a) The given function is [tex]$\frac{x^2-2x+2}{(x-1)^2(x+2)}$[/tex]. The series of this function is [tex]$\sum_{n=0}^{\infty}(-1)^n(n+1)x^n$[/tex]. Therefore, the series is alternating (-1).
b) The sum of the first four nonzero terms of the series is [tex]$-1x^1+2x^2-3x^3+4x^4$.[/tex]
c) The interval of convergence is [tex](-2, 1)[/tex]. This is because the denominator [tex]$(x-1)^2(x+2)$[/tex] has a zero at [tex]$x=-2$[/tex] and a zero at [tex]$x=1$[/tex], and the function is undefined at these two points. Therefore, the interval of convergence is the open interval [tex]$(-2, 1)$[/tex].
Convergence is the process of two or more different entities coming together and becoming one. In mathematics, it can refer to a sequence converging to a limit, or the process of a function approaching a finite value as the number of trials approaches infinity. In technology, convergence can refer to the combining of different media types into a single medium, such as the combination of audio, video, and text into a multimedia presentation.
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Jeremy has 3/4 pound of fish food if fish food is used to feed 24 fish how much food is there for each fish
Answer:
There is 1/32 pound food for each fish
Step-by-step explanation:
24 fish = 3/4 pound food
1 fish = (3/4)/24 pound food = 1/32 pound food
(Problem solved by using unitary method)
Please help me with this!
1) express the original claim in symbolic form
2) identify the null and the alternative hypotheses
The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < o
What is hypothesis?
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientists typically build their scientific ideas on prior observations that cannot be adequately explained by the current body of knowledge.
In statistics, the null hypothesis is usually denoted by letter H with subscript '0' (zero), such that H0. It is pronounced as H-null or H-zero or H-nought
At the same time, the alternative hypothesis expresses the observations determined by the non-random cause.It is represented by H1 or Ha.
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Each of the 9 reindeer have 8 jingle bells on their collar. There are 12 more bells on the reins. How many bells in all?
Answer: 84 bells
Step-by-step explanation:
12 + 9x8
84
Refer to the above diagram. Economies of scale: A) are evident over the entire range of output. B) occur over the OQ range of output. C) begin at output 03. D) occur only over the
Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.
Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.
The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.
The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.
Minimum efficient scale is the level of output where economies of scale have been fully exploited.
A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.
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A fair coin is tossed 10 times. Find the probability of satisfying the condition that that the coin does not land on tails twice in a row
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
When a fair coin is tossed 10 times, the sample size (n) is:
n = [tex]2^{10}[/tex]
This is so because a fair coin has 2 sides.
So, we have:
n = 1024
There is only one occurrence of having 10 tails in a row in the 1024 possible outcomes.
So, the probability is:
P = [tex]\frac{1}{1024}[/tex]
Therefore,
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
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A stationary shop orders a batch of pens from a factory.
The factory could make the batch of pens in 20 days using 12 machines.
Due to a fault, only 3 machines were used for the first 8 days.
All 12 machines were used from day 9 onwards.
Work out the total number of days taken to make the batch of pens
Answer:
22
Step-by-step explanation:
(8 + 20) - ((8 * 9) ÷ 12)
Using PEMDAS, let us find the product to get;
(8 + 20) - (72/12)
Next operation is to divide what is in the bracket to get:
(8 + 20) - 6
Next operation is addition of the bracket content to get; 28 - 6
Next operation is to carry out subtraction to get: 22
Thus, the total number of days taken to make the batch of pens is 22.
Reshawn read 25 pages of his book each day until he finished the book. His book was 400 pages long. Which sketch represents this solution
Graph (C) which has points (0, 400) and (16, 0) represent the solution to the given situation of Rashawn.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Graphs and charts are useful visual aids because they make information accessible and quick to understand.
Therefore, it is not unexpected that print and electronic media frequently use graphs.
When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.
So, Rashawn consumed 25 pages of his book daily till it was finished. There were 400 pages in his book.
400 / 25 = 16 days is the estimated number of days he needs to finish the book.
He will have 400 pages finished in 0 days and 0 pages in 16 days.
As a result, the situation is represented by a graph with a line segment in the first quadrant.
Days are shown on the x-axis, and Pages left are listed on the y-axis.
The line segment's ends are (0, 400) and (16, 0).
Therefore, graph (C) which has points (0, 400) and (16, 0) represent the solution of the given situation of Rashawn.
