find the flux of f = xy i yz j zxk out of a sphere of radius 2 centered at the origin.
Answers
the flux of f = xy i + yz j + zx k out of a sphere of radius 2 centered at the origin is 4 sin² θ.
The given vector field is, f = xy i + yz j + zx kThe flux of a vector field F through a closed surface S is defined as the integral of the dot product of the vector field with the outward facing unit normal vector to the surface over the entire surface.The formula for the flux is given as, Φ = ∫∫ F·dS,where dS is the outward facing unit normal vector element and the surface integral is taken over the surface S. Flux of f = xy i + yz j + zx k out of a sphere of radius 2 centered at the origin is to be found.So, the radius of the sphere is given as 2.The general equation of the sphere is given as, x² + y² + z² = r²where r is the radius of the sphere i.e., 2 in this case.The center of the sphere is at the origin i.e., (0, 0, 0).Therefore, the equation of the given sphere is x² + y² + z² = 4i.e., the sphere of radius 2 centered at the origin is given as, x² + y² + z² = 4Now, we need to find the flux of the given vector field F = f = xy i + yz j + zx k, out of this sphere.Using the formula, Φ = ∫∫ F·dS, we get, Φ = ∫∫ F·dS = ∫∫ F·n dSwhere n is the outward facing unit normal vector to the sphere x² + y² + z² = 4.We can write this normal vector as, n = (x, y, z) / 2The magnitude of the normal vector is given as, |n| = sqrt(x² + y² + z²)/2= sqrt(4)/2= 1Therefore, the unit normal vector is given as, n = (x, y, z) / 2i.e., n = (x/2, y/2, z/2)The dot product of the given vector field f and the unit normal vector n is, F·n = (xy i + yz j + zx k)·(x/2, y/2, z/2) = (xy² + yz³ + zx²)/2Thus, the flux is given as, Φ = ∫∫ F·dS= ∫∫ F·n dS= ∫∫ (xy² + yz³ + zx²)/2 dSNow, we need to evaluate this double integral over the surface of the sphere x² + y² + z² = 4.To evaluate this integral, we use spherical coordinates.Substitute x = r sin φ cos θ, y = r sin φ sin θ, z = r cos φ in the given equation of the sphere x² + y² + z² = 4.We get, r² sin² φ cos² θ + r² sin² φ sin² θ + r² cos² φ = 4r² (sin² φ cos² θ + sin² φ sin² θ + cos² φ) = 4r²sin² φ cos² θ + sin² φ sin² θ + cos² φ = 4 sin² φ (cos² θ + sin² θ) + cos² φ = 4 sin² φ + cos² φ = 4Thus, the limits of the variables are: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π, 0 ≤ r ≤ 2Using these limits and integrating the dot product of F and n over the surface of the sphere using spherical coordinates, we get, Φ = ∫∫ F·dS= ∫∫ (xy² + yz³ + zx²)/2 dS= ∫[0, 2π]∫[0, π] (r³ sin² φ cos θ sin φ + r³ sin³ φ sin² θ + r³ sin φ cos² φ cos θ)/2 dφ dθ= ∫[0, 2π] cos θ dθ · ∫[0, π] (r³ sin³ φ sin² θ + r³ sin φ cos² φ)/2 dφ= 0 (because cos θ is an odd function integrated over the limits of an even function)∫[0, π] (r³ sin³ φ sin² θ + r³ sin φ cos² φ)/2 dφ= ∫[0, π] (r³ sin φ/2 sin² θ cos φ + r³ sin φ/2 sin² θ sin φ)/2 dφ= (r³/2) sin² θ ∫[0, π] sin φ dφ= (r³/2) sin² θ (-cos π + cos 0)= (r³/2) sin² θWe know that r = 2 (because the sphere is of radius 2)Therefore, Φ = (2³/2) sin² θ= 4 sin² θ.
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The flux of F through the sphere is 16π.
To find the flux of the vector field, F= xy i + yz j + zxk out of a sphere of radius 2 centered at the origin, we shall apply the divergence theorem which states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the volume enclosed by the surface.
