do the following by paper folding using a circular cut out.
make the diameter
shade the minor and major segment
make a sector of a circle
Answers
The shaded region of segments is given in the attachment.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The diameter is the length of the line through the center that touches two points on the edge of the circle.
A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.
A sector of a circle is a pie-shaped part of a circle made of the arc along with its two radii.
Hence, the shaded region of segments is given in the attachment.
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Related Questions
when serenity goes bowling, her scores are normally distributed with a mean of 195 and a standard deviation of 14. what is the probability that the next game serenity bowls, her score will be between 183 and 218, to the nearest thousandth?
Answers
The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
Given that,
Mean = 195
Standard deviation = 14
Thus, the probability between 183 and 218 is the ρ value of z when x = 195
Subtracting by the ρ value of z when x = 183
so, x = 218
z = 218-195/14 = 1.64
when x = 183
z = 183-195/14= -0.85
Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886
Now, 0.94950 - 0.21886 = 0.73064
Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%
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Find the area of the shaded portion if we know the outer circle has a diameter of 4 m and the inner circle has a diameter of 1. 5 m. A Circle
Answers
The area of the shaded portion is given by the difference between the area of the outer circle and the area of the inner circle.
First, let's find the areas of the circles:
Outer Circle: Area = πr^2 = π (2)^2 = 4π square meters
Inner Circle: Area = πr^2 = π (0.75)^2 = 0.5625π square meters
Area of shaded portion = Area of outer circle - Area of inner circle = 4π - 0.5625π = 3.4375π square meters
So the area of the shaded portion is approximately 10.8 square meters.
Let f(x) = x³ + 2x² + 7x - 11 and g(x) = 3f(x). Which of the following describes g as a
function of f and gives the correct rule?
A.) horizontal compression; g(x) = 3x³ + 6x² + 21x - 33
B.)horizontal stretch; g(x) = 27x3 + 18x² +21x - 11
C.)vertical stretch; g(x) = 3x3 + 6x² +21x - 33
D.)vertical compression; g(x) = 27x³ + 18x² + 21x - 11
Answers
Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11 = -1 and g(x) = 3f(x) = -3
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope.
Here,
Given:
we have been provided with -
f(x) = x³ + 2x² + 7x - 11
so, x = 1
f(x) = 1 +2 +7 -11= -1
g(x) = 3f(x) = -3
Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11 = -1 and g(x) = 3f(x) = -3
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4 Which number is included in the set of integers that when added to –4 gives a sum of less than zero? Select all that apply. A 3 B 7 C 9 D –2 E 4 F 0
Answers
The number included in the set of integers that when added to -4 gives a sum less than zero are 0, -2 and 3
How to find the integers in a word expression?The question wants us to find the numbers included in the set of integers that when added to -4 gives a sum less than zero.
The options are 3, 7, 9, -2, 4 and 0.
Therefore,
let
the number added = x
Hence,
-4 + x < 0
Base on the options, the numbers that fits into the inequality are as follows:
The numbers are 0, -2 and 3.
Therefore,
-4 + 0 < 0
-4 + -2 < 0
-4 + 3 < 0
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What are two possible transformations that together could have been used to create the red figure from the blue figure?
mc023-1 (see picture for graph )
A. a translation of 2 units up followed by a translation of 4 units right
B. a rotation of 90 degrees counterclockwise about the origin followed by a translation of 2 units up
C. a reflection across the y axis followed by a translation of 2 units up
D. a translation of 2 units up followed by a reflection across the x axis
Answers
Answer:
(c) a reflection across the y-axis followed by a translation 2 units up
Step-by-step explanation:
You want to know transformations that will give the red figure from the blue one.
ObservationThe red figure is reversed left-to-right with respect to the blue figure, so a reflection across a vertical line is required. The only answer choice that has such a reflection is ...
C. a reflection across the y axis followed by a translation of 2 units up
Graph x = -4 on the graph below. What is the domain of x = -4? What is the range of x = -4?
Answers
Answer:The graph of x = -4 is a vertical line located 4 units to the left of the y-axis.