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Complete question:
Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.
Which sketch represents this situation?
a) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 400 end ordered pair and begin ordered pair 25 comma 0 end ordered pair.
b) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 16 end ordered pair and begin ordered pair 400 comma 0 end ordered pair.
c) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 400 end ordered pair and begin ordered pair 16 commas 0 ends ordered pair.
d) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y-axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 25 ends ordered pair and begin ordered pair 400 commas 0 ends ordered pair.
If sin =−0.093 and 00 ≤ <3600, then what is to the nearest tenth of a degree?
A. 5.3⁰ or 174.7⁰
B. 185.3⁰ or 354.7⁰
C. 174.7⁰ or 185.3⁰
D. 2.2⁰ or 0.9⁰
There are two angles for the sine function such that sin θ = - 0.093: (i) 185.3°, (ii) 354.7°.
What are the approximate values of a trigonometric function?
In this problem we must determine two values of the angle of the sine function such that its result is - 0.093. According to the features of the trigonometric function, sine is negative for angles between 180° and 360°.
Since trigonometric functions are trascendent functions, we can only obtain approximate values of the angle by means of inverse trigonometric functions and numerical methods. There are two possible solutions:
sin⁻¹ - 0.093
θ₁ ≈ 185.336° or θ₂ ≈ 354.664°
θ₁ ≈ 185.3° or θ₂ ≈ 354.7°
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WILL MAKE BRAINLIEST Your classmate is starting a new fitness program. He is planning to ride his bicycle 50 minutes every day. He burns 5 calories per minute bicycling at 11 mph and ! minute bicycling at 15 mph. How long should he bicycle at each speed to burn 400 calories?
He should bicycle for ———— minutes at 11 mph and ______ minutes at 15 mph
Hello,
I hope you and your family are doing well!
The classmate should bike for 50 minutes at 11 mph and at 150 minutes for 15 mph. (See explanation below)
First, let's find how many calories your classmate burns while biking at 11 mph:
calories burned = time * rate of calorie burn
Since your classmate bikes at 11 mph for 50 minutes, the number of calories he burns at this speed is:
calories burned = 50 minutes * 5 calories/minute = 250 calories
Now, let's find how many calories your classmate burns while biking at 15 mph:
calories burned = 400 calories - 250 calories = 150 calories
Since your classmate burns 1 calorie per minute while biking at 15 mph, he needs to bike at this speed for 150 minutes to burn the remaining calories:
time = calories burned / rate of calorie burn
time = 150 calories / 1 calorie/minute = 150 minutes
Please rate this answer 5 stars and brainliest if you find it helpful.
Happy Holidays!
let w represent the number of attempted experiments to get one experiment that is not successful. the random variable w has a geometric distribution with mean 4 and standard deviation 3.5. which of the following is the best interpretation of the standard deviation? responses a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selecte
The best interpretation of the standard deviation on this problem is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
How to interpret the standard deviation?The standard deviation of a data-set is calculated as the square root of the sum of the differences squared between each observation of the data-set and the mean, divided by the number of observations in the data-set.
The interpretation of this calculation is that the standard deviation represents by how much each value of the distribution is expected to vary from the mean, on average.
This means that the correct statement is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
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Determine whether the integers in each of these sets are pairwise relatively prime. a) 11, 15, 19 b) 14, 15, 21 c) 12, 17, 31, 37 d) 7, 8, 9, 11
Note that Option A is pairwise and is relatively prime.
Option B is not relatively primeOption C is also a relatively primeOption D is also relatively prime.What does it mean for a list of integers to be pairwise relatively prime?If every pair of elements in a list of integers is relatively prime, the list is pairwise relatively prime. For example, the numbers 121, 122, and 123 are relatively prime pairwise (even though they are each composite).
You can tell if a set of numbers are relatively prime if they do not share a common factor other than ±
Looking at set a:
11, 15, 19
Writing their prime factorization
11 = 11
15 = 3 x 5
19 = 19, hence since any pair of these numbers does not have any common factor, hence they are relatively prime.
Looking at set b:
14, 15, 21
Writing their prime factorization, we have:
14 = 7 x 2
15 = 3 x5
21 = 3 x 7
15, and 21 share a common factor of 3 while
14 and 21 share a common factor of 7, therefore, they are NOT relatively prime.
