Answers
The continuity of the piece-wise functions is defined as follows:
1. Not continuous.
2. Not continuous.
3. Not continuous.
How to define the continuity of the functions?A piece-wise function is a function that has multiple definitions, depending on the input.
Then the function is classified as continuous if the lateral limits at the points that the function change the definition are equal, and also equal to the numeric values of the function.
None of the functions in this problem are continuous, as:
For function 1, lim x -> 0^- = 0, lim x -> 0^+ = 2, hence different lateral limits. At x = 3, the lateral limits are also different.For function 2, lim x -> -6^- = 0, lim x -> -6^+ = 4. At x = 2, the lateral limits are also different.For function 3,lim x -> 0^- = 3, lim x -> 0^+ = -3.More can be learned about the continuity of a function at https://brainly.com/question/24637240
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Related Questions
What is the mean of 1 2 3 4 5?
Answers
Answer:
Step-by-step explanation:
answer is 3 because formula of mean is Mean = {Sum of Observation} ÷ {Total numbers of Observations}.
so 1+2+3+4+5=15/5=3
so 3
The mean or arithmetic mean* is represented with this symbol [tex]\boldsymbol{\sf{\overline{x}}}[/tex], and it is calculated by adding all the data, and dividing them in total, by the total number of data there is.
We calculate the mean.1 ➕ 2 ➕ 3 ➕4➕ 5 = 15➗5=3The mode of 1,2,3,4,5 is 3✅.
How do you tell if a slope is steeper or flatter?
Answers
Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .
Slope is the rate of change in the dependent variable with respect to the independent variable.
For an equation of line of the type - y= mx +c , the slope is given by the m value.
Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.
Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values, the lines have a flatter slope and do not have a steep nature.
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What is the coefficient of y2 in the expression 2x2y 10xy2 5y²?
Answers
Let x be the coefficient of y^2 in the expression 2x^2y+10xy^2-5y^2. So x=5.
What is co-efficient?A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.
Write an example of co-efficient.As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.
The given algebraic expression is 2yx^2+10xy^2-5y^2.
The terms are xy^2, yx^2 any y^2
So the co-efficient of y^2 is 5.
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Determine the domain and range
Answers
Answer:
Domain:
[tex]0 \leqslant x \leqslant 4[/tex]
Range:
[tex]0 \leqslant x \leqslant 64[/tex]
Range: [0, 64]
Remember, the domain is the set of all x-values that satisfy the function, meaning their is a corresponding y-coordinate for every x-coordinate in the domain. The range is the set of all y-value, showing the output range of the function. We use brackets in this case because we have defined points, hence the black dot.
A regression table mainly shows us Select one: a. How we should run the regression analysis.b. what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0)c. that the smallest coefficients always have the greatest impact on the dependent variable.d. if a large constant term is important.e. all of the above.
Answers
A regression table mainly shows us that what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0) .
A regression table is a statistical technique that describes how strongly a dependent variable and one or more independent variables are correlated (s). A field or variable you are attempting to predict or comprehend could be a dependent variable.
Regression allows researchers to predict or explain the variation in one variable based on another variable. The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.
What is interpretation of regression statistics table?In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable. When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression.
A regression table primarily reveals the values of the coefficients as well as the significance of each coefficient (how likely it is that it will depart from 0).
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Your manufacturing requires parts to go sequentially through process a, b, and c. A machine can do process a in 1 minute, b in 2 minutes, and c in 3 minutes. You have two a machines, one b machine, and three c machines. Which process is the bottleneck (can produce the fewest items per unit time)? a) process a b) process b c) process c.
Answers
Answer:
b) process b
Step-by-step explanation:
You have 2 of machine A, each of which can do its process in 1 minute; 1 of machine B, which takes 2 minutes to do its process; and 3 of machine C, each of which takes 3 minutes to do its process.
Production quantitiesIn 6 minutes, the 2 of machine A can produce 2 × 6/1 = 12 units.
In 6 minutes, the 1 of machine B can produce 1 × 6/2 = 3 units.
In 6 minutes, the 3 of machine C can produce 3 × 6/3 = 6 units.
Process B produces the fewest units in equivalent time, so process b is the bottleneck.
__
Additional comment
The production quantity of a given machine is ...
(production time)/(time/unit) = units
This will be multiplied by the number of machines doing the process.
