Prove: If two angles are supplementary, then one of the angles must be obtuse.
Which image provides a counterexample to this statement?
O A.
0 в.
о с.
O D.
A
A
A
В
M
M
M
B
В
B
В
B
м с
M
с
Answers
Option D is the counterexample of this given statement.
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees. For example, angle 110° and angle 70° are supplementary angles because the sum of 110° and 70° is equal to 180°.
Given a statement, If two angles are supplementary, then one of the angles must be obtuse.
In A, ∠BMC is an obtuse angle.
In B, ∠AMB is an obtuse angle
In C, ∠AMB is an obtuse angle.
But in D, there are two right angles. { two right angles are supplementary. }
Therefore, Option D is the counterexample of this given statement.
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Related Questions
Someone pls solve this for me and make it organized
Answers
Answer: The inner rectangles area is forty cubic feet, and the outer rectangles area is eighty cubic feet.
Two parents who are each known to be carriers of an autosomal recessive allele have four children. None of the children has the recessive condition.What is the probability that one or more of the children is a carrier of the recessive allele? Hint: The probability that one or more of the children is a carrier is the same as the sum of all probabilities minus the probability that none of the children is a carrier. The answer is 0.988. I know the answer but do not know the explanation. So, if someone could walk me through it, I would greatly appreciate it.
Answers
The probability that one or more of the children is a carrier of the recessive allele is 0.988.
The probability that one or more of the children is a carrier of the recessive allele can be calculated using the binomial theorem. The binomial theorem states that the probability of a success in a given trial is the sum of all probabilities of success minus the probability of none of the successes.
For the given scenario, we can assume that the probability of each child being a carrier is 0.25 (since each parent is known to be a carrier). The probability of one or more of the children being a carrier is then[tex](1-0.25^4) = 0.988.[/tex]
To calculate this, we first calculate the probability of none of the children being a carrier, which is [tex](1-0.25)^4 = 0.316[/tex]. We then subtract this from 1 to get the probability of one or more of the children being a carrier:[tex](1-0.25)^4 = 0.316[/tex]
Therefore, the probability that one or more of the children is a carrier of the recessive allele is 0.988.
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which of the following represents the process that an analyst goes through when performing statistical analysis?
Answers
Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.
The process of statistical analysis involves the collection of data, organizing it, and summarizing it in an understandable way. After summarizing the data, the analyst can then use a variety of techniques to analyze the data. For example, the analyst may use descriptive statistics such as the mean, median, and mode to describe the data. The analyst may also use inferential statistics such as chi-square tests or correlation tests to determine the relationships between variables. Finally, the analyst may use regression analysis to predict future outcomes based on the data. All of these techniques involve the use of mathematics, primarily algebra and calculus, to solve equations and generate the desired results. Ultimately, the goal of statistical analysis is to draw meaningful conclusions from the data that can be used to inform decision-making.
Statistical analysis involves the collection, organization and summarization of data, followed by the use of descriptive and inferential statistics, and regression analysis to draw meaningful conclusions from the data.
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1. Find the future value F of the given principal under compound interest for the
time period and interest rate specified. Round your answer to the nearest cent.
t = 13 years, r= 2.75% compounded monthly
P= $12,000,
Answers
The future value F of the given principal under compound interest for the
time period and interest rate specified is $17,149.99.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = the number of times compounded in a year.
We have,
t = 13 years
r = 2.75%
Compounded monthly
This means,
n = 12
P = $12,000
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
A = 12000 [tex](1 + 0.00229)^{156}[/tex]
A = $17,149.99
Thus,
The future value is $17,149.99.
