Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.

Answer:

cot(-x) cos(-x) + sin(-x)= f(x) = (1 point) Simplify and write the trigonometric expression in terms of sine and cosine: 1 tan u +cot u = f(u) f(u) (1 point) Simplify and write the trigonometric expression in terms of sine and cosine: |(1-cos y)(1 +cos y) (f(y) f(y)= (1 point) tings sin f If sin 1+cos t tan r then A+tan t A = 1 then (1 point) If sec t - tan t = f()+tan f)= (2 points) If tan2 t - sin2 t = sind r then cos t the positive power a = the positive power b = sec r-1 A-COS 1 (1 point) If then A+cos sec 1+1 gs A = A+sin x = B-sin x then (2 points) If (tanx + sec x)2 A = В Vx- 1 (1 point) If 0 u< r/2 and x = f(u), where sec u, then f(u) = (1 point) Simplify the expression as much as possible. cos (t)-1 help (formulas) sin(t) IS (1 point) Simplify and write the trigonometric expression in terms of sine and cosine: 2+tan2 x sec x -1 (f (x) f(x)= (1 point) Simplify completely into an expression with sin(A) or cos(A) only: sin(A) tan(A) + cos(A) = (1 point) Simplify the expression as much as possible. 1 1 + 1 + sin(t) help (formulas) 1-sin(t)

sin x + cot x cos x =

f(x)

f(x)=

(1 point) Simplify and write the trigonometric expression in terms of sine and cosine:

2 + tan2 x

- 1 (f(x)

sec x

f(x) =

The probability of guessing randomly at least 8 correct answers in a 10 question multiple choice test where each question has 4 choices is 0.0385 or approximately 3.85%.

To find the probability of guessing at least 8 correct answers, we need to use the binomial probability formula:

P(X ≥ k) = 1 - P(X < k)

where

P(X ≥ k) is the probability of getting k or more correct answers

P(X < k) is the probability of getting less than k correct answers

n is the total number of questions in the test = 10

p is the probability of guessing the correct answer = 1/4

q is the probability of guessing the incorrect answer = 3/4

Now, we need to find the probability of getting less than 8 correct answers:

P(X < 8) = Σ P(X = k) for k = 0 to 7

P(X = k) = nCk * p^k * q^(n-k)

where nCk is the binomial coefficient for choosing k items from a set of n items.

P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)

P(X = k) = nCk * p^k * q^(n-k)

P(X = 0) = 10C0 * (0.25)⁰ * (0.75)¹⁰ ≈ 0.0563

P(X = 1) = 10C1 * (0.25)¹ * (0.75)⁹ ≈ 0.1875

P(X = 2) = 10C2 * (0.25)² * (0.75)⁸ ≈ 0.2813

P(X = 3) = 10C3 * (0.25)³ * (0.75)⁷ ≈ 0.2503

P(X = 4) = 10C4 * (0.25)⁴ * (0.75)⁶ ≈ 0.1450

P(X = 5) = 10C5 * (0.25)⁵ * (0.75)⁵ ≈ 0.0586

P(X = 6) = 10C6 * (0.25)⁶ * (0.75)⁴ ≈ 0.0161

P(X = 7) = 10C7 * (0.25)⁷ * (0.75)³ ≈ 0.0028

Therefore, P(X < 8) = 0.0563 + 0.1875 + 0.2813 + 0.2503 + 0.1450 + 0.0586 + 0.0161 + 0.0028 ≈ 1.0 - 0.0385 = 0.9615 or approximately 96.15%

The probability of guessing at least 8 correct answers:

P(X ≥ 8) = 1 - P(X < 8) ≈ 1 - 0.9615 = 0.0385 or approximately 3.85%

The problem seems incomplete, it must have been...

"Steve is taking a 10-question multiple choice test where each question has 4 choices. What is the probability that guessing randomly will give him at least 8 correct answers?"

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Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

We can write quadradic equation as [tex]y=1+x^2[/tex]

Where y is number οf dοts and x is step number.

