Answer:
1387.2 ft² (nearest tenth)
Step-by-step explanation:
Formulae
Circumference of a circle = [tex]2 \pi r[/tex]Area of a circle = [tex]\pi r^2[/tex](where r is the radius of the circle)
The railing of the circular fountain is the circumference of a circle.
The area of the fountain is the area of a circle.
First, find the radius by using the circumference formula:
Given:
circumference = 132 ft[tex]\implies 132=2 \pi r[/tex]
[tex]\implies r=\dfrac{132}{2 \pi}=\dfrac{66}{\pi}[/tex]
Now input the found value of r into the formula for the area of a circle:
[tex]\begin{aligned}\implies \textsf{Area} & =\pi \left(\dfrac{66}{\pi}\right)^2\\\\ & = \dfrac{4356}{\pi}\\\\ & = \dfrac{4356}{3.14}\\\\ & = 1387.261146...\\\\ & = 1387.3 \: \sf ft^2\:(nearest\:tenth)\end{aligned}[/tex]
A carnival has a duck-pond booth. You choose a rubber duck at random. The mark on the bottom of the duck tells you whether you won a small, medium, or large prize, or no prize at all. There are 56 ducks floating in the pond. There are 5 ducks marked as large-prize winners, 10 ducks marked as medium-prize winners, and 20 ducks marked as small-prize winners. Find the theoretical probability of winning a small prize at the duck pond. Express your answer as a percent. If necessary, round your answer to the nearest thousandth.
35.714%
62.5%
280%
64.286%
The probability helps us to know the chances of an event occurring. The probability of winning a small prize in the carnival is 35.714%.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that there is a total of 56 ducks floating in the pond, out of which 20 ducks are marked as small-prize winners. Therefore, the probability of winning a small price can be written as:
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\\\\rm Probability=\dfrac{\text{Nnmber of small price ducks}}{\text{Total number of ducks}}\\\\\\Probability = \dfrac{20}{56} = 0.35714 = 35.714\%[/tex]
Hence, the probability of winning a small prize in the carnival is 35.714%.
Learn more about Probability:
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Special Triangle: Solve for x and y.
Answer:
x = 8.67 and y = 10
Step-by-step explanation:
In right angled triangle
cos 60⁰ = 5/y
1/2 = 5/y
y = 10
in right angled triangle,
tan 60⁰ = x/5
√3 = x/5
x = 5√3 = 5 × 1.73 = 8.65
x = 8.67
Angle A= ___? degrees
Angle B= ___ ?degrees
Angle C= ___? degrees
Answer:
Angle A = 45 degrees
Angle B = 64 degrees
Angle C = 60 degrees
Hope this helps!
PLS HELP I CANT FAIL
No links pls and Ty <3333!!!!!
Answer:
Option 1: 43π feet
Step-by-step explanation:
We are given that:
encloses garden with circular fence
garden measures 43 feet across = diameter
To find how much fencing is needed, we have to find the cicumference of the circular fence using the formula:
C = 2πr
C = Circumference
r = radius = half the diameter
We are given the diameter, so we just do half of it to get the radius
43 ÷ 2 = 21.5
r = 21.5
Now we substitute this into the formual:
C = 2πr
Substitute radius into formula
C = 2π(21.5)
Multiply 2 and 21.5
C = 43π
The potential energy of an object varies jointly with the mass of the object and the height of the object off the ground. a 25-kg object has 980 joules of potential energy when it is 4 meters off the ground. another object has 150 joules of potential energy at 3 meters off the ground. what is the mass of the second object? round to two decimal places. 0.32 kilogram 2.88 kilograms 5.10 kilograms 45.90 kilograms
The mass of the object which is at 3 meters off the ground (earth assumingly), with the potential energy of 150 joules is given by: Option C: 5.10 kg
What is gravitational potential energy?Gravitational potential energy is the energy which a body posses because of its position.
The gravitational potential energy of a body is given as,
[tex]U=mgh[/tex]
Here, (m) is the mass of the body, (g) is the gravitational accelaration and (h) is the height of the body.
Here, for the second object, we have:
Potential energy = 150 joulesDistance from the ground = 3 mg = gravitational acceleration = [tex]9.8 \: \rm m/s^2[/tex]Let its mass be m kg, then:
[tex]U=mgh\\\\150 = m(9.8)(3)\\\\m = 50/9.8 \approx 5.10 \: \rm kg[/tex]
Thus, the mass of the object which is at 3 meters off the ground (earth assumingly), with the potential energy of 150 joules is given by: Option C: 5.10 kg
Learn more about the gravitational potential energy here;
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HELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
(a) 10.3
(b) 11
Step-by-step explanation:
(a) Step 1: mean is the average of a set of numbers. Add them all together and then divide by how many numbers you were given
11+12+5+11+8+13+12 = 72
Step 2: There are 7 numbers so you divide 72 by 7
72/7 = 10.28
(a) The mean equals 10.3
(b) Step 1: Median is the middle number in a list of numbers. Line the numbers up in order and find the middle one.
