A carnival ride is in the shape of a wheel with the radius of 30 feet. The wheel has 30 cars attached to the center of the wheel. What is the central angle, arc length, and area of sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive full credit.

Answers

Answer 1

Answer:

α = 12°

L = 6.28 ft

[tex]A = 94.25 ft^2[/tex]

Step-by-step explanation:

The wheel contains 30 cars attached to it.

The wheel is in the shape of a circle and a circle has 360°.

Therefore, the angle between any two cars will be:

360 / 30 = 12°

The length of the arc between two cars is given as:

[tex]L = \frac{\alpha }{360} * 2\pi R[/tex]

where α = central angle of sector

R = radius of circle

Given that the radius of the wheel is 30 feet, the length of the arc is:

[tex]L = \frac{12}{360} * 2 * \pi * 30\\\\L = 6.28 ft[/tex]

The area of a sector is given by:

[tex]A = \frac{\alpha }{360} * \pi R^2[/tex]

Therefore, the area of the sector between any two cars is:

[tex]A = \frac{12}{360} * \pi * 30^2\\\\A = 94.25 ft^2[/tex]


Related Questions

If the measure of arc AB is 50 degrees what is the measure of its inscribed angle ACB?

Answers

Answer:

87

Step-by-step explanation:

or 130. let me know if I'm wrong

If the measure of arc AB is 50°, then the measure of its inscribed angle ACB is, 130°

What is an angle ?

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

The measure of arc AB = 50°

The measure of its inscribed angle ACB = ?

Here, ACBP will make a quadrilateral

And, the sum of opposite angles of quadrilateral is 180°

So, ∠ACB + ∠AB = 180°

⇒   ∠ACB = 180° - 50°

⇒   ∠ACB = 130°

Hence, the measure is 130°

To know more about angle check:

https://brainly.com/question/28451077

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This is urgent can someone please help.......

Quentin typically walks 28 yards south on Pine Street and 45 yards east on Maple Avenue in order to get to school. How much shorter would his walk be if he took the shortcut shown below?
A)73 yards
B)20 yards
C)53 yards
D)126 yards

A cone shaped tepee has a radius of 4 feet and a slant of 7 feet. If Joe is six feet tall, determine whether Joe is shorter or taller than the height of the tepee.
A)Joe is shorter than the tepee.
B)Joe is taller than the tepee.
C)Joe is the same height as the tepee.
D)There is not enough information to determine if Joe is shorter or taller than the tepee.

Which of the following could NOT be the side lengths of a right triangle?
A)3 - 4- 5
B)5 - 12 - 13
C)8 - 9 - 10
D)9 - 40 - 41

Answers

Answers are c, a, and c

Answer:

1. A

2.C

3.C

Step-by-step explanation:

What is the solution to the system of linear equations?
2x + y = 7
x - 2y = 16
A)(4,-1)
B)(-1,9)
C)(6,-5)
D)(-5,6)

Answers

Answer:

(6, -5)  (Answer C)

Step-by-step explanation:

Multiply the first equation by 2.  We get the following equivalent system:

4x + 2y = 14

 x - 2y  = 16

------------------

  5x = 30, or x = 6.

Substituting 6 for x in the second equation, we get

6 - 2y = 16, or

  -  2y = 10, so that y = -5

and the solution is (6, -5)  (Answer C)

9-1-1 Math EMERGENCY PLS HELP WILL GIVE BRAINLY AND 30 points
Pls solve just one queastion

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Give me brainly

A school organization sells T-shirts for a fundraiser. Youth sizes sell for $10 each, and adult sizes sell for $15 each. The organization sells a total of 220 shirts for $2,375. How many adult-sized T-shirts did the organization sell?

Answers

Answer:

35 adult shirts were sold

Step-by-step explanation:

10y+15a=2375

y+a=220

y=220-a

10(220-a)+15a=2375

2200-10a+15a=2375

2200+5a=2375

5a=175

a=35

35 adult shirts were sold.

