ to an improper fraction:
3¹/₂= 7/2
Now, we can write the rate of change as a fraction:
Rate of change = (7/2) / (2/3)
To divide by a fraction, we can multiply by its reciprocal:
Rate of change = (7/2) x (3/2)
Simplifying, we get:
Rate of change = 21/4
Therefore, the rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.
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A foam cube, 5 in. in width has a mass of 62 g. What is the volume and density
The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the volume of the foam cube is 5 in. x 5 in. x 5 in. = 125 cubic inches.
Density is calculated by dividing the mass of an object by its volume. In this case, the density of the foam cube is 62 g / 125 cubic inches = 0.496 g/cubic inch.
So, the volume of the foam cube is 125 cubic inches and its density is 0.496 g/cubic inch.
MARK ME BRAINLEISTExpress the following ratios in the form 1: n (a) 6:15 (b) 20:1160 (c) 30: 1500
Answer:
Step-by-step explanation:
(a)
16
36
=
4
9
36:16=9:4
(b)
144
324
=
4
9
324:144=9:4
(c)
1125
125
=
1125
125
=
45
5
=
9
1
∴125:1125=1:9
A basket contains 3 green, 4 yellow, 5 blue and 6 red tickets, one of which is randomly selected.
Giving your answer in its simplest form, what's the theoretical probability of not drawing a yellow ticket?
Probability of not drawing a yellow ticket =
Again using theoretical probability, determine the chance of getting a green or red ticket. Give your answer as a fraction in its simplest form.
Probability of drawing a green or red ticket =
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
We have,
There are a total of 3 + 4 + 5 + 6 = 18 tickets in the basket.
The probability of drawing a yellow ticket.
= 4/18
Since there are 4 yellow tickets out of 18 total tickets.
The probability of not drawing a yellow ticket is equal to the probability of drawing a green, blue, or red ticket.
There are 3 + 5 + 6 = 14 tickets that are not yellow.
The probability of not drawing a yellow ticket.
= 14/18
= 7/9
To find the probability of drawing a green or red ticket, we need to add the probabilities of drawing a green ticket and a red ticket.
The probability of drawing a green ticket.
= 3/18
The probability of drawing a red ticket.
= 6/18
Now,
The probability of drawing a green or red ticket is
= 3/18 + 6/18
= 9/18
= 1/2
Thus,
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
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Solve for radius and diameter then what is the area C=226.08in
The radius of the circle is 35.98 in, the diameter is 71.96 in. and the area of the circle is 4066.98 sq. in.
Here, the circumference of circle is C=226.08 in
We know that the formula for the circumference of circle is C = 2πr
Using this formula we find the value of radius 'r',
C = 2πr
226.08 = 2πr
r = 226.08 / 2π
r = 35.98 in
And the diameter of the circle would be,
d = 2r
d = 2 × 35.98
d = 71.96 in.
And the area of the circle would be,
A = π × r²
A = π × 35.98²
A = 4066.98 sq. in.
Therefore, the required area is 4066.98 sq. in.
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The complete question is:
Solve for radius and diameter then what is the area of the circle if the circumference of circle is C=226.08 in.
Find the value of
n so that the line that goes through the points
(8,n) and
(2,−2) is perpendicular to
y=2x+4.
Answer:
n = -5
Step-by-step explanation:
We know that when two lines are perpendicular, the slopes of the two lines are negative reciprocals as
[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we're usually not given, and m1 is the slope of the line we're given
Thus, we know that m2 must equal -1/2 from the formula since m1 is 2:
[tex]m_{2}=-\frac{1}{2}[/tex]
Of course, -1/2 is already simplified so m2 is the slope of the line passing through (8, n) and (2, -2)
To find n, we must use our knowledge of the slope formula that gives us the slope, m:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point on the line and x2 and y2 are another point on the line:
If we allow (8, n) to be our x1 and y1 point and allow (2, -2) to be our x1 and y2 point and -1/2 to be our m, we can now solve for m by plugging everything into the slope formula and solving for n (aka y1 in the formula:
[tex]-1/2=\frac{-2-n}{2-8}\\ \\-1/2=\frac{-2-n}{-6}\\ \\3=-2-n\\\\5=-n\\\\-5=n[/tex]
We can even check that we get -1/2 when we plug in -5 into the slope formula:
[tex]-1/2=(-2-(-5))/(2-8)\\-1/2=(-2+5)/(-6)\\-1/2=3/-6\\-1/2=-1/2[/tex]
2. A set of 120 test scores are normally distributed
with a mean of 82 and a standard deviation of
5.
