solve m^4 =625
m= +156.5
m= +5
m cannot be found
m= +125
Please look at picture

Answer:

Solving the inequality for y in 37<7 would be

y<2

The mean of the data-set in this problem is given as follows:

19.56 pounds.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The dot plot shows the number of times that each observation appears, hence the observations are given as follows:

Hence the mean is given as follows:

Mean = (2 x 12 + 4 x 15 + 1 x 16 + 1 x 18 + 2 x 20 + 1 x 22 + 3 x 25 + 2 x 29)/(2 + 4 + 1 + 1 + 2 + 1 + 3 + 2)

Mean = 313/16

Mean = 19.56 pounds.

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The correct answer is (a) $160.

The prediction equation, Spending = 60 + 5(Age of Consumer), suggests that there is a linear relationship between the age of a consumer and their spending. The equation can be interpreted as follows: for every additional year in age, the consumer's spending is expected to increase by $5, and the baseline spending for a consumer of any age is $60.

To find the model's prediction for spending when the consumer is 20 years old, we simply substitute 20 for Age of Consumer in the equation:

Spending = 60 + 5(20) = 60 + 100 = $160

Therefore, the correct answer is (a) $160.

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If a man swimming in a stream which flows 4 Km/h finds that in a given time he can swim 5 times as far at 12 km/h rate he can swim.

Production of upstream oil and gas is carried out by businesses that locate, mine, or create raw resources. The end-user or customer is closer to the production of oil and gas in the downstream sector. Here is a look at the upstream and downstream production of oil and gas, their individual roles, and how they fit into the larger supply chain.

Let's take swimmer speed  = x km/h.

The time is taken by the swimmer = t

The speed of the stream = 4 km/h

The speed when swimming with the stream = x+ 4 km/h

The distance covered when swimming with the stream D₁= (x+4)t

The speed when swimming against the stream = x -4

The distance covered when swimming against the stream D₂= (x-4)t

The swimmer swims 5 times when swimming against the stream

Therefore,

D₁ = 5D₂

(x+4)t = 2((x-4)t)

x+4 = 2x- 8

x = 12 km/h

12 km/h is the speed of the swimmer.

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The circumference of the area of a circle is 4π in² using the formula A = πr², in inches is 4π inches.

The formula for the area of a circle is A = πr², where A is the area and r is the radius. Given that the area is 4π in², we can solve for the radius by taking the square root of both sides:

√(A/π) = √(4π/π) = 2 in

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Substituting the value of r, we get:

C = 2π(2 in) = 4π in

Therefore, the circumference of the circle is 4π inches.

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Answer:

Informative!

Step-by-step explanation:

The correct statement is,

⇒ The unknown number is 27.

We have to given that;

Maria is solving this number riddle by using guess and check:

⇒ Fifteen less than a number is twelve.\

Now, We can write as;

⇒ x - 15 = 12

Solve for x;

⇒ x = 15 + 12

⇒ x = 27

Thus, The correct statement is,

⇒ The unknown number is 27.

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a. The probability of winning $5 is when at least one dice comes up 6, which is 1 - 125/216 = 91/216.

b. The standard deviation of X is the square root of the variance:

SD(X) = √(9.828) = 3.135

c. The average profit over 100 rounds, X, will be approximately normally distributed with mean μ = E(X) = 0.6944 and standard deviation σ = SD(X)/√(n) = 3.135/√(100) = 0.3135.

d. The probability that Y is at most $80 is approximately 0.6325.

Probability is a measure of how likely an event is to occur. Many events are impossible to forecast with absolute accuracy. We can only anticipate the possibility of an event occurring, i.e. how probable they are to occur, using it.

(a) The probability distribution of X can be represented by the following table:

| X      | -1    | 5     |

|--------|------|-------|

| P(X=x) | 125/216  | 91/216 |

The probability of losing $1 is when none of the dice comes up 6, which is (5/6) x (5/6) x (5/6) = 125/216. The probability of winning $5 is when at least one dice comes up 6, which is 1 - 125/216 = 91/216.

