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
assume one person out of 10,000 is infected with hiv, and there is a test in which 2.5% of all people test positive for the virus although they do not really have it. if you test negative on this test, then you definitely do not have hiv. what is the chance of having hiv, assuming you test positive for it?
In conclusion, the chance of having HIV, assuming a positive test result, is 0.4%. It is important to remember that this number could vary depending on the accuracy and false positive rate of the test, as well as the number of people infected with HIV in the given area.
Assuming you tested positive for HIV, the chance of having the virus is higher than 2.5%, since the test has a false positive rate of 2.5%.
Out of the 10,000 people, 250 are likely to test positive, of which only one person actually has the virus. This means that the actual chance of having HIV, assuming a positive test result, is 1 in 250 or 0.4%.
It is important to note that this calculation only applies to the specific case of the 10,000 people in question, and the false positive rate of the test. Different tests have different levels of accuracy and false positive rate, which could alter the result. Furthermore, the number of people infected with HIV may differ significantly in different areas, which could also change the probability.
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which of the following will increase the likelihood of rejecting the null hypothesis using anova? a. a decrease in sswithin b. an increase in the sample sizes c. both a and b d. none of the above
A larger sample size will result in a more reliable estimate of the population mean, lowering the variability and resulting in a higher F-ratio, which will result in the null hypothesis being rejected. As a result, both options A and B are correct.
Here we want to find,
the likelihood of rejecting the null hypothesis using anova is increased by which.
To increase the likelihood of rejecting the null hypothesis using ANOVA, a decrease in SSWITHIN and an increase in sample sizes are needed.
In statistics, analysis of variance (ANOVA) is a technique for comparing the means of two or more samples. ANOVA is an extension of the t-test and z-test methods, which can be used to compare only two means.
ANOVA compares the variation within the groups to the variation between the groups to see whether or not there is a statistically significant difference between them.
The null hypothesis ([tex]H_0[/tex]) in ANOVA is that the means of all groups are equal, while the alternative hypothesis (Ha) is that at least one group's mean is different from the others.
In ANOVA, a low value of SSWITHIN is desirable because it reflects that the data points are clustered around their respective means.
As a result, ANOVA will result in a higher F-ratio, which means that the null hypothesis will be rejected.
So, both a and b options are correct.
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Write the equation of a line perpendicular to y = 1/3 x + 5 and passing through the point (2,6).
1. y = 3x +18
2. y = 3x
3. y = -3x +12
4. y = -3x
The equation of the line perpendicular to y = 1/3 x + 5 and passing through (2,6) is y = -3x + 12, which is option 3.
EquationsTo find the equation of a line perpendicular to y = 1/3 x + 5 and passing through the point (2,6), we first need to determine the slope of the original line and the slope of y = 1/3 x + 5 is 1/3.
To find the slope of a line perpendicular to this, we can use the fact that the product of the slopes of two perpendicular lines is -1 and therefore, the slope of the line we want is the negative reciprocal of 1/3, which is -3.
Now that we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line passing through (2,6) with slope -3:
y - 6 = -3(x - 2)
y = -3x + 12
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HELP URGENT !!!A bag contains 16 red marbles, 7 yellow marbles, and 19 green marbles. What is the probability that a marble drawn
from the bag is red or yellow? Write your answer as a simplifed fraction.
Answer: 23/42
Step-by-step explanation:
your messageHELP URGENT !!!A bag contains 16 red marbles, 7 yellow marbles, and 19 green marbles. What is the probability that a marble drawnfrom the bag is red or yellow? Write your answer as a simplifed fraction.Sure, I can help you with that! The probability of drawing a red marble is 16/42 (since there are 16 red marbles out of a total of 42 marbles), and the probability of drawing a yellow marble is 7/42. To find the probability of drawing a red or yellow marble, we simply add those two probabilities: 16/42 + 7/42 = 23/42 So the probability of drawing a red or yellow marble is 23/42, which is already in simplified fraction form.
Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$
Find $f(x) - g(x) + h(x).$ Enter your answer as an expression.
Step-by-step explanation:
all he have to do is you substitute the expressions correctly
Helena drops a ball from 25 feet above a lake. The formula t= 1/4√25-h describes the time t in seconds that the ball is h feet above the water. How many feet above the water will the ball be after 1 second?
element x has a half-life of days. if we currently have a ounce sample of element x, how long will it be until only ounces remain?
It will take approximately 1.386*t days until only 1/2 ounces of element X remain.
If the half-life of element X is t days, it means that after every t days the amount of element X will be reduced by half.
Initially, we have a 1-ounce sample of element X.
After t days, the amount of element X remaining will be 1/2 ounces.
After 2t days, the amount of element X remaining will be (1/2)*(1/2) = 1/4 ounces.
Similarly, after 3t days, the amount of element X remaining will be (1/2)(1/2)(1/2) = 1/8 ounces.
After n*t days, the amount of element X remaining will be (1/2)^n ounces.
We want to find the value of n such that (1/2)^n = 1/2^(n/2) ounces.
Taking the logarithm of both sides, we get:
n*log(1/2) = (n/2)*log(1/2)
Simplifying, we get:
n = 2*log(2) = 1.386
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The total weight of 36 packets of crisps is 864 grams. There are 505 calories in 100 grams of crisps. Work out how many calories are there in one packet of crisps. 1
Answer:
121.2 calories.
Step-by-step explanation:
Weight of one packet of crisps = 864/36
= 24 grams.
So, by proportion, the number of calories in one packet
= 24 * 505/100
= 121.2 calories.
uppose that the distribution for total amounts spent by students vacationing for a week in florida is normally distributed with a mean of 650 and a standard deviation of 120 . suppose you take a simple random sample (srs) of 45 students from this distribution. what is the probability that a srs of 45 students will spend an average of between 600 and 700 dollars? round to five decimal places.
The probability of a SRS of 45 students spending an average of between $600 and $700 is approximately 0.9871.
We can use the central limit theorem to approximate the distribution of the sample mean from a normal population. Since the population standard deviation is known and the sample size is large enough (n = 45), we can use the normal distribution to approximate the sampling distribution of the sample mean.
The formula for the standard error of the mean is:
SE = σ/√n
Where σ is the population standard deviation and n is the sample size.
Plugging in the values, we get:
SE = 120/√45 ≈ 17.89
Now, we need to standardize the sample mean using the z-score formula:
z = (x - μ) / SE
Where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.
For the lower bound of 600:
z = (600 - 650) / 17.89 ≈ -2.79
For the upper bound of 700:
z = (700 - 650) / 17.89 ≈ 2.79
Using a standard normal distribution table or calculator, we can find the area between these two z-scores:
P(-2.79 < z < 2.79) ≈ 0.9871
Therefore, the probability that a SRS of 45 students will spend an average of between 600 and 700 dollars is approximately 0.9871, or 0.98710 rounded to five decimal places.
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h(x) = 3x
If you input a 2 into h(x), what do you get for the output?
h(2) = 3(2) = 6
The output is six
A spinner contains six equal sections: 3 red, 1 yellow, 1 blue, and 1 purple. What color do we expect the spinner to land on most frenquently?
A. Red
B. Yellow
C. Blue
D. Purple
Answer:
A) Red
Step-by-step explanation:
We can find the probability of the spinner landing on each color by dividing the number of sections for that color by the total number of sections.
Probability of landing on red: 3/6 = 1/2
Probability of landing on yellow: 1/6
Probability of landing on blue: 1/6
Probability of landing on purple: 1/6
The spinner is most likely to land on red because it has the highest probability, 1/2 or 50%. Therefore, the answer is A. Red.
