The length around the circular edge of the plate is 37.68 inches
How to find the circumference of a circle?The circumference of a circle can be solved as follows:
The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .
The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.
Hence, the distance around the edge of the plate is the circumference of the plate.
Therefore,
circumference of the circular plate = 2πr
circumference of the circular plate = 2 × π × 6
circumference of the circular plate = 12π
circumference of the circular plate = 12 × 3.14
circumference of the circular plate = 37.68 inches
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I have no idea how to do this
The solution for the given equation X^3 + Y^2 = 971,028. So, option A is correct.
What are multiples?A multiple of a number is the number whose remainder is 0 when divided by the given number.
Consider 'a' as the multiple of a number 'n'.
Then, a ÷ n = b (and remainder = 0)
Calculation:It is given that,
X = largest 2-digit multiple of 3 which is not a multiple of 5
⇒ X = 99
Y = smallest 2-digit multiple of 9 which is not a multiple of 6
⇒ Y = 27
Then, substituting the values in the given equation,
= X^3 + Y^2
= (99)³ + (27)²
= 970,299 + 729
= 971,028
Therefore, the value of the given equation is 971,028.
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Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Find the measure of arc CFD.
The measure of the Central Angle indicated is; 45°
How to find the central angle of a circle?
The central angle will be the angle subtended at the center by arc FE and arc CB.
Now, we see that angle ∠FOB = 135° and since we know that sum of angles on a straight line is 180°, then we can say that;
Central Angle = 180° - 135° = 45°
Angle subtended by Arc CD at the center is;
θ = 180 - (81 + 45)
θ = 54°
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The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = a sine (b (t minus h)) k. what is the height of the ball at its equilibrium?
Based on the height of the ball suspended from a spring, the height of the ball at equilibrium is K feet.
What is the ball's height at equilibrium?The model for the height of the ball when it is suspended from a spring is shown as:
= aSin(b ( t - h)) + k
Given this, we can infer the value of h by looking at the general form of the Sin function which is:
y = Asin(Bx) + c
In the above:
A = amplitude
B = (2 x pi) / Period
C = midline
Comparing the function and the general Sin function, we notice that:
C = K
If C = K then it means that K is the height of the ball at its equilibrium because C as the midline represents the equilibrium height.
In conclusion, the height of the ball at equilibrium is K feet.
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Which rule can be used to describe the growth of the y-values of the function y=12^(x) each interval from x=-1 to x=3
A rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."
How to determine the rule?By critically observing the given function, we can logically deduce that it is an exponential function. Also, the initial value of this exponential function is 1 with a growth factor is 12.
For instance, we have:
At x = -1
y = 12^(-1)
y = 1/12
At x=0
y = 12^(0)
y = 1
At x = 1
y = 12^(1)
y = 12
In conclusion, a rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."
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Suppose 60% of the freshmen at msu take a course in outdoor survival skills. the probability that a freshman selected at random who did not get lost during a hike is 90%. the probability that a freshman selected at random who took the course and did not get lost is 50%.
Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
According to the question,
Probability of freshmen who took course at MSU in outdoor survival skills is 0.6.
Probability that a freshmen selected at random who did not get lost during a hike is 0.9.
Probability that a freshman selected at random who took the course and did not get lost is 0.50
Conditional probability = P(A and B)/ P(A)
P(did not get lost/took the course) = P( freshmen did not get lost who took the course and freshmen took the course)/P(freshmen did not get lost)
= 0.5/0.6
= 0.8333
Hence, Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
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In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.
What is circuit training?A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.
Some features of circuit training exercise are-
It is a great approach to increase muscular strength and endurance as well as cardiovascular health. Due to the brief rest times, the use of major muscles in conjunction with smaller ones, and the mix of upper, lower, and whole-body movements in circuit training, your heart rate will increase and remain elevated during the entire circuit.Once all of the selected exercises have been finished, a circuit has been completed. A single training session may involve several circuits.Benefits of doing circuit training exercise-
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The complete question is -
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)
Question If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0
Answer: If the product of any two numbers in the list is equal to 0, you can't conclude that the list is composed only by zeroes. In fact, suppose that you have a list of N numbers which are all zeroes except one. Whenever you multiply two elements of this list, you either multiplies two zeroes, or you multiply the non-zero element by a zero element, and so the result is zero, but the list is not composed by zeroes only.