Thus, the problem can be solved as follows:
Integral of F over the sphere = flux of F through the sphere
= ∫∫ F . n dS,
where n is the outward normal unit vector to the sphere,
and dS is the surface area element of the sphere.
Since the sphere is centered at the origin, the vector field F has radial symmetry about the origin.
Therefore, we can write F = F(r) * r, where r is the radial unit vector.
Hence,\(F . n = F(r) * r . n = F(r) cos(θ)\),
where θ is the angle between F and n.
For the sphere, θ = 0 everywhere, so cos(θ) = 1.
Thus, F . n = F(r).
Thus, the flux can be written as
\(∫∫ F . n dS = ∫∫ F(r) dS = ∫∫∫ div F(r) dV\),
where div F(r) is the divergence of F evaluated at radial distance r.
We have, \(div F = ∂/∂x (xy) + ∂/∂y (yz) + ∂/∂z (zx)= y + z.\)
Thus, div F(r) = 3r for r ≤ 2, and is zero elsewhere.
Therefore, we have,
∫∫ F . n dS = ∫∫∫ div F(r) dV
= ∫0π ∫0π ∫0²³ 3r r² sinθ dr dθ dφ
= 3 ∫0π ∫0π (sinθ) dθ dφ ∫0²³ r³ dr
= 3 * 2 * π * (1/3) * (2³)
= 16π
Thus, the flux of F through the sphere is 16π.
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Related Questions
(1.5x10^13)^2 in standard form
Answers
The standard form of the number \((1.5*10^(13))^2\) is 2.25×\(10^(26)\) .
What is standard form of a number ?
An equation, an expression, or a set of integers can all be written in standard form using the standard form approach. It is possible to express a number in a way that adheres to certain standards by writing it in its standard form. Standard form refers to any number between 1.0 and 10.0 that may be expressed as a decimal number and multiplied by a power of 10. The term "standard form" in this context refers to the act of condensing a particularly big expanded form of a number.
Here given is ,
=> \((1.5*10^(13))^2\)
=> \(1.5^2\) × \(10^(13)^2\)
=> 2.25×\(10^(26)\)
Therefore standard form of the number is 2.25×\(10^(26)\).
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a researcher randomly draws samples of iq scores for 50 individuals. what proportion of samples will have means less than 80?
Answers
A whopping 95% of people fall within the IQ ranges of 70 and 130. 99.7% of people in the world have IQs between 55 and 145. Only about 0.3% of people have IQ scores that fall outside of this range (less than 55 or higher than 145).
According to the one-standard-deviation rule, 32 percent of the population has an IQ score that is at least 15 points off from 100: 16 percent have IQs over 115, and 16 percent have IQs below 85.
The equation IQ=mc100, where m is the mental age and c is the chromological age, determines a person's IQ. Find the range of their mental ages if a group of 12-year-old youngsters has an IQ between 80 and 140.
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u + 7 < 18
solve the inequality of u
Answers
Answer:
u < 11
Step-by-step explanation:
u + 7 < 18
u < 11
To solve the inequality:
u + 7 < 18
We need to isolate the variable u on one side of the inequality symbol.
Subtracting 7 from both sides, we get:
u < 18 - 7
Simplifying the right-hand side, we get:
u < 11
Therefore, the solution to the inequality is:
u < 11
In interval notation, the solution is:
(-∞, 11)
A right cylinder and an oblique cylinder have the same radius and the same height. How do the volumes of the two
cylinders compare?
A. The volumes are the same, based on Cavalieri's principle.
B. The volumes are not the same, because Cavalieri's principle does not apply to oblique solids.
C. The volumes are not the same, because the two solids do not have the same cross-sectional
area at every level parallel to the bases.
D. The volumes are not the same, because an oblique solid has less volume thanits corresponding
right solid with the same height.
Answers
Answer:
A. The volumes are the same, based on Cavalieri's principle.
Step-by-step explanation:
Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.