Answer

35 adult T shirt was sold

question in attachment

Answers

Answer:

a₁ = 6

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]

where a₁ is the first term and r the common ratio

Here [tex]S_{8}[/tex] = 1530 and r = 2, thus

[tex]\frac{a_{1}(2^{8}-1) }{2-1}[/tex] = 1530 , that is

a₁ (256 - 1) = 1530

255a₁ = 1530 ( divide both sides by 255 )

a₁ = 6

Is my answer to this problem right?

Answers

Answer:

Yes

Step-by-step explanation:

1/3 = 3 in 1

3(1) = 3

3 x 12 = 36

So 36 is correct

Answer:

I’m pretty sure you are correct.

how to find an unknown angle in a quadrilateral

Answers

Subtract the sum of the angles from 180 degrees to get the missing angle. For example if a triangle in a quadrilateral had the angles of 30 and 50 degrees, you would have a third angle equal to 100 degrees (180 - 80 = 100).

I need help please thanks

Answers

Answer:

1/6

Step-by-step explanation:

The answer is D. Hope this helped :)

write a function rule that relates r and t.
Input r: -2, 0, 2, 4, 6
Output t: 0, -1, -2, -3, 1

Answers

Answer: [tex]t=-\frac{1}{2}r- 1[/tex]

Step-by-step explanation:

For a lineal equation [tex]t=mr+n[/tex]

For r=0 and t=-1

[tex]-1=m(0)+n\\n=-1[/tex]

For r=-2 and t=0

[tex]0=m(-2)-1\\m(-2)=1\\m=-\frac{1}{2}[/tex]

Them [tex]t=-\frac{1}{2}r- 1[/tex]

???? The output for 6 is 1????

I need help due today online school sucks I only need the answer to 6 and 7​

Answers

6) the number of glasses is 5 times the number of boxes.
7) robert is incorrect as he only needs 24 boxes to pack 120 glasses, because 120/24=5

Answer:

6. The relationship is they multiply the first box of glasses by the amount of boxes 15glasses = x 3,

30 glasses = x6

45 glasses = x 9

60 glasses = x 12

75 glasses = x15

= 30, 45, 60,75

But in between glass amount 45 +60 they show a midpoint amount of glasses in a box where 45 = 9n  then 55 = 11n and stands out as  11 boxes as an offset amount of glasses where 5 are in each box.

7. Robert is incorrect as 25 x 5 = 125 and not 120

as 120 and 125 glasses can be divided to check

125/25  = 5 and could be correct if he wanted spare glasses = 1 spare box.

But when we check 120/25 =  4.8 so this would be too many boxes as he would only need 24 boxes.

24 x 5 = 120 glasses.

Step-by-step explanation:

For every 2 adults there are 7 kids. There are a total of 180 people. How many adults and kids are there out of the 180 total?

Answers

Answer:

40 adults and 140 kids

Step-by-step explanation:

Answer:

40 adults

Step-by-step explanation:

40 adults and 140 kids

20 times 7 is 140

40 plus 140 is 180

PLz help right answers only will give brainliest!!!!

Answers

Answer:

-48

Step-by-step explanation:

First You put The question in Order

HOPE THIS HELP

STAY SAFE:)

The answer for this question is D

What is 42.8 on its standard form???

Answers

Answer:

[tex]4.28 \times 10^{1}[/tex]

Step-by-step explanation:

[tex]42.8 \times 10^0=42.8[/tex]

[tex]4.28 \times 10^{1}=42.8[/tex]

Answer:

42.8 x 10^0

Step-by-step explanation:

A. Standard Form

Ax + By = C.

A, B, C are integers (positive or negative whole numbers)

No fractions nor decimals in standard form.

Traditionally the "Ax" term is positive.

Simplify ^4 sqrt 16x^8y^12z^4

Answers

Answer:

Step-by-step explanation:

[tex]y^{4}\sqrt{16x^{8}y^{12}z^{4}}=y^{4}\sqrt{4*4*x^{4*2}y^{6*2}z^{2*2}}\\\\ =y^{4}\sqrt{4^{2}*(x^{4})^{2}*(y^{6})^{2}*(z^{2})^{2}}\\\\=y^{4}*4*x^{4}*y^{6}*z^{2}\\\\=4x^{4}y^{4+6}z^{2}\\\\\\=4x^{4}y^{10}z^{2}[/tex]

Mouse population is 25,000 and is decreasing at a rate of 20% per year what is the population of mice after 3 years

Answers

Answer:

10,000

Step-by-step explanation:

3 years x 20% = 60%

60% of 25000 is 15000

25000 -15000 =  10,000

Can somebody help me with this question

Answers

Answer: -17 degrees

Step-by-step explanation:

109-126 = -17

Answer:

-17 degrees

Step-by-step explanation:

since it is 126 degrees lower, you minus 126 from 109.  109-126= -17

Drag each tile to the correct box. Match the expression to the exponent property that you use first to simplify the expression.