(b) The expectation of X can be calculated as:

E(X) = (-1) x (125/216) + (5) x (91/216) = 0.6944

The variance of X can be calculated as:

Var(X) = [(−1 − 0.6944)² × 125/216] + [(5 − 0.6944)² × 91/216] = 9.828

The standard deviation of X is the square root of the variance:

SD(X) = √(9.828) = 3.135

(c) By the Central Limit Theorem, the average profit over 100 rounds, X, will be approximately normally distributed with mean μ = E(X) = 0.6944 and standard deviation σ = SD(X)/√(n) = 3.135/√(100) = 0.3135.

(d) Let Y be the total profit over 100 rounds. Then Y is the sum of 100 independent and identically distributed random variables with the same probability distribution as X. Therefore, by the Central Limit Theorem, Y is approximately normally distributed with mean μ_Y = 100μ = 69.44 and standard deviation σ_Y = √(100)σ = 31.35.

To find the probability that Y is at most $80, we standardize the variable:

Z = (80 - μ_Y)/σ_Y = (80 - 69.44)/31.35 = 0.337

Using a standard normal distribution table or calculator, we find that the probability of Z being less than or equal to 0.337 is 0.6325. Therefore, the probability that Y is at most $80 is approximately 0.6325.

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We are given two sets A and B, and we are asked to describe some sets that can be formed using these sets. We will use set operations such as union and intersection to form new sets and provide descriptions of these sets in words.

a. A ∩ B: This set includes all current students who are attending both ABC and Harvard at the same time.

b. A ∪ B: This set includes all current students who are attending either ABC, Harvard, or both.

c. A ∩ B: (same as 'a') This set includes all current students who are attending both ABC and Harvard at the same time.

d. (A ∩ B): (same as 'a') This set includes all current students who are attending both ABC and Harvard at the same time.

e. (A ∪ B): (same as 'b') This set includes all current students who are attending either ABC, Harvard, or both.

3. Let A = {2 ∈ Z | x = 6a for some integer a} and B = {y ∈ Z | y = 36 for some integer b}. To prove that A ⊂ B, we need to show that every element of A is also an element of B.

Let x be an arbitrary element of A.

Since x = 6a for some integer a, we can write x as 6a = 2 * 3a.

Because 3a is also an integer (since a is an integer), we can say x = 2 * (3 * a), which implies x = 36 * a for some integer a. Thus, x ∈ B.

Since every element of A is also an element of B, we have proven that A ⊂ B.

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Answer: Answer:

3. For some x-values, the y-value of the exponential function is smaller.

4. For some x-values, the y-value of the exponential function is greater.

5. For any x-value greater than 7, the y-value of the exponential function is greater.

Step-by-step explanation:

We are given the functions,

It is required to find the true statements of the functions.

From the graphs of the functions below, we have that the graphs intersect at the point (6.32,79.878).

To the left of the point, we have that the exponential function have smaller y-values than the parabola.

To the right of the point, we have that the exponential function have greater y-values than the parabola.

Moreover, after x= 7, the y-values of the exponential function are always greater than parabola.

Thus, the correct options are 3, 4 and 5.

Step-by-step explanation:

Answer:

- For any x-value, the y-value of the exponential function is always greater. (False)

- For any x-value, the y-value of the exponential function is always smaller. (False)

- For some x-values, the y-value of the exponential function is smaller. (True)

- For some x-values, the y-value of the exponential function is greater. (True)

- For any x-value greater than 7, the y-value of the exponential function is greater. (Not enough information provided to determine)

- For equal intervals, the y-values of both functions have a common ratio. (False)

The constant of proportionality between d and h is 3.75

Any function in which the dependent variable (y) is obtained by multiplying the independent variable (x) by a constant value is called the direct proportionality function. This function is also expressed in the form  [tex]( y = m * x)[/tex] and is more commonly called a linear function.

The value m is a constant and is known as the constant of proportionality or the slope of the line. It represents the inclination of the line to the abscissa axis, that is, the x-axis. If we talk about graphic representation, this linear function is a line with slope m that passes through the origin of coordinates, that is, the point 0 in x and 0 in y, which is the point (0,0).

Bethany finds the distance d with the help of equation d = 3.75*h, she travels this distance while walking for h number of hours.  When we compare it with the direct proportionality function y = m * x, then y is represented by the distance d, x is represented by the number of hours h, and slope m or the constant of proportionality is the number 3.75.

