Therefore, the correct answer is (D) [tex]$(12.61,16.39)$[/tex]
To calculate the confidence interval for the mean age of cars in the commuter lot, we'll use the formula:
[tex]\[ \text{Confidence interval} = \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \][/tex]
where:
- [tex]\(\bar{x}\)[/tex] is the sample mean age (14.5 years),
- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years),
- [tex]\(n\)[/tex] is the sample size (16),
- [tex]\(t\)[/tex] is the critical value from the t-distribution corresponding to the desired confidence level (90% in this case).
First, we need to find the critical value \(t\) for a 90% confidence level with [tex]\(n-1 = 15\)[/tex] degrees of freedom. Using a t-distribution table or calculator,[tex]\(t \approx 1.753\).[/tex]
Now, we can plug in the values:
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \left( \frac{4.6}{\sqrt{16}} \right) \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times \frac{4.6}{4} \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times 1.15 \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 2.12595 \][/tex]
[tex]\[ \text{Confidence interval} = (12.37405, 16.62595) \][/tex]
Complete question:
Ignacio is curious about the average age of cars in the commuter lot at his large university. He takes a random sample of 16 cars and finds that their average age is [tex]$\bar{x}=14.5$[/tex] years and their standard deviation is [tex]$s_x=4.6$[/tex]years. The distribution of ages in the sample was roughly symmetric with no obvious outliers.
Based on this sample, which of the following is a [tex]$90 \%$[/tex] confidence interval for the mean age of cars (in years) in this commuter lot?
Choose 1 answer:
(A) [tex]$(6.44,22.56)$[/tex]
(B) [tex]$(12.05,16.95)$[/tex]
(c) [tex]$(12.48,16.52)$[/tex]
(D)[tex]$(12.61,16.39)$[/tex]
(E) [tex]$(13.35,15.65)$[/tex]
The 90% confidence interval for the mean age of cars in the commuter lot is (12.48, 16.52). The correct answer is: c) (12.48, 16.52)
Step 1
To determine the 90% confidence interval for the mean age of cars in the commuter lot, we can use the formula for the confidence interval of the mean for a normally distributed sample:
[tex]\[ \text{CI} = \bar{x} \pm t \left(\frac{s}{\sqrt{n}}\right) \][/tex]
Where:
- [tex]\(\bar{x}\)[/tex] is the sample mean (14.5 years)
- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years)
- n is the sample size (16)
- t is the t-value for the 90% confidence level with [tex]\(n-1\)[/tex] degrees of freedom (df = 16 - 1 = 15)
First, we find the t-value for 90% confidence and 15 degrees of freedom. Using a t-table or a calculator, the t-value (two-tailed) is approximately 1.753.
Step 2
Next, we calculate the margin of error:
[tex]\[ \text{Margin of Error} = t \left(\frac{s}{\sqrt{n}}\right) = 1.753 \left(\frac{4.6}{\sqrt{16}}\right) = 1.753 \left(\frac{4.6}{4}\right) = 1.753 \times 1.15 \approx 2.016 \][/tex]
Now, we calculate the confidence interval:
[tex]\[ \text{CI} = 14.5 \pm 2.016 \][/tex]
So, the lower bound is:
[tex]\[ 14.5 - 2.016 = 12.484 \][/tex]
And the upper bound is:
[tex]\[ 14.5 + 2.016 = 16.516 \][/tex]
Thus, the 90% confidence interval for the mean age of cars is approximately:
[tex]\[ (12.48, 16.52) \][/tex]
This interval suggests that we are 90% confident that the true mean age of cars in the commuter lot lies between 12.48 and 16.52 years.
Complete question : Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random sample of 16 cars and finds that their average age is 2 = 14.5 years and their standard deviation is 8, = 4.6
years. The distribution of ages in the sample was roughly symmetric with no obvious outliers. Based on this sample, which of the following is a 90% confidence interval for the mean age of cars (in years) in this commuter lot?
a) (6,44,22,56)
b) (12,05,16,95)
c) (12,48,16,52)
d) (12,61,16,39)
e) (13,35,15,65)
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 5 mm. What is
the volume of the composite figure? Use 3.14 for Round to the nearest hundredth.
