PLEASE PLEASEEEEEEE HELPPPPPP!! 100 POINTSSSS :)
A Ferris wheel, called the Atlanta Skyview, recently opened in Centennial Olympic Park in the Atlanta, GA area. The diameter of this Atlanta attraction is 200 feet and has 42 gondolas evenly spaced out along the circle. Each sector starts and ends at the point at which the gondola is attached to the Ferris wheel circle.
Answer the following questions about this Ferris wheel. Be sure to show and explain all work for each problem.
a. Area of the wheel?
b. measure the central angle in degrees
c. Measure of a central angle in radians
d. Arc length between two gondolas
e. Area of each sector.
Answers
The area of the wheel is 31415.9 ft².
The Central angle in degrees is 34.29°
Measure of a central angle in radians is 0.5984 radians
How to calculate the area and central angle of a circle?
A) The image shows an example of this Ferris wheel.
We are given;
Diameter; d = 200 ft
Radius; r = 100 ft
Number of gondolas = 42
Area of the circle wheel = πr²
Area = π * 100²
Area = 31415.9 ft²
B) Now, the sum of angles in a circle is 360°.
Since there are 42 gondola's, then;
Each angle = 360/42 = 60/7°
The central angle will be an angle with its vertex at the center of a circle and with sides that are radii of the circle. From the image, we see that it covers approximately 4 gondola's. Thus;
Central angle = 4 * 60/7° = 34.29°
C) Central Angle in radians will be converted as 0.5984 rad.
D) Arc length between two gondolas is;
S = rθ
S = 100 * 0.5984
S = 59.84 radians
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Related Questions
The stock of Company A lost 2% today to $73.50. What was the opening price of the stock in the beginning of the day?
Answers
The opening price of the stock in the beginning of the day will be $75.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
The stock of Company A lost 2% today to $73.50.
Let x be the opening price of the stock in the beginning of the day.
Then the opening price of the stock in the beginning of the day will be
0.98 · x = 73.5
x = 73.5 / 0.98
x = $75
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Help me with this question please!! :)
Answers
Answer: 20/63
Step-by-step explanation:
The probability that the first marble is red is 16/28.The probability that the second marble is red is 15/27.Multiplying these probabilities, we get (16/28)(15/27) = 20/63
Find X and QT. The shape is a Rhombus
Answers
Answer:
See below ~
Step-by-step explanation:
Sides of a rhombus are equal.
⇒ QT = TS
⇒ x² - 4x - 10 = 6x + 14
⇒ x² - 10x - 24 = 0
⇒ x² + 2x - 12x - 24 = 0
⇒ x (x + 2) - 12 (x + 2) = 0
⇒ (x + 2)(x - 12) = 0
⇒ x = -2 or x = 12
Substitute both values and see which gives a positive value for QT :
When x = -2 :
QT = (-2)² - 4(-2) - 10QT = 4 + 8 - 10QT = 2When x = 12 :
QT = (12)² - 4(12) - 10QT = 144 - 48 - 10QT = 86The 2 possible answers are :
x = -2, QT = 2x = 12, QT = 86Which results only in a horizontal compression of Y=1/x
by a factor of 6?
Answers
Step-by-step explanation:
[tex] y = \frac{1}{x} [/tex]
In order to compress by a factor of 6, we multiply the variable x by 6. It would compress the hyperbola
[tex]y = \frac{1}{6x} [/tex]
What is the median of this data set?
22, 37, 49, 15, 72
Answers
Steps:
Order the numbers from least to greatest.
15, 22, 37, 49, 72
The median value is the middle number.
37
Hello, thank all of you that helped me fix my math problems you helped me to succeed and get a good grade !!!
Answers
Please help!!! I will give 20 points to the correct answer !! Thanks so much
Answers
Find the measure of PR.
Answers
The length of PR = 18 .
What is a Chord ?A chord is a line segment whose both points lie on the circle.
When a chord is extended it is called secant .
When two chords meet outside the circle , the product of length of the secant and its external segment is equal to the product of length of other secant and its external segment.
According to the given data
FR and FP are the secants of the circle
To determine the measure of PR
From the secant theorem
(7+9) * 9 = (5x+8) * 8
16 * 9 = (5x+8) *8
2 *9 = 5x+8
18 = 5x+8
5x = 10
x = 2
Therefore the length of PR = 5x+8 = 10+8 = 18
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What is the surface area of the cylinder below?
Answers
Answer:
Surface Area = 378.25
Step-by-step explanation:
Comment
It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.
Area lids
diameter = 11.4
radius = d/2
radius = 11.4/2
radius = 5.7
Area = pi * r^2
Area = (3.14 * 5.7^2) * 2 There are 2 lids.
Area = 102.01 yd^2
Area body
This is found by finding the circumference of the lid and multiplying by the height
Circumference
C = 2*pi*r
2*r = the diameter
2*r = 11.4
C = 3.14*11.4
C = 35.80
Area body
Area body = C* h
h = 7.8
Area body = 35.80 * 7.8
Area body = 279.24
Total Area = 102.01 + 279.24 = 378.25
Please help, been stuck on this for ages!
