Two similar cylinders have heights 6cm and 30cm. The volume of the smaller cylinder is 90cm3. What is the volume of the larger cylinder?

Answer: 10 pencils and 5 notebooks.

Step-by-step explanation:

       We will create a system of equations using the information given. Let n be equal to the number of notebooks and p be equal to the number of pencils.

She spent $23.25 on notebooks and pencils. Notebooks cost $2.49 each and pencils cost $1.08 each.

       $2.49n + $1.08p = $23.25

She bought a total of 15 notebooks and pencils.

       n + p = 15

Next, we will solve for p by substituting.

       n + p = 15 ➜ n = 15 - p

       $2.49n + $1.08p = $23.25

       $2.49(15 - p) + $1.08p = $23.25

       $37.35 - $2.49p + $1.08p = $23.25

       $37.35 - $1.41p =  $23.25

       -$1.41p =  -$14.10

       p = 10 pencils

Lastly, we will solve for n by substituting:

       n = 15 - p

       n = 15 - 10

       n = 5

The volume of the pyramid is approximately 41.67 cubic meters.

To find the volume of the pyramid, we can use the formula:

V = (1/3) x base area x height

Since the base of the pyramid is a square with side length 5 meters, its area is:

base area = side² = 5² = 25 square meters

The height of the pyramid is also given as 5 meters.

Now, we need to find the area of one of the square cross-sections. Since the pyramid has congruent triangular sides, we know that each of these triangles is similar to the original base square.

Therefore, the side length of each square cross-section is proportional to the height of the pyramid, and we can use the ratio of corresponding side lengths to find the area of one of the squares:

5 / 5 = x / 5

where x is the side length of the square cross-section.

Solving for x, we get:

x = 5

Therefore, each of the square cross-sections has an area of 5 x 5 = 25 square meters.

Now, we can substitute the values we have found into the formula for the volume:

V = (1/3) x base area x height

= (1/3) x 25 x 5

= 41.67 cubic meters

Therefore, the volume of the pyramid is approximately 41.67 cubic meters.

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a.  You will pay 80% of the original price.

b. $14.40 is the discount price of the t-shirt.

c. The sale price of the gaming system is $288.

d. $22.50 is the regular price of the hat.

a. When a store offers a 20% discount, you will pay 80% of the original price. This is because the discount is taken off the original price, leaving you to pay the remaining percentage.

b. If the regular price of a t-shirt is $18, the discount price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.

Discount price = Regular price x (1 - Discount percentage)

Discount price = $18 x (1 - 0.20)

Discount price = $18 x 0.80

Discount price = $14.40

Therefore, $14.40 is the discount price of the t-shirt.

c. If the regular price of a gaming system is $360, the sale price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.

Sale price = Regular price x (1 - Discount percentage)

Sale price = $360 x (1 - 0.20)

Sale price = $360 x 0.80

Sale price = $288

Therefore, the sale price of the gaming system is $288.

d. If the discount price of a hat is $18 and the discount percentage is 20%, we can find the regular price by dividing the discount price by the percentage you will pay after the discount, which is 80%.

Regular price = Discount price / (1 - Discount percentage)

Regular price = $18 / (1 - 0.20)

Regular price = $18 / 0.80

Regular price = $22.50

Therefore, the regular price of the hat is $22.50.

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Answer:

V = 1,728 mi³

SA = 864 mi²

Step-by-step explanation:

We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.

First, we can solve for the area of one of the triangle sides:

A(triangle) = (1/2) · b · h

A(triangle) = (1/2) · 24 · 18

A(triangle) = 12 · 18

A(triangle) = 216 mi²

Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.

V = A(triangle) · depth

V = 216 · 8

V = 1,728 mi³

__

We can find the surface area by finding the area of each side, then adding all of those areas together.

We already know that the area of each of the triangle sides is 216 mi².

Now, we can solve for the area of the base.

A(base) = length · width

A(base) = 24 · 8

A(base) = 192 cm²

Then, we can find the area of the top side.

A(top) = length · width

A(top) = 30 · 8

A(top) = 240 mi²

Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.

SA = (2 · A(triangle)) + A(base) + A(top)

SA = 2(216) + 192 + 240

SA = 432 + 192 + 240

SA = 624 + 240

SA = 864 mi²

When the subject or predicate is missing from a sentence, the sentence error is a sentence fragment.

