The length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that a table for showing the relation between length and width of a field;
Width (w) Length (l)
0 50
100 150
200 250
300 350
We see, that, width is 50 less than the length.
Therefore, the function (w) to represent the length of the field will be =
w = l-50
Hence, the length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)
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Three workers are digging a hole. They work one by one, and every single of them works exactly
the amount of time it would have taken the other two to complete the digging of the entire hole.
They finish digging the hole by taking one turn each. How many times faster would they have
digged the hole if they worked together?
(A) 2.5 (B) 3 (C) 3.5 (D) 4 (E) 5
The work would be finished 3 times faster if they had been doing the work at the same time. The correct option is B.
Rate of doing workAssumption;
Provided each one of the workers works for an hour which is equivalent to the time it takes to finish the hole.
In essence, the total time required to finish the ditch by 2 workers is; 2 hours.
Hence, for 3 workers working simultaneously, the time required is
1hour = 60 minutes
However, since they took 1 hour turns on the job, it follows that; The total time used is;
Total time = 3 × 1hr = 3 hours = 180 hours
Hence they could have finished the work in;
R = 180/60 times faster =3 times faster.
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How do you find the slope of x =- 4?
The slope of x= -4 is unidentified.
The x= -4 is a vertical line and slope cannot be found.
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; the reason for this usage is unclear, although it may be found in O'Brien's (1844)[2] and Todhunter's (1888][3] formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope.
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Using expanded forms, explain why the following problems with unlike bases do not follow the multiplication and division rules of exponents
Pls hurry and thank you!!!!
113.778=one hundred thirteen million seven hundred seventy-eight thousand, and 11,664=eleven thousand six hundred sixty-four is the enlarged form.
What do you meant by expanded form ?1.Comprehensive Notation Form:
[tex]$$\begin{aligned}& 11,664= \\& 10,000 \\& +1,000 \\& +600 \\& +\quad 60 \\& +4 \\&\end{aligned}$$[/tex]
Increased Factors Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10,000 \\& +1 \times 1,000 \\& +6 \times 100 \\& +6 x \quad 10 \\& +4 \times \quad 1 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10^4 \\& +1 \times 10^3 \\& +6 \times 10^2 \\& +6 \times 10^1 \\& +4 \times 10^0 \\&\end{aligned}$$[/tex]
Text Format:
11,664=eleven thousand six hundred sixty-four
2. Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 100 \\& +10 \\& +3 \\& +\quad 0.7 \\& +\quad 0.07 \\& +\quad 0.008 \\&\end{aligned}$$[/tex]
Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 100 \\& +1 \times \quad 10 \\& +3 \times \quad 1 \\& +7 \times \quad 0.1 \\& +7 \times \quad 0.01 \\& +8 \times \quad 0.001 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 10^2 \\+ & 1 \times 10^1 \\+ & 3 \times 10^0 \\+ & 7 \times 10^{-1} \\+ & 7 \times 10^{-2} \\+ & 8 \times 10^{-3}\end{aligned}$$[/tex]
Text Form:
113.778=one hundred thirteen million seven hundred seventy-eight thousand,
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A line has a slope of 1/5 and passes through the point (3,10). What is its equation in point-slope form? Use the specified point-slope form.
The equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that a line has a slope of 1/5 and passes through the point (3, 10)
We can write the slope of the line as -
m = 1/5
For the point (3, 10), we can write -
y = (1/5)x + c
10 = (1/5) x 3 + c
c = 10 - 3/5
c = 47/5
Therefore, the equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).
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Donna reads 56 chapters of a book in 7 hours. What is her rate in chapters per hour?
Answer:
To find what her rate for how many chapters she reads per hour, you want to find out what times 7 gives you 56, or you can simply divide:
56/7 = 8
Donna reads 8 pages per hour.
Step-by-step explanation:
Hope it helps! =D
Simon builds this podium on a platform.
What is the combined volume of the podium and the platform?
Enter your answer in the box
The combined volume of the podium and the platform is 64 cubic feet.
This sort of figure offers several choices. We really only need to consider how to divide the front face into appropriate rectangles, since the depth of the figure is 2 feet everywhere.
The volume is the area of the front face times that depth.
1) A 2 ft × 4 ft upright atop a 12 ft × 2 ft horizontal base. The frontal area is
(2 ft)(4 ft) +(12 ft)(2 ft) = 8 ft² +24 ft² = 32 ft
so, the total volume is:
V = frontal area × depth
V= (32 ft²)(2 ft)
V=64 ft³
2) A vertical post of 2 ft × 6 ft at the left side with a horizontal protrusion of 10 ft × 2 ft from its bottom.