Answers
Answer:
[tex]\boxed {192 cm^{2}}[/tex]
Step-by-step explanation:
Find the volume of separate cuboids :
Volume (top cuboid) :
⇒ V = 2 x 6 x (10 - 2)
⇒ V = 12 x 8
⇒ V = 96 cm²
Volume (lower cuboid) :
⇒ V = 8 x 6 x 2
⇒ V = 48 x 2
⇒ V = 96 cm²
Volume (prism) :
⇒ 96 + 96
⇒ 192 cm²
what is the answer to the question?
Answers
Using logic concepts, the correct statement is given by:
[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.
What are the events in this problem?The events are:
Event P: Henry is wearing a red shirt.Event Q: Henry is wearing khaki shirts.The statement is:
Henri is wearing a red or blue shirt today with jeans.
A red or blue shirt can be represent by p or not p, that is:
[tex](p \vee \neg p)[/tex]
Jeans is not khaki, hence the second part is:
[tex]\neg q[/tex]
Combining the statements, we have that the expression is:
[tex](p \vee \neg p) \wedge \neg q[/tex]
Since p and q are true, [tex]\neg q[/tex] is false, and the entire statement is false. Hence the correct option is:
[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.
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3a =2b + -6 (solve for a)
Answers
Answer:
shown below
Step-by-step explanation:
3a = 2b - 6
a = (2b - 6) / 3 or 2b / 3 - 2
Answer:
a = (2b-6)/3
Step-by-step explanation:
3a = 2b + -6
lets make a the subject of the formula
divide both sides of the equation by 3
3a/3 = a = (2b-6)/3
a = (2b-6)/3
An electrician charges a $40 fee to make a house call plus an hourly rate for labor. If the total bill that takes 2 hours comes to $99 what is the electrician hourly labor rate?
Answers
Reason
You can use the formula y=mx+b for this
We know y is the total bill of $99
We know b is the $40 fee (y intercept or starting point)
We know x is 2 hours
We are looking for m or rate
Substitute numbers for letters in formula
99= m(2) +40
Subtract 40 from both sides to isolate m
59=2m
Divide both sides by 2 to solve for m
M=$29.50
We can prove our answer by inserting our answer for “m” in the formula
99=29.50x2+40
99=99
Answer is correct
what is the variable equal to y8=40
Answers
You can divide 40 by 8 and you get 5. y=5
Answer:
5
Step-by-step explanation:
We need to isolate the variable, aka make y on one side. So, if we divide 8 on both sides, it will be
y8=40
y8/8=40/8
y=5
Question 2(Multiple Choice Worth 4 points)
If (89)P=818, what is the value of p?
02
09
10
18
Answers
Answer:
p = 2
Step-by-step explanation:
using the rule of exponents
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](8^{9}) ^{2}[/tex] = [tex]8^{9(2)}[/tex] = [tex]8^{18}[/tex]
so value of p = 2
Calculate the gross earning for an apple picker based on the following differential pay scale: 1- 1000:$0.03 each 1001-1600:$0.06 each over 1600:$0.07 each. Calculate the Gross earning
Answers
If he picks 1965, then the Gross earning will be $85.55.
The missing part of the question is given below.
If he picks 1965, then Calculate the Gross earning.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Calculate the gross earning for an apple picker based on the following differential pay scale:
1 – 1000: $0.03 each
1001 – 1600: $0.06 each
over 1600: $0.07 each
Total apples picked by Lindbergh = 1965
So, for 1000 apples, he will get =1000 × 0.03 = $30
Now, remaining apples = 1965 – 1000 = 965
Now for next 600 apples (from 1001-1600), he will get = 600 × 0.05 =$30
Now, remaining apples = 965 – 600 = 365
So, for remaining 365 (above 1600) apples, he will get = 365 × 0.07 = $25.55
So, total gross earning = $30 + $30 + $25.55
⇒ $85.55 is total gross earning
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forty percent of participants in a math contest were boys. fifty percent of the boys revived medals. the number of boys who received the medals was equal to the number of girls who received the medals. what percent of the participants were girls who received medal?
Answers
20% of the participants are girls and got a medal, and 33% of the girls got a medal.
What percent of the participants were girls who received medal?
First, we know that 40% of the participants were boys, so the other 60% were girls.
We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:
P = (0.4)*(0.5) = 0.2
So, 20% of the participants are boys and got a medal.
We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.
Then if the percentage of girls that got a medal is x (in decimal form), we must have that:
Q = (0.6)*(x) = 0.2
x = 0.2/0.6 = 0.33
x = 0.33
This means that 33% of the girls got a medal.
