If 25 tapered pins are machined from a steel rod 15 ft long, then total 15 tapered pins can be made from a steel rod 9 ft long.
The unitary method is a method where you find the value of one unit and then find the value of the number of units you want. The formula for the units method is to find the value of a single unit and then multiply the value of the single unit by the number of units to get the desired value. We have specify that 25 tapered pins can be made up from a steel rod 15 ft long. Let 'x' represent the number of pins that can be made from 9 ft long steel rod. Now, using the unitary method,
number of pins machined from a 15 ft long steel rod = 25
number of pins machined from a 1 ft long steel rod = 25/15
So, number of pins machined from a 9 feet long steel rod, x = (25/15)×9
=> x = 3×5 = 15
Hence, required tapered pins made from a steel rod 9 ft long is equals to the 15 pins.
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Write the equation of the hyperbola using the given information, The hyperbola has vertices (-2,9) and (-2,3) and foci (-2,13) and (-2,-1)
The center of the hyperbola is the midpoint between the vertices, which is (-2,6).
The distance between the center and each vertex is 3, so the distance between the center and each focus is c = 7.
The distance between each vertex and focus is a = 4.
The equation of the hyperbola with center (h,k) is:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
where b^2 = c^2 - a^2.
Plugging in the values we have:
- Center: (h,k) = (-2,6)
- a = 4
- c = 7
- b^2 = c^2 - a^2 = 49 - 16 = 33
So the equation of the hyperbola is:
(x + 2)^2 / 16 - (y - 6)^2 / 33 = 1
As the demand for the products grew, a manufacturing company decided to hire more employees. For which they want to know the mean time required to complete the work for a worker
We can conclude after answering the presented question that Use the equation data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
The procedures that a manufacturing organisation might take to undertake a time study analysis are as follows:
List the tasks performed by the workers and describe what constitutes a complete unit of labour.
Choose a representative sample of employees to observe. The sample size should be high enough to be statistically significant, but not so large that observing all workers becomes unfeasible.
Use the data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.
By doing a time study analysis, the manufacturing organisation may acquire useful insights into their workers' productivity and find chances for process changes that will help them fulfil the rising demand for their products.
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What is the scale factor from ABC to UVW
Therefore, the scale factor of triangle ABC to triangle UVW is 5 and option C is the correct choice.
Two triangles are shown to us in the photograph. We must determine the ABC to UVW scale factor.
To find the scale factor of our given triangles, we will divide one side of triangle UVW by its corresponding side of triangle ABC.
Original side ×scale factor = new side
5 × scale factor =25
By multiplying both sides of the equation by 5, we obtain:
5/5×scale factor/5 =25/5
scale factor = 5
What exactly is scale factor?
A scale factor is a figure that, when multiplied by a certain amount, creates a smaller or bigger replica of the original figure. It is the ratio of a blueprint, map, model, or actual thing to the distance or object1. Every inch on a home layout, for instance, would correspond to 4 inches in real life if the scale factor was 1/41.
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Answer: ANSWER IS 5
Step-by-step explanation:
Martin is a hair stylist. He averages a weekly wage of $240 and
usually gets another $356 in tips. What is his average total
income?
To find Martin's average total income, we need to add his average weekly wage to his average weekly tips:
$240 (weekly wage) + $356 (weekly tips) = $596 (average total income)
Therefore, Martin's average total income is $596 per week.
What series of transformations would carry the rectangle onto itself?
O(x+0,y-4), 180° rotation, reflection over the y-axis
O(x+0, y-4), 180° rotation, reflection over the x-axis
O (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis
O (x-4, y+0), 90° counterclockwise rotation, reflection over the y-axis
The answer of the given question based on the graph transformations is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.
What is Reflection?Reflection is a transformation that flips an object over a line, plane, or point. The line, plane, or point is called the "line of reflection", the "plane of reflection", or the "point of reflection", respectively. Reflection is a fundamental concept in geometry, and it has applications in various fields of mathematics, physics, and engineering. It is often used in symmetry analysis, transformation geometry, and computer graphics.
The series of transformations that would carry the rectangle onto itself is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.
To see why, we can analyze each transformation and its effect on the rectangle:
(x-4, y+0) translates the rectangle left by 4 units.
90° counterclockwise rotation preserves the right angles and parallel sides of the rectangle.
Reflection over the x-axis preserves the right angles of the rectangle and also preserves the orientation of its parallel sides.