Answers

sorry i did the best i could

Suppose the sample space for a continuous random variable is 0 to 50. If the
area under the density curve for the variable from 0 to 38 is 0.76, what is the
area under the density curve from 38 to 50?
A. 0.34
B. 0.924
C. 0.76
D. 0.24

Answers

Your answer is D.024

Answer:

0.24

Step-by-step explanation:

15 POINTS!!!
Solve 3(−3−3x)+4=−5.

The solution is x=___

Answers

3(-3-3x)+4=-5

One solution was found :

x = 0
Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3*(-3-3*x)+4-(-5)=0

Step by step solution :

Pull out like factors :

-3 - 3x = -3 • (x + 1)

Equation at the end of step 2 :

(-9 • (x + 1) + 4) - -5 = 0


Equation at the end of step 3 :

-9x = 0
Step 4 :

Solving a Single Variable Equation :

4.1 Solve : -9x = 0

Multiply both sides of the equation by (-1) : 9x = 0


Divide both sides of the equation by 9:
x = 0

One solution was found :

x = 0

does anybody know the answer to this equation? // * ANSWER ASAP *

Answers

Answer:

radius

Step-by-step explanation:

AJ is half the distance across the circle (radius).

The answer is c, radius.

A radius is half way through and AJ is half way through the circle. Hope I helped :)

The point-slope form of a line is y-y1 = m(x-x1), where m is the slope and x1 is a point on the line.
A. True
B. False

Answers

Answer:

False.

Step-by-step explanation:

A point on the cordinate plane needs an x-coordinate and a y-coordinate.

The point is (x1, y1) not just x1.

The statement is true because the point-slope form of a line is y - y₁ = m(x -x₁), where m is the slope and x1 is a point on the line.

What is the Point-slope form?

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

The point-slope form of a line is y - y₁ = m(x -x₁), where m is the slope and x1 is a point on the line.

Hence, the statement is true.

Learn more on Point-slope form of a line here: brainly.com/question/11624671

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Billy’s Boat Rentals charges a yearly fee of $105 and $9.50 each time a member wants to rent a boat. Lisa’s Boat Rentals does not charge a yearly fee but charges $14.75 every time a member rents a boat. How many times does a person have to rent a boat for Billy’s and Lisa’s to cost the same amount?


A.10

B.15

C.20

D.30

Answers

Answer:

C. 20

Step-by-step explanation:

105 + 9.5x = 14.75x

105 = 5.25x

20 = x

Simply
(3x^2 y^3/x^3)^3

Answers

The answer is 27y^9/x^3

if multiple choice the answer is 27x^6 y^9/x^9

Pictures so you can see

Answer:

[tex]=\frac{27y^9}{x^3}[/tex]

Step-by-step explanation:

[tex]\left(\frac{3x^2y^3}{x^3}\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}\\\left(\frac{3x^2y^3}{x^3}\right)^3=\frac{\left(3x^2y^3\right)^3}{\left(x^3\right)^3}\\=\frac{\left(3x^2y^3\right)^3}{\left(x^3\right)^3}\\\mathrm{Simplify}\:\left(3x^2y^3\right)^3:\quad 27x^6y^9\\=\frac{27x^6y^9}{\left(x^3\right)^3}\\\mathrm{Simplify}\:\left(x^3\right)^3:\quad x^9\\=\frac{27x^6y^9}{x^9}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}[/tex]

[tex]\frac{x^6}{x^9}=\frac{1}{x^{9-6}}\\\frac{x^6}{x^9}=\frac{1}{x^{9-6}}\\=\frac{27y^9}{x^{9-6}}\\\mathrm{Subtract\:the\:numbers:}\:9-6=3\\=\frac{27y^9}{x^3}[/tex]

The figure is made of rectangular prisms. What is the volume?
6 cm
15 cm
10 cm
3 cm
6 cm
3 cm
3 cm
3 cm
318 cm
225 cm
13
159 cm

Answers

What are the sides of the rectangular prisms ?