So, the constant of proportionality between d and h is 3.75.

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The events "model YZ-99 is chosen" and "model XB-50 is chosen", these would be mutually exclusive events, because a bike cannot be both models at the same time.

a. To find the probability that a mountain bike is brown using the relative frequency assessment method, we need to divide the number of brown mountain bikes by the total number of mountain bikes:

Total number of brown mountain bikes = 105 + 205 = 310

Total number of mountain bikes = 302 + 105 + 200 + 40 + 205 + 130 = 982

Therefore, the probability that a mountain bike is brown is:

P(brown) = 310/982 ≈ 0.316

b. To find the probability that the mountain bike is a YZ-99, we need to divide the total number of YZ-99 bikes by the total number of mountain bikes:

Total number of YZ-99 bikes = 40 + 205 + 130 = 375

Therefore, the probability that the mountain bike is a YZ-99 is:

P(YZ-99) = 375/982 ≈ 0.382

c. To find the joint probability that a randomly selected mountain bike is a YZ-99 and brown, we need to find the number of YZ-99 bikes that are also brown, and divide by the total number of mountain bikes:

Number of YZ-99 bikes that are brown = 205

Total number of mountain bikes = 982

Therefore, the joint probability that a randomly selected mountain bike is a YZ-99 and brown is:

P(YZ-99 and brown) = 205/982 ≈ 0.209

d. Two events are mutually exclusive if they cannot occur at the same time. In this case, the events "model YZ-99 is chosen" and "a white product is chosen" are not mutually exclusive, because there are white YZ-99 bikes. Therefore, it is possible for both events to occur at the same time.

However, if the question was about the events "model YZ-99 is chosen" and "model XB-50 is chosen", these would be mutually exclusive events, because a bike cannot be both models at the same time.

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This is because there are mountain bikes that are both YZ-99 and white, so it is possible to choose a mountain bike that belongs to both events at the same time.

a. Based on the relative frequency assessment method, the probability that a mountain bike is brown is:

Total number of brown bikes / Total number of bikes

= (105 + 205) / (302 + 105 + 200 + 40 + 205 + 130)

= 310 / 982

= 0.3156 (rounded to 4 decimal places)

So the probability that a mountain bike is brown is 0.3156.

b. The probability that the mountain bike is a YZ-99 is:

Total number of YZ-99 bikes / Total number of bikes

= (40 + 205 + 130) / (302 + 105 + 200 + 40 + 205 + 130)

= 375 / 982

= 0.3819 (rounded to 4 decimal places)

So the probability that the mountain bike is a YZ-99 is 0.3819.

c. The joint probability that a randomly selected mountain bike is a YZ-99 and brown is:

Number of brown YZ-99 bikes / Total number of bikes

= 205 / 982

= 0.2088 (rounded to 4 decimal places)

So the joint probability that a randomly selected mountain bike is a YZ-99 and brown is 0.2088.

d. The events "model YZ-99 is chosen" and "a white product is chosen" are not mutually exclusive. This is because there are mountain bikes that are both YZ-99 and white, so it is possible to choose a mountain bike that belongs to both events at the same time.

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Answer: 23/45 or 0.51 rounded to the nearest hundredth

Step-by-step explanation:

4 1/9 can be written as 37/9, and 3 3/5 can be written as 18/5.

37/9-18/5 = (185/45) - (162/45) = 23/45 or 0.51

The 90% confidence interval for a sample of size 277 with 57 successes is (0.157, 0.255).

To find the confidence interval for a population proportion, we can use the following formula:

CI = p ± zsqrt(p(1-p)/n)

where CI is the confidence interval, p is the sample proportion, z is the z-score for the desired confidence level, and n is the sample size.

Since we want a 90% confidence interval, we need to find the z-score that corresponds to a 5% level of significance on each tail of the normal distribution. Using a z-table or calculator, we find that z = 1.645.

Plugging in the given values, we get:

CI = 0.206 ± 1.645sqrt(0.206(1-0.206)/277)

Simplifying this expression, we get:

CI = (0.157, 0.255)

Therefore, the 90% confidence interval for a sample of size 277 with 57 successes is (0.157, 0.255).

