evaluate the double integral ?(y^2)/(x^2 y^2)da, where r is the region that lies between the circles x^2 y^2=4 and x^2 y^2=121, by changing to polar coordinates.
Answers
The double integral is zero.
How the double integral is zero?To evaluate the given double integral using polar coordinates, we need to express the integrand and the region R in terms of polar coordinates. Let's start by finding the polar equation of the two circles.
The equation of the circle x^2 y^2 = 4 can be rewritten in polar coordinates as r^4 cos^2θ sin^2θ = 4, which simplifies to r^2 = 2/(cosθ sinθ).
Similarly, the equation of the circle x^2 y^2 = 121 becomes r^2 = 121/(cosθ sinθ).
Since the circles are centered at the origin, we can use the fact that r is non-negative and 0 ≤ θ ≤ 2π to define the region R in polar coordinates. Therefore, we have:
2/(cosθ sinθ) ≤ r ≤ 11/cosθ sinθ
0 ≤ θ ≤ 2π
To change the integrand to polar coordinates, we need to express y^2/x^2 y^2 in terms of r and θ. We know that y = r sinθ and x = r cosθ, so y^2/x^2 y^2 = (r sinθ)^2 / (r^2 cos^2θ sin^2θ) = 1/(cos^2θ). Therefore, the
∫∫r=11/cosθ sinθ r=2/cosθ sinθ 1/cos^2θ r dr dθ
Integrating with respect to r first, we get:
∫θ=0^2π ∫r=2/cosθ sinθ r=11/cosθ sinθ 1/cos^2θ r dr dθ
= ∫θ=0^2π [1/sinθ - 1/11sinθ] dθintegrand becomes:
y^2 / x^2 y^2 = 1/cos^2θ
Now we can set up the double integral in polar coordinates:
= ∫θ=0^2π [10/11sinθ] dθ
= 0
Therefor, the double integral is zero.
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Related Questions
A company is considering purchasing the mineral rights to two different mountains. The probability that it will purchase the mineral rights to the first mountain is 0.55. The probability that it will purchase the mineral rights to the second mountain is 0.4. Assuming the decisions to purchase the mineral rights to each mountain are made independently, what is the probability that it will purchase the mineral rights to exactly one of the two mountains?
a. 0.4
b. 0.45
c. 0.51
d. 0.49
Answers
Using probability of independent events, it is found that the probability that it will purchase the mineral rights to exactly one of the two mountains is given by:
c. 0.51
If two events, A and B, are independent, the probability of both happening is the multiplication of the probability of each happening, that is:
\(P(A \cap B) = P(A)P(B)\)
In this problem, these following two events result in the rights of exactly one of the two mountains being bought:
First bought(0.55 probability), second not(0.6 probability).First not bought(0.45 probability), second bought(0.4 probability).Hence:
\(p = 0.55(0.6) + 0.45(0.4) = 0.51\)
Thus, option c is correct.
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4. Determine the perimeter of a square field with an area of 800m². (Give your answer as
an exact value - mixed radical)
Helpp
Answers
The perimeter of a square field of area 800m² is 113.137
The area of the field is 800 m²
We need to determine the perimeter of the square field
The formula for area of a square is
area = side ² or a ²
a = √ area
a = √ 800
a = 20√2
a = 20 x 1. 414
a = 28.284
perimeter is the sum of all sides of a square
The formula to calculate the perimeter
p = 4 x side
p = 4a
p = 4 x 20√2 = 80√2
p = 80 x 1.414
p = 113.137
Therefore, the perimeter of a square field of area 800m² is 113.137
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What is the ratio of rise to run between the points (-2, 8) and (4, -3)?
Answers
Ratio of rise to run between the points (-2, 8) and (4, -3) = -11/6
To find the ratio of rise to run between two points, we need to calculate the difference in the y-coordinates (rise) and the difference in the x-coordinates (run) between the two points.