The frontal area calculated this way is:
(2 ft)(6 ft) +(10 ft)(2 ft) = 12 ft² +20 ft² = 32 ft²
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
3) A 6 ft × 12 ft rectangle with a 4 ft × 10 ft cutout from the upper right corner. The area calculated this way is
(6 ft)(12 ft) -(4 ft)(10 ft) = 72 ft² -40 ft² = 32 ft² . . . . . same as above
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
V=64 ft³.
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The number cube with sides labeled 1 through 6 is rolled.
Which events are likely to occur? Select all that apply. Multiple select question. A) rolling a 1 or a 2 B) rolling an odd number C) rolling an even number D) rolling a a number less than 6 E) rolling a number greater than 2
Answer:
Events D and E are likely to occur.----------------------------------------
The number cube has sides 1 through 6. The probability of each number is same, 1/6.
Given events below, see how likely they are to occur:
A) rolling a 1 or a 2,
this is a 2/6 = 1/3 < 1/2, not likely;B) rolling an odd number,
this is a 3/6 = 1/2, not likely;C) rolling an even number,
this is a 3/6 = 1/2, not likely;D) rolling a a number less than 6,
this is 5/6 > 1/2, likely to occur;E) rolling a number greater than 2,
this is a 4/6 = 2/3 > 1/2, likely to occur.What is a 2 step problem?
A 2-step problem is a mathematical problem that can be solved using two steps or operations. These types of problems are typically simple and can be solved using basic arithmetic or algebraic concepts.
For example, a 2-step problem could involve solving for one variable in one equation and then substituting that value into another equation to find the value of a second variable.
For example:
2x+3y=10 and 3x-2y=5
Here, first step would be to solve for x in the first equation by isolating x and in the second step we can substitute that value of x in the second equation to solve for y.
It can also refer to a problem that can be solved in two steps by breaking the problem down into simpler parts. For example, a 2-step problem in geometry could involve finding the area of a shape by first finding the area of one part of the shape and then adding that to the area of another part of the shape.
In general, 2-step problems are not complex and can be solved easily by breaking down the problem into simpler parts and solving each part separately.
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Find the value of each expression.
a. 1/4 • (-12)
b. -1/3 • 39
c. (-4/5) • (-75)
d. -2/5 • (-3/4)
e. 8/3• -42
By using simple arithmetic and using calculator we get:
a. 1/4 • (-12) = (-3)
b. -1/3 • 39 = -13
c. (-4/5) • (-75) = 60
d. -2/5 • (-3/4) = 3/10 = 0.3
e. 8/3• -42 = -56
What is arithmetic?Arithmetic is a branch of mathematics that deals with the manipulation of numbers and their properties. It is the study of numbers and the operations that can be performed on them, such as addition, subtraction, multiplication, and division. Arithmetic also includes concepts such as fractions, decimals, and percentages. The study of arithmetic is fundamental to many other branches of mathematics, including algebra, geometry, and calculus, as well as many practical fields like finance, engineering, and computer science.
What is calculator?A calculator is a device that performs mathematical calculations. It can be a handheld device or a software program on a computer or mobile device. Calculators typically have buttons or keys for performing basic arithmetic operations, such as addition, subtraction, multiplication, and division, as well as more advanced functions like trigonometry and logarithms. Some calculators also have the ability to store and recall numbers, perform conversions between units of measurement, and perform other specialized functions.
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What's the fewest number of people in a room where it's probable (>50%) that a pair of them share a birthday
There is a probable (>50%) that two people in a room with 23 people will share the same birthday.
What is probability?Probable means likely to occur or prove true, or having more evidence for than against, or evidence that inclines the mind to belief but leaves some room for doubt, or affording ground for belief.
Even while it may appear odd that only 23 people are needed to achieve a 50% likelihood of a shared birthdate, this conclusion is made more logical by keeping in mind that birthday comparisons will be done between all potential pairs of people.
There is a 50% chance that two people in a room with 23 people will share the same birthday. Though it may seem strange, it is mathematically accurate.
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How do you make a truth table?
If we want to create a truth table , for say expression (P ∨ Q)∧(~P⇒Q) , then we will create different columns having the column head as , P , Q , ~P , P ∨ Q,~P⇒Q and (P ∨ Q)∧(~P⇒Q) and then perform the logical operation on them.
