What is the circumference of a circular amphitheater with a diameter of 300 meters?

To find out if the fractions are proportional, we need to check if their cross-products are equal.Cross-product of 3/5 and 9/15:

3/5 × 9/15 = (3 × 9)/(5 × 15) = 27/75We can simplify 27/75 by dividing both the numerator and denominator by their greatest common factor, which is 3:

27/75 = (3 × 9)/(3 × 25) = 9/25Therefore, the cross-product of 3/5 and 9/15 is 9/25.Since the cross-products are not equal to each other, the fractions are not proportional.

The simplified expression is [tex]-2x^2 - 2x - 5.[/tex]

To simplify the expression, combine like terms:

[tex]3x^2 + 5x - 7x - 3 - 5x^2 - 2[/tex]

Combine the [tex]x^2[/tex] terms:

[tex](3x^2 - 5x^2) + 5x - 7x - 3 - 2[/tex]

Simplify the [tex]x^2[/tex] terms:

[tex]-2x^2 + 5x - 7x - 3 - 2[/tex]

Combine the x terms:

[tex]-2x^2 - 2x - 3[/tex]

This is the simplified form of the expression.

Therefore, the simplified expression is [tex]-2x^2 - 2x - 5.[/tex]

We have grouped the terms with similar variables together and performed the necessary arithmetic operations to obtain the simplified form.

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Answer:

Step-by-step explanation:

here is the solution of your problem i hope u enjoy

The length of the other diagonal of the kite is: 50 cm

We want to find the area of the given kite but It should be noted that:

The hypotenuse is usually the slanted line part in a triangle.

Area of a kite = pq/2

where:

p and q are diagonals

We are given:

Area of Kite = 180 cm²

Length of diagonal = 16 cm

Thus:

16q = 180

q = 180/16

q = 50 cm

This gives us the length of the other diagonal of the kite

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The car will travel 640 kilometers in 5 hours.

We have,

To convert miles per hour to kilometers per hour, we need to multiply by the conversion factor of 1.6:

= 80 miles/hour x 1.6 kilometers/mile

= 128 kilometers/hour

So the car's rate is 128 kilometers per hour.

Now,

To find the distance the car will travel in 5 hours, we need to multiply the rate by the time:

= 128 kilometers/hour x 5 hours

= 640 kilometers

Thus,

The car will travel 640 kilometers in 5 hours.

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Answer: 18m

Step-by-step explanation:

Volume of cylinder = area of base circle x height

16228 = [tex]\pi r^2[/tex] x 15

16228/15pi = r^2

.: r = [tex]\sqrt{\frac{16228}{15\pi} }[/tex]

r ≅ 19 m

the closest answer choice is 18m

The equation that can be used to find the nth term in the sequence, an, is: [tex]an = -4 \times 4^{(n-1)[/tex]

In a geometric sequence, each term is found by multiplying the previous term by a constant ratio.

Let's denote this ratio as "r."

Given that the first term, a₁, is -4, we can find the value of r by dividing the second term, a₂, by the first term, a₁.

a₁ = -4

a₂ = -16

r = a₂/a₁

Substituting the given values:

r = -16 / -4

r = 4

So, the common ratio, r, in this geometric sequence is 4.

To find the nth term, aₙ, in the sequence, we can use the formula:

[tex]a1= a{1 } \times r^{(n-1) }[/tex]

Substituting the given values:

[tex]a_n= -4 \times 4^{(n-1) }[/tex]

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From the distance formula

[tex]d=s \times t[/tex]

Now placing the given values

[tex]d = 25 \times 7[/tex]

[tex]d = 175[/tex]

Hence the bus traveled 175m (meters)

The correct statements are:

When a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, statement A) is true.

When a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign. Therefore, statement C) is true.

It should be noted that to represent the reflection of point A (1,-2) across the y-axis, we flip the sign of the x-coordinate to obtain the image point A' (-1,-2). Therefore, statement D) is true.