Then if x=0 and y=1

If x = 1 and y = 2

If x = 2 and y = 5

If x = 3 and y = 10

Hence Patten B fοllοws the quadratic realatiοnship.

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The correct option is A. The amount of variation in the data that is explained by the regression model is shown by the Coefficient of determination.

Regression is a statistical technique used to estimate the relationship between a dependent variable and one or more independent variables. The dependent variable is the variable we are interested in understanding or predicting, while independent variables are the predictors. The goal of regression analysis is to create a mathematical equation that describes the relationship between these variables.

Regression models can be used for prediction or understanding the relationship between variables. The simplest form of regression is linear regression, which assumes a linear relationship between the dependent and independent variables. However, there are many types of regression models that can accommodate more complex relationships, including polynomial regression, logistic regression, and ridge regression.

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The probability that a 65-year-old man will survive to reach the age of 70 is 88.4%, and also the probability man to survive till his 75th birthday is approx.59.952%.

The probability of a 65-year-old man reaching the age of 70 is the probability of surviving from age 65 to age 70, which is given as

p(70)/p(65) ⇒ 0.657/0.742 ≈ 0.88544 or 88.544%.

The probability of a man who just turned 70 dying within the next 5 years is 0.176.

Therefore, the probability of surviving for the next 5 years after turning 70 is

⇒ 1 - 0.176 ⇒ 0.824.

Thus, the probability of a man surviving till his 75th birthday is the probability of surviving from age 70 to age 75, which is given as

p(75)/p(70) ⇒ 0.657/0.903 × 0.824

≈ 0.59952 or 59.952%.

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Therefore, the net result of the transaction is a loss of $21.36. The answer is A) $21.36.

Selling price refers to the price at which a product or service is sold to customers or clients. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost of producing or acquiring the product or service, and the difference between the selling price and the cost is the profit earned by the seller. In some cases, the selling price may also include additional charges such as taxes, shipping fees, or handling fees.

by the question.

To calculate the net result of the transaction, we need to determine how many shares were purchased with the $3,200 investment.

$3,200 divided by $11.95/sh = approximately 267.36 shares (rounded to the nearest hundredth)

Therefore, the total cost of purchasing 267 shares at $11.95/sh is:

267 shares x $11.95/sh = $3,195.65

The total revenue from selling 267 shares at $11.87/sh is:

267 shares x $11.87/sh = $3,174.29

To determine the net result of the transaction, we subtract the total revenue from the total cost:

$3,174.29 - $3,195.65 = -$21.36

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Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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Therefore, the solution to the system of equations is: x = 1/5 and y = 8.

An equation is a mathematical statement that asserts the equality of two expressions. Equations contain variables, which are symbols that represent unknown or varying quantities, and constants, which are known values. The variables and constants are connected by mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and the resulting expression on both sides of the equation must have the same value. Equations are used to solve problems, find unknowns, and express relationships between quantities. Some common types of equations include linear equations, quadratic equations, polynomial equations, exponential equations, and trigonometric equations.

Here,

We have the following system of equations:

y = 10x + 6

2y + 5x = 17

Using substitution method, we can substitute the expression for y in the second equation with the expression for y in the first equation:

2(10x + 6) + 5x = 17

Simplifying:

20x + 12 + 5x = 17

25x = 5

x = 5/25 = 1/5

Now we can substitute this value of x into either of the two original equations to find the corresponding value of y. Using the first equation:

y = 10(1/5) + 6

y = 2 + 6

y = 8

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Answer:

Each student's share is 1 1 3 1\dfraction{1}{ 3 } 131​ pounds of pecans.

Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

A rectangle is a geometric shape with four edges and four angles that exists in two dimensions. Because it is a sort of quadrilateral, it has four sides that are parallel to one another. Rectangles are a form of parallelogram because they have opposite sides that are the same length and opposite angles that are the same size. A rectangle's two adjacent sides make right angles, so all four of the angles, which each measure 90 degrees, are right angles.

given

The tray has a breadth of 17 inches and a length of 12.5, according to the measurements given. The package is 13 inches by 11 inches by 11 inches in size.