Therefore, the final image after all three transformations would be congruent to the original rectangle, i.e., the rectangle would be carried onto itself.
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Erik just found an old set of reference books his grandfather gave him years ago. There are 12 same-sized books in the set, each being 6 inches long and 3 4 of an inch wide. The books are packed in a case shaped like a rectangular prism that fits them perfectly. The case has a volume of 432 cubic inches. How tall are the books?
Thus, each book has an 8-inch height.
What are some math examples of volume?
The quantity of space taken up by a three-dimensional object can also be used to describe volume. By determining the number of units cubes it contains, the volume of such a solid like such a cube or cuboid can be determined.
Get the volume of a single book in cubic centimeters to get things started. We can accomplish this by multiplying a book's length, width, and height:
Volume of one book = 6 inches x 3/4 inches x height
Volume of one book = 4.5 cubic inches x height
Since the 12 books are all the same size, their combined volume is:
Total volume of books = 12 books x Volume of one book
Total volume of books = 12 books x 4.5 cubic inches x height
Total volume of books = 54 cubic inches x height
Since we are aware that the case has a total volume of 432 cubic inches, we can construct the following equation:
Total volume of case = Total volume of books
432 cubic inches = 54 cubic inches x height
When we solve for height, we obtain:
height = 432 cubic inches / 54 cubic inches
height = 8 inches
Thus, each book has a height of 8 inches.
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USE PEDMAS
What is the correct numerical expression for "subtract the sum of 2 and 9 from the product of 4 and 3?"
2 + 9 − 4 x 3
(2 + 9) − 4 x 3
(4 x 3) − (2 + 9)
4 x (3 − 2) + 9
Answer:
The correct numerical expression using PEDMAS for "subtract the sum of 2 and 9 from the product of 4 and 3" is:
4 x 3 - (2 + 9)
Using the order of operations, first, we perform the addition inside the parentheses, then we multiply 4 and 3, and finally, we subtract the result of the sum from the product:
= 4 x 3 - 11
= 12 - 11
= 1
Therefore, the correct numerical expression is (4 x 3) - (2 + 9) = 1.
Step-by-step explanation:
A recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt write the ratio of baking soda to salt then find the value of the ratio
Answer:
Step-by-step explanation:
To write the ratio of baking soda to salt, we need to compare the amount of baking soda to the amount of salt in the recipe.
The recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt, so the ratio of baking soda to salt is:
3/4 : 3
To simplify this ratio, we can divide both numbers by the greatest common factor (GCF) of 3 and 4, which is 1.
3/4 divided by 1 = 3/4
3 divided by 1 = 3
So the simplified ratio of baking soda to salt is:
3/4 : 3 = 3: 12
To find the value of the ratio, we can divide both the numerator and denominator by 3:
3/3 : 12/3 = 1: 4
Therefore, the value of the ratio of baking soda to salt is 1:4.
The diameter of a flour tortilla is 12 inches. What is the total area of two tortillas to the nearest hundredth?
Answer: 113.10 inches squared
Step-by-step explanation:
formula for area: A=(pi)r^2
the diameter is 2x the radius so the radius would be 12/2=6. plug 6 in for r and solve. The answer is 113.097 so when you round to the nearest hundredth it becomes 113.10
24 ÷ (5 + a) when a = 3
Answer:
3
Step-by-step explanation:
do the brackets first
(5+3) = 8
24÷8=3
so the answer is 3
1. An ant walks from center A, to point
B, clockwise to point C, and then
back to center A. What is the total
distance of her walk?
B
2cm
90°
A
C
Somebody please please please help me
Answer:
a₅ = 11
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 2 , with a₁ = 3 , then
a₂ = a₁ + 2 = 3 + 2 = 5
a₃ = a₂ + 2 = 5 + 2 = 7
a₄ = a₃ + 2 = 7 + 2 = 9
a₅ = a₄ + 2 = 9 + 2 = 11
consider a routine screeing test for a disease. suppose the frequency of the disease in the population is 0.1%. the test is relatively accurate with 15% false positive rate and a 15% false negative rate. if alice takes the test and it comes back positive, what is the probability that alice has the disease?
The probability that Alice has the disease given that she tested positive is only about 0.00563
To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events. Let's define the following events
A: Alice has the disease.
B: Alice tests positive.