- The price of a gallon of regular gasoline at 75
a) What percent of the scores are between 72
and 872
b) What is the probability that a score is greater
than 77?
c) What is the probability that a score is less than
82 or greater than 92?
d) About how many students scored outside two
standard deviations of the mean?
a) What percent of gas stations sell a gallon of
It should be noted that 81.85% of the scores are between 72 and 87.
The probability that a score is greater than 77 is approximately 0.8413.
How to calculate the valuea) The z-score for 72 is calculated as:
z = (72 - 82) / 5 = -2
The z-score for 87 is calculated as:
z = (87 - 82) / 5 = 1
0.8413 - 0.0228 = 0.8185
So, approximately 81.85% of the scores are between 72 and 87.
b) The z-score for 77 is calculated as:
z = (77 - 82) / 5 = -1
1 - 0.1587 = 0.8413
Therefore, the probability that a score is greater than 77 is approximately 0.8413 (or 84.13%).
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find the compound interest on rs 6950 for 3 years if the interest is payable half yearly,the rate for the first two years being 6% p.a and for the third year 9% p.a
Answer:
Rs 2150.81.
Step-by-step explanation:
The interest rate for the first two years is 6% per annum, which is halved for each six-month period. Therefore, the interest for the first two years would be (6950*(1+(0.03))^8) - 6950 = Rs 1373.53.
For the third year, the interest rate is 9% per annum, which is also halved for each six-month period. Therefore, the interest for the third year would be (6950*(1+0.045))^2 - 6950 = Rs 777.28.
Hence, the total compound interest for three years would be Rs 2150.81.
1) m2 x m2
2) w3 x w2
3) 5k3 x 4k4 x k
4) A rectangle and square have the same area.
The rectangle has length 27x and width 3x.
Find the length of each side of the square.
Find the length of each side of the square.
5) Fully simplify the following expression
28x3 ÷ 4x
6) Simplify fully:
To multiply letters e.g., xy you must include the multiplication symbol. E.g., xy should be typed as x*y
fraction numerator 12 c to the power of 8 g to the power of 9 over denominator 4 c to the power of 4 g to the power of 4 end fraction
m² × m² is equal to m⁴.
w³ × w² is equal to w⁵.
5k³ × 4k⁴ × k is equal to 20k⁸.
The length of each side of the square is 9x.
A simplification of the expression 28x³ ÷ 4x is 7x².
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangle = (27x) × (3x)
Area of rectangle = 81x²
Note: Area of square = Area of rectangle
Area of square = (side length)²
81x² = (side length)²
Side length = √(81x²)
Side length = 9x
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The volume of a rectangular prism is (x4 + 4x³ + 3x² + 8x + 4), and the area of its base is (x3 + 3x² + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? O X+1- Gere O X+1+ O X+1- 4 x4+4x³+3x²+8x+4 O X+1+ 4 X*+4x²+3x+8x+4 4 +³+3x²+8 4 +³+3x²+8
The Height of the given rectangular prism is: (x + 1) - 4/(x³ + 3x² + 8)
How to carry out polynomial division?In algebra, polynomial long division is defined as an algorithm used in dividing a polynomial by another particular polynomial of the same or even lower degree, which is a generalized version of the common arithmetic technique called long division. It can be done easily by hand, because it separates a supposedly complex division problem into smaller ones.