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Suppose that we use Euler's method to approximate the solution to the differential equation Let f(x, y) = x5/y. We let x0 = 0.3 and y0 = 9 and pick a step size h = 0.2. Euler's method is the the following algorithm. From xn and yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing xn+1 = xn + h, yn+l = yn + h Complete the following The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.3 y(1.3)
Answers
The actual value of the function is: [tex]$$y(1.3) = \frac{1.3^6}{6} + 8.6835 = 11.6375$$[/tex]
The exact solution to the differential equation can be found using separation of variables. We first integrate both sides of the equation with respect to x and obtain: [tex]$$\int \frac{x^5}{y}dx = \int 1\,dy$$$$\frac{x^6}{6} + c = y$$[/tex]
where c is a constant. From the initial conditions, we can solve for c to get: [tex]$$c = 9 - \frac{0.3^6}{6} = 8.6835$$[/tex]
Therefore, the exact solution is:[tex]$$y(x) = \frac{x^6}{6} + 8.6835$$[/tex]
At x = 1.3, the actual value of the function is: [tex]$$y(1.3) = \frac{1.3^6}{6} + 8.6835 = 11.6375$$[/tex]
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the Richardson family
Answers
The amount of tip is $ 6.40 and the total amount including the tip is given by the equation A = $ 38.40
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount including the tip for family be A
Now , the equation will be
The total amount of the bill without the tip = $ 32.00
The percentage of tip = 20 %
So , the amount of tip is = percentage of tip x total amount of the bill without the tip
Substituting the values in the equation , we get
The amount of tip is = ( 20/100 ) x 32
The amount of tip is = $ 6.40
Now , the total amount including the tip A = total amount of the bill without the tip + amount of tip
Substituting the values in the equation , we get
The total amount including the tip A = $ 32.00 + $ 6.40
The total amount including the tip A = $ 38.40
Hence , the equation is A = $ 38.40
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What is the solution for the problem on the attachment?
Answers
The value of the variable 'x', 'y', and 'z' will be -6, -9, and -1, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
x - y - z = 4
z = x - y - 4 ....1
3x - 2y = 0
y = 1.5x ....2
-2x + 4y + 4z = - 28 ....3
From equations 1, 2, and 3, then we have
-2x + 4(1.5x) + 4(x - 1.5x - 4) = - 28
- 2x + 6x + 4x - 6x - 16 = - 28
2x = - 12
x = -6
Then the value of 'y' is given as,
y = 1.5(-6)
y = - 9
Then the value of 'z' is given as,
z = - 6 - (-9) - 4
z = - 10 + 9
z = -1
The value of the variable 'x', 'y', and 'z' will be -6, -9, and -1, respectively.
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Which frequency table should she use for the histogram?
Answers
The frequency table for the histogram is (d)
How to determine the frequency tableFrom the question, we have the following parameters that can be used in our computation:
82, 83, 89, 67, 65, 88, 66, 69, 83, 81, 94, 68, 82, 69, 86, 83, 88, 62, 64, 93
To plot the dataset on a histogram, the data points must be represented on equal intervals
From the list of options, the histogram for the given data set can be made using the interval, 60–75, 75–90, and 90–105 this is because in this case none of the intervals has a frequency of 0.
Hence, the correct option is D.
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Complete question
Fiona has to plot a histogram of the given data. 82, 83, 89, 67, 65, 88, 66, 69, 83, 81, 94, 68, 82, 69, 86, 83, 88, 62, 64, 93
Which frequency table should she use for the histogram?
A. Interval 60–70 70–80 80–90 90–100 Frequency 8 0 10 2
B. Interval 56–63 63–70 70–77 77–84 84–91 91–98 Frequency 1 7 0 5 5 2
C. Interval 50–70 70–80 80–85 85–90 90–100 Frequency 8 0 6 4 2
D. Interval 60–75 75–90 90–105 Frequency 8 10 2
pls help will mark brainliest asap
Answers
When pentagon ABCDE is translated 2 units down, dilated by a scale factor of 1/2 units and reflected over the x-axis, it will map into pentagon FGHIJ. This proves that the pentagons are similar.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The transformations to this problem are given as follows:
Translation 2 units down -> the new pentagon is closer to the origin, meaning that before being reflected it was brought closer to the origin.Dilation by a scale factor of 1/2, as the side lengths are half of what it were in the original pentagon ABCDE.Reflection over the x-axis, as the pentagon ABCDE was inclined upwards and the pentagon FGHIJ is inclined downwards.More can be learned about dilation at brainly.com/question/3457976
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determine if the following is an example of descriptive or inferential statistics. 85 randomly selected fifty-year-old americans were asked how much money they had saved for their retirement. the average for these respondents was $25,000, the minimum was $0 and the maximum was $1,200,000.