Given points:
Point 1: (-2, 8)
Point 2: (4, -3)
Rise = difference in y-coordinates = y2 - y1 = -3 - 8 = -11
Run = difference in x-coordinates = x2 - x1 = 4 - (-2) = 6
Therefore, the ratio of rise to run can be calculated as:
Ratio of rise to run = Rise / Run = -11 / 6
Thus, the ratio of rise to run between the points (-2, 8) and (4, -3) is -11/6.
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The perimeter of a square field is 900 m. Find its area.
Answers
Answer:
Given perimeter=900m
So each side = 900/4
= 225
as area of square = side^2
=225^2
=50,625 meters
A certain number is added to four result is double
Answers
Given function g, which is defined by g(x)=x to the power of 3 -x , what is the value of g(3)?
Answers
Really sorry, misunderstood the equation. This is the answer though.
Answer:
24
Step-by-step explanation:
We have our function g(x) = \(x^{3}\) - x
Now, we will substitute 3 in for x, giving us:
\(3^{3} - 3\)
Now, we will simplify our exponent, giving us:
27 - 3 = 24
So your answer is 24.
Hope this helped!
(2/3)y - 4 ≥ 2
Help, Due Today
Answers
The inequality expression (2/3)y - 4 ≥ 2 when evaluated is y ≥ 3
How to evaluate the inequalityInequality expressions are those statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.
From the question, we have the following inequality expression given as
(2/3)y - 4 ≥ 2
Add 4 to both sides of the inequality
So, we have the following representation
2/3y ≥ 2
Multiply both sides of the inequality expression by 3/2
y ≥ 3
Hence, the solution to the given inequality expression is y ≥ 3
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A ship travels from Akron (A) on a bearing of 030° to Bellvilie (B),90km away. It then travels to Comptin (C) which is 310 km due east of Akron (A).Draw a diagram showing the movement of the ship indicate:a.)Northb.)the distances travelledc.)the know angles
Answers
Given: The bearing and distance of a ship from Akron(A) through Bellville(B) to Compton(C)
To Determine: The distance travelled and the angles
Solution
The diagram of the journey can be represented as shown below
Let us solve for BC using cosine rule
\(\begin{gathered} BC^2=AB^2+AC^2-2(AB)(AC)cosA \\ BC^2=90^2+310^2-2(90)(310)(cos60^0) \\ BC^2=8100+96100-27900 \\ BC^2=76300 \\ BC=\sqrt{76300} \\ BC=276.22km \\ BC\approx276km \end{gathered}\)The total distance travelled is
\(\begin{gathered} Total-distance=AB+BC+AC \\ =90km+276km+310km \\ =676km \end{gathered}\)Using sine rule, we can determine the measure of angle C
\(\begin{gathered} \frac{AB}{sinC}=\frac{BC}{sinA}=\frac{AC}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0}=\frac{310}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0} \\ sinC=\frac{90(sin60^0)}{276} \\ sinC=\frac{155.88}{276} \\ sinC=0.5648 \\ C=sin^{-1}(0.5648) \\ C=34.39^0 \end{gathered}\)Also know that the sum of angles in a triangle is 180 degree. Therefore
\(\begin{gathered} A+B+C=180^0 \\ 60^0+B+34.39^0=180^0 \\ B+94.39^0=180^0 \\ B=180^0-94.39^0 \\ B=85.61^0 \\ B\approx85.6^0 \end{gathered}\)The bearing of Compton from Bellville(B) is
\(Bearing(C-from-B)=90^0+34.39^0=124.39^0\approx124.4^0\)The bearring of Akron(A) from Compton(C) is
\(Bearing(A-from-C)=270^0+34.39^0=304.39^0\approx304.4^0\)In summary
The total distance travelled is 676km
The bearing of Compton from Bellville is 124.4 degrees, and the bearing of Akron from Compton is 304.4 degrees
c) 4x−4/5= 2
Plss daje naj
Answers
Answer:
x = \(\frac{7}{10}\)
Step-by-step explanation:
Given
4x - \(\frac{4}{5}\) = 2 ( multiply through by 5 to clear the fraction )
20x - 4 = 10 ( add 4 to both sides )
20x = 14 ( divide both sides by 20 )
x = \(\frac{14}{20}\) = \(\frac{7}{10}\)
x=7/10
Step-by-step explanation:
4x-4/5=2
multiply all through by 5
20x-4=10
collect like terms
20x=14
divide all through by 20
x=14/20
x=7/10
Look at the triangular prism below. Each triangular face of the prism has a base of 3 centimeters (cm)and a height of 4 cm. The length of the prism is 12 cm.