The platter can fit inside the box because its length is less than the box's length, which is 13 inches. But we also need to think about the box's breadth and height.

The tray cannot fit inside the box in that dimension because its width, which is 17 inches, is larger than the box's, which is 11 inches. The tray cannot fit inside the box because the height of the box is also 11 inches, which is shorter than the length of the tray neither in that realm.

Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

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Answer:

[tex] \frac{3}{2} {x}^{8} [/tex]

Step-by-step explanation:

[tex] \frac{9 {x}^{16} }{6 {( {x}^{2} )}^{3}{x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{6} {x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{8} } = \frac{3}{2} {x}^{8} [/tex]

The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].

Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.

If a marble is randomly selected from the box, we have to find the probability that it is not blue.

Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]

The probability that a marble is not blue:-

[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)

[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]

[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]

[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)

[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]

[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]

Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].

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Answer:

83.6%

Step-by-step explanation:

Let's say the original price is x

x decreased by 12% means 88% of x is left.

0.88x decreased by 5% means 95% of 0.88x is left.

This means the answer is: 0.88x * 0.95 = 0.836

The percent of the total decrease is 83.6%

Hope this helps :)

Have a great day!

400 is the total number of toy cards in his collection. This will be the total number of toy cards in his collection if Feng keeps 324 of the toy cars on his wall which is 81% of his entire collection.

A fraction is a mathematical value that illustrates the components of a whole. In general, the whole can be any particular thing or value, and the fraction might be a portion of any quantity out of it. The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.

Based on the given conditions, formulate: 324/81%

Convert decimal to fraction: 324/81/100

Divide a fraction by multiplying its reciprocal 324 * 100 / 81

Reduce the expression to the lowest term: 4*100

Calculate the product or quotient: 400

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The distance between L1 and L2 is $\frac{1}{\sqrt{3}}$ units.

Given two lines, L1 and L2, as follows:L1: x = 1 + t, y = t, z = 2 + tL2: x - 3 = y - 1 = z - 3a. Verification of parallel lines L1 and L2L1 can be written as the vector equation, (x, y, z) = (1, 0, 2) + t(1, 1, 1)Similarly, L2 can be written as the vector equation, (x, y, z) = (3, 1, 3) + t(1, 1, 1)We can see that both the vector equation of L1 and L2 has the same direction ratios (1, 1, 1).Therefore, both lines are parallel.b. Calculation of the distance between L1 and L2To find the distance between L1 and L2, we can find a point on L1 and its perpendicular distance from L2. As L2 passes through the point (3, 1, 3), we can take this point as a point on L1 as well. The perpendicular distance of (3, 1, 3) from L1 can be calculated as follows:We can write the general equation of a plane, P, containing the line L1 as follows: x - y + z - 3 = 0The normal vector of P is (1, -1, 1). Therefore, the perpendicular distance between P and the point (3, 1, 3) is given byd = $\frac{|(1, -1, 1)\cdot (3, 1, 3) - 3|}{\sqrt{1^2 + (-1)^2 + 1^2}}$d = $\frac{|-1|}{\sqrt{3}}$d = $\frac{1}{\sqrt{3}}$Therefore, the distance between L1 and L2 is $\frac{1}{\sqrt{3}}$ units.

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In the following question, the Total cost to production 50 barstools: $1,200 Total cost to produce 51 barstools: $1,228.91 "Total cost to produce 52 barstools: $1,258.44" Total cost to produce 53 barstools: $1,288.59 Therefore, the approximate total cost of producing 53 barstools is $559.15.

The cost function for producing $x$ items of a certain brand of barstool is given by C(x)=0.01x3-0.6x2+13x+200.

(a) C(x)=0.03x3- 0.12x2+13

(b) MC(50)=-82 dollars per barstool.

It approximately represents the cost of producing the 50th barstool.

(c) The exact cost of producing the 51st barstool is C51=C50+MC(50)=$28.91 dollars.

