For which situations would it be appropriate to calculate a probability about the difference in sample means?
1) Both population shapes are unknown. n1 = 50 and n2 = 100.
2) Population 1 is skewed right and population 2 is approximately Normal. n1 = 50 and n2 = 10.
3) Both populations are skewed right. n1 = 5 and n2 = 10.
4) Population 1 is skewed right and population 2 is approximately Normal. n1 = 10 and n2 = 50.
5) Both populations have unknown shapes. n1 = 50 and n2 = 100.
6) Both populations are skewed left. n1 = 5 and n2 = 40.
Answers
It is generally appropriate to calculate a probability about the difference in sample means when the sample sizes are large (typically n ≥ 30) and the populations are approximately normally distributed.
How did we arrive at this assertion?To determine if it is appropriate to calculate a probability about the difference in sample means, consider the assumptions and conditions for conducting a hypothesis test or constructing a confidence interval. The appropriateness of calculating a probability about the difference in sample means depends on the following factors:
1) Both population shapes are unknown. n1 = 50 and n2 = 100:
- It is generally appropriate to calculate a probability about the difference in sample means when the sample sizes are large (typically n ≥ 30) and the populations are approximately normally distributed. Since the population shapes are unknown in this case, it is difficult to assess this condition. However, the large sample sizes (n1 = 50 and n2 = 100) may suggest that it is reasonable to approximate the population distributions as normal. Therefore, calculating a probability about the difference in sample means could be considered.
2) Population 1 is skewed right and population 2 is approximately Normal. n1 = 50 and n2 = 10:
- In this case, the assumption of approximately normally distributed populations is violated for population 1, which is skewed right. When the population distributions are not approximately normal, it may not be appropriate to calculate a probability about the difference in sample means. The small sample size for population 2 (n2 = 10) may also limit the accuracy of any inference made based on this sample.
3) Both populations are skewed right. n1 = 5 and n2 = 10:
- Similar to the previous case, the assumption of approximately normally distributed populations is violated for both populations. Additionally, the small sample sizes (n1 = 5 and n2 = 10) may not provide sufficient information for reliable inferences. Therefore, it is generally not appropriate to calculate a probability about the difference in sample means in this situation.
4) Population 1 is skewed right and population 2 is approximately Normal. n1 = 10 and n2 = 50:
- Similar to case 2, the assumption of approximately normally distributed populations is violated for population 1, which is skewed right. In this case, the sample size for population 1 (n1 = 10) is also small, which may limit the accuracy of any inference made based on this sample. The larger sample size for population 2 (n2 = 50) might make it more reasonable to approximate the population distribution as normal. However, the violation of the assumption for population 1 suggests caution when interpreting the results. It is not generally appropriate to calculate a probability about the difference in sample means in this situation.
5) Both populations have unknown shapes. n1 = 50 and n2 = 100:
- Similar to case 1, the population shapes are unknown. However, the large sample sizes (n1 = 50 and n2 = 100) might suggest that it is reasonable to approximate the population distributions as normal. As mentioned before, calculating a probability about the difference in sample means could be considered in this case.
6) Both populations are skewed left. n1 = 5 and n2 = 40:
The assumption of approximately normally distributed populations is violated for both populations, as they are skewed left. Additionally, the small sample sizes (n1 = 5 and n2 = 40) may not provide sufficient information for reliable inferences. Therefore, it is generally not appropriate to calculate a probability about the difference in sample means in this situation.
Summarily, it is generally appropriate to calculate a probability about the difference in sample means when the sample sizes are large (typically n ≥ 30) and the populations are approximately normally distributed. However, when the population distributions are not approximately normal or when the sample sizes are small, it is generally not appropriate to calculate a probability about the difference in sample means.