What is the volume of this triangular prism?
Answers
Answer:
chupapi muñeño
Step-by-step explanation:
Answer:
144 cm?
Step-by-step explanation:
V
\(v = l \times w \times h \\ v =12 \times 4 \times 3 \\ v = 12 \times 12 \\ v = 144\)
Refer to the Exhibit Cape May Realty. Testing the significance of the slope coefficient at a = 0.10, one can conclude that a. Because the p-value < 0.10, we can reject the null hypothesis. Therefore, there is enough evidence to say that the square footage has no effect on the property rental rate. b. Because the p-value < 0.10, we fall to reject the null hypothesis Therefore, there is enough evidence to say that there is no relationship between square footage and property rental rate. c. Because the p-value <0.10, we can reject the null hypothesis. Therefore, there is enough evidence to say that the population slope coefficient is different from zero. d. Because the p-value <0.10.we can reject the null hypothesis. Therefore, there is enough evidence to say that the population slope coefficient is greater than zero.
Answers
Based on the given information in Exhibit Cape May Realty, the question is asking to test the significance of the slope coefficient at a significance level of a = 0.10. The p-value is less than 0.10, which means that the null hypothesis can be rejected. This leads to the conclusion that the population slope coefficient is different from zero. Therefore, option C is the correct answer.
This means that there is a statistically significant relationship between square footage and property rental rate. As the slope coefficient is different from zero, it indicates that there is a positive or negative relationship between the two variables. However, it does not necessarily mean that there is a causal relationship. There could be other factors that influence the rental rate besides square footage.
In summary, the statistical analysis conducted on Exhibit Cape May Realty indicates that there is a significant relationship between square footage and property rental rate. Therefore, the population slope coefficient is different from zero. It is important to note that this only implies a correlation, not necessarily a causal relationship.
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PLEASE HELP WILL GIVE BRAINLIEST
Arrange the tiles on both boards to find the value of x.
Board sum: 3x + (-5) = 1
What x value solves the equation?
3x - 5 = 1
X =
Answers
Answer: x = 2
Step-by-step explanation:
3x - 5 = 1
add 5 to both sides
3x - 5 (+5) = 1 (+5)
3x = 6
divide by 3 on both sides
3x/3 = 6/3
x = 2
Help me please, will mark brainliest
Answers
It’s the last one. D.
Explanation:
Factor completely 3x3 − 3x2 − 18x. 3x(x 3)(x 2) 3x(x 3)(x − 2) 3x(x − 3)(x 2) 3x(x − 3)(x − 2).
Answers
3x(x^2-x-6)———-Rewrite the equation
3x(x^2+2x-3x-6)———Factor our X
3x(x(x+2)-3(x+2))——-factor out x+2
3x(x(x+2)-3(x+2))
3x(x+2) (x-3)
Write an equation to represent the following statement.
The sum of j and 47 is 55.
Answers
Answer:
j+47=55
Step-by-step explanation:
“the sum of” means adding, so you add j and 47, which is or is equal to 55
j+47=55
To rent a carpet cleaner, Tools To Go
charges $15.00 for the first hour or part of
an hour plus $3.50 for each additional half
hour or part of a half hour.
a) Tim picked up a carpet cleaner at
8:10 a.m. and returned it at 4:10 p.m.