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The solution to this system of equations is dependent.

Dependent matrix is a matrix where one or more rows can be expressed as a linear combination of the other rows. This means that the rows are not linearly independent, and there is redundancy in the information they provide.

A dependent matrix has less than full rank, which means that the rank of the matrix is less than the number of rows or columns. In a dependent matrix, one or more variables can be expressed in terms of the other variables, and the system of equations represented by the matrix has infinitely many solutions.

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The equation x² + 2x + __ = (__)² should be completed by the following:

D. 1; x + 1.

x² + 2x + 1 = (x + 1)²

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² + 2x + (2/2)² = (2/2)²

x² + 2x + (1)² = (1)²

x² + 2x + 1 = (x + 1)²

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The probability that 3 of the next 10 households that a student visits will purchase a raffle ticket is 25%

From the question, we have the following parameters that can be used in our computation:

The probability is calculated as

P(x) = nCx * p^x * (1 - p)^(n -x)

Where

n = 10

p = 25%

x = 3

Substitute the known values in the above equation, so, we have the following representation

P(3) = 10C3 * (25%)^3 * (1 - 25%)^(10 -3)

Evaluate

P(3) = 0.25

Hence, the probability value is 25%

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Answer:

C) g(x) = f(x) + 4

Step-by-step explanation:

A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A

-anumber would slide the function DOWN instead.

As for the other answers:

A) the 3multiplied in front is a vertical STRETCH.

D) the 1/2 multiplied in front is a vertical shrink (smash)

B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.

The exact values of the variables are;

x = 9

y =14.5

To determine the value of the variables, we have that the trigonometric identities are;

From the diagram shown, we can se that the triangle is an isosceles triangle

An  isosceles triangle has two of its sides and angles equal to each other.

Then, the value of the variable x would be;

x = 18/2 = 9

Using the Pythagorean theorem;

15²- 9² = y²

find the square value

y² = 225 - 16

y² = 209

Find square root

y = 14. 5

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The inverse of matrix A is:

A^-1 = |-3 -2|

|-2 -1|

Using Adjoint of a Matrix A=2 -1 0

0 1 2

1 1 0

The first step is to find the determinant of the matrix A:

|A| = 2(10 - 21) - (-1)(10 - 12) + 0(11 - 10)

= 4 + 2 + 0

= 6

Next, we need to find the adjoint of matrix A, which is the transpose of its cofactor matrix. The cofactor matrix is obtained by taking the determinant of the submatrix obtained by removing each element of the original matrix in turn and multiplying it by (-1)^(i+j), where i and j are the row and column indices of the removed element, respectively.

Cofactor matrix of A is

| 1 2 -1|

|-2 0 2|

|-1 2 1|

Taking the transpose of the cofactor matrix, we get the adjoint matrix of A as follows:

A^T = | 1 -2 -1 |

| 2 0 2 |

|-1 2 1 |

To find the inverse of A, we use the formula:

A^-1 = (1/|A|) A^T

Substituting the values, we get:

A^-1 = (1/6) | 1 -2 -1 |

| 2 0 2 |

|-1 2 1 |

Using Gauss Jordan A= |1 3|

|2 5|

We can find the inverse of a matrix using Gauss-Jordan elimination method as follows:

|1 3|1 0| |1 3|0 1|

|2 5|0 1|-> |0 1|-2/3 -1/3|

Therefore, the inverse of matrix A is:

A^-1 = |-2/3 -1/3|

| 1/3 1/3|

Using Equations and Identity Matrix A= |1 -2|

|2 -3|

We can find the inverse of a matrix A using the equations AX=I, where I is the identity matrix and X is the matrix that represents the inverse of A. The solution is given by:

|1 -2| |x11 x12| |1 0|

|2 -3| |x21 x22| = |0 1|

Multiplying the matrices, we get:

x11 = -3

x12 = -2

x21 = -2

x22 = -1

Therefore, the inverse of matrix A is:

A^-1 = |-3 -2|

|-2 -1|

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Suppose A and B are dependent events. If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

The probability of an event is described as a number that indicates how likely the event is to occur which is usually  expressed as a number in the range from 0 and 1, or preferably using percentage notation ranging  from 0% to 100%.