For comparison purposes, we used a production time of 6 minutes here.
Stefan sells Jin a bicycle for $114 and a helmet for $18. The total cost for Jin is 110% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Stefan originally spent $
Answers
Answer:
$12
Step-by-step explanation:
given:
Stefan sells jin a bicycle for $114 and a helmet for $18.
we're gonna add to get the total cost 114 + 18 = $132
The total cost is 110% of what he spent originally to buy the bike and helmet.
divide 110% by 100 to get the answer in decimal which if you calculate is 1.1
now we're gonna make a simple equation and assume what Stefan spends originally is x
1.1 * x = 132
1.1x = 132
(now we want x to be alone so we can find its value so divide both sides by 1.1 (division is the opposite of multiplication if, for example, we have 1.1 - x 1.1 is positive so take it to the other side it'll be negative))
after dividing x=120
therefore, he originally spent $120
and to find how much money Stefan made we're gonna subtract 132-120 = $12
Stefan made $12
Can anyone explain to me how to do this and what's the answer?
Answers
We can solve this question using Linear equations . The answer for the question is Option B.
What do you mean by Linear Equations?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
CalculationSo in the given question the motorboat is 55 km from the shore.
SO y =55 when x=0
where y is the distance and x is time.
after 12 minutes it is 19km from the sea shore.
So y=-3x +55 is the equation.
We can solve this question using Linear equations . The answer for the question is Option B.
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Subtraction property of equality
3
2
= k + 11
2
3
2
− 11
2
= k + 11
2
− 11
2
Addition property of equality
3
2
+ (− 11
2
) = k + 11
2
+ (− 11
2
)
The solution is k =
-7
-4
StartFraction 13 over 2 EndFraction
StartFraction 15 over 2 EndFraction
Answers
Subtraction property of equality is B, -4.
What is subtraction property?
The Subtraction Property of Equality states that if two expressions are equal, then the same expression minus any number will also be equal. In other words, if a = b, then a - c = b - c. This property is important in algebra, as it allows us to solve equations by subtracting the same number from both sides. This property is also known as the Subtraction Property of Equality or the Subtraction Property of Equality of Two Values. It is an important concept that allows us to solve equations, and it is used in all levels of mathematics.
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I need help! Is p+9=2p-3 a one solution, no solution or infinitely Many solutions?
Answers
Answer: One solution
Step-by-step explanation:
A number is doubled and then 3 is subtracted. This gives the same result as if the numbers were quadrupled. What is the number?
Answers
Answer:
-3/2
Step-by-step explanation:
Let's call the number we're trying to find "x". When we double x and then subtract 3, we get 2x-3. The statement says that this is the same as if we had quadrupled x, which would be 4x. We can set these two expressions equal to each other to create an equation:
2x - 3 = 4x
We can solve this equation by first adding 3 to both sides to get rid of the negative number:
2x - 3 + 3 = 4x + 3
This simplifies to:
2x = 4x + 3
We can now subtract 4x from both sides to get rid of the 4x term:
2x - 4x = 4x + 3 - 4x
This simplifies to:
-2x = 3
Finally, we can divide both sides by -2 to solve for x:
(-2x) / (-2) = 3 / (-2)
This simplifies to:
x = -3/2
Therefore, the number we were trying to find is -3/2.
Answer:
Let's call the number we're trying to find "x". If we double x and then subtract 3, we get the expression 2x - 3. If we quadruple x instead, we get the expression 4x. We are looking for a value of x that makes these two expressions equal, so we can set them equal to each other and solve for x:
2x - 3 = 4x
To solve this equation, we can first combine like terms on each side by adding 3 to both sides and then dividing both sides by 2:
2x - 3 + 3 = 4x + 3
2x = 4x + 3
Combining like terms on the left side gives us:
2x - 4x = 4x + 3 - 4x
0 = 3
This equation is clearly false, since no value of x can make 0 equal to 3. Therefore, there is no solution to this problem, and the original number cannot be determined.
In general, if you are trying to solve a problem involving algebraic equations and you end up with a false equation (like 0 = 3 in this case), it means that there is no solution to the problem. This can happen for a variety of reasons, but in this case it is because the original problem statement was not possible or did not make sense.
Step-by-step explanation:
Harriett baked 3 cakes. She cut each cake into equal-size pieces. Each piece was 1/ 9 of the cake. What was the total number of pieces after Harriett cut these cakes?
