Suppose that the random variables X and Y are independent and you know their distributions.
Which of the following explains why knowing the value of X tells you nothing about the value of Y?
A.
X and Y might be independent.
B.
The mean of X might be different from the mean of Y.
C.
The variance of X might be different from the variance of Y.
D.
All of the above.
Answers
A. X and Y might be independent. Knowing the value of one independent variable tells us nothing about the value of the other independent variable. The mean and variance of X and Y being different does not necessarily mean that knowing the value of one tells us nothing about the other.
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Related Questions
Work clothes costing $25.95, $23.95, $26.50, $39.95, and $41.25.
Answers
A company loses $780 as a result of shipping delay the 6 owners of the company must share the loss equally.
A:write an expression to show the change in profit for each owner
B: Evaluate the expression
Help me please
Answers
A) Change in profit for each owner = -780/8
B) Change in profit for each owner = -$130
The total loss = $780
Number of owners = 6
The 6 owners must share the loss equally
For the 6 owners to share equal loss, the total loss must be divided by the number of owners (That is, 6)
The change in profit for each owner will be the original profit less 780/6
That is -780/6
Evaluating -780/6
Change in profit for each owner = -$130
This means that each of the 6 owners will have a $130 reduction in the profit made
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Find a Möbius transformation sending 0,00 to -1,1, respectively. Note that this maps the y-axis onto the unit semicircle (b) Use the transformation from part (a) to find an infinite sequence of points on the mit semicircle that are equally spaced in the sense of non-Euclidean length. az + b (c) What map 2 is the product of reflections in the y-axis and unit cz +d circle? Does this map have a fixed point? til not provide
Answers
(a) The transformation is the identity transformation, which leaves the points unchanged.
(b) Using the transformation f(z) = z, we can map the y-axis onto the unit semicircle. Points on the unit semicircle can be represented as e^(iθ) for θ ranging from 0 to π. Mapping these points using f(z) = z gives us:
f(e^(iθ)) = e^(iθ)
(c) The fixed points of this transformation are ±i.
(a) To find a Möbius transformation that maps 0 to -1 and 1 to 1, we can use the general form of a Möbius transformation:
f(z) = (az + b) / (cz + d)
First, let's find the transformation that maps 0 to -1:
We have f(0) = -1, which gives us the equation:
(0a + b) / (0c + d) = -1
This simplifies to b / d = -1.
Next, let's find the transformation that maps 1 to 1:
We have f(1) = 1, which gives us the equation:
(a + b) / (c + d) = 1
This equation gives us a + b = c + d.
Using the condition b / d = -1, we can substitute b = -d into the equation a + b = c + d:
a - d = c + d
Now, we have two equations:
a - d = c + d
a + b = c + d
Simplifying these equations, we get:
2a = 2c + 2d
2a = 2c
From these equations, we can see that a = c = 1 and d = 0.
Therefore, the Möbius transformation that maps 0 to -1 and 1 to 1 is:
f(z) = (z + 0) / (z + 0)
Simplifying further, we get:
f(z) = z
This means that the transformation is the identity transformation, which leaves the points unchanged.
(b) Now, using the transformation f(z) = z, we can map the y-axis onto the unit semicircle. Points on the unit semicircle can be represented as e^(iθ) for θ ranging from 0 to π. Mapping these points using f(z) = z gives us:
f(e^(iθ)) = e^(iθ)
So the points on the unit semicircle that are equally spaced in the sense of non-Euclidean length are simply the points e^(iθ) for θ ranging from 0 to π.
(c) The product of reflections in the y-axis and unit circle can be represented by the transformation f(z) = -1/z. This transformation reflects points across the y-axis and then reflects them across the unit circle. To find the fixed point of this transformation, we set f(z) = z and solve for z:
-1/z = z
Multiplying both sides by z, we get:
-1 = z^2
Taking the square root of both sides, we obtain:
z = ±i
So the fixed points of this transformation are ±i.