ApplicationA right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.
How do I solve for X
Answers
Answer:
I think x equals 7.5
Step-by-step explanation:
Please let me know if this was correct or what you were looking for. Thanks!
does someone mind helping me with this problem? Thank you!
Answers
Answer:
5.20
Step-by-step explanation:
48 / 9.23 = 5.20043336945
rounded to tenth is 5.20
Hope This Helped
Answer:5.20
Step-by-step explanation:
48 / 9.23 = 5.20
Charge Q
1. =6.0nC is at (0.30 m,0), charge Q
2 =−1.0nC is at (0,0.10 m), and charge Q
3 =5.0nC is at (0,0). What is the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges? (k=8.99×10^9 N⋅m^2C ^2 )
Answers
The magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.
The value of the net electrostatic force on the 5.0-nC
charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0),
charge Q2 = −1.0 nC is at (0, 0.10 m), and
charge Q3 = 5.0 nC is at (0, 0) can be calculated as follows:
Given data,Charge Q1 = 6.0 nC is at (0.30 m, 0),
Charge Q2 = -1.0 nC is at (0, 0.10 m),
Charge Q3 = 5.0 nC is at (0, 0)
The formula to find out the force on the third charge Q3 is:
F = k * |Q1 * Q3| / r1^2 + k * |Q2 * Q3| / r2^2
Here, k = 8.99 × 10^9 N·m^2/C^2, Q1 = 6.0 nC, Q2 = -1.0 nC, Q3 = 5.0 nC
For the third charge Q3, the distance from Q1 is:
r1 = √(0.3^2 + 0^2) = 0.3 m
And the distance from Q2 is: r2 = √(0^2 + 0.1^2) = 0.1 m
Substituting all the given values in the formula:
F = 8.99 × 10^9 * [ (6.0 × 10^-9 * 5.0 × 10^-9) / 0.3^2 ] + 8.99 × 10^9 * [ (-1.0 × 10^-9 * 5.0 × 10^-9) / 0.1^2 ]F = 6.21 N
Therefore, the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.
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Find the perimeter of the figure. Round all figures to the nearest hundredths place.
Isosceles trapezoid
A 70.24 ft
B 74.48 ft
C 79.42 ft
D 92.84 ft
Answers
Answer:92.84
Step-by-step explanation: 39+27+13.5+13.5 because the two sides are longer than 12
The perimeter of the trapezium is 143.94 ft.
We have,
The perimeter of an isosceles trapezium can be found by adding the lengths of all four sides.
In this case, the trapezium has height = 12 ft and parallel sides of length 27 ft and 39 ft.
To find the length of the non-parallel sides we can use the Pythagorean theorem:
a² = (39 - 27/2)² + 12²
a² = 1440
a ≈ 37.95 ft
Therefore,
The perimeter of the trapezium is:
P = 27 + 39 + 2a
P ≈ 27 + 39 + 2(37.95)
P ≈ 143.9 ft
Rounding to the nearest hundredth place,
we get P ≈ 143.94 ft.
Thus,
The perimeter of the trapezium is 143.94 ft.
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IF U WAN BRAINLIEST PLS HELP
Answers
7) 65%
8) 5%
9) 19 pencils
10) 30 questions
7)20 - 7 = 13
13/20= 0.65
0.65= 65%
8) 40 - 38 = 2
2/40= 0.05
0.05 = 5%
9) 0.38 times 50 = 19
10) i just did 30 divided by 27 and got 90%
Jessie traveled 60 miles in 1 hour. At the same rate, how far would she travel in 10 hours?
Answers
Answer:
600 mph
Step-by-step explanation:
60 x 10 = 600
Answer:
600
Step-by-step explanation:
if she travled 60 in 1 hour you multiply that by 10 so it woupd be 600 in 10 hours
There are 6 cups of oatmeal in a box. If each serving is 1/5 of a cup, how many servings are contained in the box?
