Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.
Measures of the variation of a distribution:
Measures of the variation of distribution are used to quantify the spread or dispersion of the data points in the distribution.
Variance:The variance is a measure of the variation of distribution that represents how spread out the data points in a distribution are from the mean.
A higher variance indicates that the data points are more spread out, while a lower variance indicates that they are more tightly clustered around the mean.
The variance is useful when the data is normally distributed and there are no extreme outliers in the dataset.
Standard deviation:Standard deviation is a measure that shows how the spread or dispersion of a set of data points from the mean.
The standard deviation can tell us how tightly or loosely the data points are clustered around the mean. A smaller standard deviation indicates that the data points are tightly clustered, while a larger standard deviation indicates that the data points are more spread out.
The standard deviation is useful when the data is normally distributed and there are no extreme outliers in the dataset.
Some of the measures of the variation of distribution are Range, Interquartile range, Coefficient of variation, etc.
Therefore,
Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.
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f(x)=x^2+7
find x if f(x) = 24
Write in ascending order
x= _______ and ______
Answer:
[tex]\huge\boxed{\sf x = \pm \sqrt{17} }[/tex]
Step-by-step explanation:
Given function:f(x) = x² + 7
Given that, f(x) = 24
24 = x² + 7
Subtract 7 from both sides24 - 7 = x²
17 = x²
Take square root on both sides x = ±√17So,
x = √17 or x = -√17
[tex]\rule[225]{225}{2}[/tex]
rational number definition
A rational number is one that has a non-zero denominator and can be written as a fraction of two integers.
A rational number is one that has a non-zero denominator and can be written as the ratio of two integers. This indicates that a rational number must have an integer denominator and numerator, and that the denominator cannot be 0.
Rational numbers can be positive or negative, and they include all integers, fractions, and terminating or repeating decimals. A and b can be stated as a/b when both of them are integers and b is not equal to 0. It is essential to understand rational numbers in mathematics, and fields like computer science, physics, and engineering frequently use it in their daily work. as well as computer science.
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Amelia has 2 gallons of paint. She uses
1/3 of the paint on a fence. How many
gallons of paint does she use?
Answer:
2/3 gallons
Step-by-step explanation:
0.67 gallons or 2/3 gallons is used on the fence.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
Amount of gallons = 2 gallons
The amount used on a fence.
= 1/3 of 2 gallons
Now,
1/3 x 2 gallons
= 2/3 gallons
= 0.67 gallons
Thus,
0.67 gallons or 2/3 gallons is used on the fence.
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what is the statistical test that will be used in this week's lab
The correct option is (a) Student's t-test. The statistical test that will be used in this week's lab is Student's t-test.
Student's t-test is a statistical test used to compare the mean of two samples. It is used to determine whether there is a statistically difference among two populations or not. The t-test generally calculates the difference.
And if that difference is large till the limit, then it can be summarized that the means of two samples are very different. The t-test can be useful in comparison the means of two independent samples or the means of two dependent samples. And it is basically based on the Student's t-distribution.
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Full Question:
'What is the statistical test that will be used in this week's lab?
a. Student's t-test
b. No statistical test will be run on this data
c. Chi-square test
d. Kruskal-Walls test
e. Rank-sum test
A shipment of 8 tons of sugar is separated into containers of equal size. If the shipment fills 3 3/5 containers, how much sugar can one container hold?
THIS IS TIMED HELP ME OUT
Therefore, one container can hold 20/9 tons of sugar.
To simplify this expression, we can convert the mixed number 3 3/5 to an improper fraction:
3 3/5 = (5*3 + 3)/5 = 18/5
So the expression becomes:
8 tons / (18/5) containers
To divide by a fraction, we can multiply by its reciprocal:
8 tons / (18/5) containers = 8 tons * (5/18) containers
Now we can simplify the expression and solve for the amount of sugar in one container:
8 tons * (5/18) containers = 40/18 tons/container = 20/9 tons/container
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What is the Z Score for a 99 confidence interval?
The Z score for a 99% confidence interval is approximately 2.576.