The relationship between two dependent events is expressed in the following equation below according to the rules of probability,

P(A|B) = P(A∩B) / P(B)

we then substitute ,

0.25 = P(A∩B) / 0.8

P(A∩B)  = 0.2

In conclusion, If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

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The minimum sample size that should be taken to be 90% confident that the sample mean is within 17 emails of the true population mean is 82.

To find the minimum sample size required to estimate a population mean with a given confidence level, we need to use the following formula:

n = (Z * σ / E)^2

where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level (90% in this case)
- σ is the population standard deviation (94 emails)
- E is the margin of error (17 emails)

First, find the Z-score for a 90% confidence level. You can do this by checking a Z-table or using a calculator. For a 90% confidence level, the Z-score is approximately 1.645.

Now, plug the values into the formula:

n = (1.645 * 94 / 17)^2
n ≈ (153.63 / 17)^2
n ≈ 9.036^2
n ≈ 81.65

Since we cannot have a fraction of a person, round up to the nearest whole number. Therefore, the minimum sample size that should be taken to be 90% confident that the sample mean is within 17 emails of the true population mean is 82.

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The volume of the solid that lies within both the cylinder x2+y2=9 and the sphere x2+y2+z2=49 using cylindrical coordinates is: ∫∫∫ dV = 2∫0^2π ∫0^3 r√(49-r2) dr dθ = 2(229/3)π = 458/3π.

To find the volume of the solid that lies within both the cylinder x2+y2=9 and the sphere x2+y2+z2=49 using cylindrical coordinates, we first need to rewrite the equations in terms of cylindrical coordinates.

Recall that in cylindrical coordinates, a point is specified by (r,θ,z), where r is the distance from the origin to the point in the xy-plane, θ is the angle between the positive x-axis and the line segment connecting the origin to the point, and z is the vertical distance from the point to the xy-plane.

For the cylinder x2+y2=9, we have r2 = x2 + y2 = 9, so r = 3.

For the sphere x2+y2+z2=49, we have x2 + y2 = 49 - z2, so r2 = 49 - z2.

Therefore, the solid lies within the cylinder x2+y2=9 and the sphere x2+y2+z2=49 if and only if 0 ≤ r ≤ 3 and -√(49-r2) ≤ z ≤ √(49-r2).

To find the volume of the solid, we integrate over the region:

∫∫∫ dV = ∫0^2π ∫0^3 ∫-√(49-r2)^√(49-r2) r dz dr dθ

= ∫0^2π ∫0^3 r(√(49-r2) + √(49-r2)) dr dθ

= ∫0^2π ∫0^3 2r√(49-r2) dr dθ

= 2∫0^2π ∫0^3 r√(49-r2) dr dθ

(We can drop the factor of 2 since the integrand is even in r.)

To evaluate the integral, we use the substitution u = 49 - r2, du/dr = -2r:

∫0^3 r√(49-r2) dr = -∫49^40 1/2 √u du

= -(1/3)u3/2 |49^4

= (1/3)(49√49 - 4√4)

= (1/3)(49(7) - 4(2))

= 229/3

Therefore, the volume of the solid that lies within both the cylinder x2+y2=9 and the sphere x2+y2+z2=49 using cylindrical coordinates is:

∫∫∫ dV = 2∫0^2π ∫0^3 r√(49-r2) dr dθ = 2(229/3)π = 458/3π.

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Using the distance formula, the perimeter of the quadrilateral PQRS is equal to 15.6 to the nearest tenth.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is given by the following formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²],

where d is the distance between the points (x₁, y₁) and (x₂, y₂).

we shall evaluate the distance between the points PS and QR as follows:

distance between P and S = √[[1 - (-3)]² + (1 - 3)²]

distance between P and S = √20

distance between P and S = 4.5

distance between Q and R = √[[1 - (-3)]² + [-1 - (-2)]²]

distance between Q and R = √17

distance between Q and R = 4.1

Thus; PQ =5, SR = 2, PS = 4.5, and QR = 4.1

perimeter of quadrilateral PQRS = 5 + 2 + 4.5 + 4.1

perimeter of quadrilateral PQRS = 15.6.