Answers
This is an example of descriptive statistics. Descriptive statistics involves summarizing and describing the main features of a set of data. In this case, the data consists of the responses from 85 randomly selected fifty-year-old Americans about the amount of money they have saved for their retirement.
The statistics provided, such as the average ($25,000), minimum ($0), and maximum ($1,200,000), are all examples of descriptive statistics that summarize the data and provide information about its distribution.
Inferential statistics, on the other hand, involves making inferences about a population based on a sample. Inferential statistics allow us to use the information from a sample to make educated guesses about the characteristics of the population from which the sample was drawn.
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A rectangle has an area of 18 meters square and a perimeter of 18 meters. What are its length and width?
Answers
Answer:
6 m or 3 meters
Step-by-step explanation:
Area formula = w * L
Perimeter formula =2 x (l+w)
So, that is how I found the answer.
Hope this helps!
A table of ordered pairs is shown.
X
y
Which graph best represents these ordered pairs?
1
2
3
5
6
1
1
그를 2를 3를 5를 6를
Answers
A graph that best represents these ordered pairs is: C. Graph C.
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:
Ordered pair = (1/2, 1).Ordered pair = (1, 2).Ordered pair = (1 1/2, 3).Ordered pair = (2, 4).Ordered pair = (2 1/2, 5).Since the values on the x-coordinate (abscissa) increases by 1/2 and the values on the y-coordinate (ordinate) increases by 1, the most appropriate scale 0.5:1, which is best represented by the data points in graph C.
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Special right triangles
Answers
x = 13
y = 13√2
Step-by-step explanation:Special right triangles are right triangles with specific angle measurements whose side lengths follow a certain pattern.
45-45-90 Triangle
A 45-45-90 special right triangle is a triangle that has two 45-degree angles and one 90-degree angle. Remember that in a right triangle, the two shorter sides are called the legs. Additionally, the longest side that is directly across from the right angle is the hypotenuse. In a special right triangle, the legs are equal. Additionally, the hypotenuse is √2 times the leg length. So, if x is the leg, then the hypotenuse is x * √2.
Solving For x and y
In the problem above, x represents one of the legs and y is the hypotenuse. Since this is a 45-45-90 triangle we know that the legs are equal, and one of the legs is 13 units. So, x must equal 13 as well. Then, we know that y must equal x * √2. So, y equals 13√2. This radical cannot be simplified any further, so the final answers are:
x = 13y = 13√2Enter your answer in scientific notation.
A swimming pool is exactly 20 m long, 6 m wide, and 3 m deep. What is its volume in cubic feet to 3
significant figures?
Answers
Answer:
Step-by-step explanation:
The volume of a swimming pool can be calculated as follows:
Volume = Length * Width * Depth
In this case, the length is 20 m, the width is 6 m, and the depth is 3 m, so the volume is:
Volume = 20 m * 6 m * 3 m = 360 m^3
To convert this volume to cubic feet, we can use the conversion factor:
1 m^3 = 35.3147 ft^3
So, 360 m^3 = 360 * 35.3147 ft^3 = 12611.32 ft^3
Rounding to 3 significant figures, the volume of the swimming pool in cubic feet is:
12611.32 ft^3 ≈ 12611 ft^3
Therefore, the volume of the swimming pool in cubic feet to 3 significant figures is 12611 ft^3.
The volume of the swimming pool is 12,800 ft^3.
Explanation:To find the volume of the swimming pool in cubic feet, we need to convert the measurements to feet and then multiply them together. One meter is equal to approximately 3.281 feet. So, the length in feet is 20 m × 3.281 ft/m = 65.62 ft, the width is 6 m × 3.281 ft/m = 19.68 ft, and the depth is 3 m × 3.281 ft/m = 9.84 ft.
Now, multiply the length, width, and depth together: 65.62 ft × 19.68 ft × 9.84 ft = 12,848.156 ft3.
Rounding to 3 significant figures, the volume of the swimming pool is approximately 12,800 ft3.
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Round the numbers in each expression to the nearest whole number.
Then select the expression that can be estimated to 8.
A.