The domain of x = -4 is the set of all real numbers, since any real number can be plugged into x = -4 and the equation will be true. This is because x = -4 is a vertical line and not a function, it cuts the y-axis at one point, so it doesn't matter what value you put on x it will always be -4.
The range of x = -4 is a single point on the y-axis, y = -4.
Step-by-step explanation:
Determine the value of X
The two angles are (x+10) and the other number is 96
Answers
Answer: 43
Step-by-step explanation:
x+x+10 = 96
2x = 86
x = 43
What is the range of the function f?
f(x) = 3x² + 18x
O A. (-00,00)
O B. (-00, 18]
O C.
-6,00)
OD.
[-27,00)
A
Answers
The range for the function f(x) = 3x² + 18x is option d: [-27 , ∞).
What is the range of a function?
A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range . It is only a function in a relation if each x value has exactly one y value.
The given function is -
f(x) = 3x² + 18x
The set of values of the dependent variable for which a function is defined is a function's range.
For a parabola ax^2+bx+c with vertex (xv,yv) -
If a<0 the range is f(x) ≤ yv.
If a>0 the range is f(x) ≥ yv.
Here a=3, and vertex (xv,yv) = (-3,-27)
So, f(x) ≥ -27.
Therefore, the range is [-27 , ∞).
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Sarah, gene, and paul are proposing plans for a class fundraiser. each presents
his or her proposal for the amount of money raised, y, for x number of
hours worked, in different ways.
Answers
We can draw the conclusion that linear functions can be used to represent each of the ideas. Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).
What does "Linear Function" mean?A linear function is denoted by the equation y = mx + b, where m is the slope or unit rate between the two variables, x and y, and b is the beginning value or y-intercept.
The initial value is b.
A linear function is a graph with straight lines.
A unit rate exists for all linear functions (b).
Sarah's suggestion can be expressed by a linear function because the graph that represents it is a straight line.
Gene's Proposal's table displays the unit rate as change in y/change in x = 7. As a result, a linear function can be used to express it.
Paul's idea has a linear function as its equation.
This leads us to the conclusion that linear functions can be used to represent each of the ideas.
Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).
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Correct Question:
A rectangular swimming Pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
Answers
Answer:
Let x be the width of the pool. Then the length of the pool is 2x, since it is twice as long as it is wide.
The area of the pool is (2x)(x)=2x^2
The total area of the pool and the walkway is 2x^2+196 square feet.
We can set up the equation using this information:
2x^2 + 22x = 196
Where 22x is the area of the walkway, 22x = 2x * 2 = 4x
2x^2 + 4x = 196
2x^2 + 4x - 196 = 0
Using the quadratic formula to solve the equation above:
x = (-b ± √(b^2 - 4ac))/2a
x = (-4 ± √(4^2 - 42196))/2*2
x = (-4 ± √(16 - 1568))/4
x = (-4 ± √(-1552))/4
Since x is width of the pool, it cannot be a negative value, the x value that is negative must be rejected. Therefore x = (-4 + √1552)/4 = 8
The width of the pool is 8 feet and the length is 2x = 2*8 = 16 feet
A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns. chosse from the below option.a)Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solutionAnswer: (Type an ordered pair here _____)x1=2, x2=4, x1+x2=6b) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solutionAnswer: (Type an ordered pair here _____)x1=2, x2=4, x1+x2=8c)No, overdetermined systems cannot be consistent because there are fewer free variables than equations. For example, the system of equations below has no solution.x1=2, x2=4, x1+x2=12d)No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.x1=2, x2=4, x1+x2=24
Answers
a) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (2,4)
x1=2, x2=4, x1+x2=6
An overdetermined system of linear equations can have infinitely many solutions if the equations are dependent, meaning they are linearly dependent and can be derived from one another by a linear combination. If a system of equations is dependent, it means that the equations are not providing new information.
b) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.
x1=2, x2=4, x1+x2=8
An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.
d) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.
x1=2, x2=4, x1+x2=24
An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.
c) is not a valid option as it contains a mix of concepts of dependent and independent systems and also the system of equations is inconsistent.
