Aiden gave each member of his family a playlist of random songs to listen to and asked them to rate each song between 0 and 10. He compared his family’s ratings with the release year of each song and created the following scatterplot:
What would the linear equation be?

Answer: To calculate the total amount a buyer should save each month to cover these fees, we need to add up all the costs and divide by 12 (the number of months in a year).

Annual real estate taxes = $2046

Insurance premiums = $1236

Flood insurance premiums = $380

Annual special assessment landfill fee = $125

Quarterly trash collection costs = $65 x 4 = $260

Annual homeowner's association fee = $720

Quarterly pool maintenance costs = $45 x 4 = $180

Monthly termite and pest protection costs = $39 x 12 = $468

Total annual costs = $2046 + $1236 + $380 + $125 + $260 + $720 + $180 + $468 = $5405

Total monthly costs = $5405 / 12 = $450.42

Therefore, a buyer should save $450.42 each month to cover these fees.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The data set in order is: 11, 13, 15, 19, 19, 21, 22, 22, 25, 26, 34, 34, 41, 43, 45, 48, 49, 50, 55, 58, 60, 62.

The seventh percentile is 15.

The twenty fifth percentile is 22.

The seventy ninth percentile is 58.

The option of bank B investment will allow to reach goal of buying the car the fastest compare to bank A it will take approximately 8.4 years

Saved amount = $15,000

Value of the car = $26,795

Use the formula for compound interest to calculate the time it will take to reach $26,795 for each bank,

Bank A,

Initial investment ' P ' = $15,000

Annual interest rate ' r ' =5.45%

                                       =  0.0545

compounded continuously  'n'  = infinity

Target amount  'A' = $26,795

The formula for continuous compounding is,

A = P[tex]e^{rt}[/tex]

Substituting the values, we get,

⇒ 26,795 = 15,000 × [tex]e^{(0.0545t)}[/tex]

Solving for t, we get,

⇒ t = (log(26,795/15,000))/(0.0545)

     ≈ 9.4 years

It will take approximately 9.4 years to reach the target amount if we invest in Bank A.

Bank B,

Initial investment ' P ' = $15,000

Annual interest rate ' r ' =5.75%/12

                                       =  0.00479 (monthly interest rate)

n = 12 compounded monthly

Target amount 'A' = $26,795

The formula for monthly compounding is,

A = [tex]P\times( 1+ r/n)^{nt}[/tex]

Substituting the values, we get,

26,795 = [tex]15,000 \times(1+0.00479/12)^{12t}[/tex]

Solving for t, we get,

t = (1/12) × (log(26,795/15,000))/(log(1+0.00479/12))

  ≈ 8.4 years

It will take approximately 8.4 years to reach the target amount if we invest in Bank B.

Therefore, investment in Bank B will allow you to reach your goal of buying the car the fastest, taking approximately 8.4 years.

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First, solve the expression inside the parentheses: (-28) - (+42) = -70

Next, subtract 3 from -70: -70 - (+3) = -73

The given expression can be simplified as follows:

[( -28 )-( +42)]-(+3) = -28 - 42 - 3 = -73

So, the answer to the given expression is -73.

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The probability of getting heads and an even number is 1/4, and the probability of getting tails and a prime number less than 4 is 1/6.

To solve this, we need to use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Let's first find the probability of getting heads and an even number. Since there are two equally likely outcomes when flipping a coin (heads or tails), and three equally likely outcomes when rolling a die (1, 2, 3, 4, 5, or 6), the probability of getting heads and an even number is:

P(heads and even) = P(heads) x P(even)

= 1/2 x 3/6

= 1/4

Next, let's find the probability of getting tails and a prime number less than 4. The prime numbers less than 4 are 2 and 3. So, the probability of getting tails and a prime number less than 4 is:

P(tails and prime) = P(tails) x P(prime)

= 1/2 x 2/6

= 1/6

Therefore, the probability that Oscar gets heads and an even number is 1/4, and the probability that Oscar gets tails and a prime number less than 4 is 1/6.

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Answer:

{51

Step-by-step explanation:

10^2 - 7^2= 51

You can’t square 51 because no two same whole numbers multiplied creates 51

B= 51

Check answer

7^2 + 51= 100

{100 = 10^2

The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.