5 mm
10 mm
Recall the formulas y-Bhand V-
376.80 cubic millimeters
847 80 cubic millimeters
1.177 50 cubic millimeters
1308 33 cubic millimeters
Rounded to the nearest hundredth the volume of the composite figure is:
1308 33 cubic millimeters
Explanation:Hello! I wrote the complete question in a comment above. The volume of a cylinder is defined as:
[tex]V_{c}=\pi r^2 h \\ \\ r:radius \\ \\ h:height[/tex]
While the volume of half a sphere is:
[tex]V_{hs}=\frac{2}{3}\pi r^3[/tex]
Since we have 2 half spheres, then the volume of these is the same as the volume of a sphere:
[tex]V_{s}=\frac{4}{3}\pi r^3[/tex]
Then, the composite figure is:
[tex]V=\pi r^2 h +\frac{4}{3}\pi r^3 \\ \\ V=\pi r^2(h+\frac{4}{3}r)[/tex]
The radius of the cylinder is the same of the radius of each half sphere. So:
[tex]r=5mm \\ \\ h=10mm \\ \\ \\ V=(3.14) (5)^2((10)+\frac{4}{3}(5)) \\ \\ V=25(3.14)(10+\frac{20}{3}) \\ \\ \boxed{V\approx 1308.33mm^3}[/tex]
the crazy coaster has 3 trains , each train holds 27 people and runs 9 times in 1 hour . If the crazy coaster operates for 13 hours a day how many people can ride it each day ?
Given that the crazy coaster has 3 trains each holding 27 people and runs 9 times in 1 hour, and also operates for 13 hours a day, it can carry a total of 9,477 people in a day.
Explanation:To figure out how many people can ride the crazy coaster each day, we need to multiply all the related factors together. First, we consider the passengers each train can carry. Each of the 3 trains can hold 27 people which makes 81 people (3 trains multiplied by 27 people each). Then, each of these trains runs 9 times in 1 hour, so that's 81 people multiplied by 9 runs, which makes 729 people per hour. Since the crazy coaster operates for 13 hours a day, that's 729 people multiplied by 13 hours, which equals 9,477 people. Therefore, a total of 9,477 people can ride the crazy coaster each day, assuming every train is full on every run.
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It costs $3.45 to buy 3/4 kilogram of chopped walnuts. How much would it cost to purchase 7.5 kilograms of walnuts? Explain or show your reasoning. *
write y=3x-5 in function notation
Answer:
f(x) = 3x -5 is your answer
Step-by-step explanation:
f(x)=3x-5 is the function notation of the equation y=3x-5.
The equation y=3x−5 can be written in function notation as: f(x)=3x−5.
In function notation, we use f(x) to represent the dependent variable (usually y), and x remains the independent variable.
So, the function f(x) takes an input x, multiplies it by 3, and then subtracts 5 to determine the corresponding output y.
Hence, the equation y=3x-5 in function notation is f(x)=3x-5.
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WILL MARK BRAINLIEST! HELP PLEASE!
Ashley runs 5/8 miles in 4 minutes 30 seconds. Josh runs 3/4 miles in 5 minutes 15 seconds. Explain how you can tell who is the faster runner.
Please explain!
Answer:
Ashley is faster.
Step-by-step explanation:
I find it is easiest to convert into decimals.
Ashley ran 5/8 mile in 4 1/2 minutes.
5/8 is 0.625
Josh ran 3/4 mile in 5 minutes 15 seconds.
3/4 is 0.75
It looks like Josh won because his number is closer to 100, but, Ashley ran 0.625 mile faster than he ran 0.75 mile.
But then again, Josh ran more than her. Who won? Here is the answer.
Josh can run 0.75 mile in 5 minutes 15 seconds.
Ashley can run 0.625 miles in 4 1/2 minutes.
(4 + 1/2) ÷ 0.625 = 7.2
(5 + .15) ÷ 0.75 = 6.8
7.2 is more & closer to 10.
So to sum it up, Ashley is faster.