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Answer the screenshot
Answers
The domain of the given function f(x) = √(x⁴ - 1) include the following: C. {x|x ≤ -1 or x ≥ 1}.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. Additionally, the horizontal extent of a graph represents all domain values (input values) and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Next, we would use an online graphing calculator to plot the graph of the given function f(x) = √(x⁴ - 1). By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain:
Domain = (-∞, 1) U (1, ∞)
By using set builder notation, the domain of this function f(x) = √(x⁴ - 1) can be re-written as follows;
Domain = {x|x ≤ -1 or x ≥ 1}.
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solve for w
-5/2 + 1/4w = -5/8
Answers
Answer: 15/2
Step-by-step explanation: -5/2 + 1/4W = -5/8
- 1/4W = -5/8 + 5/2
- 1/4W = 15/8
- W = 15/8 × 4
- W = 15/2
What is 1/2 as a decimal and percent?
Answers
1/2 as a decimal is 0.5. As a percent, it is 50%. 1/2 can be written as a decimal by dividing the numerator (1) by the denominator (2).
In this case, 1 divided by 2 is 0.5. To convert this decimal to a percent, simply multiply it by 100. 0.5 multiplied by 100 is 50%, so 1/2 as a percent is 50%.
1/2 is 0.5 as a decimal and 50% as a percent.
1/2 is equal to 0.5 when written as a decimal. This means that 1 is divided by 2, resulting in 0.5. To convert this decimal to a percentage, it is necessary to multiply it by 100. When 1/2 is multiplied by 100, it comes out to be 50%, meaning that 1/2 as a percent is 50%. This shows that 1/2 is equal to 0.5 as a decimal and 50% as a percent.
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a spider is on the rim of an empty conical cup when it spies a fly one third of the way around the rim. the cone is 36 cm in diameter and 24 cm deep. in a hurry for lunch, the spider chooses the shortest path to the fly. how long is this path?
Answers
The length of the shortest path is 44.69cm.
To find the length of the shortest path, we need to calculate the distance between the two points on the rim of the conical cup where the spider and the fly are located. Since the cone is symmetric, we can find the distance by considering a cross-section of the cone through the center of the cup.
In this cross-section, the spider and the fly are located on a circumference of radius 18 cm (half of the diameter of the cone). The distance between the spider and the fly is one-third of this circumference, or (2pi18 cm)/3 = 12*pi cm.
However, since the cone is 24 cm deep, the shortest path between the spider and the fly is not a straight line, but a curved path along the surface of the cone. To find the length of this path, we need to use the Pythagorean theorem to find the distance between the two points on the surface of the cone.
The height of the cone is 24cm, and the distance between the two points on the circumference is 12pi cm. Using the Pythagorean theorem, we can calculate the length of the shortest path as the square root of (12pi)^2 + 24^2 = 12pi cm + 576 = √(144π^2+ 576)cm=44.69 cm.
So, the length of the shortest path is √(144*π^2+ 576)cm = 44.69cm
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Solve the system using the substitution method.
10x - 16y = 17
3x + 3y = 9
Answers
Answer:
x = 2.5, y = 0.5
Step-by-step explanation:
[tex]10x - 16y = 17\\3x + 3y = 9[/tex]
Isolate for x or y on the equation of choice (Just choose a random one)
[tex]3y = 9 - 3x\\y = 3 - x[/tex]
Sub new equation into the other equation
[tex]10x - 16(3-x) = 17\\10x -48 + 16x = 17\\26x = 65\\x = 2.5[/tex]
Sub x into new equation
[tex]y = 3 - x\\y = 0.5[/tex]
Three fathers-Paul, Johnson, and Nicolas have between them a total of 15 children of which 9 are boys. Paul has 3 girls and Johnson has the same number of boys. Johnson has 1 more child than Paul who has 4 children. Nicholas has 4 more boys than girls and the same number of girls as Paul has boys. How many boys each do Nicolas and Paul have?
Answers
Answer:
Nicholas has 5 boys, and Paul has 1 boy
Step-by-step explanation:
We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:
[tex]p + j + n = 15[/tex] (1st Equation)
[tex]p_{g} = j_{b} = 3[/tex] (2nd Equation)
[tex]j = p + 1 (p = 4)[/tex] (3rd Equation)
[tex]n_{b} = n_{g} +4[/tex] (4th Equation)
[tex]n_{g} = p_{b}[/tex] (5th Equation)
Whew! That was a lot. We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:
b = g + 4 and b + g = 6
So, we substitute the first equation into the second equation, giving us:
g + 4 + g = 6
2g = 2
g = 1
So, Nicholas has one girl, meaning he has 5 boys.
