Calculate the following inverse Laplace transforms (a) \mathcal{L}^{-1}\left\{\frac{e^{-3 s}}{s^{3}}\right\}
Answers
The inverse Laplace transform of ^(−3)/^3 is () = -9/(4) (), where () is the unit step function.
To calculate the inverse Laplace transform of ^(−3)/^3 , we can use the formula:
()=^{−1}{()}=lim_(→∞) 1/(2) ∫_(−)^(+) () ^() d
where is a real number such that all singularities of () are to the left of the line =.
Applying this formula, we have:
^−1{^(−3)/^3} = lim_(→∞) 1/(2) ∫_(−)^(+) ^(−3)/^3 ^() d
To evaluate this integral, we can use the residue theorem. The integrand has poles at =0 and =3, where =±1,±2,…. The pole at =0 has order 3, so we need to compute its third residue. Using the formula for the nth residue of a function () at a pole =, we have:
Res[^(−3)/^3, =0] = lim_(→0) d^2/d^2 (^3 ^(−3))
= lim_(→0) (6 ^(−3) − 9 ^(−3))
= -9/2
Thus, by the residue theorem, we have:
^−1{^(−3)/^3} = Res[^(−3)/^3, =0]/(2) = (-9/2)/(2) = -9/(4)
Therefore, the inverse Laplace transform of ^(−3)/^3 is () = -9/(4) (), where () is the unit step function.
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Related Questions
Verify that a + ( b + c) = (a + b) + c , a = (-12) , b = 4 , c = (-25)
Answers
Answer:
a + (b + c) = (a + b) + c
Step-by-step explanation:
a= (-12), b = 4, c = (-25)
\((12) + (4 + ( - 25)) = ( - 12 + 4) + ( - 25) \\ - 33 = - 33\)
Answer:
GIVEN :-
a = -12b = 4c = -25TO VERIFY :-
a + (b + c) = (a + b) + cSOLUTION :-
Find the values of L.H.S. & R.H.S.
L.H.S. :-
Put all values in → \(\boxed{a+(b+c)}\)
⇒ -12 + [4 + (-25)]
⇒ -12 + (4 - 25)
⇒ -12 + (-21)
⇒ -12 - 21
⇒ -33
R.H.S. :-
Put all values in → \(\boxed{(a+b)+c}\)
⇒ (-12 + 4) + (-25)
⇒ -8 - 25
⇒ -33
CONCLUSION :-
L.H.S. = R.H.S.
⇒ a + (b + c) = (a + b) + c
The price of an item yesterday was $140. Today, the price fell to $119. Find the percentage decrease.
Answers
Answer:
-15%
Step-by-step explanation:
15%-
Explanation
Erick sold 2 pounds of walnuts and 4 pounds of almonds for $28. The next day, he sold4 pounds of walnuts and 3 pounds of almonds for $31. Which system of equations canbe used to determine the cost per pound of walnuts x, and the cost per pound ofalmonds, y?F 2x - 4y = 284x + 3y = 31G 2x + 4y = 284x + 3y = 31H 2x + 4y = 314x + 3y = 28) 4x + 3y = 282x + 4y = 31
Answers
Let the selling price for walnuts be x and the selling price for the almonds be y.
On the first day, Erick sold 2 pounds of walnuts and 4 pounds of almonds for $28. This implies that
\(\begin{gathered} 2x\text{ + 4y =28 } \\ \text{equation 1} \\ \end{gathered}\)On the second day, 4 pounds of walnuts and 3 pounds of almonds for $31.
\(undefined\)What is the slope of the graphed line?
O
I
5/2
O
O
5/2
O
7/2
10
9
8
7
6
5
4
31
21
1
1 2 3
4
5
6
7
8
9 10
Answers
Answer:
Step-by-step explanation:
OK YOU ARE GOOD OH AND IT
5/8
42, 43, 44, 44, 49, 40, 39
What is the mean?
Answers
Answer:
43
Step-by-step explanation:
To find the mean, add up all the numbers
(42+ 43+ 44+ 44+ 49+ 40+ 39)=
301
Then divide by the number of terms
301/7
43
Answer:
mean = 43
Step-by-step explanation:
Mean is given by
mean = sum of all numbers / total no. of terms
substitute the values
mean = 42 + 43 + 44 + 44 + 49 + 40 + 39 /
Divide ,
mean = 301 / 7
mean = 43
Which of these graphs represents a function?