Therefore, using the distance formula, the perimeter of the quadrilateral PQRS is equal to 15.6 to the nearest tenth.

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The arc length of this 60 degree central angle in a circle with radius 5 units is 5π/3 units.

In geometry, a central angle is an angle whose vertex is at the center of a circle and whose rays intersect the circle at two distinct points, creating an arc between them.

A central angle is an angle whose vertex is at the center of a circle and whose rays intersect the circle at two distinct points, creating an arc between them.

Central angles can be classified into two types: minor central angles and major central angles. A minor central angle is an angle that intercepts a minor arc, while a major central angle is an angle that intercepts a major arc.

The arc measure is the degree measure of the arc between the two points where the central angle intersects the circle.

The arc length is the actual length of the arc itself, and it depends on both the radius of the circle and the degree measure of the arc. The formula is:

[tex]Arc length = (arc measure/360)[/tex] x [tex]2\pi r[/tex]

For example, if a central angle of a circle has a measure of 60 degrees and the radius of the circle is 5 units, then the arc measure is also 60 degrees, and the arc length can be calculated as:

[tex]Arc length = (60/360)[/tex] x [tex]2\pi (5)[/tex]

[tex]= (1/6)[/tex] x [tex]10\pi[/tex]

[tex]= 5\pi /3[/tex] units

So the arc length of this 60 degree central angle in a circle with radius 5 units is 5π/3 units.

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Yes, snow and "cold" weather are independent events. The probability of snow and a "cold" day is 15.

Based on the given probabilities, we can determine if snow and "cold" weather are independent events. Independent events occur when the probability of both events happening together is equal to the product of their individual probabilities.

P(snow) = 0.30
P(cold) = 0.50
P(snow and cold) = 0.15

If snow and cold are independent, then P(snow and cold) = P(snow) * P(cold).

0.15 = 0.30 * 0.50
0.15 = 0.15

Since both sides of the equation are equal, snow and "cold" weather are independent events.

Your answer: b. yes

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(a) Letting X1, ..., Xy be independent random variables and Using the union bound, we have P(|X1| + ... + |XN| ≥ t) ≤ P(|X1| ≥ t/N) + ... + P(|XN| ≥ t/N) ≤ 2N[tex]e^{(-tε/N)}[/tex] for all t > 0.

(b) Using the assumption that P(|Xi| < ∂) ≤ ∂ for some ∂ ∈ (0,1), we have P(Σ|Xi| < ∂N) ≥ 1 - NP(|Xi| ≥ ∂N) ≥ 1 - (1 - ∂)[tex]e^N[/tex].

Setting t = 2N[tex]e^ε[/tex], we obtain

which is equivalent to

By setting ∂ = 2Ne**ε/N, we get

P(Σ|Xi| < ∂) ≥ 1 - e**(-ε), and therefore,

Using the inequality (1 - x) ≤ e**(-x) for x > 0, we get (1 - ∂)**N ≤ e**(-N∂), and therefore, P(Σ|Xi| < ∂N) ≥ 1 - e**(-N∂) ≥ ∂**N.

Thus, we have shown that NP(Σ|Xi| < ∂N) ≥ ∂**N for some ∂ ∈ (0,1) and P(|X1| + ... + |XN| ≥ t) ≤ P(|X1| ≥ t/N) + ... + P(|XN| ≥ t/N) ≤ 2N[tex]e^{(-tε/N)}[/tex] for all t > 0

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The angle subtended by an arc 1.60 m in length on the circumference of a circle of radius 2.50 m is approximately 115.2°.

To find the angle subtended by an arc of 1.60 m in length on the circumference of a circle with a radius of 2.50 m, you can follow these steps:

Recall the formula for the length of an arc: Arc Length = (Central Angle × Radius)/180°, where the central angle is in degrees and the radius is in meters.

Rearrange the formula to solve for the central angle: Central Angle = (Arc Length × 180°) / Radius

Plug in the given values: Central Angle = (1.60 m × 180°) / 2.50 m

Calculate the result: Central Angle = (1.60 × 180) / 2.50 ≈ 115.2°

The angle subtended by an arc 1.60 m in length on the circumference of a circle of radius 2.50 m is approximately 115.2°.

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