Step-by-step explanation:
10 POINTS
please help me!!
This is the graph of f(x). What is the value of f(3)?
10+
2
-5
C
A. 5
B. 3
C. 6
D. 8
5
X
The value of f(3) is 8
What is the area of this triangle?
Answer:
12 units^2
Step-by-step explanation:
Area of a triangle = 1/2 * base * height
base goes from -4 to +4 = 8 units
Height goes from 1 to 4 = 3 units
area = 1/2 * 8 * 3 = 12 units^2
The equation represents an ellipse. which point is the center of the ellipse? (−9, 5) (−5, 9) (5, −9) (9, −5)
The point which is the center of the ellipse whose equation is; (y+5)²/121+(x-9)²/49=1 s in the task content is; (-5, 9).
Which point represents the center of the ellipse whose equation is given as; (y+5)²/121+(x-9)²/49=1?It follows from convention that the equation of an ellipse usually takes the form;
(y-h)²/a²+(x-k)²/b²=1 in which case, the center of the ellipse is given by the point; (h, k).
On this note, By comparison of the actual equation and the standard equation, it follows that;
+5 = -h and consequently, h = -5,
-9 = -k and consequently, k = 9.
Ultimately, the point which is the center of the
ellipse is; (-5, 9).
Remark: The equation of the ellipse which is missing in the task content is; (y+5)²/121+(x-9)²/49=1
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Answer: D. (9, −5)
Not (-5, 9)
Step-by-step explanation:
Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
77 m (nearest metre)
Step-by-step explanation:
Angle of Elevation
If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.
To find how tall the flagpole is, model as a right triangle and solve using the tan trigonometric ratio.
Tan trigonometric ratio
[tex]\sf \\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven information:
Person height = 1.6 mHorizontal distance (from person to flagpole) = 35 mAngle of elevation = 65°Therefore:
[tex]\theta[/tex] = 65°O = height of flagpole less height of personA = 35 mAs the person is 1.6 m tall, we model the line of sight as 1.6 m above ground level. Therefore, when calculating the height of the flagpole, we will need to add the height of the person to the value found using the trig ratio.
Substitute the given values into the formula and solve for O:
[tex]\implies \sf \tan(65^{\circ})=\dfrac{O}{35}[/tex]
[tex]\implies \sf O=35\tan(65^{\circ})[/tex]
Therefore the height of the flagpole is:
[tex]\implies \sf 35\tan(65^{\circ})+1.6=76.65774222...[/tex]
[tex]\implies \sf Height\:of\:flagpole=77\:m\:(nearest\:metre)[/tex]
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Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer:
They are similar. Triangle abc is similar to triangle edc.
Step-by-step explanation:
To prove that triangles are similar, you must show that the 3 angles in one triangle are equal to the 3 angles in the other triangle. We know that they both have a 50 degree angle. We can also see that they both have a right angle. That means that the 3rd angle must also equal 40 (180-90-50). So by AAA the two triangles are congruent.
Triangle ABC is similar to triangle EDC.
Answer:
triangle ABC is similar to triangle DCE
Step-by-step explanation:
Reason being that angles in triangle ABC Correspond to That of triangle DCE Eg triangle ABC=CDE
Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.
Subsets with bit strings:
001110000010100100010111001110What are subsets?A set A is a subset of a set B if all of its items are also elements of B; B is, therefore, a superset of A. A and B can be equal; if they are unequal, then A is a legitimate subset of B. Inclusion refers to the relationship of one set being a subset of another.To find the subsets with bit strings:
We need to express a) b) and c) into bit strings.
Firstly, a number of elements in the universal set represent the number of bits in the bit string.
Secondly, 1 = yes element is present in both universal sets as well as in subset.
0 = No, the element is not present in the subset but present in the universal set.
Hence, we have:
a) Subset {3,4,5} = 0011100000 (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.