A confidence interval is a range of values that, with a given degree of certainty, is likely to contain the real value of a population parameter.
For example, a 99% confidence interval means that if we were to take repeated samples of the same size from the same population
To figure the interval estimate for each sample,
Approximately 99% of these intervals would contain the true population parameter.
To find the Z score for a 99% confidence interval,
We can make use of a calculator or a conventional normal distribution table.
The Z score for a 99% confidence interval corresponds to the point on the standard normal distribution
Where the area to the right of the Z score is 0.01
(As the confidence interval is split evenly into two tails, each with a probability of 0.005).
Utilizing a standard normal distribution table or calculator,
We find that the Z score for a 99% confidence interval is approximately 2.576.
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A number z divided by 2 is at least -6.
A number z divided by 2 is at least -6 is expressed as z ÷ 2 = ≥ -6
What is division?One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal parts. Every day, we might use the division technique in various situations.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.
On a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. 7 It's not necessary for this number to be an integer.
The expression to represent this problem is:
z ÷ 2 = ≥ -6
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Rosetta drives 85 kilometres in 1 hour 15 minutes. Work out her average speed in kilometres per hour.
Answer:
68 kilometers per hour
Step-by-step explanation:
Rosetta's average speed is 85 kilometers per hour. This can be determined by dividing the total distance traveled (85 kilometers) by the total time taken (1 hour and 15 minutes, or 1.25 hours). Therefore, 85 kilometers divided by 1.25 hours is equal to 68 kilometers per hour.
Answer: 68 kilometers per hour (look at the image for the explanation)
Step-by-step explanation:
Find m∠BDC big ideas
In the triangle BCD the value of ∠BDC is 105°.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In ΔABC and ΔBCD it is given that -
∠A ≅ ∠B
∠ADC ≅ ∠BCD
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
So, by the theorem stated above -
∠ACD ≅ ∠BDC
In ΔACD he sum of angles of a triangle is 180°.
The equation will be -
∠ACD + ∠ADC + ∠A = 180°
Substitute the values in the equation -
∠ACD + 30° + 45° = 180°
∠ACD + 75° = 180°
∠ACD = 180° - 75°
∠ACD = 105°
Now, since ∠ACD ≅ ∠BDC.
So, ∠BDC = 105°.
Therefore, the measure of ∠BDC is 105°.
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what is the roman numeral l?
The Roman numeral number I means the number "1".
In roman numerals, the counting is represented by using the basic English alphabets in the Upper Case.
The roman numeral I means the number "1". For representing 10 we use "X".
When we have to write 1, 2, 3 we use I, II, III respectively and when we use want to show 5 we use "V" in roman numerals. More English letters like L, C etc. are also used to depicts certain other big numbers in the roman numbers. It is to be noted that one alphabet cannot be used more than three times in an number.
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what is 5pm military time
5:00 pm in military time is 1700 hours. Military time, also known as the 24-hour clock, is a system of timekeeping used by the military, emergency services, and other organizations around the world.
In this system, the day is divided into 24 hours, starting at midnight (0000 hours) and ending at midnight the following day (2400 hours).
To convert from standard time (AM/PM) to military time, you can simply add 12 hours to any time after 12:00 pm. For example, to convert 5:00 pm to military time, you would add 12 hours to 5:00 pm, which gives you 17:00 or 1700 hours.
Military time is commonly used in situations where time needs to be communicated clearly and without confusion, such as in aviation, transportation, and healthcare. It can also be useful in everyday life to avoid confusion and ensure accurate scheduling.
In summary, 5:00 pm in military time is equivalent to 1700 hours, and understanding how to convert between military time and standard time can be useful in a variety of contexts where clear and accurate timekeeping is important.
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how many minutes are in 24 hrs
Answer:
There are 1440 minutes in 24 hours.
Step-by-step explanation:
24 x 60 = 1440
Hope this helped. Have a good day!
how to convert 169 lbs to kg?
The value on converting 169 lbs to Kilograms (Kg) is equivalent to 76.65 Kg .