Looking at set c)
12, 17, 31, 37
Writing their prime factorization,
12 = 3 x 2²
17 = 17
31 = 31
37 = 37
In this case, no pair of these numbers have any common factor. Hence they are relatively prime.
Looking at set d)
7,8,9, 11, spelling out their prime factorization
7=7
8=2³
9=3²
11=11
Thus, any pair of these numbers do not have a common factor, hence they are relatively prime.
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A vector field F is shown. Use the interpretation of divergence derived in this section to determine whether div F is positive or negative at P_1 and at P_2.a. div F is negative at both P_1 and P_2. b. div F is positive at P_1 and negative at P_2. c. div F is positive at both P_1 and P_2. d. div F is negative at P_1 and positive at P_2.
As pre the concept of vector, div F is negative at P1 and divF is positive at P2.
In math the term vector refers the quantity that has both magnitude and direction but not position
Here we have to determine whether div F is positive or negative at P1 and at P2.
Let us consider if div F(P)>0, the net flow is outward near P and P is called a source and if div F(P)<0, the net flow is inward near P and P is called a sink.
Here by observing the graph of F, we have identified that the vectors end near the P1 are the larger than the vectors starts near the point P1,
So, the net flow is inward near P1 and div F is negative at P1
Where P1 is called a sink
Whereas, by observing the graph of F we have identified that the vectors end near P2 are shorter than the vectors starts near the point P2,
So, the net flow is outward and div F is positive at P2 and the P2 is called a source
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[(6x2.99)-1] ÷2
Please help me
Answer: Answer is 8.47
Step-by-step explanation:
[(6x2.99)-1] ÷2
16.94 / 2
8.47
Answer:
8.47
Step-by-step explanation:
[(6x2.99)-1] ÷2 16.94 /2 =8.47
Help me please ASAP (ﾒ﹏ﾒ)
Answer:
A ' ( -21, 14 )
B ' ( 28, 14 )
C ' ( -7, -7 )
Step-by-step explanation:
The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.
For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.
The dilation rule can be written as (x,y)—-> (7x,7y)
As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.
Example: side AB = 7 units, side A'B' = 49 units
Hopes this helps!!
Find the midpoint of the line segment with the given endpoints.
Answer
2x73
Step-by-step explanation:
Answer:
(11.5, 7.5)
Step-by-step explanation:
17 + 6 / 2 = 11.5
2 + 13 / 2 = 7.5
A local entrepreneur would like to know if those who live in an urban or rural community are more likely to buy a real Christmas tree. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the village and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree, and let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree. What is the p-value?
.32
.16
.07
.18
The value of p is 0.16. So the option b is correct.
A local entrepreneur takes a random sample of 100 people.
Of the urban participants, 22 buy a real tree.
Of the rural participants, 28 buy a real tree.
Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree.
Let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree.
We have to find the p-value
p1 = X1/N1
p1 = 28/100
p1 = 0.28
p2 = X2/N2
p2 = 22/100
p2 = 0.22
p = (X1 + X2)/(N1 + N2)
p = (28+22)/(100+100)
p = 0.25
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2
Test statistic
z = (p1 - p2)/√(p*(1-p)*(1/N1 + 1/N2))
z = (0.28-0.22)/√(0.25*(1-0.25)*(1/100 + 1/100))
z = 0.9798
P-value Approach
P-value = 0.16
Hence, the option A is correct. 0.16 is the p-value.
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Write the complex equation 8 + 3; in trigonometric form.
The complex equation 8 + 3; in trigonometric form is z = 8.544[cos(20.6) + isin(20.6)}.
What is trigonometric form ?
Here, we'll utilize that fundamental transformation to recast z = a + bi in a different (sometimes more practical) form that is based on the polar transformation. The trigonometric form of a complex number is the name of this new representation.
Given
8 + 3i
Required
Rewrite in trigonometric form.
The trigonometric form of a complex equation is
z = r[cosθ + isinθ]
Let a = 3 and b = 8
Where
r is calculated by
r² = b² + a²
And
θ is calculated by
θ = arctan(a/b)
Substituting 3 for a and 8 for b
r² = a² + b² becomes
r² = 3² + 8²
r² = 9 + 64
r² = 73
√r² = √73
r = √73
r = 8.544
Calculating θ
θ = arctan(a/b) becomes
θ = arctan(3/8)
θ = arctan(0.375)
θ = 20.556°
θ = 20.6 --- Approximated
Hence, z = r[cosθ + isinθ] becomes
z = 8.544[cos(20.6) + isin(20.6)}
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use the intermediate value theorem to show that there is a root of the given equation in the specified interval.