Determine his rental charge.
b) Calculate the average cost per hour for
Tim’s rental.
c) Charmaine rented a carpet cleaner from
Carpet Emporium. Her bill was $59.40
for 5.5 h. Compare the average cost per
hour for Charmaine’s rental with the
average cost per hour for Tim’s rental.
How many times as much was
Charmaine’s rental?
Answers
Answer:
A) His rental charge is $64
B)The average cost per hour for Tim’s rental is 8 dollar/hour
C) Charmaine’s average cost is 1.35 times Tim's average cost
Step-by-step explanation:
Rent for first hour of carpet cleaner = $15
Rent for each additional half hour carpet cleaner = $3.50
a)Tim picked up a carpet cleaner at 8:10 a.m. and returned it at 4:10 p.m.
Total time = 8 hours
So, Rent for first hour of carpet cleaner = $15
Now no. of half an hours in remaining 7 hours is 14
So, Rent for each additional half hour carpet cleaner = $3.50
Rent for 14 additional half hour carpet cleaner = \(3.50 \times 14 =49\)
So, Total rental charge = 49+15 = 64
Hence his rental charge is $64
b)Calculate the average cost per hour for Tim’s rental.
Average cost =\(\frac{\text{Total cost}}{\text{Total hours}}=\frac{64}{8}=8 dollar/ hour\)
c)Charmaine rented a carpet cleaner from Carpet Emporium. Her bill was $59.40 for 5.5 h.
Average cost =\(\frac{\text{Total cost}}{\text{Total hours}}=\frac{59.4}{5.5}=10.8 dollar/ hour\)
Let Tim’s rental be x times as much was Charmaine’s rental
So,8x=10.8
\(x=\frac{10.8}{8}\)
x=1.35
So, Charmaine’s average cost is 1.35 times Tim's average cost
PLEASE HELP!! Solve for y.
Answers
Answer:
hypotenuse²=base²+height²
\( \sqrt{85 } {}^{2} = 6 {}^{2} + x {}^{2} \\ \)
85=36+x²85-36=x²49=x²49½=xx=7(4 ^1/5) ^5 simplify
a4
b1/4
c4^5
d4^25
Answers
The simplified form of \((4^{(1/5))}^5\) is 4, which is option (a).
Given the expression , we need to simplify,
Simplify the expression inside the parenthesis first.
Since there is an exponent of 5 outside the parenthesis, we can use the exponent rule of power of a power to simplify it.
\((4^{(1/5)})^5\) = \(4^{(1/5 * 5)\)
= \(4^1\)
= 4
To simplify (1/5))5, we need to apply the exponential rule.
= \(4^1\)
= 4
The formula \(a^4 * b^ {(1/ 4)} * c^4 * 4^5 * d^4^{25\), with some ambiguity and missing information.
The base of "a" is unknown, so we cannot simplify \(a^4\) unless we know the base.
Similarly, to simplify \(b^{(1/4)\) we need more information about the base of 'b'.
Unclear whether '4' should be a variable or \(a^4\) as it immediately follows \(c^4\).
The exponent of "d" is written as \(d^4^25\)
To allow a more precise simplification, please provide additional information or refine the formula further
Substitute the simplified expression back into the original expression.
\((4^{(1/5)})^5\) = 4
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If two right triangles each have a 45° angle, then the
triangles must be-
Answers
find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 4y + z = 24
Answers
Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.
To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.
First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:
6x + 4(0) + 0 = 24
6x = 24
x = 4
So, the plane intersects the x-axis at (4, 0, 0).
Similarly, to find the y-intercept, we set x = 0 and z = 0:
6(0) + 4y + 0 = 24
4y = 24
y = 6
So, the plane intersects the y-axis at (0, 6, 0).
To find the z-intercept, we set x = 0 and y = 0:
6(0) + 4(0) + z = 24
z = 24
So, the plane intersects the z-axis at (0, 0, 24).