Answers
Dakota earned $15.75 in interest in Account A and $28.00 in interest in
Account B after 21 months. If the simple interest rate is 3.0% for Account A
and 4.0% for Account B, which account had the greater principal? Explain.
Answers
The principal of account A is $3 and the principal of account B is $4, Account B had the greater principal.
What is principal?
The principal is the sum that was first invested or borrowed from the bank. P stands for the principal. Rate: Rate is the interest rate at which the main sum is loaned to a person for a specific period of time; it may be 5%.
Given $15.75 in interest in Account A with interest rate 3.0% and $28.00 in interest in Account B with interest rate 4.0% after 21 months.
The formula of simple interest is I = PRT.
For account A:
R = 3.0% = 0.03
T = 21 month = 21/12 year
I = $15.75
P = I/RT
P = 15.75/ (0.03 × (21/12))
P =$3
For account B:
R = 4.0% = 0.04
T = 21 month = 21/12 year
I = $28.00
P = I/RT
P = 28.00/ (0.04 × (21/12))
P =$4
The principal of account B is more than that of account A.
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A car traveling on the highway for 4 hours used 2 gallons of gasoline each hour.
How many gallons did it use during those 4 hours?
Which choice shows the correct product and answer?
4×(−2)=−8; The car used 8 gallons of gasoline.
4×(−2)=2; The car gained 2 gallons of gasoline.
.
4×(−2)=−2; The car used 2 gallons of gasoline.
Answers
Answer: The first one is correct
Step-by-step explanation: 4x(-2)=-8; The car used 8 gallons of gasoline.
An aerial camera is suspended from a blimp and positioned at d. The camera needs to cover 125 meters of ground distance and will be flown at an altitude of 75 meters. If the camera attachment to the blimp is 20 meters in length, how low should the camera hang from the blimp, from g to d? a blimp over triangle edf with height gd and fe equals 20 meters and triangle adc with height of 75 meters and ac equals 125 meters. Triangles share point d.
Answers
Answer: 12 m
Step-by-step explanation:
If ΔTYL ~ ΔCHK, find the value of x.
Answers
Answer:
There isn't enough information to solve for x.
Step-by-step explanation:
The way the statement of similarity is written, we get this proportion:
TY/CH = TL/CK = YL/HK
Replace segment names with lengths:
TY/10 = 25/CK = (4x - 1)/(x + 5)
There isn't enough information to solve for x.
A business has a budget of $2,160 to spend on updating their technology. Each month, x, the business spends $135 on various technology updates. The amount of money remaining in the budget for technology, T(x), can be described by the function T(x) = −135x + 2160. What is the interpretation of the x-intercept in the context of the problem?
After 1 month, the business will have $2,025 remaining for technology updates.
After 16 months, the business will have $0 remaining in their technology budget.
The initial technology budget for the business is $2,160.
The business spends $135 every month updating their technology.
Answers
The interpretation of the x-intercept in the context of the given problem is: B. After 16 months, the business will have $0 remaining in their technology budget.
How to Find and Interpret the X-intercept of an Equation?To find the x-intercept of an equation, substitute the value of y = 0, and solve for x. It is the value of x when y or the output = 0.
Given the equation, T(x) = −135x + 2160, where T(x) is the amount of money remaining in the budget for technology, and x is the number of months, the x-intercept would be the number of months that the business will have $0 in their budget for technology.
To find the x-intercept, substitute T(x) = 0, into T(x) = −135x + 2160:
0 = −135x + 2160
135x = 2160
Divide both sides by 135
135x/135 = 2160/135
x = 16
This means after 16 months, the technology budget that the company will have remaining is $0.
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Sharon has a favorite video game she likes to play everyday until she hits 700 points. she knows that she can earn 10 points per star. if she has 490 points, how many days did she play
Answers
The number of days it will take Sharon to hit her target 700 points is 21 days
How many days did she play the game?Sharon's target on the game = 700 pointsAdditional points earned daily = 10 pointsPoints earned already = 490 pointsNumber of days she played the game = g490 + 10g = 700
Subtract 490 from both sides
10g = 700 - 490
10g = 210
divide both sides by g
g = 210 / 10
g = 21
Therefore, it will take Sharon 21 days to meet her target points.