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The length of one leg of the right triangle is 2 ft less than the length of the hypotenuse. The length of the other leg is 1 ft less than the length of the hypotenuse. Find the length of the sides.
Answers
Answer:
The length of the sides are 3 feet and 4 feet, respectively.
Step-by-step explanation:
Given the fact that triangle is a right triangle, it can be represented by Pythagorean Theorem:
\(r^{2} = x^{2}+y^{2}\)
Where:
\(r\) - Hypotenuse, measured in feet.
\(x\), \(y\) - Legs, measured in feet.
In addition, each leg can be determined as functions of hypotenuse:
\(x = r-2\,ft\)
\(y = r-1\,ft\)
Hence, the Pythagorean identity can be expanded and remaining variable may be solved:
\(r^{2} = (r-2\,ft)^{2}+(r-1\,ft)^{2}\)
\(r^{2} = r^{2}-4\cdot r +4 + r^{2}-2\cdot r +1\)
\(r^{2}-6\cdot r +5 =0\)
\((r-5)\cdot (r-1) = 0\)
\(r = 5\,ft\,\vee\,r = 1\,ft\)
According to the definition of hypotenuse, it must be longer than any of legs. Hence, there is just one solution that is reasonable:
\(r = 5\,ft\)
And length of the sides are, respectively:
\(x = 5\,ft-2\,ft\)
\(x =3\,ft\)
\(y = 5\,ft-1\,ft\)
\(y = 4\,ft\)
The length of the sides are 3 feet and 4 feet, respectively.
a plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone. what conic section is formed? what conic section is formed?
Answers
When a plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone, it forms a hyperbola.
A double-napped cone is a three-dimensional object with two identical nappes, or curved surfaces, that meet at a single vertex. The nappes extend infinitely in both directions away from the vertex.
When a plane intersects the double-napped cone, it cuts through both nappes, resulting in a curve that consists of two separate branches. These branches are symmetrical about the plane that contains the axis of the cone.
The resulting curve, known as a hyperbola, has two distinct arms or branches that open up in opposite directions. The hyperbola is characterized by its center, vertices, asymptotes, and foci. The plane intersects the cone at an angle, which determines the shape and orientation of the hyperbola.
Therefore, when a plane intersects both nappes of a double-napped cone but does not go through the vertex, it forms a hyperbola.
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Assessment Practice
9. The base of the prism shown is an isosceles triangle.
What is the surface area, in square centimeters, of this prism?
Answers
The surface area, in square centimeters, of this prism is 1301 cm²
How to determine the surface areaA triangular pyramid has 3 rectangular sides and 2 triangular sides.
Now, we are told that the triangular side is isosceles.
This means that two of the rectangular sides which share a side with the equal side of the triangle are equal as well as the 2 triangular sides.
Surface area of prism = 2(area of triangular face) + 2(area of rectangle sharing one side with the equal side of the triangle) + (area of rectangle sharing side with the unequal side of the triangle).
Area of triangle = ½ × base × height
Area of triangle = ½ × 9 × 13 = 58.5 cm²
Since height of prism is 32 cm, then;
Area of rectangle sharing one side with the equal side of the triangle = 32 × 14 = 448 cm²
Area of rectangle sharing side with the unequal side of the triangle = 32 × 9 = 288 cm²
Thus;
Surface area of prism = 2(58.5) + 2(448) + 288
expand the bracket and add the values, we get;
Surface area of prism = 1301 cm²
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Find the open interval(s) where f(x) is increasing and the open interval(s) where f(x ) is decreasingf(x)=3(x-2)/(x+1)^2 and f'(x)=-3(x-5)/(x-1)^3
Answers
f(x) is increasing on the open interval (-∞, 5) and decreasing on the open interval (5, +∞).
To find the open intervals where f(x) is increasing and decreasing, we need to analyze the first derivative, f'(x), which is given as -3(x-5)/(x-1)^3.