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1
43-2-1₁ 1 2 3 4 5
-2
-3
-4
-5
W.
N.
1
-5-4-3-2-1 1 2 3 4 5
JANM
-5
-2
Y.
A
X
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4
3
1
-5-4-3-2-1 1 2 3 4
-2
-3
-4
-5
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X.
V
5
4
-2
-3
-4
5
Z.
HE
४
+X
1 2 3 4 5
Answers
Answer: W
Step-by-step explanation:
The graph must pass the vertical line test.
i need help i suck at dividing decimal
Answers
453.6 divided by 8.1 answer: 56
264.684 divided by 4.2 answer: 15.004
Answer: 1. 0.185185185 keeps going
2. 56
3. 63.02
Step-by-step explanation:
Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.
Answers
Answer:
The amount she saves is 25% of her income
Step-by-step explanation:
She is paid $11 per hour
She works 9 hours per day
and for 24 days per month
So, she works 9(24) hours per month
= 216 hours per month
Now, she is paid $11 hourly, so for 216 hours,
she will have 11(216) = $2376
Total income = $2376 per month
Saving = $594 per month
As a percentage, we divide the savings by the total income,
savings/(total income) = 594/2376 = 1/4 = 0.25
Hence we get 25%
Somone please help I am completely lost...
Answers
The first one says x+2x+4y.
So the first thing you would do is combine like terms.
x and 2x are like terms.
Since x has no number you would have to put a 1 in place for it.
So you would have 1x+2x which would be 3x.
You would then put that together and have 3x+4y.
I don’t understand how to solve
Answers
By using a translation rule, the coordinates of C' are (- 1, - 2). (Correct choice: E)
How to translate the vertices of a triangle in a accordance to a vector
Triangles are defined by the locations of its three vertices on Cartesian plane and we must find the locations of the images of the three vertices after applying a translation rule. In this case, we must translate each vertex 2 units upward and 4 units to the right. The general translation formula is described below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Location of the vertex.T(x, y) - Translation vector.P'(x, y) - Location of the image of the vertex.If we know that C(x, y) = (- 5, - 4) and T(x, y) = (4, 2), then the location of the image of point C is:
C'(x, y) = (- 5, - 4) + (4, 2)
C'(x, y) = (- 1, - 2)
The coordinates of C' are (- 1, 2).
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the paths from one location to another are straight lines. one unit on the coordinate grid equals 10 yards. betsy starts at location 1 and goes to location 2, then location 3, and then location 4, and then returns back to location 1. what is the total distance betsy has traveled?
Answers
According to the given statement Betsy has traveled a total distance of 60 yards.
To find the total distance Betsy has traveled, we need to calculate the distance between each location and sum them up.
Given that one unit on the coordinate grid equals 10 yards, we can determine the distance between each location by finding the difference in their coordinates and multiplying it by 10.
The coordinates for Betsy's path are:
Location 1: (0, 0)
Location 2: (1, 0)
Location 3: (2, 0)
Location 4: (3, 0)
The distance between Location 1 and Location 2 is 1 unit, which is equal to 1 * 10 = 10 yards.
The distance between Location 2 and Location 3 is also 1 unit, which is equal to 1 * 10 = 10 yards.
The distance between Location 3 and Location 4 is 1 unit, which is equal to 1 * 10 = 10 yards.
To return back to Location 1, Betsy will need to travel from Location 4 to Location 1.
The distance between these two locations is 3 units, which is equal to 3 * 10 = 30 yards.
Summing up the distances:
10 yards + 10 yards + 10 yards + 30 yards = 60 yards
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What is the equation of the line that has a slope of 1/2 and contains the points 0,3?show work please
Answers
Answer:
Step-by-step explanation:
y - 3 = 1/2(x - 0)
y - 3 = 1/2x - 0
y = 1/2x + 3
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
Referring to Scenario D.1, assume that an optimal serving contains 0.89 ounces of chicken
and 0.52 ounces of tomatoes. Which of the following statements is BEST?
The serving costs about 20 cents.
The serving costs about 30 cents
The serving costs about 50 cents.
The serving costs about 40 cents.
Answers
the BEST statement is: The serving costs about 40 cents.
To determine the cost of the optimal serving, we need to calculate the cost per serving based on the quantities of chicken and tomatoes used.