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Related Questions
16. A population of bacteria increases by 30 every hour. Is this situation linear or exponential? Why?
A. Exponential, because the function decreases
B. Exponential, because the function grows by a common factor
C. Linear, because the function decreases
D. Linear, because the function increases by a common difference
Answers
Answer:
D. Linear, because the function increases by a common difference
Step-by-step explanation:
Since it is increasing always at the same rate it is linear.
Please mark Brainliest.
PRE CALC HELP NEEDED
Answers
Answer:
\(\dfrac{5e^2}{2}\)
Step-by-step explanation:
Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.
Given function:
\(y=x^2\ln(2x)\)
Differentiate the given function using the product rule.
\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)
\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)
\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)
Input the values into the product rule to differentiate the function:
\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)
To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:
\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)
Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:
\(\boxed{\dfrac{5e^2}{2}}\)
Let B be a 2 ×2 matrix such that
7B^2 −5B + 3I = 0.
Is B invertible? It so, what are the eigenvalues of B−1? Justify your answer.
Answers
Yes, Matrix B is invertible.
And, The eigenvalues of B−1 are;
⇒ (5 ± 7.68) / 14 - 1
What is mean by Matrix invertibility?An Invertible Matrix is a square matrix defined as invertible if the product of the matrix and its inverse is the identity matrix.
Given that;
B be a 2 ×2 matrix such that;
⇒ 7B² −5B + 3I = 0
Now,
Since, B be a 2 ×2 matrix.
And, The expression is,
⇒ 7B² −5B + 3I = 0
⇒ B² −5/7B + 3I/7 = 0
Multiply by B⁻¹, we get;
⇒ B - 5/7 + 3B⁻¹ = 0
Solve for B⁻¹;
⇒ 3B⁻¹ = - B + 5/7
⇒ B⁻¹ = - B/3 + 5/21
Thus, The matrix B is invertible.
And, The eigen value of B are;
⇒ 7B² −5B + 3I = 0
⇒ 7B² −5B + 3I = 0
⇒ B = - (-5) ± √(-5)² - 4×7×3 / 2×7
⇒ B = 5 ± √25 - 84/14
⇒ B = 5 ± √- 59 / 14
⇒ B = 5 ± 7.68 i / 14
⇒ B - 1 = (5 ± 7.68) / 14 - 1
Thus, Matrix B is invertible.
The eigenvalues of B−1 are = (5 ± 7.68) / 14 - 1
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Please help, I'm not understanding this, I will give brainliest to the person who helps answer and maybe explain :)
the best way to put the solution is to say
1 to 3/5 * 5/9 to 1/3 or something like that, that was just an example
Answers
Step-by-step explanation:
all the tasks are the same type and have the same way of solution.
Example №1:
9[girls] + 11[boys]=20 persons. Then the probability to choose the first boy is: 11/20. After this choice, 9[girls]+10[boys]=19 persons. Then the probability to choose the 2-d boy is: 10/19. The final required probability is: 11/20 * 10/19 = 11/38.
P.S. all the details are in the attachment.
P.P.S. the suggetsted way is not the only one.
Hi guys can you help me?
Answers
Answer:
(2,-3)
Step-by-step explanation:
(-2 , -5) 4 units down → (-2, -9)
(-2, -9) reflected across y-axis → (2, -9)
The rule for a reflection over the y -axis is (x, y) → (−x, y)
(2, -9) 6 units up → (2, -3)
Brainiest this
Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing. How much is the total amount paid for the used car plus expenses?
Answers
The total amount paid for the used car plus expenses will be $6,914.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Zaida purchased a used car for $6,500.
State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.
Now,
Since, Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.