Sentence Errors are errors related to grammar and mechanics within sentences in Standard Written English.

An example of a sentence error will be "The children re us"

The phrase "re" is the error word in this sentence.

The three types of sentence errors we have are run-on sentences, sentence fragments and overloaded sentence.

In this problem, the type of sentence error that occurs when a sentence is missing a subject of predicate is a sentence fragment

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The next number in the sequence is 9.

The given sequence of numbers are perfect squares of decreasing numbers in descending order. Specifically, the given sequence consists of the squares of the first five counting numbers in descending order, starting from 8², then 7², 6², 5², and 4².

Therefore, the next number in the sequence should be the square of the next counting number in descending order, which is 3. Thus, the next number in the sequence should be 3², which is equal to 9.

To further explain, the sequence can be written as follows:

64 = 8²

49 = 7²

36 = 6²

25 = 5²

16 = 4²

The next number in the sequence is the square of the next counting number in descending order, which is 3. Therefore, the next number in the sequence should be 3², which is equal to 9. Thus, the next number in the sequence is 9.

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U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:

Find the slopes of sides UQ, QA, and UA:

Determine which segments are perpendicular and how we know they are perpendicular:

To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.

Find the lengths of each side:

Use the Pythagorean Theorem to show that it is a right triangle:

Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.

Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.

U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

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The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).

Percent of defective rate in manufacturing machine = 80%

Random number of items chosen = 109

The correct wording for the random variable in this situation is,

The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.

Number of defective items is successes.

A common symbol for the number of successes in a binomial distribution is X.

Use X to represent the random variable in this situation.

The notation for the binomial distribution is usually written as,

X ~ B(n, p)

where X is the random variable,

n is the sample size,

and p is the probability of success on each trial.

X ~ B(109, 0.8).

Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to  X ~ B(109, 0.8).

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The answer is 2143.6.

The magnitude of the resultant force is approximately 119.89 pounds, and the direction angle is approximately S12.2°W.

To solve the problem, we can use vector addition.

Let F1 be the vector representing the first force, and F2 be the vector representing the second force. Then, we can find the resultant force R by adding the two vectors:

R = F1 + F2

To add two vectors, we need to resolve them into their x and y components. Let's do that first.

For F1:

Magnitude = 80 pounds

Direction = S58°E

To resolve F1 into its x and y components, we can use trigonometry:

Fx1 = 80 cos 58° = 42.57 pounds (east)

Fy1 = 80 sin 58° = 68.13 pounds (south)

For F2:

Magnitude = 50 pounds

Direction = N76°E

To resolve F2 into its x and y components, we can again use trigonometry:

Fx2 = 50 cos (180° - 76°) = -16.92 pounds (east)

Fy2 = 50 sin (180° - 76°) = 48.76 pounds (north)

Note that we used (180° - 76°) for the angle because the direction is N76°E, which means it is 76° east of due north.

Now we can add the x and y components separately:

Rx = Fx1 + Fx2 = 42.57 - 16.92 = 25.65 pounds (east)

Ry = Fy1 + Fy2 = 68.13 + 48.76 = 116.89 pounds (south)

To find the magnitude and direction of the resultant force, we can use trigonometry again:

Magnitude = sqrt(Rx^2 + Ry^2) = sqrt(25.65^2 + 116.89^2) = 119.89 pounds (rounded to the nearest hundredth)

Direction angle = atan(Rx/Ry) = atan(25.65/116.89) = 12.2° (rounded to the nearest tenth)

The direction angle is approximately S12.2°W, and the resultant force has a magnitude of about 119.89 pounds.

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To find the average temperature of the coffee during the first half hour, we need to find the temperature of the coffee at t = 0 (when the coffee is just brewed) and at t = 30 (after half an hour has passed).

At t = 0, T(0) = 20 + 75e^0/50 = 20 + 75 = 95 C. At t = 30, T(30) = 20 + 75e^-30/50 ≈ 42.5 C.

So, the temperature of the coffee decreases from 95 C to 42.5 C during the first half hour.

The average temperature during this time period can be found by taking the average of the initial and final temperatures:

Average temperature = (95 C + 42.5 C) / 2 = 68.75 C.