Given that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes, we can calculate the cost as follows:
Cost of chicken =\(0.89 ounces * $0.40/ounce\)
Cost of tomatoes = \(0.52 ounces * $0.08/ounce\)
Total cost = Cost of chicken + Cost of tomatoes
Total cost =\((0.89 * $0.40) + (0.52 * $0.08)\)
Total cost =\($0.356 + $0.0416\)
Total cost ≈\($0.3976\)
Rounding to the nearest cent, the cost of the optimal serving is about 40 cents.
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Use Trigonometric substitution to eliminate the roots 1.1. 164+2 + 1 Use Trigonometric substitution to eliminate the roots 1.1. V64+2 + 1 1.2. V4z2 – 49
Answers
To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.
1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:
V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49
We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:
V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)
Here is a more detailed explanation of the substitution:
In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.
When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3
In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.
When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)
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2x - x + 7 = x + 3 +4
Answers
Answer:
Infinite amount of solutions.
Step-by-step explanation:
Step 1: Write equation
2x - x + 7 = x + 3 + 4
Step 2: Solve for x
Combine like terms: x + 7 = x + 7Subtract 7 on both sides: x = xHere, we see that x is infinite amount of solution. We can plug in any number x and it will render the equation true.
The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student.
Construct a 95% Confidence Interval for the true mean age of Winter Foothill College students by working out then answering the next two exercises. How much area is in each tail? /2= The 95% confidence interval is:
In one complete sentence, explain what the interval means.
Using the same mean, standard deviation, and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?
Answers
With a smaller error bound, the confidence interval narrows, increasing confidence in the estimated mean age with a more precise range of values.
To construct a 95% confidence interval for the true mean age of Winter Foothill College students, we need to calculate the margin of error and then determine the interval.
First, let's calculate the standard error, which is the standard deviation divided by the square root of the sample size:
Standard Error = (Population Standard Deviation) / sqrt(sample size)
Standard Error = 15 / sqrt(25)
Standard Error = 15 / 5
Standard Error = 3
The margin of error is then calculated by multiplying the standard error by the appropriate critical value from the t-distribution. For a 95% confidence level, the critical value is 2.063 (assuming a sample size of 25 and using a t-distribution).
Margin of Error = (Critical Value) * (Standard Error)
Margin of Error = 2.063 * 3
Margin of Error = 6.189 (rounded to three decimal places)
To calculate the confidence interval, we subtract and add the margin of error to the sample mean:
Confidence Interval = Sample Mean ± Margin of Error
Confidence Interval = 30.4 ± 6.189
Confidence Interval = (24.211, 36.589)
The area in each tail is determined by the confidence level. In this case, it's a 95% confidence interval, so there is 2.5% of the total area in each tail.
In one complete sentence, the 95% confidence interval means that we are 95% confident that the true mean age of Winter Foothill College students falls within the interval of (24.211, 36.589).
If the confidence level were reduced to 90%, the critical value from the t-distribution would change. With a smaller critical value, the margin of error would decrease.
Therefore, the error bound would become smaller, resulting in a narrower confidence interval. This means that we would have a higher level of confidence in the estimated mean age, but the interval would be less wide, providing a more precise range of potential values for the true mean age.
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A teachers monthly gross pay is $5,321. The federal government withholds 15% of the teachers monthly gross pay from income taxes. How much does the teacher pay in income tax every month??
Answers
Answer:
$798.15Step-by-step explanation:
Given
Monthly gross pay is $5,321Income tax = 15%Amount of tax paid every month:
$5321*0.15 = $798.15Tracy has a cell phone plan that provides 250 free minutes each month for a flat rate of 29$. For any minutes over 250 tracy us charged 0.35$ per minute. Which of the following picewise functions represents charges based on tracy’s cell phone plane?
Answers
Answer:
Since Tracy is charged $29 for 250 free minutes so:
For x ≤ 250, f(x) = $29
tracy is charged an extra $0.35 per minute for calls over 250 minutes, so:
For x ≥ 250, f(x) = 29 + 0.35(x - 250)
QUESTION 34 Use the following to answer questions 34-36: Distribution 1: Normally distributed distribution with a mean of 100 and a standard deviation of 10 Distribution 2Normally distributed distribution with a mean of 500 and a standard deviaton of 5. Question 34: True or False. Both distributions are bell-shaped and symmetric but where the peak falls on the number line is determined bythe mean, OTrue OFalse 2points
Answers
True. Both distributions are bell-shaped and symmetric, which means they exhibit the characteristic shape of a normal distribution. The peak of a normal distribution represents the highest point of the curve and corresponds to the mean of the distribution. In other words, the mean determines where the peak falls on the number line.