Hence, The total amount paid for the used car plus expenses is,
⇒ $6500 + 4% of 6500 + $72 + $45 + $37
⇒ $6500 + $260 + $154
⇒ $6,914
Thus, The total amount paid for the used car plus expenses = $6,914
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y − 6 =3/5(x + 5); (0, 8)
Answers
The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40
Equation of a lineThe equation of a line in point-slope form is expressed as;
y - y0 = m(x -x0)
where
m is the slope
(x0, y0) is the point on the line
Given the following parameters
Point (0,8)
Slope from the equation = 3/5
Substitute
y - 8 = 3/5(x - 0)
5(y -8) =3x
5y - 40 = 3x
5y - 3x = 40
Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40
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The voltage of an audio speaker can be represented by V=3 √P, where P is the power of the speaker. An engineer wants to design a speaker with 225 watts of power. What will the voltage be?
Answers
We are given the model for the voltage,
\(V=3\sqrt[]{P}\)This depicts the relationship between the voltage, V and the power, P.
This way, we can find the value for one variable given the other.
Given power of 225 watts, we can find V.
\(V=3\sqrt[]{225}=3\times15=45V\)Voltage = 45V
Boxes of Valentine’s Day chocolate truffles come in a variety of sizes. The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches. If each truffle in this box has a volume of 2 cubic inches, how many truffles are included in the box?
Answers
The no. of truffles than can be included in the box is 135.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches.
∴ The volume of the box is,
= (15×12×1.5) inches³.
= 270 inches³.
Given each truffle has a volume of 2 iches³.
∴ No. of truffles than can be included in the box is,
= (270/2).
= 135.
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Which number has a 4 with a value ten times less than the 4 in the number 123,469?
Answers
The number that has a 4 in the hundred places.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A 4 with a value ten times less than the 4 in the number 123,469.
First, the value of the 4 in the number 123,469 can be found by separating each digit as:
123,469 = 100,000 + 20,000 + 3,000 + 400 + 60 + 9
Then the value of the 4 is 400.
Now we want a number that has a 4 with a value then times less than 400. Then we have
400/10 = 40
Then we want a number that has a 4 in the hundred places.
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A-line passes through the points (2, -2) and (-6,2). the point (a,-4) is also in the line. what is the value of A
A. -6
B. -1
C. 1
D. 6
Answers
Answer:
d 6
it is not A B or c its
Step-by-step explanation:
edge 2020
The range of y = –2x to the 4th power + 7?
Answers
Answer: y ≤ 7
Step-by-step explanation:
brainlest
x is called the _____ When using scientific notation the _____ is 10.
Answers
Answer:
X is called the power of
1 is 10
Thank you and please rate me as brainliest as it will help me to level up
( PLEASE I NEED HELP AASP!!)
Answers
Answer:
2/3 * 660
Step-by-step explanation:
If we convert 65% to a decimal, we get 0.65.
First, it will helpful to find exactly what is 65% of 668:
0.65 * 668 = 434.2 and thus 65% of 668 is exactly 434.2.
Similarly, if you convert 2/3 to a decimal, you get 0.66 repeating.
2/3 * 660 = 440 which is only 10.2 units larger than 434.2. Thus, 2/3 * 660 is the most accurate estimate of 65% of 668.
It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon. A recent survey was conducted from 1000 of these individuals. For the sampling distribution of the sample proportion to be reasonably Normal, the sample must have been obtained in the right way (ideally, a simple random sample) and the sample size must be large (so that at least 10 or more successes and failures). Are these conditions met
Answers
Answer:
Random sample, \(np \geq 10\) and \(n(1-p) \geq 10\), so yes, both conditions were satisfied.
Step-by-step explanation:
60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.
This means that \(p = 0.6\)
A recent survey was conducted from 1000 of these individuals.
This means that \(n = 1000\)
Also, a random sample, so the first condition was satisfied.
The sample size must be large (so that at least 10 or more successes and failures).
\(np = 1000*0.6 = 600 \geq 10\)
\(n(1-p) = 1000*0.4 = 400 \geq 10\)
So yes, both conditions were met.
If 23 is added to a number, the result is 43 less than twice the number. Find the number.
Answers
9514 1404 393
Answer:
66
Step-by-step explanation:
Let n represent the number.
n +23 = 2n -43
66 = n . . . . . . . . add 43-n to both sides
The number is 66.