The Pound (lbs) and Kilogram (Kg) are both the units of measurement used for weight or mass.
They both belong to different systems of measurement. Pound is a unit of measurement in the Imperial and US Customary systems, whereas kilogram is a unit of measurement in the International System of Units (SI).
We know that One pound is = 0.4535 kilograms,
We have to convert 169 lbs to Kg ,
We write ;
⇒ 169 lbs = 169 × 0.4535 Kg ;
⇒ 169 lbs = 76.6415 Kg ≈ 76.65 Kg .
Therefore , 169 lbs is approximately equal to 76.65 Kg .
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Use <,>, or =
1.9 ? 1.90
0.05 ? 0.2
3.88 ? 6.38
The comparision between decimal number are 1.9 = 1.90, 0.05 < 0.2, 3.88 < 6.38
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcd.efg and belongs to the decimal numerical system.
Therefore, one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.
Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.
Here we can see that
1.9 = 1.90
0.05 < 0.2
3.88 < 6.38
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Find the solution of the system of equations. -5x+7y= −5x+7y= \,\,40 40 10x+7y= 10x+7y= \,\,25 25
The quadratic equation of x2-6x+9=0 is C) (x-2)(x+3).
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
This equation is an example of a quadratic equation, which is an equation of the form ax2+bx+c=0, where a, b, and c are real numbers, and a is not equal to 0. In this equation, a is equal to 1, b is equal to -6, and c is equal to 9. To solve this equation, we need to use the quadratic formula, which states that the solutions to the equation are x= -b ± √b2-4ac / 2a. Therefore, the solutions to this equation are x= -(-6) ± √(-6)2-4(1)(9) / 2(1), which simplifies to x=3 ± √3 /2, or x=3 ± √9 /2. This simplifies to x=3 ± √3, or x=3 ± 1. Therefore, the solutions to this equation are x=2 and x=4. The factored form of this equation is (x-2)(x+3), which is option C.
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What is the equation of the line that is parallel to the given line and passes through the point (−2, 2) ?
A. y=1/5x+4
B. y=1/5x+12/5
C. y=−5x+4
D. y=−5x+12/5
As a result, option B is the equation of the line parallel to the specified line and passing through the point (2, 2): y = 1/5x + 12/5.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equals sign (=). The two sides represent the same value, so any operation performed on one side must also be performed on the other side to maintain equality.
Here,
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Two lines are parallel if and only if they have the same slope.
The given line has a slope of 1/5, so any line that is parallel to it must also have a slope of 1/5.
We want to find the equation of a line that is parallel to the given line and passes through the point (-2, 2). We can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line. Substituting the values we have:
y - 2 = (1/5)(x - (-2))
y - 2 = (1/5)(x + 2)
Multiplying both sides by 5 to eliminate the fraction, we get:
5(y - 2) = x + 2
5y - 10 = x + 2
x = 5y - 12
This is the equation of the line that is parallel to the given line and passes through the point (-2, 2).
However, we can also rewrite the equation in slope-intercept form if we prefer. Solving for y in terms of x, we get:
x = 5y - 12
x + 12 = 5y
(1/5)(x + 12) = y
y = (1/5)x + 12/5
So, the equation of the line that is parallel to the given line and passes through the point (-2, 2) is:
y = (1/5)x + 12/5
Therefore, the equation of the line that is parallel to the given line and passes through the point (−2, 2) is option B: y = 1/5x + 12/5.
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What is r?
150°
115⁰
130⁰
O
110°
105°
r
Answer:
r = 110
Step-by-step explanation:
We can see that we have a polygon that has 6 sides. So we can use the formula [tex]S = (n-2) * 180[/tex] to get the answer to create our algebraic equation, n being the number of sides of the polygon.
[tex]S=(6-2) * 180[/tex]
Solve
[tex]4*180[/tex]
[tex]s=720[/tex]
Now that we have our number, we just have to create an algebraic equation to solve for r
[tex]r+110+150+115+130+105=720[/tex]
Add like terms
[tex]r+610=720[/tex]
Subtract 610 on both sides
[tex]r=110[/tex]
To check our work, we can add all of our angle measurements together.