A, red
It would frequently land on 3 because 3 takes up the bigger portion of the spinner
Please help!!!!! Other than itself, which angle is congruent to angle FCE?
Answer:
<ICJ
Step-by-step explanation:
Vertical angles are congruent.
Answer: <ICJ
Answer: ∠JCI
Step-by-step explanation:
∠JCI and ∠FCE are vertical angles. We know that vertical angles are congruent, so the answer to this question is;
∠JCI
it takes a printer 6 minutes to print 40 pages at this rate how much can they print in 15 minutes
Answer:
100
Step-by-step explanation:
[tex]\frac{40}{6} = \frac{x}{15}[/tex]
x = (40 x 15) / 6
x = 100
i’m confused and would love help.
The final equation of the line is y = (-2/3)x - 3 in the coordinate system.
what is coordinate system?
A coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the position of a point or an object in space. In mathematics, the most common coordinate system is the Cartesian coordinate system
what is equation ?
In mathematics, an equation is a statement that shows the equality between two expressions. It contains an equals sign (=) between the two expressions that are being compared. Equations can be used to describe relationships between variables, to solve problems, or to represent real-world situations.
In the given question,
To draw the line going through (-6,1) with a slope of -2/3, we can follow these steps:
Plot the point (-6,1) on a coordinate system. This will be one point on the line.
From that point, use the slope to find another point on the line. A slope of -2/3 means that for every 3 units to the right we move, we must move 2 units down. So starting from (-6,1), we can move 3 units to the right and 2 units down to get to the point (-3,-1). This is another point on the line.
Draw a straight line through the two points to represent the line going through (-6,1) with a slope of -2/3.
To write the equation of the line, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1,y1) is one point on the line, m is the slope, and (x,y) are the coordinates of any other point on the line. Let's choose (-6,1) as our point:
y - 1 = (-2/3)(x - (-6))
Simplifying, we get:
y - 1 = (-2/3)x - 4
Adding 1 to both sides, we get the final equation of the line:
y = (-2/3)x - 3
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Need help please
Which of the following systems of inequalities matches the word problem? You are on the planning committee for the prom You have an 80 budget for food You decide to cater the prom with Little Cesar's $5 pizzas and McDonald's McChicken's, which cost 2 each. Based on a survey given to students, you will need at least 8 Little Cesar's pizzas to feed everyone that wants pizza Let x represent the number of pizzas bought and y represent the number of McChicken's bought
The system of inequalities that matches the given word problem is:
5x + 2y <= 80
x >= 8
What is system of inequalities?A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.
Equation:Let's break down the problem and identify the key information:
The budget for food is 80 dollars
Little Cesar's pizzas cost 5 dollars each
McDonald's McChicken's cost 2 dollars each
At least 8 Little Cesar's pizzas are needed to feed everyone that wants pizza
Let x represent the number of pizzas bought and y represent the number of McChicken's bought. The total cost of pizzas and McChicken's should be less than or equal to 80 dollars, which gives us the first inequality:
5x + 2y <= 80
Additionally, we know that at least 8 pizzas should be bought, which gives us the second inequality:
x >= 8
Therefore, the system of inequalities that matches the word problem is:
5x + 2y <= 80
x >= 8
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Which phrase describes the linear relationship between the x and y
values in this table?
X3
4
5
y
9
12
15
OA) X is 3 times y
OB) y is 3 times x
OC) y is 3 less than x
OD) y is 3 more than x
We can conclude that the linear relationship between x and y in this table is described by the phrase "y is 3 more than x."
What is the linear function?
A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
The given table shows two variables, x, and y, with corresponding values. A linear relationship between two variables means that a change in one variable causes a proportional change in the other variable.
If we look at the table, we can see that as the value of x increases by 1 unit from 3 to 4, the value of y also increases by 3 units from 9 to 12. Similarly, as the value of x increases by 1 unit from 4 to 5, the value of y increases by 3 units from 12 to 15.