The given function is:

d(t) = 40|t-1.25|

Here, t represents the time elapsed in hours and d represents the distance from the river in miles.

To find Mia's distance from the river, we need to plug in values of t into the function.

For example, if t=2, then:

d(2) = 40|2-1.25|

d(2) = 40|0.75|

d(2) = 30

So Mia's distance from the river after 2 hours of driving is 30 miles.

Similarly, we can find Mia's distance from the river at other points in time.

To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.

Graph of the function d(t) = 40|t-1.25|

The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.

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Answer:

C = 52

Step-by-step explanation:

sin(c/4) = sin(104/8)

sin(c/4) = 0.22495

c/4 = 13

c = 52

Each car on Mabel's train is a little less than half a foot long i.e., 3/8 feet long, or 0.375 feet long. This is solved by using simple mathematical operations.

To find the length of each car on Mabel's train, we can use the formula:

Total length of train = length of one car × number of cars

We are given that Mabel's train has 8 cars and is 3 feet long, so we can substitute those values into the formula and solve for the length of one car:

3 = x × 8

where x is the length of one car.

To solve for x, we can divide both sides by 8:

3/8 = x

Therefore, each car on Mabel's train is 3/8 feet long, or 0.375 feet long.

In other words, each car is a little less than half a foot long.

To help visualize this, imagine dividing the 3-foot length of the train into 8 equal parts. Each part would be 3/8 feet long, which is the length of one car. So when Mabel puts all 8 cars together, they form a train that is 3 feet long.

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These values (x4, y4) represent the coordinates of the missing vertex of Lana's square.

To determine the missing vertex of Lana's square, we need to know the location of the three given vertices. Let's assume that Lana plotted the vertices in a clockwise direction, starting from the top left.

If we denote the coordinates of the first vertex as (x1, y1), the second vertex as (x2, y2), and the third vertex as (x3, y3), then the coordinates of the missing vertex can be found as follows:

1. Calculate the distance between the first and second vertices:

d1 = sqrt((x2 - x1)^2 + (y2 - y1)^2)

2. Calculate the distance between the second and third vertices:

d2 = sqrt((x3 - x2)^2 + (y3 - y2)^2)

If the square is regular (i.e., all sides are of equal length), then d1 = d2. Otherwise, the shape is not a square.

3. Calculate the midpoint between the first and second vertices:

xm = (x1 + x2) / 2

ym = (y1 + y2) / 2

4. Calculate the vector that goes from the midpoint to the third vertex:

vx = x3 - xm

vy = y3 - ym

5. Calculate the coordinates of the missing vertex by adding the vector to the midpoint:

x4 = xm + vx

y4 = ym + vy

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Answer:

Ryan spent $72 on his shopping trip.

Step-by-step explanation:

To find out how much money Ryan spent, we need to add up the cost of the shirts and the sneakers.

First, we know that Ryan purchased two shirts for $16 each. So we can find the total cost of the shirts by multiplying the cost per shirt by the number of shirts:

So the total cost of the shirts is $32.

Next, we know that Ryan purchased a pair of sneakers that cost 2 1/2 times as much as a shirt. We can use this information to find the cost of the sneakers.

If the cost of a shirt is $16, then we can find the cost of the sneakers by multiplying $16 by 2 1/2:

So the cost of the sneakers is $40.

Finally, we can find the total cost of Ryan's shopping trip by adding up the cost of the shirts and the sneakers:

Therefore, Ryan spent $72 on his shopping trip.

One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.

The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.

At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.

By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)[tex])^12[/tex] pounds, using the formula for compound interest. This simplifies to (1+1/12[tex])^12[/tex] pounds or (1.0833[tex])^12[/tex] pounds, which is approximately equal to 2.613 pounds.

Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)[tex])^12[/tex] pounds or approximately 2.613 pounds by the end of the year.

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The measure of angle D is 25°

Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the opposite interior angles.

Angle D and angle C are the two opposite angles.

Therefore;

40+9x-2 = 20x +5

38+9x = 20x +5

38-5 = 20-9x

11x = 33

divide both sides by 11

x = 33/11

x = 3

Therefore since angle D = 9x-2

substitute 3 for x

D = 9(3) - 2

D = 27 -2

D = 25°

Therefore the measure of angle D is 25°

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The required answer is the double declining-balance method is $9,840.