3
1
5
+
5
7
9
B.
1
5
8
+
5
2
5
C.
15
5
7
−
8
2
9
D.
10
1
4
+
1
11
15
Answers
Answer: A, and B
A) 894
B) 728
Step-by-step explanation:
Please help! space space sppace!
Answers
Answer:
C
Step-by-step explanation:
Determine the area of each composite figure. Round to the nearest tenth if necessary.
Answers
Answer:
169m^2
Step-by-step explanation:
8m x 8m =64m^2
(the area of square = side length x side length)
15m x 7m= 105m^2
(the area of parallelogram= length x height)
so the are of the figure is: 64m^2 + 105m^2= 169m^2
use the problem below discuss, and illustrate with examples, how to solve differential equations of the forms dy/dx
Answers
dy/dx = f(x,y)
where f(x,y) is some function of x and y. To solve a differential equation, we need to find the function y that satisfies this equation. There are different methods to solve differential equations, including:
Separation of Variables: In this method, we separate the variables x and y on opposite sides of the equation and then integrate both sides to find the solution.
Example:
dy/dx = x^2 + y^2
Separate the variables:
dy/y^2 = dx/x^2
Integrating both sides:
∫(dy/y^2) = ∫(dx/x^2) + C
-1/y = ln|x| + C
y = C/x
Exact Equations: In this method, we try to find a function F(x,y) such that its partial derivative with respect to x is equal to the right-hand side of the differential equation.
Example:
(x + y) dx + x dy = 0
Find F(x,y) such that ∂F/∂x = x + y and ∂F/∂y = x:
F(x,y) = x^2/2 + xy
Integrating both sides with respect to x:
F(x,y) = x^2/2 + xy + g(y)
Taking the partial derivative with respect to y:
∂F/∂y = x + g'(y)
Comparing with the original differential equation:
x + g'(y) = x
g'(y) = 0
g(y) = C
Therefore, F(x,y) = x^2/2 + xy + C.
Numerical Methods: In this method, we approximate the solution by using computational algorithms, such as the Euler method or the Runge-Kutta method.
Example:
dy/dx = x^2 + y^2
Use the Euler method with step size h:
y_n+1 = y_n + h * (x_n^2 + y_n^2)
x_n+1 = x_n + h
Iterate this process until x_n+1 reaches a desired value.
These are some of the most common methods to solve differential equations. The choice of method depends on the form of the equation and the desired level of accuracy
3. problem 3: vectors spaces. determine if the following sets with operations defined over the given fields are valid vector spaces.
Answers
Out of the given three sets, only set a and C are valid vector spaces because A produces vectors in the same subspace on calculative operations and C produces a 0 on one of its function's values.
Because A is a subspace of [tex]R^{4}[/tex] (a vector space), it satisfies the requirement that vector addition and scalar multiplication produce vectors in the same subspace, making it a vector space. The zero vector's inclusion in the set is a further given. The zero-function is not a part of the set; hence B is not a vector space.
F(x)=0 on the range [-1,1] implies that f(x)=0 someplace on that range, hence C must be a vector space. We know that continuous functions satisfy the requirements for a subspace of a vector space since they have clearly defined function addition and scalar multiplication.
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Complete question is:
Determine if the following sets with operations defined over the given fields are valid vector spaces.
A = {(a,b,c,d) ∈ R4: a+5c+d=0}
B = {f ∈ C [0,1]: f (0) =1}
C = {f ∈ C [−1,1]: ∫1−1 f(x) dx=0}
The perimeter of a rectangular garden is 64 centimeters. The length of the garden is 3 times the width. Find the length and the width.
Answers
Answer:
l=24, w=8
Step-by-step explanation:
64/2=32 for one length and one width
l=3w
l+w=32
3w+w=32
4w=32
w=8
8*3=24=l
One popular model had a front wheel with a 52 in. diameter and one spoke on the back wheel measuring 9 in. Hint: A bicycle spoke is a rod bl that connects the edge (rim) of a wheel to the center ot the wheel. Determine the diameter of the back wheel.
Determine the diameter of the back wheel.
Answers
The diameter of the back wheel is 163.68 inches.