To use the intermediate value theorem to show that there is a root of the given equation in the specified interval, we first need to find the values of the function at the two endpoints of the interval. Let's say the function is denoted by f(x) and the interval is [a, b].
If f(a) and f(b) have opposite signs (one is positive and the other is negative), then by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [a, b]. This is because the intermediate value theorem states that if a function is continuous on a closed interval and the function takes on different values at the endpoints of the interval, then there must be at least one point in the interval where the function takes on the value of the intermediate value between the two endpoints.
For example, suppose we have the equation f(x) = x^2 - 3 and we want to show that there is a root of the equation in the interval [1, 2]. We can evaluate the function at the two endpoints of the interval:
f(1) = 1^2 - 3 = -2
f(2) = 2^2 - 3 = 1
Since f(1) and f(2) have opposite signs, by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [1, 2]. To find the root, we can use a root-finding algorithm such as bisection or Newton's method.
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Does the histogram appear to depict data that have a normal distribution? O A. The histogram appears to depict a normal distribution. The frequencies generally decrease to a minimum and then increase. O B. The histogram does not appear to depict a normal distribution. The frequencies generally increase and the histogram is roughly symmetric. O C. The hidtogram does not appear to depict a normal distribution. The frequencies generally decrease to a minimum and then increase, and the histogram is roughly symmetric. OD. The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Frequency Weight (g) 6.000-6.049 6.050-6.099 6.100-6.149 6.150-6.199 6.200-6.249 6.250 6.299 6.300-6.349 6.350-6.399 Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
The histogram appears to roughly estimate a normal distribution. The frequencies normally increase to a maximum and then decrease, and the histogram is symmetric.
The Graph of Normal Distribution is bell-shaped. Here the value of y is less for the lower value of x and then the value of y is increased for a larger value of x, but after some time value of y again getting decreases as the value of x increases.
For the Histogram to appear to be a normal distribution, the graph of the histogram must have the same nature. Thus, option B is only the correct option.
The histogram is made up of many columns and bars that are vertical with no gaps between bars with different labels of numeric data of different heights showing the size of the group of different labels.
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Can you help me with this
2. Natalie is selling candles to raise money for her softball team. The team has two different options for selling the candles. The first option is to sell a package of 5 candles for $18. The second option is to sell individual candles for $4 each.
(a) The team wants to earn $1404. How many candles do the members need to sell if they sell candles only in packages? How many candles do they need to sell if they sell only single candles? Explain your answer using an equation for each situation.
(b) Describe at least one advantage of selling the candles in packages. Describe at least one disadvantage of selling the candles in packages
a) The amounts that the team needs to sell is given as follows:
Packages: 390 candles.Single candles: 351 candles.b) The advantage and disadvantage is given as follows:
Advantage: Better opportunity cost when a person needs one candle, the person will have to purchase the entire package.Disadvantage: Lower revenue per candle.How to obtain the amounts?The amounts needed are found applying the proportion, considering the costs and the number of candles.
A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:
5 candles - $18
n candles - $1404
Applying cross multiplication, we have that:
18n = 5 x 1404
n = 5 x 1404/18
n = 390 candles.
With a single candle, the number of candles is calculated as follows:
1404/4 = 351 candles.
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Which expression is equivalent to (m−2n−4)−4? m8n16 m−8n−16 m−6n−8 1 over the quantity m raised to the sixth power times n raised to the eighth power end quantity
Answer: C m-6n-8
Step-by-step explanation:
Which expression is equivalent to (m−2n−4)−4?
A m8n16
B m−8n−16
C m−6n−8
D 1 over the quantity m raised to the sixth power times n raised to the eighth power end quantity
(m-2n-4)-4
(2n-4)
(2x-4)
(n-8 )
(m- 4)-4
4+4
m-6
which = C m−6 n−8
19
Select the correct answer.
What is the solution to this equation?
log₃(4 x)-2log₃ x=2
A. 1/36
B. 9/4
C. 4/9
D. 36
If f(x) = x³ + 14x² + 61x + 84, which of the following is not a factor of f(x)?
can someone help me with this pre calc question? and show work so I know how to do it please :)
[tex]$$(x-h)^2+(y-k)^2=r^2$$[/tex]
This is the general standard equation for the circle centered at (h, k)
with radius r.