To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:

Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400

Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate

The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.

Therefore:

Depreciation expense (2020) = $24,600 x 0.40 = $9,840

So the amount of depreciation expense for 2020, the second year of the asset's life,

using the double declining-balance method is $9,840.

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Mr. Ream has 7 cups of paint left in the bowl.

There are 12 cups of paint, which is equivalent to 192 fluid ounces of paint (1 cup = 16 fluid ounces). Mr. Ream filled 40 small dishes with 2 fluid ounces of paint each, for a total of 80 fluid ounces of paint used (40 x 2 = 80).

Therefore, Mr. Ream has 192 - 80 = 112 fluid ounces of paint left in the bowl.

To convert this to cups, we divide by 16 (1 cup = 16 fluid ounces):

112/16 = 7 cups

Therefore, Mr. Ream has 7 cups of paint left in the bowl.

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Answer:

Si Antoni comió 7/9 del pan francés y Miguel Eduardo comió 5/9, entonces la cantidad total de pan que comieron juntos es 7/9 + 5/9 = 12/9.

Esto significa que los tres amigos comieron 12/9 del pan, lo cual es equivalente a 4/3 del pan francés.

Para encontrar la cantidad de pan que quedó para Fabian, podemos restar 4/3 del pan francés de la cantidad total del pan francés, que es 1. Entonces:

1 - 4/3 = 3/3 - 4/3 = (3 - 4)/3 = -1/3

Esto significa que Antoni y Miguel Eduardo comieron más del pan francés de lo que había disponible, lo que no es posible. Por lo tanto, no hay una cantidad del pan francés que quedó para Fabian.

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Answer:

[tex] \: \frac{11}{1620} \: \pi^{2} [/tex]

Step-by-step explanation:

I think this is it. But if you find a mistake somewhere let me know? I'm confused because the answer seems a little weird. Like 11/1620 pi² really?

Also at the bottom I wrote "area of sector =" but the area got cut off

The frog will travel a total distance of 1650 cm before she cannot jump anymore. None of the options given are correct.

To find the total distance the frog will travel, we need to add up the distances of all her jumps. Given that her first jump is her longest at 300 cm and her second jump is 270 cm, we can assume that each subsequent jump is shorter than the one before it.

The difference between the first jump and the second jump is 30 cm. So let's assume that the common difference between each jump is 30 cm. So the frog takes a total of 10 jumps before she cannot jump anymore.

The total distance the frog will travel is:

300 + 270 + (240 + 210 + 180 + 150 + 120 + 90 + 60 + 30) = 1650 cm

So here none of the options are correct.

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The t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is

(a) Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 is ±1.711.

To find the t-test statistic value for a given P-value and alternative hypothesis, we need to use a t-distribution table or a statistical software program. Here, we will use a t-distribution table to find the t-test statistic value for a sample of 24 observations and a P-value of 0.10 for each alternative hypothesis.

(a) Ha: μ ≠ 0 (two-tailed test)

The critical t-value for a two-tailed test with a P-value of 0.10 and degrees of freedom (df) of 23 (sample size - 1) is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

(b) Ha: μ > 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = 1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ > 0 is 1.319.

(c) Ha: μ < 0 (one-tailed test)

The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:

t = -1.319

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ < 0 is -1.319.

(d) Ha: μ ≠ 0 (two-tailed test)

To find the t-test statistic value when Ha: μ ≠ 0, we can use the inverse t-distribution function in a statistical software program or a calculator. The t-test statistic value that corresponds to a P-value of 0.10 with 23 degrees of freedom is:

t = ±1.711

Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.

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The derivative of the function f(x) = [tex]x^{0,9}[/tex] is f'(x) = [tex]0.9x^{-0.1}[/tex].

To find the derivative of f(x), we use the power rule of differentiation, which states that if f(x) = [tex]x^n[/tex], then f'(x) = [tex]nx^{(n-1)}[/tex].