This means that for every 1 unit increase in x, the value of y increases by a constant amount of 3 units.
In other words, the slope of the line connecting these points is constant and equal to 3.
Therefore, we can conclude that the linear relationship between x and y in this table is described by the phrase "y is 3 more than x."
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What’s is the perimeter and area of 14.3 yds and 12 yds
Answer:
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:
perimeter = 2(length + width)
In this case, the length is 14.3 yards and the width is 12 yards. Substituting these values into the formula, we get:
perimeter = 2(14.3 + 12)
perimeter = 2(26.3)
perimeter = 52.6 yards
Therefore, the perimeter of the rectangle is 52.6 yards.
The area of a rectangle is given by the formula:
area = length x width
Substituting the length and width values, we get:
area = 14.3 x 12
area = 171.6 square yards
Therefore, the area of the rectangle is 171.6 square yards.
HELP ME QUICK
what is 6:12 in the simplest form
Answer:
1 : 2
Step-by-step explanation:
First, find the GCF of 6 and 12, which is 6.
So divide both sides by 6:
6 / 6, 12 / 6
= 1 : 2
how do you write 2350 million in standard form
Answer:
WE CAN WRITE IN STANDARD FORM IN THE FOLLOWING WAY..
LMX0
Describe the range of the relationship shown here
Outside of this range, the relationship's range may differ, and outliers or other significant points may also have an impact.
what is variable ?A variable in mathematics is a symbol or letter that designates a number or value that is subject to change or variation. In order to solve problems and generate expressions and equations that represent the relationships between different quantities, variables are employed. X and Y are variables in the equation y = 3x + 2, for instance. The variable value of x determines the value of y. In order to express unknown numbers that we want to solve for, we can also utilize variables.
given
The scatterplot's depicted relationship is a positive linear relationship. These are some possible descriptions of the relationship's scope:
As the independent variable (x-axis) rises, so too does the dependent variable (y-axis).
There is not much scatter around the trendline, suggesting that the link is reasonably strong. From the lowest value on the y-axis to the greatest value on the y-axis, the relationship's range is defined.
The scatterplot only depicts the relationship between the two variables within the observed range of the data, it is crucial to remember this. Outside of this range, the relationship's range may differ, and outliers or other significant points may also have an impact.
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In a circle of radius 3, an arc has length 5.
What's the central angle of the arc?
Answer: 300/π°, or ~95.49°
Step-by-step explanation:
In order to find the central angle of the arc, we first find the ratio of the arc length to the circumference of the circle, since it is proportional to the ratio of the central angle to the total inside angle, 360°.
Finding the circumference
Circumference is equal to 2πr, and r (radius) in this case is 3, so
C=2π*3, or 6π
The ratio of the arc length to circumference is then 5/6π
Finding the angle
Since the ratio of lengths and ratio of angles are proportional, we can set up this equation:
5/6π=x/360
solving for x gets us:
x=300/π°, or ~95.49°
what is the range of the function graphed?
The correct option is A.
y ≥ -3
what is the range of the grapherd function?The range is defined as the set of possible outputs, so just look at the vertical axis, you can see it goes from x = -3 up, then the range is just the set of all values larger than -3
it is written as:
y ≥ -3
The correct option is a-.
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The table gives the number of students in a seventh-grade class enrolled in each elective.
Elective Number of Students
Art 2
Music 4
Health 3
Computer Science 5
If a student from this group is randomly selected, what is the probability that the student is enrolled in music?
Enter a number in the box.
Answer:
2/7 or 4/14
Step-by-step explanation:
we add all the people in the various electives and get 14.
then, we put 4 over 14 to get 4/14, which simplifies to 2/7 people.
I hope this helps!
Good luck for future math questions!
~Cain
Describe the type, direction, and strength of the correlation shown in the scatterplot below
show how you did the work
The Scatterplot has no correlation.
What is scatterplot?