We want to find P(A|B), the probability that Alice has the disease given that she tested positive. Bayes' theorem tells us that
P(A|B) = P(B|A)× P(A) / P(B)
where
P(B|A) is the probability of testing positive given that Alice has the disease, which is 1 - the false negative rate = 0.85.
P(A) is the frequency of the disease in the population, which is 0.1% or 0.001.
P(B) is the overall probability of testing positive, which can be calculated using the law of total probability
P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)
where
P(B|not A) is the probability of testing positive given that Alice does not have the disease, which is the false positive rate = 0.15.
P(not A) is the complement of P(A), i.e., the probability that Alice does not have the disease, which is 1 - P(A) = 0.999.
Therefore,
P(B) = 0.85 × 0.001 + 0.15 × 0.999 = 0.15084
Now we can substitute these values into Bayes' theorem
P(A|B) = 0.85 × 0.001 / 0.15084 = 0.00563
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I don't understand this could someone help I will give brainliest!
Answer: c
Step-by-step explanation:
The graph above shows quadrilateral ABCD. Which set of vertices represents a rotation? a glide reflection? a translation? a similarity transformation? Write a rule for each of these transformations. 1. A'(-3, 1), B'(-1, 4), C'(-3, 6), D'(-6, 3) 2. A'(-5, -5), B'(-3, -8), C'(-5, -10), D'(-8, -7) 3. A'(-8, 0), B'(-4, -6), C'(-8, -10), D'(-14, -4) 4. A'(1, -3), B'(4, -1), C'(6, -3), D'(3, -6) 5. A'(-1, -3), B'(-4, -1), C'(-6, -3), D'(-3, -6) 6. A'(6, 1), B'(8, 4), C'(6, 6), D'(3, 3)
Note that the transformation for the above vertices are given as follows.
What is the transformation for the above vertices ?From the given graph, we can determine the transformations as follows:
A'(-3, 1), B'(-1, 4), C'(-3, 6), D'(-6, 3) - This set of vertices represents a reflection across the line y = 3. Rule: (x, y) -> (x, 6 - y)A'(-5, -5), B'(-3, -8), C'(-5, -10), D'(-8, -7) - This set of vertices represents a glide reflection. Rule: (x, y) -> (x - 2, -y)A'(-8, 0), B'(-4, -6), C'(-8, -10), D'(-14, -4) - This set of vertices represents a translation. Rule: (x, y) -> (x - 4, y - 4)A'(1, -3), B'(4, -1), C'(6, -3), D'(3, -6) - This set of vertices represents a rotation of 270 degrees counterclockwise about the origin. Rule: (x, y) -> (y, -x)A'(-1, -3), B'(-4, -1), C'(-6, -3), D'(-3, -6) - This set of vertices represents a reflection across the line y = -2. Rule: (x, y) -> (x, -4 - y)A'(6, 1), B'(8, 4), C'(6, 6), D'(3, 3) - This set of vertices represents a similarity transformation (rotation and dilation). Rule: (x, y) -> (2x - 9, 2y + 1)Learn more about transformation at:
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
The measure of each interior angle of a regular polygon is eight times that of an exterior angle. How many sides does the polygon have?
Answer:
18 sides
Step-by-step explanation:
We know the relation between exterior angle, interior angle. Given that each interior angle is 8 times the exterior. So, there are 18 sides for such a polygon given in question.
Help! I have a take home test due Tommorow please give me answers
This is the simplified ratio of lengths DE:EF as (2/√(29))√(34) : 1.
What is ratio?A ratio is a relationship between two or more quantities that indicates how many times one quantity is contained in another. It is a way of comparing quantities of the same kind, such as lengths, areas, volumes, or numbers. A ratio is usually expressed as a fraction or a colon (:). Ratios can be simplified by dividing both terms of the ratio by their greatest common factor (GCF). Ratios are used in many fields such as mathematics, finance, science, engineering, and statistics, among others. They are used to compare different quantities, to express proportions or rates, and to solve various mathematical problems.
Here,
We can use the distance formula to find the lengths DE and EF, and then calculate their ratio:
Length DE = √[(xE - xD)² + (yE - yD)²]
= √[(10 - 4)² + (15 - 4)²]
= √(6² + 11²)
= √(136)
= 2√(34)
Length EF = √[(xF - xE)² + (yF - yE)²]
= √[(12 - 10)² + (20 - 15)²]
= √(2² + 5²)
= √(29)
Therefore, the ratio of lengths DE:EF is:
DE:EF = (2√(34)) : (√(29))
We can simplify this ratio by dividing both sides by √(29):
DE:EF = (2√(34))/√(29) : (√(29))/√(29)
= (2/√(29))√(34) : 1
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The nineteenth term in an arithmetic
sequence is 243, and the eleventh term is 147.