[tex]110+110+150+115+130+105=720[/tex]
Because this equals 720, we know for sure r = 110.
Measurement math word problems. 25 pts, show working out!
Answer:
bumps down
Step-by-step explanation:
65+82+14+0=161/4=40.25
40.25/65=0.619 this is lowest, so highest accurate
40.25/82=.490
40.25/14=2.875
what is 3 4 as a decimal
3/4 in a decimal, divide the denominator by the numerator to get 3/4 as a decimal 3/4 is 0.75.
We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.
3/4
3[1/2 x 1/2]
3 x [0.5 x 0.5]
3 x 0.25
0.75
To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.
Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.
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Name one math concept that you struggle with initially but you eventually understood it?????????
A football club increases the number of seats in its stadium to 66,000 The manager of the club states they can now seat exactly 45% more people than previously. Explain why the manager cannot be correct
The manager's claim that the new stadium can seat exactly 45% more people than previously is not correct. Instead, the new stadium can accommodate 145% of the previous number of seats, which is an increase of 45% over the original capacity
If a football club increases the number of seats in its stadium by 45%, it means that the new stadium can accommodate 145% of the previous number of seats.
Suppose the previous capacity of the stadium was x seats. Then, the new capacity of the stadium can be calculated by multiplying the previous capacity by 1.45 (which represents the 45% increase in capacity):
New capacity = x × 1.45 = 1.45x
However, the manager of the club claims that the new capacity of the stadium is exactly 45% more than the previous capacity, which means that the new capacity should be:
New capacity = x + (0.45x) = 1.45x
This equation suggests that the increase in capacity is not 45%, but rather an increase of the original capacity by 45%. This is not the same as the increase of 45% over the original capacity.
Therefore, the manager's claim that the new stadium can seat exactly 45% more people than previously is not correct. Instead, the new stadium can accommodate 145% of the previous number of seats, which is an increase of 45% over the original capacity.
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What is the solution to this equation?
25
= 15
O A. x = 20
OB. x = 3
OC. x = 10
OD. x =
75
The solution to the equation 25 - x = 15 is x = 10.
This question is incomplete, the complete question is;
What is the solution to this equation?
25 - x = 15
What is the solution to the given equation?Given the equation in the question;
25 - x = 15
To solve for x, collect like terms and solve for x.
25 - x = 15
Subtract 25 from both sides
25 - 25 - x = 15 - 25
-x = 15 - 25
-x = -10
Divide both sides by -1
-x / -1 = -10 / -1
x = -10 / -1
x = 10
Therefore, the value of x is 10.
Option C) 10 is the correct answer.
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determine if the columns of the matrix form a linearly independent set.[1 4 -3 0 -2 -2 4 1 -4 -5 7 5]
A circular table top of radius 1m has an inner section of radius 75cm which Is made of glass and outer section of wood.if the glass costs #2500per m²,and wood costs #1500per m²,what is the cost of the top of the table,correct to nearest naira
The cost of the top of the table, to the nearest naira, is 7678.
What is area of circle ?Area of circle can be defined as the product of pi and square of radius of circle.
The area of the circular table top can be found using the formula for the area of a circle:
[tex]A = pi*r*r[/tex]
where r is the radius of the entire circle.
[tex]A = π(1m)^2 = π m^2[/tex]
The area of the inner glass section can also be found using the same formula, but with the radius of the glass section:
A_glass =[tex]π(0.75m)^2 = 0.5625π m^2[/tex]
The area of the outer wooden section can be found by subtracting the area of the inner glass section from the area of the entire circle:
A_wood = A - A_glass = [tex]π m^2 - 0.5625π m^2 = 0.4375π m^2[/tex]
The cost of the glass section is 2500 per m², so the cost of the glass section can be found by multiplying the area of the glass section by the cost per square meter:
Cost_glass = [tex]0.5625π m^2 × 2500/m² ≈ 4418.60[/tex]
Similarly, the cost of the wooden section can be found by multiplying the area of the wooden section by the cost per square meter:
Cost_wood [tex]= 0.4375π m^2 × 1500/m² ≈ 3259.68[/tex]
The total cost of the table top is the sum of the cost of the glass section and the cost of the wooden section:
Total cost = Cost_glass + Cost_wood ≈ 7678.28
Therefore, the cost of the top of the table, to the nearest naira, is 7678.
