Answer:
11.17 ft
Step-by-step explanation:
Since the swing hangs from a beam 10 feet high with the seat hanging 2 feet above the ground, the swing moves in an arc of radius r = 10 ft - 2 ft = 8 ft.
Now, since the swing moves back and forth from -130° to -50° to the horizontal, the length of arc L it moves in is given by
L = Δθ/360 × 2πr where Δθ = change in angle of the swing = θ₂ - θ₁ where θ₁ = -50° and θ₂ = -130°. So, Δθ = θ₂ - θ₁ = -130° -(-50°) = -130° + 50° = -80°.
Substituting r and Δθ into L, we have
L = -80°/360° × 2π(8 ft)
= -8/36 × 16π ft
= -32π/9 ft
= -100.53/9 ft
= -11.17 ft
Ignoring the negative sign, the length of arc L = 11.17 ft. So, the swing moves back and forth 11.17 ft
Identify the volume of the composite figure. Round to the nearest tenth.
Answer:
474.5 ft ³
Step-by-step explanation:
1) Find the volume of the cube
[tex]A=l^3[/tex] where l is the side length
Plug in 9 ft as l
[tex]A=9^3\\A=729[/tex]
Therefore, the volume of the cube is 729 ft³.
2) Find the volume of the cylinder
[tex]A=\pi r^2h[/tex] where r is the radius of the base and h is the height of the cylinder
Plug in 3 ft as the radius and 9 as the height
[tex]A=\pi (3)^2(9)\\A=\pi (9)(9)\\A=81\pi \\A=254.5[/tex]
Therefore, the volume of the cylinder is approximately 254.5 ft ³.
3) Subtract the volume of the cylinder from the volume of the cube
729 ft³ - 254.5 ft ³
= 474.5 ft ³
Therefore, the volume of the figure is 474.5 ft ³.
I hope this helps!
Answer:
I think It's A
Step-by-step explanation:
Rosa conducted a survey of students' favorite types of music. The results are shown in the table. Of the 550 students in the whole school, how many would you expect to prefer Pop/Rock?
Answer: 264
Step-by-step explanation:
A rectangular piece of metal 12 cm long 18 cm wide and 10 cm high is melted and recast into 45 cylindrical plates,each of radius 1.2 cm.Find the thickness of each plate giving your answer correct to 2 decimal places?
Answer:
10.61 cm
Step-by-step explanation:
From the question,
The volume of the rectangular piece of metal = Volume of the 45 cylindrical plates.
Volume of a cuboid = 45×volume of a cylinder
lwh = 45×πr²h..................... Equation 1
Where l = length of the rectangular piece of metal, w = width of the rectangular piece of metal, h = height of the rectangular piece of metal, r = radius of the cylindrical plates, h = thickness of the cylindrical plates.
make h the subject of the equation
h = lwh/(45πr²).................... Equation 2
Given: l = 12 cm, w = 18 cm, h = 10 cm. r = 1.2 cm
Constant: π = 3.142.
Substitute these values into equation 2
h = (12×18×10)/(45×3.142×1.2²)
h = 2160/203.60
h = 10.61 cm.
A shape is made of 9 right triangles of equal size and three identical rectangles.
Each rectangle measures 7 mm wide by 3 mm high. The rectangles are each
7 mm wide by 3 mm high. What is the total area, in square millimeters,
of the shape?
Answer:
The area of the figure is 157.5 square millimeters.
Step-by-step explanation:
Since a shape is made of 9 right triangles of equal size and three identical rectangles, and each rectangle measures 7 mm wide by 3 mm high, while the rectangles are each 7 mm wide by 3 mm high, to determine what is the total area, in square millimeters, of the shape, the following calculations must be performed:
Area of a rectangle: base x height
Area of a triangle: (base x height) / 2
7x3 = 21 = Rectangle area
7x3 / 2 = 10.5 = Triangle area
21 x 3 + 10.5 x 9 = 157.5
Thus, the area of the figure is 157.5 square millimeters.
Suppose that appoximately 261,000,000 people live in the united states. Of these people 37,600,000 speak a language other than english at home who speak another lanague at home over 45 percent speak spanish
Answer:
16,920,000 people speak Spanish at home in the United States, which represents 6.48% of the country's population.
Step-by-step explanation:
Given that approximately 261,000,000 people live in the United States, and of these people 37,600,000 speak a language other than English at home, of which over 45 percent speak Spanish, to determine the number of people who speak Spanish in the United States, the following calculation has to be done:
37,600,000 x 0.45 = X
16,920,000 = X
261,000,000 = 100
16,920,000 = X
16,920,000 x 100 / 261,000,000 = X
6.48 = X
Thus, some 16,920,000 people speak Spanish at home in the United States, which represents 6.48% of the country's population.
which of the following is the solution to the equation 25(z-2 )= 125?