_____
Check
23 added to the number is 89
43 less than twice the number is 132 -43 = 89 . . . . as it should be
geometry question, after 3.1) suppose we are given the unit square a in the plane with corners (0, 0), (1, 0), (1, 1) and (0, 1). (a) find a linear transformation t that sends a to the parallelogram b with corners (0, 0), (1, 2), (2, 2) and (1, 0). (b) is the linear transformation t unique? why or why not? (c) what linear transformation s, other than the identity, would send a to itself? (d) is there a linear transformation whose overall effect would be to send a to b and then translate b in the horizontal direction by one unit? explain. (e) find a linear transformation that will send a to a parallelogram c of area 4 while still keeping (0, 0) and (1, 0) as two of its corners. (f) what is the general formula for the linear transformation that sends a to a parallelogram of area k while still keeping (0, 0) and (1, 0) as two of its corners?
Answers
a) The linear transformation that sends the unit square a to the parallelogram is T = [1 2 | 1 0]
b) The linear transformation is not unique
c)The transformation matrix S = [1 0 | 0 1]
d) The overall transformation T' is given by: T' = T_trans * T = [1 0 | 1 0] * [1 2 | 1 0] = [1 2 | 2 0]
e) To keep the area of parallelogram c as 4, the vectors CD' and C
a) We need to find the matrix representation of the transformation. Let's call the unit square vertices A, B, C, and D, and the parallelogram vertices A', B', C', and D'. To find the matrix representation, we can use the following procedure
So, let's start with step 1:
A = (0, 0), B = (1, 0), A' = (0, 0), and B' = (1, 2).
The transformation matrix T that maps AB to A'B' is given by:
T = [A'B' | AB] = [1 2 | 1 0]
Step 2:
C = (1, 1), D = (0, 1), C' = (2, 2), and D' = (1, 0).
To verify that this transformation maps the remaining vertices of the unit square to the remaining vertices of the parallelogram, we can calculate T(C) and T(D) and compare them with C' and D', respectively.
T(C) = T * C = [1 2 | 1 0] * [1, 1]^T = [2, 2]^T = C'
T(D) = T * D = [1 2 | 1 0] * [0, 1]^T = [1, 0]^T = D'
So, the linear transformation that sends the unit square a to the parallelogram b is given by the matrix representation:
T = [1 2 | 1 0]
b) No, the linear transformation is not unique. There could be multiple matrices that represent the same linear transformation.
c) The transformation matrix S that sends a to itself is given by:
S = [1 0 | 0 1]
This is known as the identity transformation, which maps every point in the plane to itself.
d) Let's call this transformation T'. We know that the transformation T that maps a to b is given by:
T = [1 2 | 1 0]
transformation T' is given by:
T' = T_trans * T = [1 0 | 1 0] * [1 2 | 1 0] = [1 2 | 2 0]
e) To find a linear transformation that sends a to a parallelogram c of area 4 while still keeping (0, 0) and (1, 0) as two of its corners, Let's call the two other corners of parallelogram c D' and C'. To keep the area of parallelogram c as 4, the vectors CD' and C
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What was your recommended intake of carbohydrates (grams), and how far were you from it? Show the mathActual Intake Recommended Intake Percentage159.00 115-166 100%
Answers
The actual intake of carbohydrates is 138% as compare to recommended intake.
Recommended intake of carbohydrates or any other nutrient are,
Based on the information provided,
Consumed 159 grams of carbohydrates,
Recommended intake is between 115 and 166 grams.
Calculate the percentage of actual intake compared to the recommended intake, use the following formula,
Percentage = (Actual Intake / Recommended Intake) x 100%
Substituting the values in the formula we have,
⇒Percentage = (159 / 115) x 100%
⇒Percentage ≈ 138.3%
Therefore, the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.