5, 8, 11, 11, 12, 12, 13
(b) the median equal 11
Write in slope intercept form an equation of the line that passes through (-2,5),(-1,1)
Answer:
y=-4x-3
Step-by-step explanation:
Hi there!
We are given the following two points: (-2,5) and (-1,1)
We want to write the equation of the line that passes through these two lines in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, let's find the slope
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to calculate the slope, but let's label the value of the points to avoid any confusion
[tex]x_1=-2\\y_1=5\\x_2=-1\\y_2=1[/tex]
Now substitute into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{1-5}{-1--2}[/tex]
Simplify
m=[tex]\frac{1-5}{-1+2}[/tex]
Subtract
m=[tex]\frac{-4}{1}[/tex]
Divide
m=-4
Now substitute -4 as m into the equation:
y=-4x+b
Now we need to find b
As the equation passes through both (-2, 5) and (-1, 1), we can use either point to help solve for b.
Taking (-2,5) for example:
Substitute -2 as x and 5 as y:
5=-4(-2)+b
Multiply
5=8+b
Subtract 8 from both sides
-3=b
Substitute -3 as b.
y=-4x-3
Hope this helps!
See more on this topic here: https://brainly.com/question/27304092
Someone help me please
Answer:
Step-by-step explanation:
From the observation deck of a skyscraper, Meena measures a 48∘ angle of depression to a ship in the harbor below. If the observation deck is 1068 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Using the slope concept, it is found that the horizontal distance from the base of the skyscraper out to the ship is of 961.6 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The angle is of 48º.The vertical change is of 1068 ft.The horizontal change is of x.Hence:
[tex]\tan{48^\circ} = \frac{1068}{x}[/tex]
[tex]x = \frac{1068}{\tan{48^\circ}}[/tex]
x = 961.6
The horizontal distance from the base of the skyscraper out to the ship is of 961.6 feet.
More can be learned about the slope concept at https://brainly.com/question/18090623
As an estimation we are told £3 is €4. Convert £7. 50 to euros
What was her speed?
0. 1 mile per minute
0. 5 mile per minute
5 miles per minute
10 miles per minute
Question :
The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged. what was her speed?
Answer:
The Answer is A. 0.1 mile per minute
Help ulitt ihihihihi
Answer:
1.A , 2.B , 3.D , 4.B , 5.C
Step-by-step explanation:
hope this helped! :)
A right triangle has an area of 33 mm2 and a height of 12mm. How long is the base of the triangle
Answer:
5.5
Step-by-step explanation:
There are 23 pennies on one side of a balance and 17 pennies on the other
side. Levi thinks 3 pennies should be added to the higher pan, Arjan thinks 4
Pennies should be added, and Charlotte thinks 6 pennies should be added. Who Is correct and why?
To have the same number of pennies in both sides, we should add 6 pennies, so Charlotte is correct.
How many pennies should we add?We want to have the same number of pennies on both sides, on one side we have 23 pennies, and in the other 17. So we will add x pennies to the last side, such that we get:
23 = 17 + x
This is a linear equation. To solve it, we need to isolate the variable x, we can do that by subtracting 17 in both sides:
23 - 17 = 17 + x - 17
6 = x
This means that the solution is 6, so we should add 6 pennies, meaning that Charlotte is correct.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/1884491
what is 7/-13 + 4/-13
Answer:
7/-13 + 4/-13 = -7/13 - 4/13 = - 11/13
Shirley and Jena, working together, can paint the deck in 6 hours. Working alone, Jena takes three times as long as Shirley. How long does it take Shirley to paint the deck alone
Answer:
18 hours
Step-by-step explanation:
Jena takes three times as long as Shirley.
3 Times 6 = 18
Rebbeca needs a box with a rectangular base of 36 cm^2 and a volume of 180 cm^3. What would be the height
of the box?
Answer:5cm
Step-by-step explanation: Area =length × breadth
Volume = length ×breadth ×height
180= Area ×height
180 = 36×h
180÷36=h
Ans 5
What is the range of the function f(x) = 3x2 6x – 8?
The domain of the function is a real number and the range of the function will be (-11, ∞).
What are domain and range?The domain means all the possible values of the x and the range means all the possible values of the y.
The function is given below.
f(x) = 3x² + 6x – 8
The range of the function will be
f(x) = 3x² + 6x – 8
f(x) = 3x² + 6x + 3 – 11
f(x) = 3(x² + 2x + 1) – 11
f(x) = 3(x + 1)² – 11
Then the range of the function will be from -11 to infinity.