A. z= 5.5
B. z = 3.5
D. z = -2.5
E. z = -0.5
Answer:
The answer is z = 7.
Step-by-step explanation:
1) Divide both sides by 25.
[tex]z - 2 = \frac{125}{25} [/tex]
2) Simplify 125/25 to 5.
[tex]z - 2 = 5[/tex]
3) Add 2 to both sides.
[tex]z = 5 + 2[/tex]
4) Simplify 5 + 2 to 7.
[tex]z = 7[/tex]
Thus, the answer is z = 7.
The diagram shows a cuboid.
8 cm
15 cm
20 cm
What is the volume of the cuboid?
Answer:
mdndmdkdkdkdkd
Step-by-step explanation:
kdkdkdjfjfk
Solve the system of linear equations by substitution.
3x – 2y = 23
x + 2y = 13
The solution of the system is
Answer:
point form : (9,2) equation form : x=9 y=2
Step-by-step explanation:
More trig ratios see attachment
Answer:
TanX = 9/12, WX = 15, TanW = 12/9, CosX = 12/15
Step-by-step explanation:
Tan = opposite/adjacent, so 9/12
WX is the missing side, so solve it by taking the square root of (9^2) +( 12^2) and you get 15
Tan again, is opposite/adjacent, so 12/9
Cos is adjacent/hypotenuse, so 12/15
Hopefully this helps! Let me know if you have any questions
6x – 64 = 2x - 44
solve for x
Answer: x= 5
Step-by-step explanation: subtract 2x from both sides eliminating 2x.
4x-64=-44 add 64 to both sides eliminating -64
4x=20 divide by 4
20/4 = 5
4x/4 = x
x= 5
Hope this helps :)
Please help me with the question please ASAP ASAP please please help ASAP ASAP please please help please
Answer:
x = 15 ft
Step-by-step explanation:
Triangle ACD is similar to triangle ABE based on the information given, therefore we can set up a proportion to compare the sides:
side AE / side EB = side AD / side DC
4/6 = 10/x
Solve for x
x = (10)(6) / 4
x = 60 / 4
x = 15 ft
Please Show your work.
Answer:
Equation: y = 2.5x
Answer: 43.75 drawers
Step-by-step explanation:
Equation: 10 - 7.5 = 2.5 and when you subtract 2.5 until the Number of Drawers (x) is 0, then you get 0 for Total Volume (y), so y =2.5x+0 or y = 2.5x
Answer: Substitute 17.5 into x.
y = 2.5(17.5)
y = 43.75 drawers
pls help I beg you pls
Answer:
The cost can be 15,000 and anything below that
A parallelogram has vertex at (-5 , -1) (-2, -1), (-3,-4), and (-6,-4). What is the approximate perimeter of the parallelogram round your answer to the nearest hundredth
Answer:
12.4 units
Step-by-step explanation:
We have to find the length of the sides of the parallelogram which is calculated using the formula for Distance
= √(x2 - x1)² + (y2 - y1)² where we are given the vertices (x1, y1) and (x2, y2)
For side A
(-5 , -1) (-2, -1)
= √(-2 -(-5))² + (-1 - (-1))²
= √(-2 + 5)² + (-1 + 1)²
= √3² + 0
= √9
= 3 units
For side B
(-2, -1), (-3,-4)
= √(-3 -(-2))² + (-4 -(-1))²
= √(-3 + 2)²+ (-4 + 1)²
= √-1² + -3²
= √1 + 9
= √10 units
= 3.1622776602 units
Approximately = 3.2 units
For side C
(-3,-4), (-6,-4).
= √(-6 -(-3))² + (-4 - (-4))²
= √(-6 + 3)² + (-4 + 4)²
= √-3² + 0²
= √9
= 3 units
For side D
(-5 , -1), (-6,-4)
= √(-6 - (-5))² + (-4 - (-1))²
= √(-6 + 5)² + (-4 + 1)²
= √-1² + -3²
= √1 + 9
= √10 units
= 3.1622776602 units
Approximately = 3.2 units
From the above calculation , we can see that,
side A = side C
side B = side D
The formula for the Perimeter of a Parallelogram is = 2(Side a + Side b)
= 2(3 + 3.2) units
= 2(6.2) units
= 12.4 units
HELPPME PLEASE ASAP i will give brainliest
Answer:
don't know but I think these is the answer =
17
Step-by-step explanation:
90 - 73 = 17
|(x-19)+11| considr all posibilyties
ill give you brainlyest
Answer: Here Is the answer
Step-by-step explanation: hoep this helps :)
Ivan had 1,500 flyers printed to announce the opening of his new coffee shop. He paid $0.06 per flyer he's paying his friends $0.25 cents per flyer to deliver them. How much will Ivan pay to have all the flyers printed and delivery
HELP PLZ
1. A new bicycle sells for $300. It is on sale for off the regular price. Select all the
expressions that represent the sale price of the bicycle in dollars.