In this case, we have f(x) = [tex]x^{0,9}[/tex]. Applying the power rule, we get:

f'(x) = [tex]0.9x^{0.9-1} = 0.9x^{-0.1}[/tex]

Note that [tex]x^{-0.1}[/tex] can be rewritten as [tex]1/x^{0.1}[/tex]. So we have:

f'(x) =[tex]0.9/x^{0.1}[/tex]

This expression tells us the slope of the tangent line to the curve of f(x) at any given point. For example, at x = 1, we have:

f'(1) = [tex]0.9/1^{0.1} = 0.9[/tex]

This means that the slope of the tangent line to the curve of f(x) at x = 1 is 0.9. As x increases or decreases from 1, the slope of the tangent line changes accordingly.

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The total population of all three states combined is 24,126,000 or 2.4126 × 10⁷ in scientific notation.

To find the total population of all three states combined, we simply need to add up the population of each state. In this case, we are given the populations of Connecticut, New York, and Rhode Island, so we can simply add those numbers together to get the total population.

When working with numbers that are very large or very small, scientific notation can be a helpful way to express them. In scientific notation, a number is expressed as a coefficient multiplied by a power of 10. The coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 indicates how many places the decimal point has been moved to create the coefficient.

In this problem, we are given the populations of the three states in scientific notation. Connecticut's population is given as 3.6 × 10⁶, which means that the coefficient is 3.6 and the power of 10 is 6. To convert this number to standard notation, we simply move the decimal point 6 places to the right to get 3,600,000. Similarly, New York's population is given as 1.947 × 10⁷, which means that the coefficient is 1.947 and the power of 10 is 7, and Rhode Island's population is given as 1.056 × 10⁶, which means that the coefficient is 1.056 and the power of 10 is 6.

To find the total population, we add the populations of the three states together:

Total population = Connecticut population + New York population + Rhode Island population

Total population = 3.6 × 10⁶ + 1.947 × 10⁷ + 1.056 × 10⁶

Total population = (3.6 + 19.47 + 1.056) × 10⁶

Total population = 24.126 × 10⁶

We can simplify this expression by multiplying the coefficient by 10⁶:

Total population = 24.126 × 10⁶ = 2.4126 × 10⁷

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The estimated surface area of the bead is 52π square millimeters.

To estimate the  face area of the blob, we need to find the  face area of the sphere and abate the  face area of the spherical hole.   The  face area of a sphere is given by the formula   A =  4πr2   where r is the compass of the sphere.

 The radius of the sphere is: r = 8 mm / 2 = 4 mm.

The surface area of the sphere is: S_sphere = 4π[tex]r^{2}[/tex] = [tex]4π(4 mm)^{2}[/tex] =64 [tex]mm^{2}[/tex]

The radius of the cylinder is: r = 2 mm / 2 = 1 mm.

The height of the cylinder is: h = 8 mm - 2 mm = 6 mm.

The surface area of the cylinder is: S_cylinder = 2πrh = 2π(1 mm)(6 mm) = 12π [tex]mm^{2}[/tex]

The estimated surface area of the bead is: S_bead = S_sphere - S_cylinder = 64π [tex]mm^{2}[/tex] - 12π [tex]mm^{2}[/tex] = 52π [tex]mm^{2}[/tex]

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Answer:

Step-by-step explanation:

you multiply 5 by 50 and that would equal 250

5 x 50 = 250

Answer:

It's 14⁹.

Add the powers in the process of multiplying.

Which is -3 + 12 answer is 9.

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The family with 8 pets cannot be used to represent the whole because it is an outlier

Given that we have

A dot plot that represents the display

On the dot plot, we have

Outlier = 8

This data value is considered an outlier because it is relatively far from other values

As a general rule, outliers cannot be used to represent the whole

Here, we have

Of the three displays, the bar chart is used to represent data such that users may readily recognize patterns or trends.

So, the bar chart is to be used

Here, we have

Of the three displays, the circle graph does not show that users  patterns or trends.

So, the circle graph is to be used

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The perimeter of the 8 feet by 6 feet rectangular garden is 28 feet.

We will need to install chicken wire along this entire length to satisfy the customer's requirements. Good luck with your project!

To find the perimeter of a rectangular garden, you can use the formula:

Perimeter = 2(Length + Width). In this case, the garden measures 8 feet by 6 feet,

so the length is 8 feet and the width is 6 feet.
Add the length and width.
8 feet + 6 feet = 14 feet
Multiply the sum by 2.
2(14 feet) = 28 feet.
The perimeter of the rectangular garden is 28 feet.