Answers
We have:
1 box has 6 cups
and 1 serving is 1/5 of 1 cup
Then:
Since there is 1/5 of a cup of oatmeal in a serving, this means that each of the 6cups contains 5 servings.
The total number of servings is seen to be
\(5\times6=30\)as there are 6 groups of 5 servings
Answer: 30
Write the polynomial f(x) that meets the given conditions. Answers may vary. Degree 2 polynomial with zeros of 4+6i and 4-6i. 2 f(x) = x² - 2x + 52 X 5
Answers
The polynomial that meets the given conditions is:
f(x) = (x - (4 + 6i))(x - (4 - 6i))(5(x² - 2x + 52))
Simplifying this expression, we have:
f(x) = (x - 4 - 6i)(x - 4 + 6i)(5x² - 10x + 260)
Using the difference of squares formula, we can simplify the complex conjugate terms:
(x - 4 - 6i)(x - 4 + 6i) = (x - 4)² - (6i)² = (x - 4)² - 36i² = (x - 4)² + 36
Substituting this simplified form back into the polynomial:
f(x) = ((x - 4)² + 36)(5x² - 10x + 260)
Expanding further:
f(x) = 5x⁴ - 10x³ + 260x² + 36x² - 72x + 9360
Combining like terms:
f(x) = 5x⁴ - 10x³ + 296x² - 72x + 9360
Therefore, one possible polynomial that satisfies the given conditions is f(x) = 5x⁴ - 10x³ + 296x² - 72x + 9360. Note that other valid polynomials may exist as well.
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6. The following table shows the weight (in kilograms) of 50 sacks of sugar in a shop. 10.37, 12.82, 11.05, 13.26, 10.65, 11.24, 15.58, 16.55, 19.47, 18.22, 29.36, 24.639, 38, 37.30, 22.01, 19.72, 10.67, 10.33, 10.05, 31.57, 10.06, 8.70, 39.49, 10.98, 26.01, 19.92, 11.36, 38.93, 20.08, 29.53, 23.36, 29.91, 27.67, 24.21, 28.18, 10.61, 18.83, 30.11, 35.41, 29.73, 9.27, 11.69, 9.66, 29.52, 11.40, 16.72, 20.63, 12.86, 10.62, 35.26 Make a grouped frequency distribution table for the data and then construct a histogram.
Answers
A grouped frequency distribution table for the data is [5, 10), [10, 15), [15, 20), [20, 25), [25, 30), [30, 35), and [35, 40).
We are given that;
The weight (in kg) of 50 sacks of sugar
Now,
To find the frequency of each class, we can use a tally mark system or a calculator. For example, the frequency of the first class [5, 10) is 3, because there are 3 data values that are greater than or equal to 5 but less than 10: 8.70, 9.27, and 9.66. The frequency of the second class [10, 15) is 16, because there are 16 data values that are greater than or equal to 10 but less than 15: 10.37, 10.65, 10.67, 10.33, 10.05, 10.06, 10.98, 10.61, 10.62, 11.05, 11.24, 11.36, 11.69, 11.40, 12.82, and 12.86.
We can repeat this process for the remaining classes and fill in the table as follows:
Class Frequency
[5, 10) 3
[10, 15) 16
[15, 20) 7
[20, 25) 4
[25, 30) 9
[30,35) 6
[35,40) 5
Therefore, by the given frequency the answer will be [5, 10), [10, 15), [15, 20), [20, 25), [25, 30), [30, 35), and [35, 40).
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What is the value of x in reduced radical form? (us sqrt)
Answers
Answer:
sin theta= p/h
here, 40√3/x=x sin 60
40√3/x=x √3/2
40/x= x/2
x^2=80
=√80=4√5
Ninety five percent of students in statistics scored between 62 pts and 90 pts. Assuming this data is normally distributed, what are the mean and standard deviation?.
Answers
The mean is 76 and the standard deviation is 7.
What is mean and standard deviation?
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.
In mathematics, particularly in statistics, there are various types of means. Each mean summarizes a particular set of data, frequently to help determine the overall significance of a particular data set.