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The statement that best describes the fairness of the coin is the coin is biased

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

Flipping of a coin

Number of times it lands on head = 1352

Number of times it was flipped = 5200

using the above as a guide, we have the following:

P(Head) = 1352/5200

So, we have

P(Head) = 26%

This value is far from 50%

Hence, the fairness of the coin is the coin is that it is biased

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From the vertices provided, the area of the parallelogram is 42cm².

The area of a parallelogram remain

Area = base×height

we need to start by creating two vectors using the given vertices. We can use LM and LN.

Vector LM = M - L = (-12, -2, -4) - (-5, -2, -4) = (-7, 0, 0)

Vector LN = N - L = (-12, -8, -10) - (-5, -2, -4) = (-7, -6, -6)

LM x LN = (0×(-6) - 0×(-6), 0×(-7) - (-7)×0, -7×(-6) - 0×0)

= (0, 0, 42)

Area = ||LM x LN|| =√(0² + 0² + 42²) = √(0 + 0 + 1764)

= √(1764) = 42 cm²

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The maximum number of staff at the school, given the distribution of bangles and sweets, is 38 staff.

The principal has distributed 90 bangles and 108 sweets equally among her female staff includng herself. This means that the total number of female staff in the school is a number that can divide both 90 and 108 evenly, as each staff member must receve an integer number of bangles and sweets.

Find the greatest common divisor (GCD) of 90 and 108. The GCD of 90 and 108 is 18.

So, the princpal's school has 18 female staff including herself. In addition to the 20 male staff, this implies a maxmum of:

18 (female staff) + 20 (male staff) = 38 staff in total

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The required length of the base of the triangular pane of glass is 22 inches.

We know that the formula for the area of a triangle is:

Area = 1/2 * base * height

We are given that the height of the triangular pane of glass is 32 inches and the area is 352 square inches. Substituting these values into the formula, we get:

352 = 1/2 * base * 32

Multiplying both sides by 2 and dividing by 32, we get:

base = 22

Therefore, the length of the base of the triangular pane of glass is 22 inches.

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The diameter of the reservoir is:

Part (a): 112.86 m

part (b): 56. 44 m

The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius and h is the height or depth

Part (a):

We have:

h = 10 cm = 0.1 m

V = 1000,000 litres = 1000 m³  (Remember: 1 litre = 1000 cubic metre)

V = πr²h

1000 = 3.14 * r² * 0.1

1000 = 0.314 r²

r² = 1000 / 0.314

r² = 3184.71

r = √3184.71

r = 56.43 m

Since diameter = 2 * r

diameter =  2 * 56.43

diameter = 112.86 m

part (b):

We have:

h = 10 cm = 0.1 m

V = 250,000 litres = 250 m³

V = πr²h

250 = 3.14 * r² * 0.1

250 = 0.314 r²

r² = 250 / 0.314

r² = 796.18

r = √796.18

r = 28.22 m

Since diameter = 2 * r

diameter =  2 * 28.22

diameter = 56. 44 m

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Answer:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Step-by-step explanation:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Answer: 5

Step-by-step explanation:45

The nearest tenth, the surface area of the given cylinder is approximately 175.9 cm².

To find the surface area (SA) of a cylinder, we need to calculate the sum of the lateral surface area (arl) and the base area (B).

The formula for the lateral surface area of a cylinder is given by:

arl = 2πrh,

where r is the radius and h is the height of the cylinder.

The formula for the base area of a cylinder is given by:

B = πr^2.

Let's calculate the values:

Given:

Height (h) = 5 cm

Radius (r) = 4 cm

First, we calculate the lateral surface area (arl):

arl = 2πrh

= 2 * 3.14159 * 4 cm * 5 cm

≈ 125.66368 cm²

Next, we calculate the base area (B):

B = πr^2

= 3.14159 * (4 cm)^2

≈ 50.26544 cm²

Finally, we find the surface area (SA):

SA = arl + B

≈ 125.66368 cm² + 50.26544 cm²

≈ 175.92912 cm²

Rounded to the nearest tenth, the surface area of the given cylinder is approximately 175.9 cm².