We are given:
Volume of a rectangular prism = (x⁴ + 4x³ + 3x² + 8x + 4), and the area of its base is (x³ + 3x² + 8)
Thus, height is:
x + 1
x³ + 3x² + 8|x⁴ + 4x³ + 3x² + 8x + 4
- x⁴ + 3x³ + 0 + 8x
x³ + 3x² + 4
- x³ + 3x² + 8
-4
Thus:
Height = (x + 1) - 4/(x³ + 3x² + 8)
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For questions 18-19, describe the end behavior of the graph for each function.
18. f(x) = x³ +2x² - 5x+1
19. g(x) = -2x³-8x2 +18x+72
Answer:
18. The end behavior of the graph of f(x) = x³ + 2x² - 5x + 1 is as follows: as x approaches negative infinity, the function f(x) approaches negative infinity, and as x approaches positive infinity, the function f(x) approaches positive infinity. This is because the leading term of the polynomial is x³, which has a positive coefficient, so the graph of the function will have a "smile" shape, with the ends of the graph pointing upwards.
19. The end behavior of the graph of g(x) = -2x³ - 8x² + 18x + 72 is as follows: as x approaches negative infinity, the function g(x) approaches negative infinity, and as x approaches positive infinity, the function g(x) approaches negative infinity. This is because the leading term of the polynomial is -2x³, which has a negative coefficient, so the graph of the function will have a "frown" shape, with the ends of the graph pointing downwards.
Step-by-step explanation:
In this figure, the two angles are complementary.
(2x + 6)°
(1/2x )°
What is the value of x?
Answer:
Step-by-step explanation:
Complementary means angles that add up to 90°
Based on that you can write and equation by adding the 2 angles and making equal to 90
2x+6+1/2x=90 combine like terms on left
5/2x+6=90 subtract both sides by 6
5/2x=84 multiply by the reciprocal of 5/2 => 2/5
x=168/5 or 33.6
Find the missing angle.
92° 78°
Answer:
[tex]\huge\boxed{\sf x = 10\°}[/tex]
Step-by-step explanation:
Statement:Angles on a straight line add up to 180 degrees.Solution:According to the statement,
92° + x + 78° = 180°
170° + x = 180°
Subtract 170° from both sidesx = 180° - 170°
x = 10°[tex]\rule[225]{225}{2}[/tex]
Solve the following for θ, in radians, where 0≤θ<2π.
5cos2(θ)−8cos(θ)+2=0
Select all that apply:
2.85
5.03
1.26
1.37
1.86
0.61
Answer:5.03
1.26 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
5u^2 - 8u + 2 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 5, b = -8, and c = 2. Substituting these values, we get:
u = (8 ± sqrt(64 - 40)) / 10
u = (8 ± 2sqrt(6)) / 10
Therefore, either:
0
Determine whether the curve is the graph of a function of x.
OYes, it is a function.
O No, it is not a function.
If it is, state the domain and range of the function. (Enter your answers in interval notation. If the curve is not the graph of a function of x, enter DNE.)
domain
range
The correct statement regarding whether the graph represents a function is given as follows:
No, it is not a function.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.
In the graph, we have that at x = 0 = y-axis, the function has three numeric values, which is a case of vertically aligned points, hence the graph does not represent a function.
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Area of triangles
Look at the image below.
6
What is the area of the triangle?
units²
3
Answer:
Please help me by marking me the brainliest.
The area of the triangle is 9 units^2
Step-by-step explanation:
Area of triangle = 1/2(6*3)
=1/2(18)
=9
A music festival sold two types of tickets, day passes and weekend passes. The day passes were $61, and the weekend pass was $110. The total ticket sales for the festival were $307,745. They sold 257 more day passes than weekend passes. How many day passes and how many weekend passes were sold?
Answer:
day passes: 1965weekend passes: 1708Step-by-step explanation:
You want the number of day passes sold for $61 and weekend passes sold for $110 if 257 more day passes were sold, and sales totaled $307745.
SetupLet w represent the number of weekend passes sold. Then w+257 is the number of day passes sold. The total revenue is ...
61(w+257) +110(w) = 307745
SolutionSimplifying the equation, we have ...