To determine who's the faster runner, we calculate the speed of each runner by dividing the distance they run by the time it takes. Josh is slightly faster than Ashley because he covers more distance per minute.
Explanation:In this problem, we are comparing the speeds of Ashley and Josh. Speed is calculated by dividing the distance traveled by the time it took to travel that distance. In Ashley's case, she runs 5/8 miles in 4 minutes and 30 seconds, or 4.5 minutes. So, her speed is (5/8) / 4.5 = 0.139 miles per minute.
Josh runs 3/4 miles in 5 minutes and 15 seconds, or 5.25 minutes. His speed is then (3/4) / 5.25 = 0.143 miles per minute.
We can see that Josh is slightly faster than Ashley because his speed (0.143 miles per minute) is higher than Ashley's speed (0.139 miles per minute).
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-BRAINLIEST ANSWER! Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse?
6 cm
6 StartRoot 2 EndRoot cm
12 cm
12 StartRoot 2 EndRoot cm
Answer:
The legs are 12 cm each, so the hypotenuse is
√(144+144)=12√2
So it would be the last one
Answer:
12√2
Step-by-step explanation:
Which of the following does not represent a function?
Answer:
It would be the third one
Answer:
The third one.
Step-by-step explanation:
Prove: If a point on a circle is equidistant from two radii, then the radius from the point bisects the angle formed by the two given radii.
Answer:
see the explanation
Step-by-step explanation:
see the attached figure to better understand the problem
we have that
OA+OB=radii of circle O
Point P is equidistant from radii OA and OB ----> given problem
so
PA=PB
OP is a common side
Triangle OAP is congruent to Triangle OBP by SSS Postulate Theorem
Remember that
If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent
That means
[tex]m\angle POA=m\angle POB[/tex]
therefore
The radius from the point (PO) bisects the angle formed by the two given radii (angle ∠AOB)
WILL GIVE BRAINLIEST!!!!
1. Find the slope of the line through each pair of points (-11, -15) and (1,14)
2. Find the slope of the line through each pair of points (16, -19) and (-9,12)
3. Find the slope of the line through each pair of points (-18, -3) and (8, -3)
Slope formula: y2-y1/x2-x1
Question 1:
= 14-(-15)/1-(-11)
= 29/12
= 2 5/12
Therefore, the slope is 2 5/12 or 29/12.
Question 2:
= 12-(-19)/-9-16
= 31/-25
= -31/25
= 1 6/25
Therefore, the slope is 1 6/25 or -31/25.
Question 3:
= -3-(-3)/8-(-18)
= 0/26
Therefore, the slope is 0.
Best of Luck!
patsy's pizzeria sold 3 5/6 vegetables pizzas yesterday. they sold 3 times as many pepperoni pizzas. how many pepperoni pizzas did they sell?
Answer:
11.5
Step-by-step explanation:
3 x 3 5/6
3 x 23/6
=69/6
=11.5
To find out how many pepperoni pizzas Patsy's Pizzeria sold, we need to multiply the number of vegetable pizzas by 3. They sold 11 1/2 pepperoni pizzas.
Explanation:To find out how many pepperoni pizzas Patsy's Pizzeria sold, we need to multiply the number of vegetable pizzas by 3. If they sold 3 5/6 vegetable pizzas, we can represent this as a mixed number of 3 + 5/6. To multiply this by 3, we first convert the mixed number to an improper fraction: 3 + 5/6 = (3 * 6 + 5) / 6 = 23/6. Next, multiply the improper fraction by 3 to get: (23/6) * 3 = 69/6 = 11 1/2. Therefore, Patsy's Pizzeria sold 11 1/2 pepperoni pizzas.
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Can three segments with length 4 cm, 6 cm, and 11 cm be assembled to form an acute triangle, a right triangle, or an obtuse triangle? Explain.
Answer:
No
Step-by-step explanation:
Three segments 4cm, 6cm, and 11cm cannot form a right triangle because if they could, then by Pythagorean theorem, 4^2 + 6^2 = 11^2, which is not true.
Moreover, the three segments cannot form an acute or obtuse triangle because by Triangle Inequality Theorem, the sum of two sides has to be greater than the third side. Here, (4cm + 6cm) is NOT larger than 11cm, and thus you cannot form a triangle.