Therefore, the average temperature of the coffee during the first half hour is 68.75 C.

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The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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Answer:

The answer is 5.8cm to 1 d.p

Step-by-step explanation:

volume of cube=L³

200=L³

cube root both sides

³√200=³√L³

L=5.8cm to 1 d.p

The two types of transformations that are produced by the matrix include:

We can see that a 90° counter-clockwise rotation followed by a dilation produces a transformation that stretches and rotates the figure.

On the other hand, a 90° counter-clockwise rotation followed by a reflection in the vertical axis produces a transformation that reflects and rotates the figure.

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The constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.

To find the area of the part with cement, we need to find the area of the entire rectangle and then subtract the area of the part with grass.

The area of the rectangle is: length x width = 5 m x 4 m = 20 m²

The area of the part with grass is: length x width = 3 m x 2 m = 6 m²

So the area of the part with cement is:

20 m² - 6 m² = 14 m²

Therefore, the area of the part with cement is 14 square meters.

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Yes, if there are more concordant pairs in the rank order, it makes sense that the Kendall correlation will be positive, as it suggests a tendency for the two variables to move in the same direction more often.

In Kendall correlation,

Rank values of each observation for the two variables are compared to determine the level of agreement or disagreement between them.

A concordant pair is when the rank order of the two variables is the same both increase or decrease together.

A discordant pair is when the rank order is different one variable increases while the other decreases.

If there are more concordant pairs, it means that the two variables tend to move in the same direction more often.

Which suggests a positive correlation relationship between them.

Conversely, if there are more discordant pairs, it means that the two variables tend to move in opposite directions more often.

Which suggests a negative  relationship between them.

Example ,

two variables, X and Y, that are positively correlated.

If we plot the observations of X and Y on a scatter plot.

Expect to see a pattern where as the values of X increase, the values of Y also tend to increase.

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Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.

Let's start by using variables to represent the unknown quantities in the problem. Let m be the number of slices of pizza Michael received, a be the number of slices Amy received, and au be the number of slices Mr. Au received.

We know that Miss Chang gave Michael 60 slices of pizza in total, so we can write:

m = 60

We also know that Amy received twice as many slices of pizza as Michael, so we can write:

a = 2m

Finally, we know that Mr. Au received three times the sum of what Miss Chang gave to Michael and Amy, so we can write:

au = 3(m + a)

We also know that Miss Chang gave 60 slices of pizza in total, so we can write:

m + a + au = 60

Now we can substitute the expressions we found for a and au into the last equation to get:

m + 2m + 3(m + 2m) = 60

Simplifying this equation, we get:

m + 2m + 3m + 6m = 60

12m = 60

m = 5

So Michael received 5 slices of pizza, and we can use the equations we found for a and au to determine how many slices Amy and Mr. Au received:

a = 2m = 2(5) = 10

au = 3(m + a) = 3(5 + 10) = 45

Therefore, Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.

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The value of Isabel's investment after 5 years is 2512.08 euros.

To calculate the value,

The formula for calculating compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have

P = 2000 euros

r = 0.043 (4.3% as a decimal)

n = 2 (compounded biannually)

t = 5 years

So, the formula becomes:

A = 2000 (1 + 0.043/2)^(2*5) = 2512.08 euros

Therefore, after 5 years, Isabel's investment will be worth 2512.08 euros.

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The solution to the equation 30 + q = 43 is q = 13.

Given the equation in the question:

30 + q = 43

To determine the value of q in the equation 30 + q = 43, isolate q on one side of the equation by performing the same operation on both sides of the equation.

30 + q = 43

q + 30 = 43

Next, we can isolate q by subtracting 30 from both sides of the equation:

q + 30 - 30 = 43 - 30

q = 43 - 30

Subtract 30 from 43

q = 13

Therefore, the value of q is 13.

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The numbers chocolate chip cookie would be assigned to the group is equals to the 40 belongs to 60-100. So, right choice is option(a).

We have a data values for a random number ranges within 1 to 100 need to be assigned for each event.

Probability for the chocolate cookies purchased for a fundraiser = 0.40

Probability for the butter cookies purchased for a fundraiser = 0.15

Probability for the peanuts butter cookies purchased for a fundraiser = 0.15

Probability for the lemon cookies purchased for a fundraiser = 0.30

The number would be assigned to the chocolate chip cookie group = 0.40× 100

= 40%

The difference between 60-100 is 40.