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What is the value of the expression when a = 5 and b = 2?
2a+b−3
A. 6
B. 9
C. 11
D. 24
Answers
9
Step-by-step explanation:Hi there !
2a + b - 3 =
replace a = 5 ; b = 2
= 2(5) + 2 - 3
= 10 + 2 - 3
= 12 - 3
= 9
Good luck !
Answer: 9
2a and b - 3 = ?
a = 5 ; b = 2
2(5/a) + 2/b - 3
Now we solve this.
10 + 2/b - 3
Subtract 3.
12 - 3
The answer is 9.
6 math books weigh 24 pounds. How much does 18 math books weigh?
Answers
Answer:
72 pounds
Step-by-step explanation:
6/24=18/x
cross multiply
Answer:
5 book because divide weight 24 for 1 and you go multiplication for 2 3 4 5 6
Step-by-step expl.klanation:
Please help me understand how to do this
Answers
Answer:
-1
Step-by-step explanation:
First, find g(3), g(3) is 5.
Next, plug in 5 for g(3).
So we have f(5), f(5) is -1
Any help? I don’t get this q can anyone help me do this
Answers
For number 5 - .3 ( 3.60 ÷ 12 = .3)
For number 6 - .32 ( 2.56 ÷ 8 = .32)
For number 7 - 2 ( 2.36 ÷ 2 = 1.18)
Find the Surface Area of the following figure. 9.5 m 16m 14m 12.7m 11m
Answers
The total surface area of the figure will be 1968.85 square meters.
To determine the surface area of the figure, we need to find the area of each face and then add them together.
Surface Area of the rectangular prism = 2(lb + bh + hl)
= 2(16 × 9.5) + 2(9.5 × 14) + 2(16 × 14)
= 2(152 + 133 + 224) = 2(509)
= 1018 m²
Next, we need to find the area of the triangular prism on the front with dimensions 11 m, 12.7 m, and 14 m:
Surface Area of the triangular prism;
= (11 × 14) + 2(0.5 × 11 × 12.7) + 2(0.5 × 12.7 × 14)
= (154 + 350.35 + 445.5)
= 950.85 m²
Therefore, the total surface area of the figure will be;
Total Surface Area = Surface Area of rectangular prism + Surface Area of triangular prism
= 1018 m² + 950.85 m²
= 1968.85 m²
So, the surface area of the figure is 1968.85 square meters.
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Consider the following system of two linear equations:
4y + 3x = 0
4y - x = 16
What is the point of intersection?
Answers
Answer: The two lines intersect at (-4,3)
Step-by-step explanation:
So our first step would be to turn both of these into standard slope-intercept form.
1.)
4y + 3x = 0
4y = -3x
y = -3/4x
2.)
4y - x = 16
4y = x + 16
y = 1/4x + 4
Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)
“What happens to our balloon when we add a positive number (puffs of air)?” need help ASAP!!
Answers
each puff of air added will make the balloon rise one unit
Need help, pls!!!
ty!
Answers
The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.
The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.
The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.
The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).
Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.
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Bo kept track of his cookie sales. He
discovered that 3 out of 5 people who
came into his bakery for cookies bought
chocolate chip cookies.
If 400 customers bought cookies at Bo's
Bakery last month, how many of them
bought chocolate chip cookies?
Answers
Answer:240
Step-by-step explanation:
400/5 = 80
80 x 3 = 240
240/400 people bought choc chip
26. Tyler has been saving his winning lottery tickets. He has 23 tickets that are worth a total of $175. If each ticket is worth either $5 or $10, how many of each does he have?
Answers
A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
The total weight of the liquid in the tank is approximately 12,628 pounds.
To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.
Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.
In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.
By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.
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the dimension of the confirms room or 7.2 M * 11 M what is the area of the conference room
Answers
Step-by-step explanation:
Just multiply the two dimensions to get m^2 area
7.2 m * 11 m = 79.2 m^2