So, Nicholas has 5 boys, and Paul has 1 boy.
Hope this helped!
How many solutions can a system of 3 linear equations have?
Answers
A system of 3 linear equations can have 0, 1, or an infinite number of solutions.
A system of linear equations is a group of equations with multiple variables. The number of solutions to the system of equations depends on how many equations and how many variables are in the system. A system of 3 linear equations can have 0, 1, or an infinite number of solutions.
If the number of equations is greater than the number of variables, the system is said to be overdetermined and has no solutions.
If the number of equations is equal to the number of variables, the system is said to be determined and has either one or an infinite number of solutions, depending on if the equations are dependent or independent.
If the number of equations is less than the number of variables, the system is said to be underdetermined and has an infinite number of solutions.
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what does 안녕하세요 mean??
Answers
Answer:
I hope my answer is helpful!
"안녕하세요" is a formal and polite way of saying "hello" in Korean. It is commonly used as a greeting, both when meeting someone for the first time and when meeting someone again after a period of time. The literal translation of 안녕하세요 is "Are you at peace?"
A grocery store sells a bag of 6 oranges for $5.22. What is the cost of oranges, in dollars per orange?
Answers
For each given situation, determine if the method of randomization is either appropriate or not appropriate
Answers
Determining if the method of randomization is either appropriate or not for each given situation includes:
A. Inappropriate
B. Appropriate
C. Appropriate.
Randomization is what?
The technique of randomly assigning study participants to various treatment groups is known as randomization.
Randomization can take the form of selecting names at random to place people in groups or flipping a fair coin to place participants in the experimental or control groups.
In contrast to experiments B and C, the randomization strategy used in experiment A is incorrect.
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The number four letter combination that can be formed with the English alphabet is 26 to the fourth power. The number of six letter combination that can be formed is 26 to the sixth power. how many times more six letter combinations can be formed than four letter combinations.
Answers
The times more six letter combinations can be formed than four letter combinations will be 26² times.
How to calculate the scientific notation?It should be noted that scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.
Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.
In this case, the number four letter combination that can be formed with the English alphabet is 26 to the fourth power. The number of six letter combination that can be formed is 26 to the sixth power.
The number of times more six letter combinations can be formed than four letter combinations will be:
= 26^6 / 26^4
= 26^2
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Answer:
26^2
Step-by-step explanation:
Subtract 1/2 and 2/4 using fraction strips
Answers
Answer:
0
Step-by-step explanation:
1/2 = 2/4
1/2-2/4 = 0
Find the solutions of the given equation.
25x² +64 = 289
O A. x =
-√√3, √3
OB.
x =
-9,9
OC.
x = -3, 3
O D. x = -3√3, 3√/3
Answers
The solution of the given equation is x = -3,3. Hence option C is the correct option.
What is a quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in a standard form where x represents an unknown value and a, b, and c represent known numbers, with a ≠ 0.
The number of solutions of a quadratic equation is 2. The degree of a quadratic equation is also 2.
Given equation is
25x² +64 = 289
Subtract 64 from both sides of the equation:
25x² +64 -64 = 289 -64
25x² = 225
Divide both sides by 25:
25x²/25 = 225/25
x² = 9
Take square root on both sides:
√x² = √9
x = ±3.
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10001000 students took a test and the scores are normally distributed, with a mean of 7676 and standard deviation of 55. approximately how many students scored between 8181 and 8686?
Answers
The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.
How is this calculated?z1 = (8181-7676)/55 = 1.89
z2 = (8686-7676)/55 = 3.04
Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.
What is the difference between a standard normal distribution and a non-standard normal distribution?A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.
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Quizz guyz •^•
What is the minimum length runway needed to accommodate airplanes that can accelerate uniformly at 2.7 m/s2 and must reach a ground velocity of 64 m/s before they can?