Data visualization that depicts the relationship between two numerical variables is known as a scatterplot. The values for the two variables are used to depict each member of the dataset as a point with ( x , y ) coordinates that correspond to those values.
We know that A positive correlation between the variables is present when the y variable tends to grow as the x variable increases and a negative correlation is when x variables increase but y variable decreases.
No correlation means there is no clear relationship between two variables.
In the given scatter plot represent the relationship between month and cost.
Here for 6 months cost is $0.5 , for 7 months cost is $1 and for 5 months cost is also $1. Then there is no clear relationship between month and cost.
Hence the scatterplot has no correlation.
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Prove that X^n + Y^n is divisible by X + Y for any odd natural number n, where n ≥ 1.
Step-by-step explanation:
We can prove that X^n + Y^n is divisible by X + Y for any odd natural number n, where n ≥ 1, using mathematical induction.
Base case: n = 1 When n = 1, we have X^1 + Y^1 = X + Y, which is clearly divisible by X + Y.
Inductive step: Assume that X^k + Y^k is divisible by X + Y for some odd natural number k ≥ 1. We will show that X^(k+2) + Y^(k+2) is divisible by X + Y.
We can expand X^(k+2) + Y^(k+2) using the binomial theorem: X^(k+2) + Y^(k+2) = (X^2)(X^k) + (Y^2)(Y^k)
We can factor out X + Y from the first term and Y + X from the second term, since X + Y = Y + X: X^(k+2) + Y^(k+2) = (X + Y)(X^k + XY^k) + (X + Y)(Y^k + XY^k)
We can then simplify this expression by factoring out XY^k from the first term and X^kY from the second term: X^(k+2) + Y^(k+2) = (X + Y)XY^k + (X + Y)X^kY X^(k+2) + Y^(k+2) = (X + Y)XY^k + (X + Y)X^kY
We can then factor out (X + Y) from this expression to get: X^(k+2) + Y^(k+2) = (X + Y)(XY^k + X^kY)
Since X + Y is a common factor of X^(k+2) + Y^(k+2), we have shown that X^(k+2) + Y^(k+2) is divisible by X + Y.
Therefore, by mathematical induction, we have proven that X^n + Y^n is divisible by X + Y for any odd natural number n, where n ≥ 1.
the relative frequency of a class is computed by: group of answer choices dividing the frequency of the class by the number of classes dividing the frequency of the class by the class width dividing the frequency of the class by the total number of observations in the data set subtracting the lower limit of the class from the upper limit and multiplying the difference by the number of classes adding the lower limit of the class to the upper limit and multiplying the sum by the number of classes
The relative frequency of a class is computed by dividing the frequency of the class by the total number of observations in the data set. This statement (C) is true.
What is the relative frequency?
The relative frequency is a statistical term that represents the percentage of times a certain event occurs in an experiment or study. It is calculated by dividing the number of times an event occurred by the total number of trials in the experiment or study.
The class width is the difference between the upper limit and lower limit of a class. Class width is used to construct frequency histograms, cumulative frequency curves, and frequency polygons.The frequency of a class is the number of times the data falls within a certain class.
So, to compute the relative frequency of a class, divide the frequency of the class by the total number of observations in the data set. Therefore, option c, "dividing the frequency of the class by the total number of observations in the data set," is correct.
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I NEED HELP ASAP CAN SOMEONE SOLVE THESE ILL GIVE BRAINIEST
Using composite figures, we can find the value of area as:
In the 1st image,
Area of 1st triangle =70m².
Area of 2nd triangle = 24unit².
Area of 3rd triangle = 30unit².
In the 2nd image,
Area of the composite figure = 144unit²
In the 3rd image,
Area of the trapezium = 54unit².
Define composite figures?The area of composite shapes refers to the space any composite shape occupies. The composite shape is a shape made by combining a few polygons together to generate the required shape. Certain geometric forms, such as triangles, squares, quadrilaterals, etc., can be combined to create other geometric forms. Dividing a composite item into straightforward forms like a square, triangle, rectangle, or hexagon will allow you to compute its area.