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When completing the square on the equation c^2 + 11c = 12, the resulting solution is
Answers
Answer:
Attached file is the solutions
Step-by-step explanation:
6x -8=16 solve equation
Answers
Answer:
x = 4
Step-by-step explanation:
6x - 8 = 16 (add 8 to both sides)
6x = 24 (divide by 6 on both sides)
x = 4
Brainliest, please :)
Step-by-step explanation:
6x=16+8
6x=24
6x/6=24/6
x=4
so the answer is 4
In your own words, explain the discriminant test. Use the discriminant test to decide whether the equation represents a parabola, ellipse or a hyperbola and explain why you know this is true. x^2 − 4xy + 3x + 25y − 6 = 0
Answers
A discriminant test is one that tells whether a formula has one, two or no solutions.
The equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
What is a discriminant test?A discriminant test is a test that tells whether there are one, two or no solutions for a formula.
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.
The discriminant of a quadratic equation is given as ax2 + bx + c = 0
A discriminant is said to be a parabola either x or y is squared and not both unlike that of an eclipse and a hyperbola.
With the given equation, x^2 − 4xy + 3x + 25y − 6 = 0, only x is squared and not both x and y.
Thus, the equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
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Find the value of x.
Answers
Answer:
Step-by-step explanation:
plug in x try numbers
x = 14.2
list 4 factors of 24. list 4 multiples of 24.
Answers
Answer:
Factors of 24: 1, 2, 3, 4, 6 etc.
Multiples of 24: 48, 72, 96, 120
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
Factors of 24:24 can be written as:
= 1 × 24
= 2 × 12
= 3 × 8
= 4 × 6
So, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.
Multiples of 24 are:1 × 24 = 24
2 × 24 = 48
3 × 24 = 72
4 × 24 = 96
and so on...
So, the first 4 multiples of 24 are 24, 48, 72 and 96.
[tex]\rule[225]{225}{2}[/tex]
Based on the vertical bar chart below, in which of the following months were just over 10% of professional European soccer players
born?
March
B) January
April
May
Professional European soccer player birth months
Relative frequency (%)
20%
15%
10%
5%
Jan Feb Mar Apr May Jun
ایل
Month
....
Aug Sep Oct Nov Dec
Answers
By critically observing the vertical bar chart, only the month of May had a birth of just over 10%.
What is a bar chart?A bar chart refers to a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.
Based on the vertical bar chart (see attachment), the relative frequency (&) with the birth of over 10% are:
Jan Feb Mar Apr MayHowever, only the month of May had a birth of just over 10%.
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What is an undefined term in geometry?
OA. A sentence that asserts a fact
OB. A term that has no formal definition, but is used to define other
terms
OC. A clause preceded by "if" in a conditional statement
OD. A statement in which the hypothesis and conclusion are switched
Answers
An undefined term in geometry is (b) A term that has no formal definition, but is used to define other terms
How to define the term?In geometry, there are four undefined terms.
These terms are:
PointLinePlaneSet.The above items do not have a specific or formal definition. However, they are used to define other terms in geometry
This is the reason they are referred to as undefined terms.
Hence, an undefined term in geometry is (b)
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If f(x) = 3x − 1 and g(x) = x + 2, find (ƒ– g)(x)
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]
[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]
Simple procedure :
[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]
[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]
[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Which statements are true from the graph ? Check all that apply:
the line is horizontal the line is vertical
Answers
The statements that are true from the graph are:
The line is horizontalThe line goes through (4, 4 )The y- values are all 4Calculations and ParametersGiven the graph, we can note some things:
There is a line with a slope of zero.This is a horizontal line parallel to the x-axis.The equation of the line is y = cc is the value of the y- coordinates the line passes through.
The line passes through (0, 4 ) with a y- coordinate of 4
Therefore, the equation of the line of y= 4
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Factor out the GCF from the polynomial.
r(2²-24) + (2²-24)
Answers
Answer: -20
Step-by-step explanation: i hope its right
What is the value of the expression 24 + 3²? What is the value of the expression 24 + 3² ?
Answers
Answer:
33
Step-by-step explanation:
3² = 3.3 = 9 => 24 + 9 = 33
A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?
Answers
The worker's expected weekly bonus is $30.0
How to determine the worker's expected weekly bonus?The amounts and the probabilities are given as:
x $10 $50
P(x) 0.75 0.25
The worker's expected weekly bonus is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = $10 * 0.75 + $50 * 0.25
Evaluate the product
E(x) = $17.5 + $12.5
Evaluate the sum
E(x) = $30.0
Hence, the worker's expected weekly bonus is $30.0
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The sequence an = 1(3)n − 1 is graphed below: coordinate plane showing the points 1, 1; 2, 3; and 3, 9 Find the average rate of change between n = 1 and n = 3. (6 points)
Answers
Answer:
4
Step-by-step explanation:
[tex] \frac{9 - 1}{3 - 1} = 4[/tex]
The average rate of change on the interval [3, 9] will be 4.
How to find the average rate of change?The average rate of change between two points is given by the slope formula:
m = average rate of change = (y2 -y1)/(x2 -x1)
The sequence an = 1(3)n − 1 is graphed below:
m = (9 -1)/(3 -1) = 8/2
m = 4
The average rate of change on the interval [3, 9] will be 4.
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