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Graph g(x)=-2|x -5|-4g(x)=−2∣x−5∣−4
Answers
The graph of the given function is attached below.
What is a absolute function?
A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The definition of the absolute value parent function is given as follows: f(x)=x if x > 0 and f(x) = -x if x 0.
Given function is g(x)= - 2|x -5|-4.
Finding some points on the graph:
Putting x = 5
g(5)= - 2|5 -5|-4
g(5) = -4
Putting x = 0
g(0)= - 2|0-5|-4
g(0) = -2 ×5 - 4
g(0) = -14
Putting x = 10
g(10)= - 2|10 -5|-4
g(10) = -2 ×5 - 4
g(10) = -14
The points on the graph are ( 5,-4), (0,-14), (10,-14).
Plot the points and joint them.
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A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.
What is the multiplicative rate of change of the exponential function represented in the table?
1.5
2.25
3.0
4.5
A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.
What is the multiplicative rate of change of the exponential function represented in the table?
1.5
2.25
3.0
4.5
Answers
The multiplicative rate of change of the exponential function represented in the table is given as follows:
1.5.
How to obtain the multiplicative rate of change of the exponential functions?For an exponential function, when x is increased by one, the output variable y is multiplied by a constant, called multiplicative rate of change of the exponential function.
Then, given a table of values, the rate of change is obtained by the division of two outputs(output with the greater input divided by output with the smaller input) when their inputs have a difference of 1.
Thus, for the table, the rate of change is obtained as follows:
6.75/4.5 = 1.5.
(the difference of the inputs is of 2 - 1 = 1).
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A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation.y''-y'=t, yp(t)=-tAnswer: y= -t+c1et+c2e-t but how?Thank you
Answers
The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]
When the vector of constants to the right of the equals sign is not zero, an equation system is said to be non-homogeneous. A broad description of the solutions to a non-homogeneous system is presented in this solution.
General solution for the equation: [tex]y''-y'=t[/tex] , [tex]yp(t)=-t[/tex]
Consider the equation [tex]y''-y'=t[/tex]. The corresponding homogeneous equation has the associated auxiliary equation [tex]r^2-1=0[/tex] which has [tex]r= -1[/tex] and [tex]r=1[/tex] as solutions.
The solution of an n[tex]^{th}[/tex]-order differential equation or difference equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.
Hence the general solution for a homogeneous equation is [tex]y(t)=-t+c_{1}e^t+c_{2}e^-t[/tex]
Combining the general solution [tex]y(t) = c_{1}e^t+c_{2}e^t[/tex] of [tex]y"-y'=0[/tex] with the particular solution [tex]y_{p}(t)=-t[/tex] of [tex]y"-y'=t[/tex], we find that the general solution to [tex]y"-y'=t[/tex] is [tex]y(t)=c_{1}e^-t+c_{2}e^t-t[/tex]
The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]
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To Write Equations of Parallel or perpendicular Lines Write the equation of the line that is parallel to y=2x + 4 and passes through the point (-4,-1). Geometry question
Answers
Answer:
Equations of parallel and perpendicular lines The equation of a straight line is represented as \ (y=ax+b\) which defines the slope and the \ (y\)-intercept. Here \ (a\) represents the slope of the line. Since two parallel lines never intersect and have the same slope, their slope is always equal.
Step-by-step explanation:
What are the intercepts of the graphed function? Group of answer choices x-intercept = (–1, 0) y-intercept = (–3, 0) x-intercept = (0, –1) y-intercept = (0, –3) x-intercept = (0, –1) y-intercept = (–3, 0) x-intercept = (–1, 0) y-intercept = (0, –3)
Answers
The x and y intercepts of the graphed function are (–1, 0) and ( 0,-3 ) respectively.
What are intercepts?A graph's intersections with an axis, or at least touches on it, are known as intercepts.Where the graph crosses or touches the x-axis is known as an x-intercept.When the graph touches the y-axis is known as a y-intercept.When the y-value is zero, the equation has a solution known as the y-intercept.When the x-value is zero, the equation has a solution known as the x-intercept.As a result, the graphic idea of x- and y-intercepts is quite straight forward. When we are forced to attempt to handle intercepts algebraically, issues arise.Here, the x and y intercepts of the graphed function are (–1, 0) & ( 0,-3 ) respectively. Refer image for graph.So, option D is correct.To learn more about intercepts, refer:
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i need help, who has the answers?