(d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately C50+(53-50) MC(50)=$229.82.

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Yes, the distribution of heights for all adults is approximately normal because normal distribution has a bell-shaped curve. The bell curve indicates that the majority of the data points are located around the mean, with fewer data points on either side. Furthermore, normal distribution has certain characteristics that are relevant to this question.

The average height of men is 69.2 inches, while the average height of women is 63.7 inches. Therefore, we can assume that the mean height for both genders would be approximately 66.45 inches, assuming the distribution is equal (i.e., half male, half female).

If we plot the data of both males and females together, the plot will likely resemble a bell curve as per the properties of normal distribution. Since most adults would fall within the average height range, the distribution of heights for all adults is considered approximately normal. Therefore, we can conclude that the distribution of heights for all adults is approximately normal.

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Answer:

$245

Step-by-step explanation:

15h+2.50d

= 15(15)+2.50(8)

= 225+20

= $245

Maria's amount of land first exceeds Lucia's amount of land after 3 months.

To solve this problem, we need to find out when Maria's total amount of land first exceeds Lucia's total amount of land. Let's start by writing out the formulas for the amount of land each woman has after n months

Lucia's land after n months = 11 + 5n

Maria's land after n months = 6 × 1.4^n

Now we want to find the month, n, when Maria's amount of land first exceeds Lucia's amount of land. So we need to solve the following inequality

6 × 1.4^n > 11 + 5n

We can solve this inequality by using a trial-and-error approach or by using a graphing calculator. Here's one way to solve it using trial-and-error

Let's start by plugging in n = 1 and see if Maria's land is greater than Lucia's land:

6 × 1.4^1 = 8.4

11 + 5 × 1 = 16

Since 8.4 < 16, we know that Maria's land is not greater than Lucia's land after 1 month.

Now let's try n = 2

6 × 1.4^2 = 11.76

11 + 5 × 2 = 21

Since 11.76 < 21, we know that Maria's land is still not greater than Lucia's land after 2 months.

Let's keep trying larger values of n until we find the first month when Maria's land is greater than Lucia's land:

n = 3

6 × 1.4^3 = 16.384

11 + 5 × 3 = 26

Since 16.384 > 26, we know that Maria's land is greater than Lucia's land after 3 months.

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The given question is incomplete, the complete question is:

Lucia and Maria are business women who decided to invest their money by buying farmland in Brazil. They started their investments at the same time, and each month they buy more land. Lucia bought 11 hectares of land in the first month, and each month afterwards she buys 5 additional hectares. Maria bought 6 hectares of land in the first month, and each month afterward her total number of hectares increases by a factor of 1.4. In which month will Maria's amount of land first exceed Lucia's amount of land?

The  cd = ab · (an integer), and so ab | cd by definition of divisibility.

The question wants us to prove the following statement using the definition of divisibility. For all integers a, b, c, and d, if aſc and bld, then ab|cd.Definition of divisibility: Let a and b be integers. We say that b divides a or b is a divisor of a if there exists an integer k such that a = bk.

If b divides a, then we write b | a.Let a, b, c, and d be any integers such that alc and b | d. Then by definition of divisibility, c = ar and d = bs for some integers r and s. Then cd equals the product of ab and a number that can be written in terms of r and s as follows:cd = ab · rs, which is an integer because products of integers are integers.

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Answer:

Step-by-step explanation:

I think a calculator is the only way to solve this question:

[tex]\sqrt{7} +\sqrt{3} = 2.96\\\\\sqrt{6} +\sqrt{4} = 2.54\\\\\sqrt{8} +\sqrt{2} =3.07[/tex]

So (c) is the greatest.