Using triangle concepts, it is found that the sides with these lengths cannot form a triangle.
In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the larger side.
In this problem:
The smaller sides have lengths: 4 cm and 6 cm.The larger side has length: 11 cm.[tex]4 + 6 = 10 < 11[/tex]
Since the larger side length is greater than the sum of the lengths of the smaller sides, a triangle cannot be formed.
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What is the slope of the linear function represented in
the table?
-7
Answer:
The function is linear; therefore, the slope of the line joining any two points is the same. We take any two points from the table and compute the slope or rise/ run between them— let is take points (-4, -2) and (-2, -10).
Answer:
1/7
i took the quiz already
In the Volume of Pyramids section, a right square pyramid has a slant height of 5cm and a base edge length of 6cm. Select all that apply. *
B = 6cm
B= 36cm squared
The height and the slant height form a right triangle.
h = 4cm
h= 7cm
h = 3cm
V = 1/3Bh
V = Bh
V = 144 cm cubed
V = 48 cm cubed
Answer:
B= 36cm squared
h = 4 cm
V = 48 cm cubed
Step-by-step explanation:
A square pyramid has a square base. The edge length are all equal.
Given that:
base length (b) = 6 cm and slant height (l) = 5 cm.
The height and the slant height form a right triangle i.e the slant height is the hypotenuse, the base of the triangle is the distance from the center of the square to the edge which is half of the base length (b/2). The height of the pyramid (h) is given as:
l² = h² + (b/2)²
h² = l² - (b/2)²
h² = 5² - (6/2)²
h² = 25 - 9
h = √16 = 4 cm
The area of the base = b² = 6² = 36 cm²
The volume of the pyramid (V) = 1/3 × b² × h = 1/3 × 6² × 4 = 48 cm³
(Express each rate in lowest term)
6 + 4 2/3
Final answer:
The rate 6 + 4 2/3 in lowest terms is 32/3 or, as a mixed number, it is 10 2/3.
Explanation:
The student asked to express the rate 6 + 4 2/3 in lowest terms. To do this, we will first convert the mixed number 4 2/3 into an improper fraction. The mixed number 4 2/3 can be converted by multiplying the whole number 4 by the denominator 3 and then adding the numerator 2, which gives us 14/3. So now we have the expression 6 + 14/3.
To add the whole number and the fraction, we can convert the whole number 6 into a fraction with the same denominator as 14/3. This means converting 6 to 18/3 (since 6 times 3 equals 18). Now we can add the fractions directly: 18/3 + 14/3 equals 32/3. Therefore, the rate 6 + 4 2/3 expressed in lowest terms is 32/3 or 10 2/3 when represented as a mixed number.
WILL MARK BRANLIESTTT
What is the value of x?
A. 42°
B. 48
C. 64°
D. 84
Answer:
D.84Step-by-step explanation:
*It's an isosceles triangle so 2 of the angles are going to be the same degrees
*Every triangle is 180 degrees
(48)+(48)=96 then 180-96=84
Which of the following describes a positive correlation? As the number of hours spent on homework increases, the tests scores increase. As the number of times going to bed early increases, the number of times waking up late decreases. As the number of apples eaten per year increases, the number of times visiting the doctor every year remains the same. The amount of time a team spent practicing increases, the number of games lost in a season decreases.
Answer:
As the number of hours spent on homework increases, the tests scores increase.
Step-by-step explanation:
because the independent variable and dependent variable are both increasing.
Final answer:
The statement "As the number of hours spent on homework increases, the test scores increase" best describes a positive correlation, where two variables increase together.
Explanation:
A positive correlation is described as a relationship in which the increase in one variable leads to the increase in another variable. Looking at the situations you provided, the scenario, "As the number of hours spent on homework increases, the test scores increase," clearly illustrates a positive correlation. More hours of homework tend to result in higher test scores, suggesting that the two variables change in the same direction.
A negative correlation involves an inverse relationship where an increase in one variable leads to a decrease in the other. For example, "As the number of times going to bed early increases, the number of times waking up late decreases," is a negative correlation because the variables move in opposite directions.