More about the domain and range link is given below.
https://brainly.com/question/12208715
In the triangle ABC, angle C is a right angle. Find the value of the trig function indicated. Find sin A if a = 3013, b = 2
[tex]Given: Statement\\ To\ find: Correct\ optician\\ tan\theta=\frac{2}{30\sqrt{13}}[/tex]
[tex]sin\ B=\frac{2}{33}[/tex]
[tex]sin A=\frac{1}{7}=\frac{30\sqrt{13}}{3311}=\frac{3\sqrt{13}}{11}[/tex]
I hope this helps you
:)
A base of a trapezoid is 16 feet, and the height is 3 feet. The area of the trapezoid is 36 square feet. Find the length of the other base
Answer:
8 feet
Step-by-step explanation:
Area of a trapezoid: h(a + b)/2
height, h = 3 ft
base 1, a = ?
base 2, b = 16 ft
area, A = 36 ft^2
36 = 3(a + 16)/2
72 = 3(a + 16)
24 = a + 16
8 = a
I hope this helps!
A washing machine has the following cycle: soak for 15 minutes, wash for 30 minutes, and rinse for 10 minutes. If you approach the machine at a random during the cycle, what is the probability that the cycle will be in the rinse phase when you arrive at the machine
pls need help in math<3
Answer: 12 minutes
Step-by-step explanation:
Time taken by 2 people = 60 minutes
The time taken by 1 person is double that = 60 x 2 = 120 minutes
So the time taken by 10 people = 120 minutes / 10 people = 12 minutes
Answer: 12 minutes.
Step-by-step explanation: For two people, it takes an hour to paint a fence. With ten people, however, it takes very little time to paint a fence. 10 people are 5 times more people than when you have only 2. It would only take 12 minutes because it takes 5 times less time with 10 people than with only two.
Let me know if this is right! :)
50 PTS 2. Consider the following line plot.
(a) What is the general trend of the graph?
(b) What is the median of the data? Explain.
(c) What is the mean of the data? Explain.
(d) Would the mean or median be affected more with a data point of 20? Explain.
Answer:
Picture so I can solve it
need some help with the question in the image
Cheers
HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
The answer is (A) or 3/4.
Step-by-step explanation:
By plugging in a through d, the only one that gave an acurate answer was A.
2(6-2x) - 2x = 2(5+x)-4
turns into
2(6-2[3/4]) - 2[3/4] = 2(5+[3/4]) -4
Hope this helps!
Answer:
x = 3/4Therefore , option A is correct .Step-by-step explanation:
In the question we're given with an equation i.e.,
2 ( 6 - 2x ) - 2x = 2 ( 5 + x ) - 4And we are asked to find the value of x .
Solution :
[tex] \longmapsto \: 2 ( 6 - 2x ) - 2x = 2 ( 5 + x ) - 4 [/tex]
Step 1 : Solving parenthesis by multiplying it with 2 on both the sides :
[tex] \longmapsto \: 12 - \bold{4x} - \bold{2x} = \bold{10} + 2x - \bold{4}[/tex]
Step 2 : Adding like terms on left hand side and subtracting like terms on right hand side :
[tex] \longmapsto \: 12 - 6x = 2x + 6[/tex]
Step 3 : Transposing 12 to right hand side and 2x to left hand side :
[tex] \longmapsto \: -2x - 6x = 6 - 12[/tex]
On further calculations we get :
[tex] \longmapsto \: \cancel{ - }8x = \cancel{- }6[/tex]
Step 4 : Transposing 8 to right hand side :
[tex] \longmapsto \: x = \frac{\cancel{6}}{\cancel{8}} [/tex]
Step 5 : Cancelling 6/8 to their simplest form :
[tex] \longmapsto \: \pink{\boxed{x = \frac{3}{4} }}[/tex]
Therefore , value of x is 3/4 and it will make the equation true .#Keep Learningwhat is 500x150 help please
Answer: 75,000, (Ignore for 20 characters)
Answer:
75000
Step-by-step explanation:
using Pythagorean theorem we can conclude that the sun is facing north of the south pole which leads to the basic formula of planks leagth which is the smallest thing in the universe so far but it is not a thing it is but a leagth
Write an equation in slope-intercept form for the line that passes through (-1, -2) and (3, 4).
Answer:
y = 3/2x - 1/2
all steps explained in pic attached below :)
Point A is an element of a direct variation. Select two points, other than A, that are elements of this direct
A
variation.
No links please
Answer:
Step-by-step explanation:
B and C is crorect answer tha ks
WHAT IS THE ANSWER??? PLEASE QUICKLY
Answer:
A = lateral face B = base C = 132
Step-by-step explanation:
this has to be one of the most random question i seen
144 Inches or 12 Feet
Step-by-step explanation
7 feet converted to inches is 84 So 84+60=144
And if you convert 60 inches into feet it would be 5
Answer:
144 inches
Step-by-step explanation:
1 ft = 12 inches
7 ft = 12 x 7 inches
7ft = 84 inches
Ice path you are floating on = 84 inches
other ice path = 60 inches
all together = 84 + 60
=> 144 inches
Hope this helps!