First, find the critical points by setting f'(x) = 0:
-3(x-5)/(x-1)^3 = 0
(x-5) = 0
x = 5
Now, let's analyze the intervals based on the critical point x = 5:
1) Interval (-∞, 5): Choose a test point, say x = 0. Plug it into f'(x):
f'(0) = -3(0-5)/(0-1)^3 = 15 > 0
Since f'(0) > 0, f(x) is increasing on the interval (-∞, 5).
2) Interval (5, +∞): Choose a test point, say x = 6. Plug it into f'(x):
f'(6) = -3(6-5)/(6-1)^3 = -3 < 0
Since f'(6) < 0, f(x) is decreasing on the interval (5, +∞).
In conclusion, f(x) is increasing on the open interval (-∞, 5) and decreasing on the open interval (5, +∞).
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Find the value of x. Round to the nearest tenth if necessary.
Answers
Answer:
x
Step-by-step explanation:
Consider the standard form of an exponential function:
y = a (b)^x
1. How does changing the base number (inside the parentheses) change your graph? (10 points)
2. How does changing the number outside the parentheses change your graph? (10 points)
3. Create three new exponential equations to represent Alison, Cindy, and Javier. (30 points)
Alison loves social media and likes for her posts to be shared as much as possible while Cindy and Javier prefer for their posts to stay amongst their friends primarily.
I have number one please help with 2 and 3.
Answers
Answer:
2. If we plug in X = 0 into our problem ( Y = A(B)^X ) I would get Y = A which drastically changes the initial value, the Y-intercept, and the point on the graph. The point changes to (0,a) which becomes the new Y-intercept.
3. Cindy and Javier would be ln(x) and x^(1/2) as they will grow somewhat fast at first and then die out.
While Alison would be 1/(1+e^-x) representing an s curve showing a lot of growth and later evening out.
Step-by-step explanation:
The answer to part [2] and [3] are given above.
What is a mathematical function? What is an exponential function? Differentiate between equation and expression? exponential function : An exponential equation is given by -y = A(B)ˣ
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the standard form of an exponential function -
y = a (b)^x
[2] - Changing the number outside the parenthesis will determine the amplitude scaling of the graph of (A)ˣ. For -
a > 1 (Magnitude will increase)
a < 1 (Magnitude will decrease)
a = 0 (Magnitude will become zero)
[3] - For Alison, we can write the expression as -
y{A} = 5000(1000)ˣ
For Cindy and Javier, we can write -
y{C} = (2)ˣ
y{J} = (3)ˣ
where -
[x] represents the number of posts.
Therefore, the answer to part [2] and [3] are given above.
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Consider the quadric surface given by ( 3
x
) 2
−y+( 2
z
) 2
=0. (a) State the type of quadric surface defined by the above equation. (b) Sketch the trace obtained by intersecting the surface with the xy-plane. You do not need to sketch the surface. Just sketch the trace in the xy-plane. Describe the trace. (c) Describe the trace obtained by intersecting the surface with the plane y=1. You do not need to sketch the trace.
Answers
The major axis lies along the z-axis, while the minor axis lies along the x-axis.
Given quadric surface is ( 3x)² − y + (2z)² = 0.
The equation of a quadric surface can be given by Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0, where A, B, C, D, E, F, G, H, I, J ∈ ℝ and (x, y, z) ∈ ℝ³.
(a) Type of quadric surface defined by the above equation is an elliptic paraboloid.
(b) The trace obtained by intersecting the surface with the xy-plane can be obtained by replacing z with 0. So, the equation is 9x² - y = 0, which can be written as y = 9x².
The trace is a parabola which opens upwards and intersects the y-axis at the origin.
(c) The trace obtained by intersecting the surface with the plane y = 1 can be obtained by replacing y with 1.
So, the equation is 9x² + 4z² = 1.The trace is an ellipse in the xz-plane, centered at the origin.
The major axis lies along the z-axis, while the minor axis lies along the x-axis.