What is diameter?Diameter is a straight line passing through the center of a circle, connecting two points on the circumference of a circle. It is the longest possible distance between any two points on the circle and is used to measure the size of a circle. The length of the diameter is twice the radius of the circle. The diameter is also the measure of the distance across a circle, rather than the circumference.
To do this, we first need to calculate the circumference of the front wheel, which is the distance around the edge of the wheel. The circumference of a circle is calculated using the formula C = π x D, where C is the circumference and D is the diameter. Therefore, the circumference of the front wheel is 3.14 x 52 = 163.68 inches.
Next, we need to divide the circumference of the front wheel by the number of spokes on the back wheel. Since there is only one spoke on the back wheel, we can divide the circumference of the front wheel by 1. Therefore, the diameter of the back wheel is 163.68 inches.
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-2x + 5 < 2 and 3y - 3 > 1
Answers
The combined inequality for the conditions is 2x + 3y > 7.
What is linear inequality?The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).
Given inequalities,
-2x + 5 < 2 and 3y - 3 > 1
-2x + 5 < 2
subtract 2 from both sides
-2x + 5 - 2 < 2 - 2
-2x + 3 < 0
multiply by -1 to change the sign,
-1(-2x + 3) > 0
2x - 3 > 0 .......(1)
and 3y - 3 > 1
subtract 1 from both sides
3y - 3 - 1 > 1 - 1
3y - 4 > 0..........(2)
since both equations are greater than zero we can add both equations,
2x - 3 + 3y - 4 > 0
2x + 3y > 7
Hence combined equation is 2x + 3y > 7.
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The complete question is -2x + 5 < 2 and 3y - 3 > 1,
find the combined equations.
Total Cups in Boxes:
18
36
54
66
72
84
Total Numer of Boxes: 3
6
9
1.) How many boxes are needed for 66, 72, and 84 cups?
Answers
Answer:
Step-by-step explanation:
For 66 cups, 9 boxes are needed.
For 72 cups, 9 boxes are also needed.
For 84 cups, 9 boxes are also needed.
Please can someone help me Im stuck
Answers
Solving an exponential equation we will see that the correct option is C.
How to find the interest rate?We know that if the 1is P ( a percentage) and the initial value is A, then the value after x years is:
A' = A*(1 + P/100%)^x
We want the value $70 to be doubled after 5 years, sowe can write the equation:
$140 = $70*(1 + P/100%)^5
Now we need to solve that for P.
$140/$70 = (1 + P/100%)^5
2 = (1 + P/100%)^5
2^(1/5) = 1 + P/100%
(2^(1/5) - 1)*100% = P
14.8% = P
Then the correct option is C.
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Write a system of equations for this word problem. DO NOT SOLVE IT
Tickets to the movie theater are $5.50 for children
and $7.00 for adults. On Saturday, 1,250 people
attended the movie theater (adults and children)
The movie theater received $7,979 in ticket sales.
How many children and how many adults
attended the theater on Saturday?
Put answer here⬇️
Equation
TOPIC—
# of tickets—
$ earned—
PLEASE HELP ASAP
Answers
A system of equations for this word problem is
x + y = 1,2505.5x + 7y = 7,979.What is a system of equations?A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.
A system of equations is also called simultaneous equations.
The cost of movie theater tickets per child = $5.50
The cost of movie theater tickets per adult = $7.00
The total attendees on Saturday = 1,250
The total ticket sales = $7,979
Let the number of children who attended = x
Let the number of adults who attended = y
Equations:x + y = 1,250... Equation 1
5.5x + 7y = 7,979... Equation 2
Multiply Equation 1 by 5.5:
5.5x + 5.5y = 6,875... Equation 3
Subtract Equation 3 from Equation 2:
5.5x + 7y = 7,979
-
5.5x + 5.5y = 6,875
1.5y = 1,104
y = 736
x = 1,250 - y
x = 1,250 - 736
x = 514
Thus, we can conclude that 514 children and 736 adults attended the movie theater on Saturday.
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pls help and give an explanation :)
You mix 4/5 quart of blue paint for every 1/3 quart of red paint to make 3 2/5 quarts of purple paint. How much blue paint and how much red paint do you use?