Similarly,
b) Subset {1, 3, 6, 10} = 1010010001
c) Subset {2, 3, 4, 7, 8, 9} = 0111001110
Therefore, Subsets with bit strings:
001110000010100100010111001110Know more about subsets here:
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Complete question:
Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.
a) {3, 4, 5}
b) {1, 3, 6, 10}
c) {2, 3, 4, 7, 8, 9}.
Using Euler's formula, how many
edges does a polyhedron with 6
faces and 8 vertices have?
[?] edges
Euler's Formula: F + V = E + 2
Answer:
F+V=E+2
F=6
V=8
E=?
PUT THEIR VALUE
6+8=E+2
= 14=E+2
=14-2=E
=12=E
VALUE OF E IS 12
A boss plans a business meeting at Starbucks with the two engineers below him. However, he fails to set a time, and all three arrive at Starbucks at a random time between and p.m. When the boss shows up, if both engineers are not already there, he storms out and cancels the meeting. Each engineer is willing to stay at Starbucks alone for an hour, but if the other engineer has not arrived by that time, he will leave. What is the probability that the meeting takes place
The probability that the meeting takes place is 7/24.
What is the probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes(sample space) of the event.
It is given by
P(A) = n(A)/n(S)
Where A - event, S - sample space
Calculation:From the given data,
The probability, if the engineers arrive in the first hour and the boss arrives in the second hour is 1/8,
So, the meeting will be held i.e., p = 1.
The probability, if all the three arrive in the same hour (first or second)
= 1/8 + 1/8
= 1/4
So, the meeting will be held only if the boss (he may arrive first, second, or last) arrives last, the probability is 1/3
The probability, if one of the engineers arrives in the first hour while the other engineer and the boss arrive in the second hour is
= 1/4
So, the meeting will be held only if the second engineer arrives before the boss and before the first engineer leaves, the probability is 1/3
Thus, the final probability for the meeting to take place is
= (1/8) × 1 + (1/4) × (1/3) + (1/4) × (1/3)
= 7/24
Therefore, the required probability is 7/24.
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Which could be the missing data item for the given set of data if the median of the complete data set is 14?
10 11 10 19 16 14 12 12 15 11 18 19
A. 10
B. 11
C. 12
D. 18
The missing data item for the given set of data if the median is 14 is 18.
How to find the median of a data sets?The Median is the "middle" of a sorted list of numbers.
Therefore, the missing data item for the given set of data if the median is 14 can be calculated as follows:
10 10, 11, 11, 12, 12, 14, 15, 16, 18, 19, 19,
Therefore, if you add 18 the middle number of the sorted numbers will be 14.
10 10, 11, 11, 12, 12, 14, 15, 16, 18, 18, 19, 19,
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Identify the relationship between the variable:_____ is a function of __
Ps need asap
A correlation is simply used to determine whether a relationship exists between the variables.
How to illustrate the information?The information is incomplete and an overview will be given. The correlation shows the relationship between the variable.
This can be explained in a numerical form that's known as the correlation coefficient. This shows that strength of the relationship.
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WILL MARK BRAINLIEST!!!
1. Describe three different ways to solve a quadratic equation. Describe the strengths and limitations of each method, and explain how you would decide which one to use to solve a particular problem.
2. Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
Divide all terms in the equation by a.
Subtract the constant (the term without an x) from both sides.
Add a constant (in terms of a and b) that will complete the square.
Take the square root of both sides of the equation.
Solve for x.
3. Write a linear equation that intersects y = x2 at two points. Then write a second linear equation that intersects y = x2 at just one point, and a third linear equation that does not intersect y = x2. Explain how you found the linear equations.
Thank You!!
The ways that can be used to solve a quadratic equation include:
Factorization
Using the quadratic formula.
Completing the squares.
What is a quadratic equation?It should be noted that a quadratic equation simply means an algebraic equation of the second degree in x.
Here, the factorization, using the quadratic formula, and completing the squares method can be used.
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Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.
The true statement about the plane include:
Points A, B, and D are on both planes. Point H is not on plane R.The line containing points F and G is on plane R.The line containing points F and H is on plane R.What is a vertical plane?It should be noted that a vertical plane simply passes through a vertical line.