Let, 95% of students in statistics scored between 62 and 90 points.
Here,
Mean = \(\frac{62+90}{2} = \frac{152}{2} = 76\)
And the standard deviation is,
SD = \(\frac{90-76}{2}= \frac{14}{2} = 7\)
Hence, the mean is 76 and the standard deviation is 7.
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A pizza restaurant is offering a special price on pizzas with
2
22 toppings. They offer the toppings below:
Pepperoni
Sausage
Ham
Chicken
Green pepper
Onion
Mushroom
Pineapple
Pepperoni
Chicken
Mushroom
Sausage
Green pepper
Pineapple
Ham
Onion
Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose
2
22 different toppings.
What is the probability that Rosa's mom chooses sausage and onion?
Answers
The probability that Rosa's mom chooses sausage and onion is: 1/8C₂.
What is the probability?Probability refers to the chance of an event occurring. It is given by the formula: number of favorable outcomes/number of total outcomes. The total number of groups from which Rosa's mom can make her choice is 1 and this is the number of favorable outcomes.
But, the total number of outcomes that Rosa can hope to expect are 2 two toppings(sausage or onions) out of 8. So, the selected answer is the representation of the probability.
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Classify the triangle.
Answers
Answer: Triangles can also be classified by their angles. In an acute triangle all three angles are acute (less than 90 degrees). A right triangle
Step-by-step explanation:Classification of triangles according to the length of their sides · Isosceles triangle · Equilateral triangle · Scalene Triangle.
Which is the value for 54 . 3 ÷ 10 0 54.3÷100? A. 0.543 B. 5.43 C. 54.3 D. 543
Answers
Answer: The answer is acually 54.3
Step-by-step explanation: cause I did it
Which of the following is the additive inverse of -4x + 13?
A) 4x – 13
B) 4x + 13
C) –4x – 13
D) –4x + 13
Answers
-13+4x
Step-by-step explanation:
Determine the opposite number of -4x +13 :
⬇️
-13 + 4x
A discrete uniform distribution has the following characteristics except:
(a) Equal probability for each possible outcome
(b) Finite number of possible outcomes
(c) Continuous random variable
(d) Uniform distribution
Answers
The correct answer is (c) Continuous random variable.
A discrete uniform distribution is characterized by the following:
(a) Equal probability for each possible outcome: In a discrete uniform distribution, each possible outcome has an equal probability of occurring.
(b) Finite number of possible outcomes: The distribution has a finite number of possible outcomes, which are typically integers or a discrete set of values.
(d) Uniform distribution: The distribution is uniform, meaning that the probabilities of each outcome are the same.
However, a discrete uniform distribution is not characterized by a continuous random variable. In a discrete distribution, the random variable can only take on a finite or countable number of distinct values, while a continuous random variable can take on any value within a specified range.
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Please help me I would appreciateeeeeeeeeeeeee
Answers
The value of the variable x in first figure will be 15.
The value of the variable x in second figure will be 20.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
There are two figure is shown in figure.
Now,
In first figure;
The sum of all the interior angle in a triangle is 180°.
So, We can formulate;
⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°
Solve for x as;
⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°
⇒ 6x - 10 + 2x + 20 + 3x + 5 = 180°
⇒ 11x + 15 = 180
⇒ 11x = 180 - 15
⇒ 11x = 165
⇒ x = 15
Thus, The value of the variable x in first figure will be 15.
For second figure;
We can formulate by the corresponding angle of the parallel lines as;
⇒ x + 50 = 70
⇒ x = 70 - 50
⇒ x = 20
Thus, The value of the variable x in second figure will be 20.
Therefore,
The value of the variable x in first figure will be 15.
The value of the variable x in second figure will be 20.
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle.
y = ex, y = x2 − 1, x = −1, x = 1
Find the area of the region.