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help lolololol marking brainliest
Answers
Answer:3216.99088
Step-by-step explanation:V=πr2h=π·82·16≈3216.99088
PLS HELP ASAP WILL MARK BRAINLIEST
How do natural resources impact the economies of countries in Southern and Eastern Asia?
*Choose 2
Group of answer choices
Countries specialize in industries that require hard-to-find natural resources.
Countries usually specialize in industries that make use of natural resources they have available.
Industrialized countries usually sell their natural resources to underdeveloped countries.
Many countries specialize in growing rice because their climate and land is well suited for it.
Answers
Answer:
C
Step-by-step explanation:
for Japan and South Korea it's more about high tech industry and services. but they also import all the resources other countries lack.
Add the two numbers. Express your answer in scientific notation.
Answers
Answer:
theres nothing? :/
Step-by-step explanation:
Please help me find the answer ASAP
Answers
Answer:C Because there the same sides
how to find the rate of change
Answers
Answer:
Step-by-step explanation:
rate of change is essentially slope
\(Rate Of Change = \frac{rise}{run}\) or
\(Rate Of Change = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\) or
\(Rate Of Change = \frac{f(x_{2})- f(x_{1}) }{x_{2} -x_{1} }\)
indica los monomios semejantes en cada uno de las siguientes series: por favor ayudenmen aaaaaaa D':
Answers
Answer:
Do you have this in english so that I can help :)
Step-by-step explanation:
what is the measure of x if angle 6 equals 4x and angle 7 equals 2x + 34
112°
64°
17°
68°
Answers
Answer:
17°
Step-by-step explanation:
6 = 4x
7 = 2x + 34
4x - 2x = 2x
Since 6 and 7 are vertically opposite angles, they have the same angle.
2x = 34
X = 34 ÷ 2 = 17
Step-by-step explanation:
< 6 and < 7 are vertically opposite angles so.
< 6 = < 7
4x = 2x + 34°
4x - 2x = 34°
2x = 34°
x = 17°
Hope it will help :)
a robotic machine fills containers with an acid solution at the rate of 140 3 t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 . how many ml are put into a container in 60 seconds? round to the nearest whole number.
Answers
The container put 320 ml amount of the acid in 60 seconds.
Given, a robotic machine fills containers with an acid solution at the rate of 140 + 3t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 .
we have to find the amount of acid solution put into the container in 60 sec
As, Amount of acid be A(t)
A(t) = 140 + 3t
A(60) = 140 + 3(60)
A(60) = 140 + 180
A(60) = 320
So, the container put 320 ml amount of the acid in 60 seconds.
Hence, the container put 320 ml amount of the acid in 60 seconds.
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Patrice found a book that was 2 1/4 inches thick. She stacked it with another book that was the same thickness. How tall was the stack ?
Answers
Answer:
4.5. inches
Step-by-step explanation:
Given that:
Thickness of first book = 2 1/4 inches
Thickness of second book = same as first = 2 1/4 Inches
Stacking both books together, height of stack will be :
2 1/4 inches * 2
Height of stack = 9/4 * 2
Height of stack = 18 /4 = 4.5 inches
Click on a factor pair of 32.
Answers
Answer:
1, 2, 4, 8, 16, 32
Step-by-step explanation:
Mark me Brainllest
A CD was originally priced at $10.93, and is marked down to $10.39. What is the percentage decrease in price?
Answers
Answer:
0.96%
Step-by-step explanation:
10.39/10.93
Pls. Help find these answers?!
Answers
Answer:
12
Step-by-step explanation:
Answer:
1) 12 boxes
2) 3, 6, 12
3) 12
4) 110 degrees
Step-by-step explanation:
1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.
Length: 4 boxes
Width: 3 boxes
4 x 3 = 12
12 boxes
2)
10% of 30 is 0.1 times 30.
0.1 x 30 = 30/10 = 3
20% of 30 is 0.2 times 20.