In this case, Point H is not on plane R and the e line containing points F and G is on plane R.
The correct options are 1,2,4, and 5.
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Answer:
a,b,d,e
Step-by-step explanation:
Suppose that E and F are two events and that P(E)=0.3 and P(F|E)=0.5. What is P(E and F)?
P(E and F)=
(Simplify your answer.)
E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15
Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.
P(F|E)=P(E and F)÷P(E)
It is given that P(E)=0.3,P(F|E)=0.5
Using Bayes' formula,
P(F|E)=P(E and F)÷P(E)
Rearranging the formula,
⇒P(E and F)=P(F|E)×P(E)
Substituting the given values in the formula, we get
⇒P(E and F)=0.5×0.3
⇒P(E and F)=0.15
∴The correct answer is 0.15.
If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.
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A car can travel 161 miles on 7 gallons of gas. how much gas will it need to go 368 miles?
Answer:
16 gallons of gas
Step-by-step explanation:
Two ways to answer this
1:
Find how many miles per gallon the car can go. Then, divide the amount the car needs to go with the miles per gallon. This gets you the gallons of gas needed to go the amount. In this case, 161 ÷ 7 = 23. 368 ÷ 23 = 16.
2:
Make a proportion. [tex]\frac{161}{7} = \frac{368}{x}[/tex]. Solve for x. 161 and 7 cancel out to get 23. [tex]\frac{23}{1} = \frac{368}{x}[/tex]. Now you can either divide 368 and 23 and multiply the quotient by 1 to get x, or you can cross multiply to get an equation you can solve. In the first case, 368 ÷ 23=16. 1*16=16. x=16. In the second case, 23x=368. Divide both sides by 23 and you get x = 16.
Please please please help with b
The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.
a. Angle a = 72.54 degrees
b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys
The length of the belt around the two pulleys is approximately 49.2 centimeters.
How to determine the length of the belt around the two pulleys?
In this question we must determine the perimeter of a belt around two pulleys, whose centers are 10 centimeters apart. This perimeter is the sum of part of the circumference of small pulley, part of the circumference of the big pulley and two times the segment tangent to the two pulleys.
Now we proceed to determine the parts of the perimeter of the belt:
Big pulley
s' = (214.92° / 180°) · π · (6 cm)
s' ≈ 22.506 cm
Small pulley
s'' = (145.08° / 180°) · π · (3 cm)
s'' ≈ 7.596 cm
Tangent segments
l = (10 cm) · sin 72.54°
l ≈ 9.539 cm
Lastly, the perimeter of the belt is:
L = s' + s'' + 2 · l (1)
L = 22.506 cm + 7.596 cm + 2 · (9.539 cm)
L = 49.180 cm
The length of the belt around the two pulleys is approximately 49.2 centimeters.
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A research team collects both quantitative and qualitative data. They code the qualitative data and examine how variations in the themes are related to the quantitative data. What type of mixing is this
Its related to the mixing in the Analysis.
Quantitative data:
They are used when a researcher is trying to quantify a problem, or address the "what" or "how many" aspects of a research question. It is data that can either be counted or compared on a numeric scale.
Qualitative data :
It describes qualities or characteristics. It is collected using questionnaires, interviews, or observation, and frequently appears in narrative form. For example, it could be notes taken during a focus group on the quality of the food at Cafe Mac, or responses from an open-ended questionnaire.
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A student found the MAD of the data shown. What was the student’s error?
A.When calculating the mean, the student divided the sum by the wrong number.
B.When calculating the MAD, the student divided the sum by the wrong number.
C.When calculating the distances to the mean, the student forgot to take the absolute values.
D.When calculating the MAD, the student forgot to take the absolute value of the result.
The error made while find the mean absolute deviation was: C. When calculating the distances to the mean, the student forgot to take the absolute values.
What is the Mean Absolute Deviation?The mean absolute deviation is simply the average of the sum of the "absolute difference" of the mean and each data point.
In the calculation of the student, after getting the difference of the mean and each data point, the student failed to take the absolute value, and still kept the minus sign included.