Answers
The total amount of paint used is x + 12/5 * x = 17/5 * x quarts.
Since the total amount of paint used is 3 2/5 quarts, we have 17/5 * x = 3 2/5, which gives us x = 2/5 quarts of red paint.
So, the amount of blue paint used is 12/5 * 2/5 = 2 2/5 quarts.
Therefore, you use 2/5 quarts of red paint and 2 2/5 quarts of blue paint
Answer:
You would use one quart of red paint and 2.4 quarts of blue paint.
Step-by-step explanation:
You first want to make 3 2/5 into a decimal. To do that you multiply 3x5 and add 2 which equals 17/5. Then you divide 17 by 5 and you get 3.4. So, now you know that you want your blue paint plus your red paint to equal 3.4 So, add 4/5 and 1/3 which equals 1.13333333333. Multiply 1.13333333333 and 3 which equals 3.4. So use the equation (4/5+1/3)x3 and you'll get 3.4. This shows that everything that you do was right.Then multiply just 1/3 x 3 and you'll get your answer which is 1. Then multiply just 4/5 x 3 and you'll get 2.4.
Find the standard deviation of the data set. (Do not round until the final answer. Round final answer to 1 decimal place.) You must do this problem without using the standard deviation capabilities of a calculator. Ages of Last 6 Presidents at Inauguration
George Bush
64
Bill Clinton
46
George W. Bush
54
Barack Obama
47
Donald Trump
70
Joe Biden
78
Answers
The mean of the data set is 58.3. The standard deviation of the data set is 10.8.
What is the standard deviation?In descriptive statistics, the standard deviation measures how widely the data points vary from the mean. It describes how values are distributed throughout the data sample and measures how widely apart data points are from the mean.
Sum of all values divided by the number of values.
Mean = ( 64 + 46 + 54 + 47 + 70 + 78 ) / 6
Mean = 58.3
The mean of the data set is 58.3.
The square root of the sum of the difference squared between each value and the mean is divided by the number of values subtracted by 1. So
[tex]\sigma =\sqrt{\dfrac{(X-\bar X)^2}{n- 1 }[/tex]
[tex]\sigma = \sqrt{\dfrac{(64 - 58.3)^2+(46 - 58.3)^2+(54 - 58.3)^2+(47-58.3)^2+(70-58.3)^2+(78-58.3)^2}{6-1}\\[/tex]
σ = 10.8
The standard deviation of the data set is 10.8.
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PLEASE HELPP it needs to be done by the 3rd!
Answers
Answer:
20 because the breathe is 18 to get it length
A puffin leaves a cliff and flies 38 km due east then 54 km due north to an island.
Work out the bearing from the cliff to the island.
Give your answer to the nearest degree.
Answers
The bearing here is given as 54.89 degrees degrees
How to solve for the bearingThe distance that the puffin flies is 38 km due to the east
Then the distance is 54 km due to the north
We would have the height h = √(p²+b²)
We would have to solve this out such that :
=√54²+38²
h = 66.03 units
From here we would have to solve for sine θ
sin θ = 54 / 66.03
sine θ = 0.818
θ = sin ⁻¹0.818
= 54.89 degrees
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Chebyshev’s Theorem
For any set of data:
At least 75% of the data fall in the interval from __________ to __________. At least 88.9% of the data fall in the interval from __________ to __________. At least 93.8% of the data fall in the interval from __________ to __________.
Answers
Answer:
Step-by-step explanation:
At least 75% of the data fall in the interval from the first quartile (Q1) to the third quartile (Q3).
At least 88.9% of the data fall in the interval from the first decile (D1) to the ninth decile (D9).
At least 93.8% of the data fall in the interval from the second percentile (P2) to the 98th percentile (P98).
Note: The quartiles, deciles, and percentiles divide a set of data into 100 equal parts and provide information about the distribution of the data. The first quartile (Q1) is the 25th percentile, the third quartile (Q3) is the 75th percentile, the first decile (D1) is the 10th percentile, the ninth decile (D9) is the 90th percentile, the second percentile (P2) is the 2nd percentile, and the 98th percentile (P98) is the 98th percentile.