No correlation occurs when the changes in one variable do not relate to changes in another variable, such as "As the number of apples eaten per year increases, the number of times visiting the doctor every year remains the same." Here, there is no consistent pattern of increase or decrease between apple consumption and doctor visits.
A cylindrical bucket can hold approximately 301.44 in. The height of the bucket is about 6 inches. What is the diameter of the bucket to the nearest inch?
Answer:
The diameter is 8 inches
Step-by-step explanation:
This problem bothers on mensuration of solid shapes, this in particular a cylindrical
Given data
Volume of cylinder in inches v=301.44in^3
Height of the bucket h= 6 inches
Radius r=?
To solve for the diameter we neeed to solve for the radius and multiply It by 2 to get the diameter
We know that the volume of a cylinder is given as
v= πr^2h
301.44= 3.142*r^2*6
301.44= 18.85*r^2
r^2= 301.44/18.85
r^2= 15.99
r=√15.99
r=3.998in
We know that the
diameter d =2r
Therefore d= 3.99*2
d= 7.997in
≈ d = 8 inches
Use grid paper to find the median of the data.
9,7,2,4,3,5,9,6,8,0,3,8
The median is....
The median of the data is 5.5.
Calculation of the median:Since the sequence is 9,7,2,4,3,5,9,6,8,0,3,8
We have to arrange the above sequence in the smaller to largerst number
i.e.
0,2,3,3,4,5,6,7,8,8,9,9
So since 5 and 6 are in middle
So, the median is
[tex]= (5 + 6)\div 2[/tex]
= 5.5
Therefore, The median of the data is 5.5.
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It was 75.5 degrees Fahrenheit and 2 hours later, the temperature dropped 15.1 degrees Fahrenheit. What is the new temperature?
Answer:
60.4
Step-by-step explanation:
75.5-15.1=60.4
Answer:
60.4*F.
Step-by-step explanation:
75.5-15.1=60.4
What equation has a constant of proportionality equal to 1/2
Answer:
Y = 10/5x
10 divided by 5 = 2
Step-by-step explanation:
An office building has the dimensions shown.
What is the volume of the building?
2. 50 m
10 m
110 m
90 m
70 m
For the angles shown in the diagram, which statements are true? Select all that apply.
A.The sum of m∠3 and m∠4 is 180°.
B.The sum of the measures of the adjacent interior angle and one of the remote interior angles is equal to the measure of the exterior angle.
C.∠3 is supplementary to ∠1.
D.m∠4 = m∠1 + m∠2.
E.m∠1 + m∠2 + m∠3 = 180
Answer:
A, D, E
Step-by-step explanation:
i just did it
The statements that are true include:
A.The sum of m∠3 and m∠4 is 180°.D.m∠4 = m∠1 + m∠2.E. m∠1 + m∠2 + m∠3 = 180°It should be noted that the sum of angles that are in a triangle equals 180°. Therefore, m∠1 + m∠2 + m∠3 = 180°.
Also, the sum of m∠3 and m∠4 is 180°. This is because the angle on a straight line equals 180°.
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WILL MARK BRAINLIEST
In which quadrants do solutions for the inequality y>1/5x+3
A) l and ll
B) I,ll, and lll
C)l,lll, and lV
D) All four quadrants
Answer:B is your correct answer
Step-by-step explanation:
I TOOK THE TEXT AND GOT A HUNDRED
helllloo plss help asap it would mean alottttt
plss helppp asap
Answer: The point will move across the Y- axis
Step-by-step explanation:
When the X coordinate's sign is changed, then the coordinate will be reflected over the Y-axis, becoming equidistant from the Y-axis.
For the data set below which of the following measures is greatest? 3,3,4,5,6,8,16,20
In this question, the student is asked to compare mean, median, mode, and range for a given data set. Among these measures, the range, being 17, is the greatest.
The question given is asking for the greatest measure among the data set, which is 3,3,4,5,6,8,16,20. The measures being referred to are likely statistical measures such as mean, median, mode, and range.