We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).
To find the volume of this tetrahedron, we can use the formula:
Volume = (1/3) * base area * height
The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.
The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.
Plugging these values into the volume formula:
Volume = (1/3) * 12 * 24
= 96 cubic units
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complet the table of inputes and outputs for given function. g(x) = -4x-1 x g(x) 70 -13-1
Answers
To complete the first space on the table, we need to replace g(x) by 7 and solve for x as:
g(x) = -4x - 1
7 = -4x - 1
7 + 1 = -4x - 1 + 1
8 = - 4x
8/(-4) = -4x/(-4)
-2 = x
So, the first space is -2
Then, for the second space, we need to replace x by 0 and calculate g(x) as:
g(x) = -4x - 1
g(x) = -4*0 - 1
g(x) = 0 - 1
g(x) = -1
So, the second space is -1
The third space is calculated as the first one, replacing g(x) by -13 and solving for x:
g(x) = -4x - 1
-13 = -4x - 1
-13 + 1 = -4x - 1 + 1
-12 = - 4x
-12/(-4) = -4x/(-4)
3 = x
So, the third space is 3
Finally, the fourth space is calculated as the second one, replacing x by -1, so:
g(x) = -4x - 1
g(x) = -4*(-1) - 1
g(x) = 4 - 1
g(x) = 3
So, the fourth space is 3
Answer:
x g(x)
-2 7
0 -1
3 -13
-1 3
What’s the answer for this question?
Answers
Answer:
D
Step-by-step explanation:
The last one- monetary support that is used to help pay educational costs
:)
itz D :)
Give the other person brainliest cause they answered first and they’re correct :D
please help. i will brainlist you
Answers
Answer:
first question:
range-22
IQR-13
second question:
range-26
IQR-15.5
I hope this helped bestie!
A sandwich is 2 12 feet long. You decide to cut the sandwich into pieces that are 1 14 feet long. How many pieces will you cut?
Answers
Answer:
Im assuming you meant 2 1/2 and 1 1/4, so the answer would be 2 pieces
Step-by-step explanation:
2 1/2-1 1/4=1 1/4, so 2
Using the division operation, the number of pieces of sandwich that can be cut is 2
Given the Parameters :
Length of sandwich = 2.5 feets Length per piece cut = 1.25 feetsThe number of pieces that can be cut out of the sandwich can be calculated thus :
Length of sandwich ÷ Length per piece cutNumber of pieces = (2.5 ÷ 1.25) = 2
Therefore, there are 2 pieces of sandwich that can be cut.
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A soft-drink machine dispenses only regular Coke and Diet Coke. Sixty percent of all purchases from this machine are diet drinks. The machine currently has 10 cans of each type. If 15 customers want to purchase drinks before the machine is restocked, what is the probability that each of the 15 is able to purchase the type of drink desired? (Hint: Let x denote the number among the 15 who want a diet drink. For which possible values of x is everyone satisfied?)
Answers
we need to find the probability that each of the 15 customers is able to purchase the type of drink they desire from a soft-drink machine that dispenses regular Coke and Diet Coke. The machine currently has 10 cans of each type, and 60% of all purchases are diet drinks.
To calculate the probability, we consider the number of customers who want a diet drink, denoted by x. For everyone to be satisfied, the number of customers wanting diet drinks (x) must be less than or equal to the number of available diet drinks (10), and the number of customers wanting regular Coke (15 - x) must be less than or equal to the number of available regular Coke cans (10).
We can calculate the probability by summing the probabilities for all possible values of x that satisfy the above conditions. In this case, x can range from 0 to 10, since there are a maximum of 10 diet drink cans available. For each value of x, we calculate the probability as (0.6)^x * (0.4)^(15-x), since the probability of a customer wanting a diet drink is 0.6 and the probability of wanting regular Coke is 0.4.