A. 300 •1/4
B. 300 • 3/4
C. 300 - (1 - 1/4)
D. 300 – 1/4
E. 300 – 1/4•300
Answer:
Step-by-step explanation:
All of them beside D and A
PLZZZ HELP. Celeste makes 6% Commission on her sales, if her sales for a week total %4580 what is her commission
1. $274
2. $274.50
3. $275.80
4. $272.00
Answer: 3
Step-by-step explanation:
1 p
1.) On Tuesday at lunchtime, it was 29°C. By sunset, the temperature had
dropped to 16°C. How much did the temperature change by?
Answer:
Expression is; 29 - x = 16
Step-by-step explanation:
I've attached an image showing the number line
Step-by-step explanation:
We are told that at lunchtime, it was 29 degrees Celsius and that by sunset, the temperature had dropped to 16 degrees Celsius.
Let the drop be x.
Thus;
29 - x = 16
I've attached an image showing the number line
5.
Loren is running in a long distance race. She is able to keep a steady pace of 10 feet per second.
Answer:
a or c Im not sure
Step-by-step explanation:
I think b though
The line which represents the speed as 10 feet per second is line B thus none of the given options are correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given,
Loren is running at speed of 10 feet per second.
Speed = distance covered/time taken
10 = distance covered/time taken
In line B, the ratio of distance covered/time taken is 10.
Thus, line B will be correct.
Hence "The line which represents the speed as 10 feet per second is line B thus none of the given options are correct".
To learn more about graphs,
brainly.com/question/16608196
#SPJ5
Write the standard equation of a circle with center (-2, -1) and radius 2.
Answer:
(x+2)^2+(y+1)^2=4
Step-by-step explanation:
(x-h)^2+(y-k)^2=r^2 is the standard equation for a circle
Plug in point at (h,k) Negative points= positive in equation due to (x-h),(y-k) All equal to radius squared
5)
A coach is ordering jerseys for the school.
• The coach pays a one-time fee of $10.
• The coach also pays $12 for each shirt ordered.
Which function can be used to find t, the total amount the coach pays in dollars when c shirts
are ordered?
A t = 12c + 10
Bt = 100 - 12
Ct = 120 - 10
D t = 10c + 12
Answer:
10c + 12
Step-by-step explanation:
I believe that is the answer please let me know if I am wrong
decrease
133 in the ratio 7:2
Answer:
38
Step-by-step explanation
2/7× 133=38
can someone help with this i don't get it
Answer:
Lord have mercy thats a bunch of numbers I woud help but i dont know how to start
Step-by-step explanation:
Is 8, 11.5, 8.5 a right triangle?
Answer:
Monkey says NO
Step-by-step explanation:
It was close, but banana was 1.7 banana short. sorry for your loss.
The number of bus riders was recorded on one route. The data have these values: minimum = 18, lower quartile = 22, median = 26, upper quartile = 29, and maximum = 37.
Which box plot represents the data?
Answer:
b cause its b
Step-by-step explanation:
Answer:
Step-by-step explanation:
THe guy is correct its B
The shaded portion of the bar model in Part A shows 38. What percent is equivalent to 38? Enter the correct answer in the box.
Question:
The shaded portion of the bar model in Part A shows 3/8. What percent is equivalent to 3/8? Enter the correct answer in the box.
Answer:
The equivalent is 37.5%
Step-by-step explanation:
Given
[tex]\frac{3}{8}[/tex]
Required
The equivalent
The model is not shown, but the question can still be solved.
We have:
[tex]\frac{3}{8}[/tex]
Multiply by 100%
[tex]\frac{3}{8} = \frac{3}{8} * 100\%[/tex]
[tex]\frac{3}{8} = 0.375 * 100\%[/tex]
[tex]\frac{3}{8} = 37.5\%[/tex]
find the value of given expression
[tex] \sqrt{99 - ( - 1)} [/tex]
Answer:
10
Step-by-step explanation:
Note that when there are two negative signs directly next to each other, you are adding:
[tex]\sqrt{99 - (-1)} = \sqrt{99 + 1} = \sqrt{100}[/tex]
Simplify:
[tex]\sqrt{100} = \sqrt{10 * 10} = 10[/tex]
10 is your value for the given expression
Answer:
± 10Step-by-step explanation:
[tex]\sqrt{99 - (-1)} = \sqrt{99 + 1} = \sqrt{100}[/tex] = ± 10select all of the trips that would take 2 hours
Answer:
a field trip
a road trip
a trip to a far antique museum
Uhm I would also appreciate if i had options.