As a contractor, you will need to install chicken wire along this entire 28 feet of the garden's perimeter to meet the customer's request.
Remember to choose the appropriate type of chicken wire, considering factors such as durability, mesh size, and material (e.g., galvanized steel or plastic).

Additionally, we may need to install supporting posts at regular intervals to ensure the stability and effectiveness of the chicken wire fence.

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5.13 U. S. Dollars will it cost to buy a gallon of gas in Canada. The correct answer to the question is A

Given in the question,

Cost of 1 liter gasoline = 1.50 Canadian dollars

1 gallon = 3.8 liters

Thus, to calculate the price of 1 gallon we multiply the cost of 1 liter by 3.8

Cost of 3.8 liters of gasoline = 1.5 * 3.8

= 5.70 Canadian dollars

1 Canadian dollar = 0.9 U. S. dollars

5.70 Canadian dollars = 5.70 * 0.9

= 5.13 U. S. dollars

That is the cost of 1 gallon of gas in Canada is 5 U S dollars and 13 cents.

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The result of this equation will give us the numerical value representing the difference between the amounts Anna ate and the amount she gave to her brother. In this case, the difference would be 20.

To find the difference between the amount of orange Anna ate and the amount she gave to her brother, we can use the equation: 58 - 38 = x
Here, x represents the difference between the two amounts. We can solve for x by subtracting 38 from 58.
58 - 38 = 20

Therefore, the difference between the amount of orange Anna ate and the amount she gave her brother is 20. Anna ate 58 of an orange and gave 38 to her brother, so the remaining 20 must be the difference between the two amounts.

In summary, the equation that can be used to find the difference between the amount Anna ate and the amount she gave her brother is 58 - 38 = x, where x represents the difference. The answer is 20.

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Step-by-step explanation:

5 + 6 + 3   = 14 marbles     5 are red

1st marble red =  5 out of 14   = 5/14

 now there are 13 marbles   4 are red

     2nd marble red             4/13

         and finally ,  3rd marble red = 3/12

5/14  * 4/13  * 3/12 =   5/182  chance for three reds

Answer:

  5.  0

  6. a: π/3; b: 45π/2 m ≈ 70.69 m; c: 30/π min ≈ 9.549 min; d: π/900 rad/s; e: 0.2°/s

Step-by-step explanation:

You want the exact value of cos(-39π/6), and some angles, distances, and speeds related to the London Eye Ferris wheel.

The argument of the cosine function can be reduced:

  [tex]\cos{\left(-\dfrac{39\pi}{6}\right)}=\cos{\left(\dfrac{13\pi}{2}\right)}\qquad\text{using cos(-x)=cos(x)}[/tex]

We notice this is an odd multiple of π/2, so its value is 0.

  cos(-39π/6) = 0

The rate of movement is given as 2π radians (one revolution) in 30 minutes. Then the angle in 5 minutes is ...

  (5 min)(2π rad)/(30 min) = (2π/6) rad = π/3 rad

The passenger will travel π/3 radians in 5 minutes.

The arc length is given by ...

  s = rθ . . . . . . where r is the radius and θ is the central angle in radians

For a radius of (135/2 m) and an angle of π/3 radians, the distance traveled is ...

  s = (135/2 m)(π/3) = 45π/2 m ≈ 70.69 m

We know that 2π radians takes 30 minutes, so the time for 2 radians is ...

  t = (2 rad)·(30 min)/(2π rad)

  t = 30/π min ≈ 9.549 min . . . . about 9:32.96 min

The angular velocity is ...

  (2π rad)/(30 min) = (2π rad)/(30 min) × (1 min)/(60 s) = 2π/1800 rad/s

  = π/900 rad/s

360 degrees in 1800 seconds is ...

  360°/(1800 s) = (1/5)°/s

The wheel turns at the rate of 1/5 degree per second.

__

Additional comment

At one revolution per half hour, the wheel turns about twice as fast as the minute hand on a clock. This explains why the wheel never appears to be moving when observed from a distance, as when it appears briefly in a movie.