What is the value of the eighty-sixth term?
Answer:
1047
Step-by-step explanation:
a_n = a_1 + (n - 1)d
a_19 = 243
a_11 = 147
243 = a_1 + (19 - 1)d
147 = a_1 + (11 - 1)d
243 = a_1 + 18d
147 = a_1 + 10d
a_1 = 243 - 18d
a_1 = 147 - 10d
243 - 18d = 147 - 10d
-8d = -96
d = 12
a_1 = 147 - 10d
a_1 = 147 - 10(12)
a_1 = 27
The first term is 27. The common difference is 12.
a_86 = a_1 + (n - 1)d
a_86 = 27 + 85(12)
a_86 = 1047
Select the equation that correctly describes the following real-world situation. 10 pieces of candy are given to s students from a bag of candy containing 225 pieces. There are 5 pieces left over.
(s x 10) ÷ 5 = 225
(s x 10) = 225 ÷ 5
225 ÷ (s + 10) = 5
(225 − 5) ÷ 10 = s
The arithmetic equation that correctly describes the following real-world situation is (s x 10) ÷ 5 = 225.
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given: 10 pieces of candy are given to s students from a bag of candy containing 225 pieces. There are 5 pieces left over.
We have to find the equation that correctly describes the following real-world situation.
(s x 10) ÷ 5 = 225
2s = 225
s = 112.5
Hence, the value of s is 112.5
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Answer: ( s x 10 ) `-. = 225
Step-by-step explanation:
There are 65,450 people under the age of 14 years old
There are 214,965 people age between 15 and 64 years old
There are 40,809 people over the age of 65 years old
What is the Old Age Dependency Ratio as a decimal rounded to the Thousandths place?
The old age dependency ratio as a decimal is 0.190.
What is old age dependency ratio ?
The old age dependency ratio is a measure of the number of people who are considered "dependent" on those who are of working age.
Specifically, it is the ratio of the number of people aged 65 years and over to the number of people aged 15 to 64 years old.
Old Age Dependency Ratio = (Number of people over 65) / (Number of people aged 15-64)
Old Age Dependency Ratio = 40,809 / 214,965 = 0.1895
Therefore, Rounding this to the thousandths place the Old Age Dependency Ratio as a decimal is 0.190.
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let g be a function such that g(4)=8 and g’(4)=-3
let h be the function h(x)=sqrt
Answer:If (2t+1)is a factor then t=2−1 must be one of the zeroes of the given polynomial. Substituting in the given equation.
q((2−1))=4(2−1)3+4(2−1)2−(2−1)−1=4(8−1)+4(41)+(21)−1=(2−1)+1+(21)−1=0
Hence(2t+1) is a common factor of q(t)
Step-by-step explanation:
3x − 2y = –17
–x − 9y = –4
Answer: x = -5, y = 1
Step-by-step explanation:
These are simultaneous equations
I will use the substitution method
BTW [1] means the top equation, and [2] the bottom equation
Rearrange [2] for x
-x = -4 + 9y
x = 4 - 9y
Substitute 4 - 9y into [1]
3(4 - 9y) - 2y = -17
Expand the bracket
12 - 27y - 2y = -17
Simplify
12 - 29y = -17
Rarrange for y
12 = 29y - 17
29y = 12 + 17 = 29
y = 1Now substitute y into either equation to solve for x
I will use [2] as it looks easier
-x - 9(1) = -4
Expand the bracket
-x -9 = -4
-x = 5
x = -5Now lets substitute x and y into [1] to check our answer
3(-5) - 2(1) = -17
-15 - 2 = -17
Using the quadratic formula, solve 0 = 2x² 2x² - 10x + 7 Give each of your answers to 2 d.p.
Answer:
x1 ≈ 0,84; x2 ≈ 4,16
Step-by-step explanation:
Find the discriminant and then both values of x according to the formulas (I added a photo of my solution)
a cylinder is leaking water at an unknown rate. the cylinder has a height of 6 meters and a radius of 5 meters. find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters.
The rate at which the volume of water in the tank is changing is 58π(dr/dt).