• Use Method
• Neat
• No nonsense
• No alien language
Notes : Hi, I'm actually originally from Indonesia, sorry if my words are a bit lacking. Greetings from Indonesia guys
Answers
Answer:
758.295 meters
Step-by-step explanation:
If for any reason my answer is wrong, feel free to correct me.
As per your question,
The airplanes accelerate uniformly at 2.7 meters per second^2
And they must reach a ground velocity of 64 m/s.
Therefore
S(Displacement) = u(initial velocity) x time + 1/2(acceleration x time^2)
Initial Velocity = 0 m/s(airplane is at rest)
Acceleration is 2.7m/s^2
Time = ?
Acceleration = Final Velocity - Initial Velocity / Time(t)
2.7 m/s^2 = 64 m/s - 0 m/s / t
2.7(t) = 64
t = 64/2.7
t = 23.703703... rounded to 23.7
S = 0(23.7) + 1/2[2.7 x (23.7)^2]
S = 1/2(2.7 x 561.7) 561.69 is the original answer rounded to 561.7
S = 758.295 meters
Final Answer - An airport would require a runway of minimum length of 758.295 meters to accommodate aircraft of the respective specifications.
2.7 m/s^2 = 64 m/s 0 m/s/t
2.7(t) = 64
t = 64 ÷ 2,7
t = 23.703
or => 23,7
S = 0×(23.7) + 1/2[2,7 × (23,7)²]
S= 1/2(2.7 × 561.7)
S = 758.295 meters
In conclusion:the speed of the plane is 758.295 meters
For every 4 girls in Mr Hegarty's class there are 5 boys. What is the ratio of boys to girls in the class?
Give your answer in its simplest form.
Answers
Answer:
5:4
Step-by-step explanation:
girls = 4
boys = 5
ratio = boys:girls = 5:4
HOPE THIS HELPED
Ben is x cm tall.
Kieran is 8 cm taller than Ben.
Bianca is 2 cm shorter than Ben.
Write an expression, in terms of x, for the mean of their heights in centímetres.
Give your answer in its simplest form.
Answers
hope this helps you understand !!
Answer:
x + 2
Step-by-step explanation:
Ben : x cm
Kieran: (x + 8) cm
Bianca: (x - 2) cm
Mean of their heights = [tex]\frac{Sum of their heights}{Number of people} = \frac{x + (x + 8) + (x - 2)}{3}[/tex]
= [tex]\frac{x + x + 8 + x - 2}{3}[/tex] (Expand the brackets)
= [tex]\frac{x + x + x + 8 - 2}{3}[/tex] (Bring all the like terms together)
= [tex]\frac{3x + 6}{3}[/tex] (Simplify the two sets of like terms)
= [tex]\frac{3(x + 2)}{3}[/tex] (Extract the common factor '3' in the numerator)
= (x + 2) cm ([tex]\frac{3}{3} = 1[/tex])
The ratios from parts A and B are equivalent. Write an equation by setting the ratios equal to one another.
Answers
Answer:
the solution is 9/2 = X24
Two boats left the harbour at the same time. One travelled at 10km/h on a bearing N47degreeE. The other traveled at 8km/h on a bearing of N79degreeE. How far apart are the boats after 45min? Round the distance to nearest tenth of a km.
Answers
Answer:
4.0 km
Step-by-step explanation:
You want the distance between two boats after 45 minutes if they left at the same time and traveled 10 km/h at N47E, and 8 km/h at N79E.
Law of cosinesThe distances the boats traveled in 3/4 hour can be found by multiplying the speed by the time:
distance = speed · time
distance = {10 km/h, 8 km/h} · (3/4 h) = {7.5 km, 6 km}
The distance between their positions can be found from the law of cosines:
c² = a² +b² -2ab·cos(C)
Here, the angle between the vectors is 79° -47° = 32°, so the distance is given by ...
c² = 7.5² +6² -2·7.5·6·cos(32°) ≈ 15.925671
c ≈ √15.925671 ≈ 3.9907
To the nearest tenth km, the distance between the boats is 4.0 km.
__
Additional comment
It can be helpful to draw a diagram. A geometry app can measure the distance for you (attachment 1), or a calculator app can calculate it based on the speed vectors (attachment 2).