For Distribution 1, with a mean of 100, the peak will be centered around 100 on the number line. This indicates that the majority of the data points in the distribution cluster around the mean value of 100.
Similarly, for Distribution 2, with a mean of 500, the peak will be centered around 500. This means that the data points in this distribution are concentrated on the mean value of 500.
The symmetry of the distributions implies that the data is equally likely to fall on either side of the mean, resulting in a balanced and symmetric bell-shaped curve. This characteristic is a fundamental property of normal distributions.
Therefore, the peak of a normal distribution is determined by the mean, and both Distribution 1 and Distribution 2 are bell-shaped and symmetric, with the peak aligned with their respective means.
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Card 1 has a current balance of $8,312.69 with an APR of 24.16%, and the credit limit on the card is $10,000.
Card 2 has a current balance of $1,180.34 with an APR of 21.15%, and the credit limit on the card is $7,500.
In your own words, tell which credit card you should focus on paying off first and why?
Be sure to include the credit card AND the reason for paying that card off first.
Answers
Answer:
The focus should be on paying off Card 1 first
Step-by-step explanation:
The credit limit for card 1 is $10,000,invariably the cardholder only $ 1,687.31
($10,000-$8,312.69) to reach its limit,hence available balance to draw from and also the annual percentage rate is higher for card card 1.
For every balance in card 1, the cardholder pays 24.16% APR annually compared to 21.15% applicable to card,as a result,card is cheaper.
Besides,the cardholder still has an available credit of $ 6,319.66
($7,500-$1,180.34) on card 2 which comes at a lower APR
The amount of time required to download a song from Michael's computer to his music player is the same for each song he downloads.
A linear model of this situation contains the values (138 , 96.6) and (238 , 166.6), where x represents the number of songs he wants to download to his music player, and y represents the total amount of time, in minutes, it will take him to download the songs.
What is the rate of change in this linear model?
A.
100 minutes per song
B.
0.35 of a minute per song
C.
1.4 minutes per song
D.
0.7 of a minute per song
Answers
This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).
What is a linear model?A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.
A linear equation is so named because plotting the graph of a given linear model yields a straight line.
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Resercher believed that patients who received heart pacemakers seemed to snore less. Among 40 randomly selected patients with a pacemaker, 12 snored. Among 60 randomly selected patients without a pacemaker, 25 snored. Which of the following statements is NOT correct?
I. The evidence supports the theory at the 10% level.
II. The 95% confidence interval for the difference between the proportion of those who snore in the two groups is (-0.31, 0.07).
III. Since the confidence interval contains 0, there is a significant difference between the two proportions.
a. I only
b. II only
c. III only
d. I and III
e. I, II, and III are correct
Answers
The statement that is NOT correct is: "The evidence supports the theory at the 10% level."
According to the given data, Among 40 randomly selected patients with a pacemaker, 12 snored.Among 60 randomly selected patients without a pacemaker, 25 snored. The proportion of patients who snored in the group with a pacemaker = 12/40 = 0.3
The proportion of patients who snored in the group without a pacemaker = 25/60 = 0.42
To find out if there is a significant difference between the two proportions, we can calculate the confidence interval for the difference between two proportions.
A confidence interval gives a range of values that is likely to contain an unknown population parameter. A 95% confidence interval is a range of values that we are 95% sure contains the true population parameter.The 95% confidence interval for the difference between the proportion of those who snore in the two groups is given as (-0.31, 0.07).
Since this interval contains 0, there is not a significant difference between the two proportions.The statement that is NOT correct is "The evidence supports the theory at the 10% level." because the 95% confidence interval is provided, not the 10% level.
Therefore, option a) is the correct answer.
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Among 40 randomly selected patients with a pacemaker, 12 snored. Among 60 randomly selected patients without a pacemaker, 25 snored.The evidence supports the theory at the 10% level.II.