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A cylinder is sliced parallel to its base. The area of the cross section is 36π in2 . What is the radius of the cylinder?
If a cylinder is sliced parallel to its base. The area of the cross section is 36π inch square, then the radius of the cylinder is 6 inches
If we slice a cylinder parallel to its base, we get a circle with the same radius as the cylinder.
We are given that the area of the cross section is 36π in square units. Since the cross section is a circle, we can use the formula for the area of a circle to find the radius.
The formula for the area of a circle is:
A = πr^2
where A is the area of the circle and r is the radius of the circle.
We are given that the area of the cross section is 36π. So, we can set A = 36π and solve for r:
36π = πr^2
Dividing both sides by π:
36 = r^2
Taking the square root of both sides:
r = ±6 inches
Since radius cannot be negative, the radius of the cylinder is 6 inches
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What is the conversion of 45 c to fahrenheit ?
The converted value of Celsius to Fahrenheit represented as 45 Celsius equals to 113 Fahrenheit.
Temperature is measured by the standard units which is defined as Celsius and Fahrenheit .
Formula which defines the relation of Celsius and Fahrenheit is equal to
(°C × 9/5) + 32 =°F
Now Substitute the given value 45 degree Celsius and convert into Fahrenheit we have,
(45°Celsius × 9/5) + 32
= ( 405 / 5 ) + 32
= ( 81 ) + 32
= 113°Fahrenheit
Therefore, the converted value from Celsius to Fahrenheit for the given temperature 45 Celsius is given by 113 Fahrenheit.
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Thuli invests R5000 for 3 years at 8% p.a simple interest.What is the total value of Thuli's investment after 3 years?Calculate the answer.
The total value of Thuli's investment after 3 years is R6200
What is the total value of Thuli's investment after 3 years?From the question, we have the following parameters that can be used in our computation:
principal, P = 5000
Rate = 8%
Time = 3 years
Using the above as a guide, we have the following:
Amount = P * (1 + RT)
Substitute the known values in the above equation, so, we have the following representation
Amount = 5000 * (1 + 8% * 3)
Evaluate
Amount = 6200
Hence, the amount is R6200
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Alex and his father took a taxi cab that charges $2.60 per mile plus $3.00 for the two passengers, and they paid a total of $18.60. Alex wrote the equation 18.60=2.60b+3.00 for this situation and found b=6, where b represents the number of miles the taxi traveled. How could Alex correctly solve this problem without using the equation?
Answer:
Answer is explained Below
Step-by-step explanation:
He could subtract 3 from both sides of the equation first. Then he could divide both sides to get D alone. When you do the D=
how to convert 20 lb to kg
Answer:
20 lbs = 9.07185 kg
20 x 0.45359237
Step-by-step explanation:
multiply the given lbs value by 0.45359237 kg and you’ll get your answer.
Please help
The step function g(x) is defined as shown
For given Step function also known as piecewise function, The range of g(x) is {-3,2,5} i.e. C.
What exactly is a piecewise function?
A piecewise function has several definitions in various x intervals. The graph of a piecewise function is split into sections that correspond to each of its definitions. The absolute value function is an outstanding example of a piecewise function. Let us look at why it was given that name. We know that an absolute value function is defined as f(x) = |x|.
f(x)=(x if x x≥0)
-x if x<0)
This piecewise function should be interpreted as
When x is higher than or equal to 0, f(x) equals x.
When x is less than zero, f(x) equals -x.
Now,
As range of a given function is given by its y values, here it will be given by values of g(x) and as we can see from question for values of x, g(x) is always equal to -3,2,5.
Hence,
The range of g(x) is {-3,2,5}.
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