171w +15677 = 307745
171w = 292068 . . . . . . . . subtract 15677
w = 1708 . . . . . . . . . . . divide by 171
w+257 = 1965 . . . day passes sold
1965 day passes and 1708 weekend passes were sold.
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Determine if the two expressions are equivalent and explain your reasoning. 8m+4-3m and 3+ m+2m+1+2m
The two expressions "8m+4-3m" and "3+ m+2m+1+2m" are equivalent because they simplify to the same-value.
To determine if the two expressions are equivalent, we can simplify each expression and then compare them.
Simplifying the first -expression,
We have,
⇒ 8m + 4 - 3m can be simplified by combining like terms;
⇒ 8m - 3m + 4 = 5m + 4
Next, Simplifying the second-expression,
we have,
⇒ 3 + m + 2m + 1 + 2m can also be simplified by combining like-terms:
⇒ (1 + 3) + (m + 2m + 2m) = 4 + 5m
So we have:
(i) 8m + 4 - 3m = 5m + 4
(ii) 3 + m + 2m + 1 + 2m = 4 + 5m
Since both simplified expressions are equal to "5m + 4", we can conclude that the two original expressions are equivalent.
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Graph the line with slope 2/3 and y-intercept -6.
A line on the graph which could represent this scenario is shown in the image attached below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this line, it can be modeled by this equation:
y = mx + c
y = 2x/3 + (-6)
y = 2x/3 - 6
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The point J is a centroid for the triangle SZU. What is SV?
1. 21
2. 9
3. 6
4. 12
The value of SV, given that point J is the centroid, would be A. 9.
How to find the value of SV?Seeing as we have point J as the centroid for triangle SZU, we can then tell that JV would be:
JV = 1 / 3 x SV
Knowing this, we can make SV the subject of the formula to become:
(JV = 1 / 3 x SV ) / 1 / 3
3 x JV = SV
SV = 3 JV
SV would then be:
SV = 3 x JV
SV = 3 x 3
SV = 9
In conclusion, SV would be 9.
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Answer:
answer is B. 9 :)
Step-by-step explanation:
For question number 5
Answer: A' will be at (-2,0)
Step-by-step explanation:
Reflecting things over a line can be done in several different ways, I will try to explain the one I use and the easiest one. What I use is to look at it and find the shortest distance between the line and A, in this case, the shortest distance is at (-.5,1.5), since A is at (1,3) the distance between them is (-1.5,-1.5) If you double this change you will find how far away the new point A is from the Old point, so its a change of (-3,-3). (1,3)+(-3,-3) gets you to the final points of (-2,0)
Another, probably easier, method is to go down from point A until you hit the line, and then go over that many points. In this case, you go down 3 from A to hit the line, and then go 3 to the left which reflects it over the line. Either way you do it, you get (-2,0)
Need help fast I will rate
The formula for p(x) is p(x) = -0.1(x - 5)²(x + 3).
What is a polynomial graph?In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Also, the graph has a zero of multiplicity 2 at x = 5 and zero of multiplicity 1 at x = -3;
x = 5 ⇒ x - 5 = 0.
(x - 5)²
x = -3 ⇒ x + 3 = 0.
(x + 3)
In this context, an equation that represent the polynomial function is given by:
p(x) = a(x - 5)²(x + 3)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -7.5), we have;
-7.5 = a(0 - 5)²(0 + 3)
-7.5 = a75
a = -7.5/75
a = -0.1.
Therefore, the required polynomial function is given by:
p(x) = -0.1(x - 5)²(x + 3)
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A circular patio has diameter of 4 yards . What is the area of the patio?
The area of the circular pateo is 50.24 square yards.
What is the area of the patio?Remember that for a circle of radius R, the area is given by the formula:
A = pi*R²
Where pi = 3.14
Here we know that the patio is circular, and it has a diameter of 4 yards, then the radius is:
R = 4yd/2
R = 2 yd
Replacing that in the area formula we will get:
A = 3.14*(2yd)²
A = 50.24 yd²
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