0.2 x 30 = 30/5 = 6
40% of 30 is 0.4 times 20.
0.4 x 30 = 30/2.5 = 12
3) Count the cubes. Reminder there are 2 boxes you cannot see.
Top Layer: 2
Middle Layer: 4
Back Bottom Layer: 4
Front Bottom Layer: 2
2 + 4 + 4 + 2 = 12
4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.
180/18 (The angle of each section)
10
11 Sections
10 x 11 = 110
2/-3 divided by -1 2/7 =
pls explain the answer
Answers
Answer:
\(\frac{14}{27}\)
Step-by-step explanation:
\(-1\frac{2}{7} = -\frac{9}{7}\) Plug -9/7 in: \(-\frac{2}{3}\) ÷ \(-\frac{9}{7}\) -2/3 ÷ -9/7 = 2/3 ÷ 9/7 = 2/3 × 7/9\(\frac{2}{3}\) × \(\frac{7}{9} = \frac{14}{27}\)I hope this helps!
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\( \frac{2}{ - 3} \div (- 1 \frac{2}{7}) = \\ \)
\( - \frac{2}{3} \div ( - \frac{ 7}{7} - \frac{2}{7} ) = \\ \)
\( - \frac{2}{3} \div ( \frac{ - 7 - 2}{7} ) = \\ \)
\( - \frac{2}{3} \div ( - \frac{9}{7} ) = \\ \)
Negatives simplifies
\( \frac{2}{3} \div \frac{9}{7} = \\ \)
\( \frac{2}{3} \times \frac{7}{9} = \\ \)
\( \frac{14}{27} \\ \)
Done...
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barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. the sums of the two numbers on each of the three cards are equal. the three numbers on the hidden sides are prime numbers. what is the average of the hidden prime numbers?
Answers
The average of the three hidden prime numbers is 5, as the sum of any two of the numbers is equal to 10, and since all three numbers are prime, the only possible values are 3, 5, and 7.
3 + 5 + 7 = 15
15/3 = 5
The average of the three hidden prime numbers is 5. This means that the sum of any two of the numbers on the cards must be equal to 10. Since all three numbers are prime,as the sum of any two of the numbers is equal to 10 the only possible values are 3, 5, and 7. Therefore, the three numbers on the hidden sides of the cards are 3, 5, and 7. To calculate the average, we add the three values together and divide by three. 3 + 5 + 7 = 15, and 15 divided by 3 is 5. Therefore, the average of the hidden prime numbers is 5.
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(look at image) can i get help on this problem
Answers
Answer:
where is the image??? u should paste the image tooo.
if you multiply the number by to end at 4 the results you gave will be the same of three times the number decreased by 7
Answers
Answer:
11
Step-by-step explanation:
Let the number be x,
2x+4 = 3x-7
Collect like terms
2x-3x= -4-7
-x =. -11
Multiply both sides by -1
x. =. 11
Oh and I think you made a typo and missed the 2, " if you multiply the number by 2 to end at 4..........."
Hope This Helps :)
Evaluate the following integral using integration by parts. 18x sin x cos x dx Let u = 18x sin x. Use the integration by parts formula so that the new integral is simpler than the original one. S -SO
Answers
the integral ∫18x sin(x) cos(x) dx is equal to 1/2 x sin^2(x) - 1/4 x + 1/4 sin(2x) - 1/2C1 + C, where C is the constant of integration.
To evaluate the integral ∫18x sin(x) cos(x) dx using integration by parts, we can choose u = 18x sin(x) and dv = cos(x) dx.