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The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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Answer:

B

Step-by-step explanation:

[tex]tan^{2}\alpha (sec^{2} \alpha + cosec^{2} \alpha )\\\frac{sin^{2}\alpha}{cos^{2}\alpha} (\frac{1}{cos^{2}\alpha}+\frac{1}{sin^{2}\alpha})\\ \frac{sin^{2}\alpha}{cos^{2}\alpha} (\frac{1}{cos^{2} \alpha . sin^{2}\alpha} )\\\frac{1}{cos^{4}\alpha}\\= sec^{4}\alpha[/tex]

The equation of the data table of values is y = 2ˣ

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

The data table with the values

x values 1, 2, 3, 4, 5

y values 2, 4, 8, 16, 32

From the above, we can see that the relationship between x and y is that

The number 2 takes the variable x as its exponent to get the variable y

Mathematically, this can be expressed as

y = 2ˣ

This represents an exponential function with a base of 2

Hence, the equation of the data table is y = 2ˣ

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This revision uses transitional words (first, next, finally) to indicate a clear sequence of events helps to create coherence and improve the flow of the passage.

The revision that most effectively uses transitions to create coherence is:

Javier trained for his first marathon for months.

He learned to pace himself and to push through the pain.

He developed blisters and shin splints.

It broke his heart not to finish.

This revision uses transitional words (first, next, finally) to indicate a clear sequence of events helps to create coherence and improve the flow of the passage.

The use of these transitions also helps the reader understand the chronological order of events in the story.

In addition, the other options have some issues.

The first revision uses "after" to indicate a time sequence but it is not clear what event this refers to.

The second revision uses "finally" is a good transition but it does not provide any other transition words to clarify the order of events.

The third revision uses "but" to contrast the two events creates a bit of confusion as there is no clear cause-and-effect relationship between the two.

The fourth revision uses "also" to indicate a connection but it does not clearly indicate the sequence of events.

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Answer:

Step-by-step explanation:

Set h=0 for ground height, then solve for t

-16t^2 -20t +240 = 0

divide by -4

4t^2 +5t - 60 = 0

use the quadratic formula

t= -5/8 + or - (1/8)square root of (25 +4(4)(60)).  Ignore the negative square root

 =-5/8 + (1/8)sqr(960+25)

= -5/8 + (1/8)sqr(985)

 =-5/8 + (1/8)sqr(5(197))= slightly less than -5/8 +(10/8)(sqr10) = about -5/8 +32/8 = 27/8 = 3.3 seconds

the ball's initial velocity is negative, meaning the ball was thrown downward. Then add the effect of gravity, and it should hit the ground in a short time, even when thrown from an initial height of 240 feet.

plug t=2 into the original equation for height.  You should get slightly above ground, near zero

-16(2)^2 -20(2) +240 = -64 -40+240 = 136

try t=3

-16(9) -20(3) +240 = -144 -60 +240 = 36

try t=4

-16(16) -20(4) +240 =-256 -80 +240 =-96

the time to hit ground should be between t=3 and 4, but closer to t=3, maybe about 3 1/3 seconds

Answer:

if you make 413 dollars a second, in 30 minutes you would make 743,400 dollars.

Step-by-step explanation:

If you make 413 dollars a second, in 30 minutes you would make:

30 minutes = 30 x 60 = 1800 seconds

So, the amount of money you would make in 30 minutes can be calculated as follows:

1800 seconds x 413 dollars/second = 743,400 dollars

(a) The height of the larger box is determined as 2 cm.

(b) The volume of the smaller box is determined as 384 cm³.

The height of the larger box is calculated by applying the following formula as follows;

Volume = surface area x height

V = Ah

h = V / A

h = ( 1728 cm³ ) / ( 864 cm²2)

h = 2 cm

The volume of the smaller box is calculated by applying the following formula as follows;

V = Ah

where;

V = 96 cm²  x  4 cm

V = 384 cm³

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The area of the region that lies inside both curves is 11π/3 - 9√3/2 square units.