Hence, required number is 60-100.

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Complete question:

The above figure complete the question.

the probability distribution table shows the probability for the type of cookies purchased for a fundraiser. to conduct a simulation to determine the type of cookies purchases, random number ranges within 1 to 100 need to be assigned for each event. what numbers would be assigned to the chocolate chip cookie group?

a) 60-100

b) 71-100

c) 20-100

The value of the gauge needle is, 9.01 cm

Given that;

The fuel gauge of a car represents how much gasoline is left in the tank. If the area of the sector represented by the fuel gauge is 10.6 square centimeters.

Now, We can formulate;

A = θ/360 πr

10.6 = (135/360) 3.14 x r

3816 = 423.5r

r = 9.01

Thus, The value of the gauge needle is, 9.01 cm

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The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.

The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.

Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]

Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for  [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]

Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]

So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

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The missing lengths of BE and IJ using the concept of similar quadrilaterals are:

BE = 32

IJ = 18

Similar quadrilaterals are defined as quadrilaterals that have the same shape, but their sizes may vary. Thus, if two quadrilaterals are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

From the image, we are told that Quadrilateral GHIJ is similar to Quadrilateral BCDE.

Thus:

GJ/BE = IJ/DE = HI/CD

Thus:

12/BE = 6/16

BE = (16 * 12)/6

BE = 32

Similarly:

IJ/48 = 6/16

IJ = (48 * 6)/16

IJ = 18

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The number of bows Lulu can make  from the remaining ribbon is 13 bows.

To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.

10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.

She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:

(26/3) * 12 = 104 inches of ribbon remaining.

Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:

104 / 8 = 13 bows.

Lulu can make 13 bows with the remaining ribbon.

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Answer:

Let's start by drawing a diagram of the cornfield with the plowed strip around it:

markdown

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_____________________________

|                             |

|                             |

|                             |

|                             |

|        _____________________|__

|       |                       |

|       |                       |

|       |                       |

|       |                       |

|_______|_______________________|

The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.

The total area of the cornfield is:

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12 km x 9 km = 108 km^2

If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:

scss

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(12 + 2w) km x (9 + 2w) km

The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:

scss

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(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2

We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:

scss

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108 + 42w + 4w^2 = (1/2)(108)

Simplifying, we get:

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4w^2 + 42w - 54 = 0

We can solve this quadratic equation using the quadratic formula:

css

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w = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 4, b = 42, and c = -54. Substituting these values, we get:

scss

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w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8

arduino

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w = (-42 ± sqrt(1936)) / 8

makefile

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w = (-42 ± 44) / 8

So we have two possible solutions:

makefile

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w = 1/2 km (discarded since it does not satisfy the given condition)

or

makefile

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w = 11/2 km

Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.

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After 666 days, the video will receive approximately 33,621,452 views.

We are given the function V(d) = 4^(1.25d), where d represents the number of days since the video was uploaded and V(d) represents the number of views the video has received at that time. To find the number of views the video will receive after 666 days, we need to evaluate V(666).

Plugging in d = 666 into the function, we get V(666) = 4^(1.25*666). Using a calculator, we can simplify this to V(666) ≈ 33,621,452. Therefore, after 666 days, the video will receive approximately 33,621,452 views.

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It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.

A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.

On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.

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The amount of  bird food in cubic centimeters will fit in the container is

11, 398. 2 cubic centimeters

The formula that is used for calculating the volume of a cylinder is expressed with the equation;

V = π(d/2)²h

Such that the parameters of the given equation are;

Now, substitute the values into the formula, we have;

Volume = 3.14 (22/2)² 30

divide the values

Volume = 3.14(121)30

Now, multiply the values and expand the bracket

Volume = 11, 398. 2 cubic centimeters

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The statement "the first number of my ordered pair is 50" implies that all the points are of the form (50, y), where y can be any real number.

Therefore, the set of points that satisfy this statement is infinite, and it is not possible to list all of them.

However, if you need 20 specific points, you can choose any 20 values for y and pair them with 50 to obtain 20 points that satisfy the given condition.

For example, some of the points that satisfy this statement are (50, 0), (50, 1), (50, -2), (50, π), and (50, 10^6).


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