Using the integration by parts formula ∫u dv = uv - ∫v du, we have:
du = (18 sin(x) + 18x cos(x)) dx
v = ∫cos(x) dx = sin(x)
Applying the integration by parts formula, we get:
∫18x sin(x) cos(x) dx = 18x sin(x) sin(x) - ∫sin(x) (18 sin(x) + 18x cos(x)) dx
= 18x \(sin^2\)(x) - 18∫\(sin^2\)(x) dx - 18∫x sin(x) cos(x) dx
Now we need to evaluate the integrals on the right-hand side. The first integral, ∫sin^2(x) dx, can be rewritten using the identity sin^2(x) = 1/2 - 1/2 cos(2x):
∫\(sin^2\)(x) dx = ∫(1/2 - 1/2 cos(2x)) dx = 1/2 x - 1/4 sin(2x) + C1
The second integral on the right-hand side is the same as the original integral, so we can substitute it back in:
∫18x sin(x) cos(x) dx = 18x \(sin^2\)(x) - 18(1/2 x - 1/4 sin(2x) + C1) - 18∫x sin(x) cos(x) dx
Simplifying, we have:
∫18x sin(x) cos(x) dx = 18x \(sin^2\)(x) - 9x + 9/2 sin(2x) - 18C1 - 18∫x sin(x) cos(x) dx
Next, we move the remaining integral to the left-hand side:
∫18x sin(x) cos(x) dx + 18∫x sin(x) cos(x) dx = 18x \(sin^2\)(x) - 9x + 9/2 sin(2x) - 18C1
Combining the integrals, we have:
∫(18x sin(x) cos(x) + 18x sin(x) cos(x)) dx = 18x \(sin^2\)(x) - 9x + 9/2 sin(2x) - 18C1
Simplifying further:
∫36x sin(x) cos(x) dx = 18x \(sin^2\)(x) - 9x + 9/2 sin(2x) - 18C1
Dividing both sides by 36:
∫x sin(x) cos(x) dx = 1/2 x \(sin^2\)(x) - 1/4 x + 1/4 sin(2x) - 1/2C1
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Write The First 4 Terms Of The Power Series Representation For The Function Tan−1(2x) Centered At 0 . −2x+3!2x3−5!2x5+7!2x7−⋯ 2x−3(2x)3+5(2x)5−7(2x)7+⋯ 2x−32x3+52x5−72x7+⋯ 2x−3!2x3+5!2x5−7!2x7+⋯ 2x−3!(2x)3+5!(2x)5−7!(2x)7+⋯
Answers
The power series representation for the function **tan^(-1)(2x)** centered at **0** is given by:
**tan^(-1)(2x) = (-1)^(0) * (2x)^(0) / 0! - (-1)^(1) * (2x)^(1) / 1! + (-1)^(2) * (2x)^(3) / 3! - (-1)^(3) * (2x)^(5) / 5! + ...**
Simplifying this expression, we get:
**tan^(-1)(2x) = (2x)^(0) / 0! - 2x / 1! + (2x)^(3) / 3! - (2x)^(5) / 5! + ...**
Now, let's write out the first four terms of this power series:
The first term when **n = 0**:
**(-1)^(0) * (2x)^(0) / 0! = 1**
The second term when **n = 1**:
**(-1)^(1) * (2x)^(1) / 1! = -2x**
The third term when **n = 2**:
**(-1)^(2) * (2x)^(3) / 3! = 8x^3 / 6 = 4x^3 / 3**
The fourth term when **n = 3**:
**(-1)^(3) * (2x)^(5) / 5! = -32x^5 / 120 = -8x^5 / 15**
Putting it all together, the first four terms of the power series representation for **tan^(-1)(2x)** centered at **0** are:
**1 - 2x + (4x^3 / 3) - (8x^5 / 15)**
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Consider the difference below.
x-3/x^2-x-5 - 5/8x
Place the steps require to simplify the given difference of two expressions into one, simplified rational expression in the correct order.
Answers
Answer:
x=3/8
Step-by-step explanation:
^2×5×3÷5/8=×3/8
Find the area of the triangle below, express your answer in simplest radical form.
Answers
Answer:
Look below.
Step-by-step explanation:
256√3
128√3
64√3
8√3
Credit: Yelison25 avatar