To find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters, we need to use the formula for the volume of a cylinder, which is given by:
V = πr²hwhere V is the volume of the cylinder, r is the radius, and h is the height.
We also need to differentiate the formula for the volume of a cylinder with respect to time to get an equation for the rate of change of the volume of the cylinder. Differentiating the formula for the volume of a cylinder with respect to time, we get:
dV/dt = πr²dh/dt + 2πrhdr/dt
where dV/dt is the rate of change of the volume of the cylinder, dh/dt is the rate of change of the height of the cylinder, and dr/dt is the rate of change of the radius of the cylinder.
Substituting the given values into the formula and simplifying, we get:
dV/dt = π(5²)(-8/100) + 2π(5)(6)(dr/dt) = -2π + 60π(dr/dt) = 58π(dr/dt)
Therefore, the changes in water volume in the tank is 58π(dr/dt).
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What is measurement angle S to the nearest degree?
The unknown angle in the triangle is as follows;
m∠S = 38 degrees
How to find the angle measure of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
In the triangle QRS,
m∠Q = 4m∠R
m∠R = 3 / 4 m∠S
Therefore, let's find the angle m∠S in the triangle as follows:
Therefore,
m∠Q + m∠R + m∠S = 180°
let
m∠R = x
4x + x + 4 / 3 x = 180
5x + 4 / 3 x = 180
15x + 4x / 3 = 180
19x / 3 = 180
19x = 180 × 3
19x = 540
x = 540 / 19
x = 28.42
Therefore,
m∠S = 4 / 3 (28.42)
m∠S = 37.8947368421
m∠S = 38 degrees
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Mr.jibril is four times as old as his son. four years,he was seven times as old as his son. In how many years will Mr.Jibril's age be twice his son's age
Answer:
After 16 years Mr. Jibril will be twice as old as his son.
Step-by-step explanation:
t - age Mr. Jibril
s - son age
t=4s (father is 4 times older than son)
t-4=7(s-4) (4 years ago they both have 4 year old less and father was 7 times older than son)
t=7s-28+4
t=7s-24
7s-24=4s
3s=24
s=8
t=32
x- years after Mr. Jibril will be twice as old as his son.
32+x=2(8+x)
32+x=16+2x
16=x
x=16
What's the volume of this shape?
The volume of the pyramid is 4480ft³
What is volume of pyramid?A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.
The volume of a pyramid is expressed as:
V = 1/3 b × h
b = base area
h = height
Here, base are = 17.5 × 32
= 560ft²
Height = 24ft
V = 1/3 × 560 × 24
V = 560 × 8
V = 4480 ft³
Therefore the volume of the pyramid is 4480ft³
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David’s phone has about 10,000 songs. The distribution of play time for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time ¯
of these songs.
How many songs would you have to sample if you wanted the standard deviation of the sampling distribution of ¯
to be 30 seconds?
The standard deviation of the sampling distribution of 30 seconds songs then the total number of songs are 36.
The mean and the standard deviation of the sampling distribution of x:
The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:
The mean is the same as the population mean. The standard deviation is the division of the population standard deviation by the square root of the sample size. The central limit theorem states that as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution for the mean will be normal whether the population is normally distributed, Poisson, binomial, or any other distribution.
Now,
The parameters for this problem are given as follows:
Population mean of 225 seconds.
Population standard deviation of 60 seconds.
Sample size of 10 seconds.
Hence the standard deviation for the sampling distribution of x is given as follows:
s = 60/√(10) = 19 seconds.
if the sampling distribution of the songs is 30second tehn the tottal number of songs are 36
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What are the solutions to 3(x-10)2=243?
x=1 and x=19
x=-1 and x=-19
x=343/3 and x=-343/3
x=1 and x=19
x=50.5 and x=30.5
Answer:
1 and 19
Step-by-step explanation:
3(x-10)^2 = 3(x^2-20x+100) = 3x^2 - 60x + 300
If 3x^2 - 60x + 300 = 243, 3x^2 - 60x + 57 = 0
Divide by 3 to get x^2 - 20x + 19 = 0
use the quadratic equation (-b±√(b²-4ac))/(2a) to get
(20±√324)/2 = (20±18)/2 = 1 and 19
Find the area and circumference of a circle with diameter 7 feet use the value 3.14 for pi
Answer:
Circumfrance= 21.991
area= 38.48
Step-by-step explanation:
2piR
R=3.5
:)