Truth table is a medium used to perform logical operations on expressions. These operations consists of Boolean algebra or Boolean functions expressions.
On performing these logical operation we get to know whether the propositional expression is correct or incorrect, based on the input values. This entire process is based on Boolean algebra and the table is made up of rows and columns for one or more input values.
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Explain how the Distributive Property can be used to solve the equation.
3(x + 4) = 36.
Answer: x=8
Step-by-step explanation:
3(x+4) = 36
3x+12= 36
3x-12= -12
3x = 24
— —
3 3
X=8
Researchers were interested in the season records of the Major League baseball teams, including the Los Angeles Dodgers, and the Cincinnati Reds Baseball team. Researchers collected the data at the end of the season. This sample data collection method is considered to be:
On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.
what are statistical data?Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts
data across time numbers about the population
The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.
Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.
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Identify a method of developing systems that is well-suited to traditional project management tools and technique
The waterfall model has equivalent flexibility to other approaches. suitable for conventional project management tools and methods.
The waterfall model of the software development life cycle is the greatest technique for creating systems.
This includes the following elements:
1. The requirements phase, which takes into account the needs needed to build the product
2. The product's design is created
3. The programmers who wrote the code to put the product into action built the product.
4. The product is examined and all flaws are fixed to ensure that it responds correctly to inputs.
5. The systems are periodically maintained to ensure continued operation and proper output
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Solve for x in this triangle. Round your answer to the nearest tenth. 37⁰ X 14
Answer:
x ≈ 18.6
Step-by-step explanation:
using the tangent ratio in the right triangle
tan37° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{14}{x}[/tex] ( multiply both sides by x )
x × tan37° = 14 ( divide both sides by tan37° )
x = [tex]\frac{14}{tan37}[/tex] ≈ 18.6 ( to the nearest tenth )
Lucy ran the triangular route represented by ABDF. Kaitlyn starts from point H and wants to run the same distance as Lucy. What triangular route can Kaitlyn run? Explain.
Answer: Kaitlyn can run the triangular route represented by HEDF. This route is the same distance as Lucy's route, ABDF, because it is composed of three sides of the same length. H is the starting point, E is the midpoint, and F is the endpoint. The route starts at point H, travels to point E, then to point D, and finally to point F, completing the triangle.
An operator works a basic fortnight at a basic
rate of $8. 95 and earns $671. 25. Determine the
basic fortnight for the operator.
just the answer pls
To determine the basic fortnight for the operator, we need to divide the operator's earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
The basic fortnight for an operator is the number of fortnights the operator has worked at their basic rate of pay. In this case, the operator has earned $671.25 at a basic rate of $8.95 per fortnight. To determine the basic fortnight, we need to divide the operator's total earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
So, the operator has worked 75.05 basic fortnights. It means he has been working for 75.05*14=1053 days. This is the number of days the operator has worked at their basic rate of pay. It is important to note that this calculation assumes that the operator has not earned any overtime pay or other bonuses.
$671.25 ÷ $8.95 = 75.05
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What type of lines will be presented by the system of equations 2x 3y 6 and 4x 6y 11?
The system of equations 2x+3y=6 and 4x+6y=11 will present two lines in the coordinate plane.
The linear equation is a mathematical expression that describes a straight line in a coordinate plane. It is of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be expressed in other forms, such as ax + by = c, where a, b, and c are constants.
Since each equation represents a line, and the system has two equations, it will have two lines. The lines will be in slope-intercept form (y = mx + b), with different slopes and y-intercepts. The lines will intersect at one point, which is the solution to the system of equations.
The system of equation will present the unique straight line as the solution in two-dimensional coordinate plane.
Two lines in the coordinate plane will present the system of equations 2x+3y=6 and 4x+6y=11 .
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Please help!
ponential functions are in the form y = a(b)'.
What values of b make it an exponential growth function?
What values of make b it an exponential decay function?
What is the median of the following 9 numbers: 23, 15, 32, 27, 19, 11, 30, 19, 22?
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
What is a median?The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.
The median for odd data will be
Median = [(n + 1) / 2]th
The median for even data will be
Median = {[n / 2 + (n + 2)/ 2] / 2}th
The data is given below.