Answers
The area of the region is rectangles
The given curves are y = x2 and y = 2 − x2. They intersect at x = 1, y = 1. See the graph below. The shaded region enclosed by the curves is the region whose area we wish to find.To find the area of the shaded region,
The left part of the region is the part bounded by the x-axis, the curve y = x2, and the line x = 1. This region is shown below. To find the area of this region, we integrate with respect to y from y = 0 to y = 1. Along the curve y = x2, the values of x are ± y1/2. So we have to integrate from x = −y1/2 to x = 1.
Thus the area of the right part of the region isThus the total area of the shaded region is Approximating rectangle The area of each approximating rectangle is given by height times width. Since we are dividing the region into two parts we
A typical rectangle is shown below. The value of x corresponding to the lower end of the rectangle is x = −y1/2 and the value of x corresponding to the upper end of the rectangle is x = 1. So the height of the rectangle is x2 and the width is Δy = 1/n. Therefore, the area of the rectangle isSince the rectangle is located below the curve, this approximation underestimates the true area of the region.
Therefore, the area of the rectangle is Since the rectangle is located above the curve, this approximation overestimates the true area of the region. By computing the sum of the areas of all the approximating rectangles and taking the limit as n approaches infinity, we can find the exact area of the region.
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please give the correct answer and no links!
Answers
Answer:
KL ≈ 16.6 ft
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos25° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{MK}{KL}\) = \(\frac{15}{KL}\) ( multiply both sides by KL )
KL × cos25° = 15 ( divide both sides by cos25° )
KL = \(\frac{15}{cos25}\) ≈ 16.6 ft ( to the nearest tenth )
On a map 4.5 inches is equal to 99 miles. How many miles would represent 1 inch?
Answers
Answer:
22 inches is the answer
someone pls help it’s due today :(
Answers
180 - 28 - 14 = 138
so 12x - 18 = 138
x = 13
i need help with Which is a kind of federal payroll tax?
Answers
The FICO is a type of federal payroll tax
Given data ,
One type of federal payroll tax is the Federal Insurance Contributions Act (FICA) tax. This tax is a combination of Social Security and Medicare taxes, which are used to fund these programs. The current Social Security tax rate is 12.4%, with 6.2% paid by the employee and 6.2% paid by the employer.
The Medicare tax rate is 2.9%, with 1.45% paid by the employee and 1.45% paid by the employer. However, there is an additional 0.9% Medicare tax that is paid by employees who earn over a certain amount.
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h 10 yd.
L 14 yd.
W 3 yd.
Volume=
Answers
Answer:
10yd x 14 yd x 3yd = 420yd ^3
Step-by-step explanation:
When calculating for the volume you multiply all three numbers. That’s why when you write your answer you cube it.
4−0.25g+0.5h4-0.25g+0.5h 4−0.25g+0.5h 4, minus, 0, point, 25, g, plus, 0, point, 5, h when g=10g=10 g=10 g, equals, 10 and h=5h=5 h=5 h, equals, 5 .
Answers
Answer:
The value of the expression is 4
Step-by-step explanation:
Given:
Evaluate 4 - 0.25g + 0.5h
When g = 10 and h = 5
Substitute the value of g and h into the expression
4 - 0.25g + 0.5h
= 4 - 0.25(10) + 0.5(5)
= 4 - 2.5 + 2.5
= 4
Therefore, the value of the expression is 4
The margin of error of a confidence interval about the difference between the means of two populations is equal to Group of answer choices the width of the confidence interval half the width of the confidence interval 1.5 times the width of the confidence interval twice the width of the confidence interval
Answers
The correct answer is "half the width of the confidence interval."
The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.
In a confidence interval, the width represents the range between the upper and lower bounds of the interval. The margin of error indicates the maximum amount by which the sample estimate can deviate from the true population parameter.
To calculate the margin of error, you divide the width of the confidence interval by 2. This is because the margin of error represents the distance from the sample estimate to the upper or lower bound of the interval. By dividing the width by 2, we determine the maximum amount of deviation from the estimate allowed on either side.
Therefore, the correct answer is "half the width of the confidence interval."
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100 point please help. It's not 28 or 52
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The answer is 39 ...........