Therefore, the error was: C. When calculating the distances to the mean, the student forgot to take the absolute values.
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Find a polynomial function of lowest degree with
rational coefficients that has the given numbers
as some of its zeros.
- 5i, 4
Answer:
x^3-4x^2+25x-100
Step-by-step explanation:
We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root
Combining the roots into a polynomial gives us:
(x+5i)(x-5i)(x-4)
Expand:
(x^2 + 25)(x-4)
x^3-4x^2+25x-100
Is it possible to make a number out of 8 different digits that is
divisible by each of the eight digits?
Answer:
1,123,449,768
Step-by-step explanation:
The smallest number composed from 8 different digits that is divisible by each of those digits appears to be the 10-digit number ...
1,123,449,768
RestrictionsIf the number is to be divisible by an even digit, it must be even. That means it cannot end in the digit 5, so 5 cannot be one of the digits. We disallow division by 0, so 0 cannot be one of the digits.
The remaining 8 digits total 40, so cannot form a number divisible by 3, 6, or 9. In order to make such a number, we must add 5 to the digit total, but cannot do so using the single digit 5.
Choices for added digits include {1, 4} and {2, 3}. Adding 9+5 = 14 to the digit total would also work but would guarantee the resulting number is not the minimum possible.
Further divisibility restrictionsThe digits we have to work with are now {1, 1, 2, 3, 4, 4, 6, 7, 8. 9}. We know that an even number constructed from these digits will be divisible by 1, 2, 3, 6, and 9. To make it divisible by 4, 7, and 8, it must be a multiple of the LCM of those numbers.
The least possible number will use the smallest digits first, so will start ...
112344...
The remaining digits, 6, 7, 8, 9, need to form a number that will be divisible by 56 when appended to the 6 digits already used. Those 6 digits form a number, 1123440000, that has a remainder of 32 when divided by 56. Hence we need to use the digits 6, 7, 8, 9 to make a number with a remainder of 24 when divided by 56. There are 24 permutations of the digits 6, 7, 8, 9. Half of these are odd numbers
The one number formed from digits 6, 7, 8, 9 that is divisible by 56 with a remainder of 24 is 9768.
Smallest NumberThe smallest number comprised of 8 different digits and divisible by each of them is the 10-digit number 1,123,449,768.
Year: %Households:
1999 12.3
2000 18.2
2001 24.4
2002 25.7
2003 27.9
Estimate the instantaneous rate of change in percent of households that played games over the internet in the year 2000. Use the method of averaging a preceding and following interval AND the method of choosing a surrounding interval.
Based on the table showing the percentage of households playing games over the net, the average rate of change from 1999 to 2003 is 3.9% per year.
What is average rate of change?This can be found as:
= (27.9 - 12.3) / 4 years
= 3.9% per year
In 2000, the instantaneous rate of change would be:
= (Rate in 2001 - Rate in 1999) / difference in years
= (24.4 - 12.3) / (2001 - 1999)
= 6.05%
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In a mathematics test, Jack scored 17 marks more than Yazid while Susan scored twice Yazid's score. If their total score is 161, what is Jack's score?
Answer:
53
Step-by-step explanation:
Let yazid's score be x
x + x + 17 + 2x = 161
4x + 17 = 161
4x = 144
x = 36
jack = x + 17
jack = 53
Answer:
Jack: 36
Bonus: Yazid: 53 and Susan: 72
Step-by-step explanation:
Let J, Y, and K stand for Jack, Yazin, Susan's scores.
We are told that:
J = Y + 17 [Jack scored 17 marks more than Yazid]
S = 2Y [Susan scored twice Yazid's score]
J + Y + S = 161 [total score is 161]
Substitute the first two expressions into the last equation:
J + Y + S = 161
(Y+17) + Y + (2Y) = 161
4Y = 144
Y = 36
Use Y = 36 to find the other scores:
J = Y + 17
J = 36 + 17
J = 53
S = 2Y
S = 2*(36)
S = 72
CHECK:
Does 36+53+72 = 161?
YES
the central angle of the arc of 75
Answer:
75 degrees.
Step-by-step explanation:
Central angle = subtending arc.