23, 15, 32, 27, 19, 11, 30, 19, 22
Arrange the data in ascending order. Then we have
11, 15, 19, 19, 22, 23, 27, 30, 32
Then the median of the following 9 numbers is calculated as,
Median = [(9 + 1) / 2]th
Median = (10 / 2)th
Median = 5th
Median = 22
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
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The sum of the interior angles of a polygon is 20 x 180.
Work out the number of sides of the polygon.
sides
So the polygon has 22 sides.
A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle with three sides is an example of a polygon.
The sum of the interior angles of a polygon can be calculated using the formula:
(n-2) * 180 = sum of the interior angles
Where n is the number of sides of the polygon.
We know that the sum of the interior angles is 20*180, so we can substitute this into the formula:
(n-2) * 180 = 20 * 180
Solving for n, we get:
n = (20 * 180) / 180 + 2
n = 20 + 2
n = 22
So the polygon has 22 sides.
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A sample of fish from a river showed
that of the fish were less than one
year old. If there are an estimated
8,000 fish in the river, about how
many of them are less than one year
old?
What is the 4th interval called?
The 4th interval is called perfect. It is also called consonant.
What is interval in mathematics?
In mathematics, interval means the gap between two particular numbers in where some numbers can be located. The numbers that are kept between two particular numbers are all real and their ranges must be maintained between two particular number.
What is the 4th interval called?The 4th interval is called perfect. The fourth interval is always consonant because it is maintained by earlier third and next fifth.
Other perfect intervals along with fourth are unison, fifth and octave. The intervals listed above are all consonant. The fourth interval is called perfect because it behaves just like the unison interval.
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Identify like terms
24a - 12b + 4 - 8a
Answer:
The like terms in this expression are 24a and -8a, and -12b and 12b.
Step-by-step explanation:
The like terms 24a and -8a can be combined by adding the coefficients and the variables, which gives us 24a - 8a = 16a.
The like terms -12b and 12b can be combined by adding the coefficients and the variables, which gives us -12b + 12b = 0.
So the like terms in this expression are 24a, -8a, and -12b, 12b.
he distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.b.The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours..c.The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.d.The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.
The option a "The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance." is correct.
In the given question, we have to write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.
As we know that the distance formula is the multiplication of of speed and time.
So, the distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
So the option a is correct.
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The complete question is:
The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hours while hiking. Write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.
a. The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
b. The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours.
c. The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.
d. The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.
A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.Which of the following is the best interpretation of the probability 0.20 ?
"For all finance workers, 20% will have a tattoo" is the best interpretation of the probability 0.20.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
This can be calculated by taking the number of finance workers with tattoos and dividing it by the total number of finance workers, and then multiplying by 100 to express the result as a percentage.
(Number of finance workers with tattoos / Total number of finance workers) x 100 = 20%.
Here,
"20% of all finance workers will have a tattoo," is the best explanation of the probability 0.20.
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Complete question: A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.
Which of the following is the best interpretation of the probability 0.20 ?
A- For all workers in the United States, 20% will work in finance.
B- For all finance workers, 20% will have a tattoo.
C- For all people with tattoos, 20% will work in finance.
D- For a specific group of 5 finance workers, 1 will have a tattoo.
E- For a specific group of 5 people with a tattoo, 1 will work in finance.
a wall is measured as 5m to the nearest metre find the actual length and the percentage error
Actual length is 5.5m and percentage error is 20%.We can find by using percentage error formula.
What do you mean by percentage error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words the percent error is the relative error multiplied by 100.
How do we calculate percentage error?Subtract the actual value from the estimated value.And then divide the results with the real value. Multiply the results by 100 to find the total percentage.The formula represent it as a percentage of the exact value.Percent error = |Approximate value – Exact Value|/Exact value * 100.
Now we find
wall is measured 5m to the nearest so
approximate value= 4.5
actual value =5.5
putting value in the formula
Percentage error = 5.5- 4.5/5 *100
= 20%
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please assist with helping in the image below!!
It takes 126 cubes that have edge lengths of 1/3 ft to completely fill a plastic bin. What is the area of the base of the bin?
The area of the base of the bin is 9 ft^2.
The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.
Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.
We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.
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How do you find the mean and standard deviation of a simple random sample?
The steps of finding mean and standard deviation of a simple random sample are given below.
What is standard deviation and mean?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.
The steps of finding mean and standard deviation of a simple random sample are:
Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX): = σ/n.
How to determine sample means
Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...
Sum divided by the quantity of samples.
The outcome is the mean.
To determine the variance, use the mean.
To determine the standard deviation, use the variance.
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