The area of the region that lies inside both curves first need to find the points of intersection.

The two equations equal to each other and solve for θ:

6sin(2θ) = 6sin(θ)

Dividing both sides by 6 get:

sin(2θ) = sin(θ)

The identity sin(2θ) = 2sin(θ)cos(θ) can rewrite this as:

2sin(θ)cos(θ) = sin(θ)

Dividing both sides by sin(θ) we get:

2cos(θ) = 1

Solving for θ we get:

θ = π/3, 5π/3

The area of the region by integrating the function r with respect to θ from θ = π/3 to θ = 5π/3:

A = ∫[π/3, 5π/3] 1/2 r² dθ

r = 6sin(2θ) when 0 ≤ θ ≤ π and r = 6sin(θ) when π ≤ θ ≤ 2π.

Substituting the appropriate values of r and integrating, we get:

A = ∫[π/3, π] 1/2 (6sin(2θ))² dθ + ∫[π, 5π/3] 1/2 (6sin(θ))² dθ

= ∫[π/3, π] 27sin²(2θ) dθ + ∫[π, 5π/3] 18sin²(θ) dθ

= [9θ - 3/4 sin(4θ)]π/3π + [6θ - 9/2 cos(2θ)]π/5π

= (π/3)[9π/2 - 3√3] + (2π/3)[5 - 9√3/2]

= 11π/3 - 9√3/2

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Step-by-step explanation:

If the lines are parallel then    3x + 9x = 180 degrees

                                                12 x = 180

                                                    x = 15

Answer:

third option represents a function.

Step-by-step explanation:

for the ordered pairs to represent a function.

each value of x must only map to one unique value of y

in the first option

(- 2, 0 ) and (- 2, 2 )

the same x- coordinate maps to 2 different values of y

thus not a function.

in the second option

every value of x = - 5 maps to 5 different values of y

thus not a function.

in the third option

each value of x maps to a unique value of y.

thus a function.

in the fourth option

(- 6, - 3 ) and (- 6, - 2 )

the same x value maps to 2 different values of y

thus not a function.

Drag the solution of each inequality as shown below:

3(x - 5) + x < 13 : x<7

2(x + 8) > 4x + 2 : x<7

3x + 2(x - 8) > x : x > 4

2(x + 6) < 3x + 8 : x > 4

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

3(x - 5) + x < 13

3x -15 + x < 13

4x -15 < 13

4x < 13 + 15

4x < 28

x < 28/4

x < 7

2(x + 8) > 4x + 2

2x + 16 > 4x + 2

2x - 4x > 2 - 16

-2x > -14

x < -14/(-2)     (Note: Sign will change if you divide with negative numbers)

x < 7

3x + 2(x - 8) > x

3x + 2x -16 > x

5x - 16 > x

5x - x > 16

4x > 16

x > 16/4

x > 4

2(x + 6) < 3x + 8

2x + 12 < 3x + 8

2x - 3x < 8 - 12

-1x < -4

x > -4/(-1)

x > 4

Therefore, drag the solution of each inequality accordingly.

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The value of the function, h(0) is -4.

A function relates input and output. In other words, a function is a special relationship among the inputs (independent variable) and their outputs (dependent variable).

Therefore, let's solve the function.

Given the function h(x) = 5x - 4

Let's find the value of the function h(0). To find the value of the function h(0), we have to substitute the value of x as 0 in the function.

Therefore,h(0) = 5(0) - 4h(0) = 0 - 4h(0) = -4

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Answer:

0.72/20.  1.98/20.  17.3/20.

Step-by-step explanation:

1000/20 = 50

for blue:

36/1000. divide top and bottom by 50 to get 0.72/20

for green:

99/1000. divide top and bottom by 50 to get 1.98/20

for yellow:

865/1000. divide top and bottom by 50 to get 17.3/20