Answers
(4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .
What does greater than (>) mean ?
Greater than means that the variable or number is more than the given limit. On the other hand, greater than or equal to states that the number or variable is either equal to or more than the given limit. The greater-than symbol is represented as >, whereas the greater than or equal to sign is represented as ≥.
Given :
(4,3)
(4,4)
(0,-4)
(4,3.9)
(0,0)
Since , all the ordered pairs are in the (x,y) form , we can clearly see that (4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .
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7. The height of a candle decreases d centimeters for every hour it burns.
a. Independent Variable:
b. Dependent Variable:
Answers
Answer:
Below
Step-by-step explanation:
The height of the candle DEPENDS on how many hours it has burned.
Dependent variable = height
Independent = hours
Which inequality is represented by the graph below?
Answers
Answer:
2) y ≥ 2x - 3
Step-by-step explanation:
3 and 4 would be eliminated because the line does not intersect at (0, 2), but rather (0, -3).
How do you write all real numbers?
Answers
The set of all the real numbers are written as R.
The term set in set theory can be written as the well-defined collection of objects called elements or members of the set.
Here we have to find the way to write all real numbers.
Here we have considered that all the real numbers are collectively put on to the set.
And the set that contain all the real numbers are called R.
We all know that the real number contain all the number like negative , positive numbers.
So, Here we consider that if the domain of a function is all real numbers, then here we can represent this using interval notation as (−∞,∞).
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The correlation coefficient, r, is a number between 0 and 1 O and on O-o and o 0-10 and 10 0 and 10 0 and 100 0-1 and 1
Answers
The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. It ranges from 0 to 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. A value of 0.5 or higher is considered a strong correlation.
The correlation coefficient is calculated by taking the covariance between two variables and dividing it by the product of the standard deviations of the two variables. The formula is as follows:
r = covariance(x,y) / (stdDeviation(x) * stdDeviation(y))
The correlation coefficient is a statistical measure used to quantify the strength of the linear relationship between two variables. It takes a value between 0 and 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. The correlation coefficient is calculated by taking the covariance between the two variables and dividing it by the product of their standard deviations. A negative correlation coefficient means that as one variable increases, the other decreases. A value of 0.5 or higher is considered a strong correlation. The correlation coefficient can be used to determine the strength of the relationships between variables, whether they are linear or non-linear. It is an important tool for data analysis and can help to identify relationships between different variables.
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Can a 12 year old learn algebra?
Answers
Yes, it is generally considered appropriate for a 12-year-old to learn algebra. Algebra is a branch of mathematics that involves working with variables and equations to solve problems. It is usually introduced to students in middle school or junior high school, which is around the age of 12 or 13.
What is the rationale for the above response?According to studies, depending on the teaching technique and intellectual maturity: between 5 and 13. Algebra is a theoretical algebra with fewer techniques for demonstrating tangible lessons.
A youngster who develops abstract comprehension at a young age might learn extremely quickly, but a pupil who has difficulties with abstract notions may struggle well into their adolescence.
It is crucial to recognize that each student learns at a different rate and may have distinct arithmetic talents and weaknesses. It is critical that students receive the necessary support and adjustments in order to study algebra and excel in their math studies.
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What is standard deviation of the set of observations 32 28 29 30 31?
Answers
The set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.
You must take the following actions to determine the standard deviation of a set of observations:
Determine the set of observations' mean. Divide the total number of observations by the sum of all the observations to arrive at this result. The mean in this situation would be 30.To determine each observation's departure from the mean, deduct the mean from each observation.Each deviation should be squared.4The squared deviations are totaled.5Subtract the number of observations from the total of the squared deviations. Therefore, the standard deviation for the set of observations 32 28 29 30 would be:Mean: (32 + 28 + 29 + 30 + 31) / 5 = 30
Deviations: 32 minus 30 = 2, 28 minus 30 = 2, 29 minus 30 = 1, 30 minus 30 = 1, etc.
Squared deviations are as follows: 22 = 4, (-2)2 = 4, (-1)2 = 1, and 02 = 0.
Sum of squared deviations: (Sum of squared deviations) / (number of observations) = 10 / 5 = 2
Standard deviation is square root of sum of squared deviation.
so, [tex]\sqrt{2}[/tex] is 1.41.
As a result, the set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.
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