Circles can also be given in expanded form, which is simply the result of expanding the binomial squares in the standard form and combining like terms.
For example, the equation of the circle centered at (1,2) with radius 3 is [tex]$(x-1)^2+(y-2)^2=3^2$[/tex]. This is its expanded equation:
[tex]$$(x-1)^2+(y-2)^2=3^2$$[/tex]
[tex]\begin{array}{r}\left(x^2-2 x+1\right)+\left(y^2-4 y+4\right)=9 \\x^2+y^2-2 x-4 y-4=0\end{array}[/tex]
We know that the general equation for a circle is[tex]( x - h )^2 + ( y - k )^2 = r^2[/tex], where ( h, k ) is the center and r is the radius.
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Which model shows the problem 1 divided by 1/6 ?
The model that shows the problem 1 divided by 1/6 is option 1.
What is meant by circle?Every point in a plane that is at a specific distance from the center, or the circle's center, forms a shape. To put it another way, it is the curve that a moving point in a plane draws to keep a constant distance from another point. The radius of a circle is the separation of any point from the center. A positive integer is typically necessary for the radius. Except as specifically stated, this article discusses circles in the Euclidean plane and other aspects of Euclidean geometry.
In particular, a circle is a straight, closed curve that separates the plane into its inner and exterior.
Therefore, The model that shows the problem 1 divided by 1/6 is option 1.
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Two sides of a triangle are 17 and 53. The third side is?
Answer:
the answer would be e because you can't determine the side length
Answer: (B)
Step-by-step explanation:
Step 1: Find minimum values of the third side.
53-17 = 36
Step 2: Find maximum values of the third side.
17+53 = 70
Step 3: Find equation
36 < x < 70
A volunteer for a political campaign makes phone calls to raise funds for the candidate. The number of calls that she has left to make can be estimated with the equation C = 80-7h, where C is the number of calls left to make that day and h is the number of hours she has worked that day. How many calls does she have to make per day?
The number of calls she makes per day is 12
What is a function?A function can be defined as an expression, law or rule that describes the relationship between two variables.
These expressions are termed;
The dependent variableThe independent variableFrom the information given, we have that the function is;
C = 80-7h
Where;
C is the number of calls to make per dayh is the number of work hoursI day = 24 hours
Now, substitute the value into the formula
C = 180 - 7(24)
expand the bracket
C = 180 - 168
Subtract the values
C = 12
Hence, the value is 12
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4p2 divided by 2! - 4c2
Answer:
Step-by-step explanation:
12.5663706144
3. "Seventeen less than twice a number is -49."
Answer: the number is -16
Step-by-step explanation: if you add 17 to -49, you will get -32. you do this because it is 17 less than NOT more than. that would be called inverse operations. then, you divide that number by 2 to get -16. again, you use inverse operations because you are going backwards to try and find the number.
Answer: -16
Step-by-step explanation: So, to solve, we should write an equation. It should look like this:
2x - 17 = -49
So, using inverse operations, we would add 17 to - 49, which is -32, then divide that by 2, which would be -16. I hope this helped!
P.S. our new equation would look like 2(16) - 17 = -49
32-17 = 49
32 + -17 = 49
49 = 49
It checks out.
silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. the success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. an article reported that for a sample of 20 (newly deceased) adults, the mean failure strain (%) was 26.0, and the standard deviation was 3.4.a. Assuming a normal distribution for failure strain, estimate true average strain in
a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about
precision and reliability. How does the prediction compare to the estimate
calculated in part (a)?
A true average strain in a way that converys information about precision and reliability (24.33, 27.67)
From given information we have:
the sample size n = 20
the mean failure strain x(bar) = 26.0
the standard deviation s = 3.4
Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.
A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.
c = 0.95 or 95%
In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.
Here, the degree of freedom :
df = 20 - 1
df = 19
and α = (1-c)/2
= 0.025
To find the t-value:
t_(α/2) = 2.145
Therefore, the error margin is:
E = t_(α/2) × s/√n
E = 2.145× 3.4/√19
E ≈ 1.67
And the confidence interval would be,
(x{bar} - E, x{bar} + E) = (24.33, 27.67)
Therefore, the confidence interval is: (24.33, 27.67)
Learn more about the confidence interval here:
brainly.com/question/13067956
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