When you make an estimate in statistics, whether it is a summary statistic or a test statistic, there is always uncertainty around that estimate because the number is based on a sample of the population you are studying.The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.The confidence level is the percentage of times you expect to reproduce an estimate between the upper and lower bounds of the confidence interval, and is set by the alpha value.The 95% confidence interval for the difference between the proportion of those who snore in the two groups is (-0.31, 0.07).III. Since the confidence interval contains 0, there is a significant difference between the two proportions.Out of the three statements, the statement that is NOT correct is statement III. Since the confidence interval contains 0, it does not necessarily mean that there is a significant difference between the two proportions. Therefore, the correct answer is c. III only.
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James earns $13 an hour. John earns $4 an hour. If, after working for a whole number of hour, they both earned the same amount, what is the lowest amount they could have earned in dollars.
Answers
Help !!!! heres the picture for it
Answers
Using the proportional rule of Similar Triangles, the length of SD is 12 m.
Given a truss bridge.
From it,
The triangles BCD and RSD are similar.
For similar triangles, corresponding sides are proportional.
Corresponding sides are,
BC and RS, CD and SD, BD and RD.
BC / RS = CD / SD = BD / RD.
Consider BC / RS = CD / SD.
2 / 1 = 24 / SD
2 (SD) = 24
SD = 12
Hence the length of SD is 12 m.
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PLEASE ANSWER ASAP !!!!!
Answers
Answer:
slope =-1
Step-by-step explanation:
i dont think there is any steps for this problem ;-;
use order of operations to solve 2 1/2 + 3 1/5 x 5 5/8
Answers
Answer: decimal form 20.5
Step-by-step explanation:
What are the 7 types of hazards in the home?
Answers
The 7 types of hazards in the home are Psychosocial Risks,Physical
Dangers , Chemical Dangers, Biological risks, Constrained Areas,
Changing Equipment and Biohazards
Psychosocial Risks
Physical dangers include a subgroup called psychosocial hazards. For some workers, these risks might be more severe or restrictive than for others. Poor management or a lack of feedback may be the cause of these risks.
Physical Dangers
Environmental and occupational hazards are two different categories of physical risks. These include unguarded machines, heat, cold, vibration, noise, and temperature extremes. Engineering controls can lessen some physical dangers.
Chemical Dangers
Toxic, flammable, explosive, self-reactive, oxidizing, or corrosive compounds are considered chemical dangers. Chemical risks can have negative health impacts and need special handling techniques and equipment.
Biological risks
Many workplaces have biological risks, which can be harmful to people. They include waste debris, food, fungi, food, hair, skin, and saliva.
Constrained Areas
Flammable gases can accumulate in small places. These gases tend to gravitate toward lower elevations, yet they can rise to the surface if a lid is closed or if they are hanging in the air.
Changing Equipment
For workers, the moving machinery hazard provides a distinct set of mechanical risks. Injuries caused by it include crushing, shearing, tangling, air being ejected, striking, abrading, and trapping.
Biohazards
There are many danger thresholds for biohazards. Agents of biohazard level I pose little risk to people. On the other hand, biohazard class II agents may be extremely contagious and may result in serious sickness if consumed or dispersed through the air.
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if the roof building is 46 feet off the ground and the floor of the basement is 15 feet under ground what is the total distance from roof to basement floor
Answers
Answer:
61
Step-by-step explanation:
46 then you have to add another 15 feet for underground and you get 61 because it is asking form the roof to the basement floor
hope this helps
Which data set contains an outlier?
O {9, 10, 10, 11. 4, 12. 1, 12. 6}
O {15, 15, 15, 16, 16, 17, 18}
O {16, 42, 45, 45, 46, 48}
O {45, 46, 47, 47, 49, 49}
Answers
Answer:
O {16, 42, 45, 45, 46, 48}
Step-by-step explanation:
To determine if a data set contains an outlier, we need to look for values that significantly deviate from the rest of the data.
Looking at the given options:
Option O {9, 10, 10, 11.4, 12.1, 12.6} does not contain any values that stand out as outliers.
Option O {15, 15, 15, 16, 16, 17, 18} does not contain any values that stand out as outliers.
Option O {16, 42, 45, 45, 46, 48} contains the value 42, which is significantly different from the other values. Therefore, this data set contains an outlier.
Option O {45, 46, 47, 47, 49, 49} does not contain any values that stand out as outliers.
Therefore, the data set that contains an outlier is:
Option O {16, 42, 45, 45, 46, 48}
Triangulation is a method of finding the location of an object based on measurements made from two other locations.
Answers
Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.
Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.
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