The mean is the sum of all the numbers divided by the total count of the numbers, the median is the middle value when the numbers are arranged in order, the mode is the number that appears most frequently, and the range is the difference between the largest and smallest numbers.
To find the mean, we calculate (3+3+4+5+6+8+16+20)/8=7.875. The median is the average of the two middle numbers since we have an even count, (5+6)/2 = 5.5. This data set's mode is 3 since 3 repeats only. The range is 20 - 3 = 17.
Comparing these measures, we see that the range, with a value of 17, is the greatest.
Calculate the exact lengths of segment e and segment f. Which is longer?
Answer:
Step-by-step explanation:
(We use the pythagorean theorem)
3-(-1) = 4
-2-1 = -3
4x4 + -3 x -3 = 16 x 9 = 144
line e: 12
2-(-1) = 3
2-(-1) = 3
3x3 + 3x3 = 9 x 9 = 81
line f: 9
Therefore, line e is longer!
Hope this helps! .ω.
Please give me brainliest :<
Without specific figures or numerical data, we cannot conclusively calculate the exact lengths of segments e and f. However, geometric principles suggest that segment f, if similar to a hypotenuse, would be longer. Accurate measurement or calculations based on the context (geometry, trigonometry, physical surveying) are required to determine the length of segments.
Explanation:To calculate the exact lengths of segment e and segment f, we need more specific information from the given figures. However, based on the information provided, we can infer certain principles that could lead us to a conclusion. The hypotenuse of a right-angle triangle, as mentioned, is always the longest side, which implies that the length of segment f, being akin to a hypotenuse, would be longer than segment e if these segments were sides of a right-angled triangle. Additionally, the concept of eccentricity described for an ellipse informs us about the ratio of distances and could be applied if the segments were part of an elliptical geometry. The surveyor's tapes information suggests that lengths must be measured accurately, taking into account environmental factors such as temperature, because this can affect the length measurements. Without specific numerical data or figures to reference, we cannot determine with certainty which segment is longer, but the principles outlined can guide us to make an educated conclusion once all data is available.
In general, when comparing two segments to determine which is longer, measurement tools or mathematical calculations are utilized based on the context, such as geometry, trigonometry, or physical measurement in the case of surveying. As per the given text, if the discussion revolves around visual illusions where segments appear different in length despite being the same, then careful measurement is necessary to establish their actual lengths.
Please Help, Look at attachments. Could you Please explain also.
Answer:
true, false, true, false
Step-by-step explanation:
On a graph, you can see wether or not you have a function by doing the VLT, or vertical line test. Hold a pen or pencil vertically on the paper on move it from left to right. If no 2 points touch the pencil at once, it's a function.
Another way to find out is if any two different points have the same x coordinate. If there is a match, this is not a function. For example, 3,4 and 3,9 cause the graph to not be a function.
The five-number summary suggests that about 75\%75%75, percent of salons in Jamesville have fewer than how many stylists employed?
Answer:
15
Step-by-step explanation:
khna academy
What is the area of 1 = 8 inches
w = 4.5 inches
Answer: 36 in²
Step-by-step explanation:
A=length times width
4.5 times 8 = 36
Answer:
[tex] 36.0 \: {inches}^{2} [/tex]
Step-by-step explanation:
[tex]area = l \times w = 8 \times 4.5 \\\hspace {65 pt} = 36.0 \: {inches}^{2} \\ [/tex]
Find the area of the figure. PLEASSEEEEEEEE!!!!!!!!
Given:
side length = 6 ft
To find:
The area of the figure
Solution:
Area of the square = side × side
= 6 × 6
Area of the square = 36 ft²
Diameter of the semi-circle = 6 ft
Radius of the semi-circle = 6 ÷ 2 = 3 ft
Area of the semi-circle = [tex]\frac{1}{2} \pi r^2[/tex]
[tex]$=\frac{1}{2} \times 3.14 \times 3^2[/tex]
Area of the semi-circle = 14.13 ft²
Area of the figure = Area of the square - Area of the semi-circle
= 36 ft² - 14.13 ft²
= 21.87 ft²
Area of the figure = 21.9 ft²
The area of the figure is 21.9 ft².