What is the value of 4x- 7 when x=4?

Answers

Answer:

9

Step-by-step explanation:

4x- 7

Let x=4

4*4 - 7

16 -7

9

Answer:

9

Step-by-step explanation:

4(4)-7=16-7=9

Five times the smallest of three consecutive odd integers is seven more than twice
the largest. Find all three consecutive odd integers.

Answers

Answer:

5, 7, 9

Step-by-step explanation:

Using the information given we get:

[tex]5x-7=2z[/tex]

[tex]x+2=y\\y+2=z\\x+4=z[/tex]

[tex]5x-7=2(x+4)\\5x-7=2x+8\\[/tex]

Add 7 to both sides

[tex]5x=2x+15[/tex]

Subtract 2x from both sides

[tex]3x=15[/tex]

Divide both sides by 3

[tex]x=5[/tex]

Using these equations:

[tex]x+2=y\\y+2=z\\x+4=z[/tex]

and

[tex]x=5[/tex]

We get:

[tex]x=5\\y=7\\z=9[/tex]

please help me i’ve been stuck on this

Answers

Answer:

The odd that B draws an ace is 3/51 or 1/17

No, it is independent because they don't know if the card they draws is an ace or not. Because if B take the card first also it would be ace so it isn't dependent i think

What is the length of the unknown leg in the right triangle?

A right triangle has a side with length StartRoot 23 EndRoot yards and hypotenuse with length StartRoot 87 EndRoot yards

Answers

Answer:

8

Step-by-step explanation:

A right angled triangle is made of three sides with the longest side being the hypotenuse. According to pythagoras theorem;

[tex]hyp^{2} = adj^{2}+opp^{2}[/tex]

Given hypotenuse = [tex]\sqrt{87}[/tex] and another side = [tex]\sqrt{23}[/tex], the third side can be gotten according to the formula above. On substituting;

[tex](\sqrt{87} )^{2} = (\sqrt{23} )^{2} + x ^{2} \\x^{2} = (\sqrt{87} )^{2} - (\sqrt{23} )^{2}\\x^{2} = 87-23\\x^{2} = 64\\x =\sqrt{64}\\ x = 8[/tex]

The length of the unknown leg in the right triangle is 8

Answer:

a. 8 yd

Step-by-step explanation:

Hypotenuse = [tex]\sqrt{87}[/tex]

Length = [tex]\sqrt{23}[/tex]

x² + ([tex]\sqrt{23}[/tex])² = ([tex]\sqrt{87}[/tex])²

x² = ([tex]\sqrt{87}[/tex])² - ([tex]\sqrt{23}[/tex])²

x² = 87 - 23

x² = 64

[tex]\sqrt{x}[/tex]² = [tex]\sqrt{64}[/tex]

x = 8 yd

12. Building codes regulate the steepness of stairs. Homes must have steps that are at least 13 inches wide for each 8 inches
that they rise.
a. Discuss how to find the slope of the stairs.
b. Describe how changing the width or height affects the steepness of the stairs.

Answers

Answer:

Slope tells you about the steepness of a line. It can is the ration of vertical change to horizontal change and you can solve this by using the slope formula:

a. So in your case, starting from the bottom, the slope is:

If you want to use coordinates, you can think of the first point (bottom of the stairs} would be at the point of origin (0,0). The next point would be at the top of the first stair 13 inches wide (horizontal or x) and 8 inches high (vertical or y)

So the coordinates of the two points would be:

(0,0) and (13, 8)

Using the formula we would have:

b. Looking at the answer above, you can see that the slope with increase if the vertical change is greater, so if you increase the height of the stairs, the stair would be steeper. The opposite is true if you would increase the width.

However, if you proportionally increase the width and the height, then the slope will remain the same.

Step-by-step explanation:

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