Answer: 1/3

Step-by-step explanation:

The probability of selecting a chocolate cream pie can be found by dividing the number of chocolate cream pies by the total number of pies:

Probability of selecting a chocolate cream pie = Number of chocolate cream pies / Total number of pies

Probability of selecting a chocolate cream pie = 4 / 12

Simplifying this fraction by dividing the numerator and denominator by 4 gives:

Probability of selecting a chocolate cream pie = 1/3

Therefore, the probability of selecting a chocolate cream pie from Annie's Pie Shop is 1/3.

a. The probability of guessing a wrong answer is 4/5

Since there are three guesses, the probability of the first 2 guesses being wrong and the 3rd being correct can be calculated using the multiplication rule as follows: P(2 wrong and 1 correct) = (4/5)^2 * 1/5 = 0.128.

b. The complete list of possibilities for 2 wrong and 1 correct is: WWC, WCW, CWW.

The probability of each can be calculated using the multiplication rule as follows: P(WWC) = (4/5)^2 * 1/5 = 0.128, P(WCW) = (4/5) * (1/5) * (4/5) = 0.128, and P(CWW) = 1/5 * (4/5)^2 = 0.128.

c. The probability of getting exactly one correct answer when 3 guesses are made is the sum of the probabilities of the three possible outcomes of 2 wrong and 1 correct, which is 0.128 + 0.128 + 0.128 = 0.384.

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Answer:

its 126 and 54 hope this helps

The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.

To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:

Volume of cylinder = πr²h

Surface area of cylinder = 2πrh + 2πr²

Substituting the given values, we get:

Volume = π × 6² × 11

Volume = 1,026.72 cubic centimeters (rounded to two decimal places)

Surface area = 2π × 6 × 11 + 2π × 6²

Surface area = 452.39 square centimeters (rounded to two decimal places)

Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.

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Therefore, the measure of the manila angle is 110 degrees.

The term "degree" can have several different meanings depending on the context. Here are a few possibilities:

Academic degree: This refers to the title or certificate awarded to a student upon the completion of a course of study at a college, university, or other educational institution. Examples of academic degrees include bachelor's degrees, master's degrees, and Doctoral degrees.

by the question.

Assuming that the pink, blue, and manila arcs are all part of the same circle, the sum of their measures must be 360 degrees.

Let's denote the measure of the manila arc as x degrees. Then we can set up an equation to solve for x:

200 degrees (pink arc) + 50 degrees (blue arc) + x degrees (manila arc) = 360 degrees

Simplifying the equation, we can solve for x:

x = 360 degrees - 200 degrees - 50 degrees

x = 110 degrees

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Let m and n be two arbitrary integers. We want to prove that the relation R is an equivalence relation, i.e. it is reflexive, symmetric, and transitive.

Reflexive:  We must show that mRm for all m ∈ Z.

Since the difference of m and m is 0, which is an even number, we have mRm.

Therefore, the relation R is reflexive.

Symmetric: We must show that if mRn, then nRm.

Let mRn, i.e., the difference of m and n is an even number.

Then the difference of n and m is also an even number.

Therefore, nRm, and the relation R is symmetric.

Transitive: We must show that if mRn and nRp, then mRp.

Let mRn and nRp, i.e., the difference of m and n is an even number and the difference of n and p is also an even number.

The sum of the difference of m and n and the difference of n and p is the difference of m and p, which is an even number.

Therefore, mRp, and the relation R is transitive.


Since the relation R is reflexive, symmetric, and transitive, it is an equivalence relation.

Conclusion: The relation R is an equivalence relation.

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To triple the area of a square, the new side lengths must be the length of the old sides multiplied by the square root of three (√3).

A square is a two-dimensional (2D) geometric shape that has four equal sides, and its angles are right angles, i.e., they measure 90°. The perimeter of a square is the sum of the length of all its sides, and its area is the product of its length and width. The diagonals of a square are equal in length and intersect at right angles.

To triple the area of a square, you need to increase the length of the square's sides by a certain factor. That factor is the square root of three, which is approximately 1.732. This implies that if the old side length of the square is "x," then the new side length of the square will be 1.732x.

This ratio of new side length to old side length of the square will triple the square's area (since (1.732x)² = 3x²). Therefore, to triple the area of a square, the new side lengths must be the length of the old sides multiplied by the square root of three (√3).

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