In the 1st image,
Base of 1st triangle = 14m
Height of triangle = 10m.
Area of 1st triangle = 1/2 × b × h
= 1/2 × 14 × 10
= 70m².
In the 2nd triangle,
Base = 12
Height = 4
Area = 1/2 × b × h
= 1/2 × 12 × 4
= 24unit².
In the 3rd triangle,
Base = 12
Height = 5
Area = 1/2 × b × h
= 1/2 × 12 × 5
= 30unit².
Coming to the 2nd image we have a composite figure,
We have a rectangle with length = 9 and breadth = 6.
We have a triangle with base = 9 and height = 6.
And we have a trapezium with opposite sides as, a = 6, b = 15 with a height = 6.
So, the total area will be area of rectangle + area of triangle + area of trapezium.
= (9 × 6) + (1/2 × 9 × 6) + ((6+15)/2 × 6)
= 54 + 27 + 63
= 144unit².
Coming to the last image:
From the graph we can see that the polygon is a trapezium.
The height of the trapezium = 6 units.
Opposite sides,
a = 7 and b = 11.
So, area of trapezium = (a+b)/2 × h
= (7+11)/2 × 6
= 18/2 × 6
= 54unit².
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Describe what happens to the graph of y=a(x-2)^2+5 as ‘a’ varies
Varying 'a' in the equation og graph [tex]y = a(x-2)^2 + 5[/tex] changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).
What is graph?A graph is a visual representation of data or information that displays a relationship or pattern between two or more variables.
The graph of [tex]y = a(x-2)^2 + 5[/tex] is a quadratic function that has been shifted 2 units to the right and 5 units up from the standard form of [tex]y = x^2.[/tex] The variable 'a' represents the vertical stretch or compression factor of the parabola.
As 'a' varies, the shape of the parabola remains the same, but the steepness of the curve changes. When 'a' is positive and increases, the parabola becomes narrower, or more steeply curved, and the vertex moves higher up. This is because the larger value of 'a' causes the parabola to stretch vertically. When 'a' is negative and increases, the parabola also becomes narrower and the vertex moves lower down, but the orientation of the parabola is flipped upside down.When 'a' equals zero, the graph becomes a horizontal line at y = 5. This is because the parabola has been flattened completely, so there is no curvature in the graph.In summary, varying 'a' in the equation [tex]y = a(x-2)^2 + 5[/tex] changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).
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an angle measures 18 degrees less than the measure of its supplementary angle what is the measure of each angle
The measure of the angle is 81 degrees, and the measure of its supplementary angle is 99 degrees.
Let x be the measure of the angle in question, and let y be the measure of its supplementary angle.
By definition, supplementary angles add up to 180 degrees, so we have:
x + y = 180
We also know from the problem statement that:
x = y - 18
We can substitute the second equation into the first equation to eliminate y, giving:
(y - 18) + y = 180
Simplifying this equation, we get:
2y - 18 = 180
Adding 18 to both sides, we get:
2y = 198
Dividing both sides by 2, we get:
y = 99
Finally, we can use the equation x = y - 18 to find the measure of the angle in question:
x = 99 - 18 = 81
Therefore, the measure of the angle is 81 degrees, and the measure of its supplementary angle is 99 degrees.
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The circumference of a circle is 14 pi meters find its radius in meters
Answer: 7 meters
Step-by-step explanation:
1. Identify the given information: Circumference = 14 pi meters
2. Use the formula for calculating the circumference of a circle: Circumference = 2 pi * radius
3. Rearrange the formula to solve for the radius: Radius = (Circumference) / (2 pi)
4. Substitute the given information into the formula: Radius = (14 pi meters) / (2 pi)
5. Calculate the radius: Radius = 7 meters