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PLEASE HELP ME ANSWER THIS: The solution to the inequality 89 – 9.8t < 10.6 is
Answers
Answer:
The solution to the inequality 89 – 9.8t < 10.6 is ?
t > 8
The solution to the inequality 89 – 9.8t > 20.4 is?
t < 7
To determine when the projectile hits the ground, solve 89 – 9.8t = 0 for t.
t = 9.08163265306
Rounding to the nearest whole second, t is about ?
9 seconds.
The viable solution set is ?
[0, 7) or (8, 9]
TRUE/FALSE. the variance is the simplest measure of dispersion and is computed as the difference between the maximum value and the minimum value in the data set.
Answers
It is true that the variance is the simplest measure of dispersion and is computed as the difference between the maximum value and the minimum value in the data set.
What is variance?Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed. The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.
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Please guys this is due
Julian forgot his bat when he left for baseball camp. His mother finds a box to ship it to him with the dimensions shown. If the bat measures 34 inches long, will the bat fit inside the box? Drag words to complete the statements about the diagonal of the base and the interior diagonal of the box. Words may be used once, more than once, or not at all.
Answers
The diagonal of the base of the box is shorter than the bat.
The length of the interior diagonal of the box is shorter than the bat.
Juilian's bat will not fit in the box.
What is diagonal?The line connecting the opposite vertex of the geometric figure like cube or cuboid or square or rectangle is called the diagonal.
The diagonal of the base `= sq rt (32² + 8²) = 33 in.
The length of the interior diagonal = sq rt (32² + 8² +6²) =33.5 or 34 in.
Thus, The diagonal of the base of the box is shorter than the bat.
The length of the interior diagonal of the box is shorter than the bat.
Juilian's bat will not fit in the box.
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Answer:
1. Shorter than
2. Shorter than
3. Will not fit in the box
Step-by-step explanation:
Can someone help me solve this please?
Answers
The segment lengths for this triangle are given as follows:
PX = 7.5.XQ = 22.5.XY = 9.ZW = 21.6. What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.There are three triangles in this problem, all of which are similar.
PQR.PZW.PXY.The length of segment PX can be obtained with triangles PQR and PXY, as follows:
PX/30 = 10/40
PX/30 = 1/4
4PX = 30
PX = 7.5.
The length of segment XQ is found applying the segment addition postulate, as follows:
PQ + XQ = 30
7.5 + XQ = 30
XQ = 22.5.
The length of segment XY can also be obtained with the similarity of triangles PXY and PQR, as follows:
XY/36 = 10/40
XY/36 = 1/4
4XY = 36
XY = 9.
The length of segment ZW is obtained with the similarity of triangles PZW and PQR, as follows:
ZW/36 = 24/40
ZW/36 = 0.6.
ZW = 36 x 0.6
ZW = 21.6.
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while conducting a study on the growth rates of mice on a copper deficient diet, dr. ambrose recorded the following weights in grams of the mice after three weeks on the diet. 12, 11.3, 15.9, 12.5, 12 what is the standar deviation (s) in this set of samples? (calculate to 2 decimal places)
Answers
The standars deviation (s) in this set of samples is: s = 1.62
In this question we have been given set of the weights in grams of the mice after three weeks on the diet recorede by Dr. Ambrose while conducting a study on the growth rates of mice on a copper deficient diet.
We need to find the the standard deviation (s) in this set of samples.
First we find the mean,
μ = (12 + 11.3 + 15.9 + 12.5 + 12)/5
μ = 12.74
We know that the formula for standard deviation,
s = √[∑(x - μ)²/N]
First we find ∑(x - μ)²
= (12 - 12.74)² + (11.3 - 12.74)² + (15.9 - 12.74)² + (12.5 - 12.74)² + (12 - 12.74)²
= 13.21
So, the standard deviation,
s = √(13.21 / 5)
s = 1.62
Therefore, the standard deviation is 1.62
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