Find the product. (a - 8)(a + 2) A. 2a - 6 B. a2 - 16 C. a2 - 10a + 16 D. a2 - 6a - 16

Answer:

(a) 95% of people have an IQ score between 66 and 134.

(b) 32% of people have an IQ score of less than 83 or greater than 117​.

(c) 16% of people have an IQ score greater than 117.

Step-by-step explanation:

We are given that scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 17.

Let X = scores of an IQ test

SO, X ~ Normal([tex]\mu=100, \sigma^{2} = 17^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                      Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

Now, the empirical rule states that;

(a) The percentage of people having an IQ score between 66 and 134 is given by;

     z score for 66 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{66-100}{17}[/tex]  = -2

     z score for 134 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{134-100}{17}[/tex]  = 2

This means that the percentage of people having an IQ score between 66 and 134 is 95%.

(b) Firstly, we have to find the percentage of people having an IQ score between 83 and 117;

     z score for 83 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{83-100}{17}[/tex]  = -1

     z score for 117 =  [tex]\frac{X-\mu}{\sigma}[/tex]  =  [tex]\frac{117-100}{17}[/tex]  = 1

This means that the percentage of people having an IQ score between 83 and 117 is 68%.

This means that the percentage of people having an IQ score of less than 83 or greater than 117 = 100% - 68% = 32%.

(c) In the above part, we find that there are 32% of the values that have an IQ score of less than 83 or greater than 117.

This means that half of this will be less than 83 and half of this will be greater than 117.

So, the percentage of people having an IQ score greater than 117​ = [tex]\frac{32\%}{2}[/tex] = 16%.

Answer:

Step-by-step explanation:

Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...

  10d +5(d-9) = 180

  15d -45 = 180 . . . . . simplify

  d -3 = 12 . . . . . . . . . .divide by 15

  d = 15

  15 -9 = 6 = number of nickels

Sue has 15 dimes and 6 nickels.

Answer:

15 dimes, 6 nickels

Step-by-step explanation:

D = # of dimes, and N = # of nickels

10D + 5N = 180

D = N + 9

Substitute:

10 (N + 9) + 5N = 180

10N + 90 + 5N = 180

15N = 90

N = 6

D = 15

Answer:

Step-by-step explanation:

1). [tex](\frac{-4}{9})\times (\frac{7}{4})=(-1)(\frac{4}{9})(\frac{7}{4} )[/tex]

                [tex]=-\frac{7}{9}[/tex] [Negative]

2). [tex](-2\frac{3}{4})(-1\frac{1}{5})=(-1)(2\frac{3}{4})(-1)(1\frac{1}{5})[/tex]

                        [tex]=(-1)^2(2\frac{3}{4})(1\frac{1}{5})[/tex]

                        [tex]=(2\frac{3}{4})(1\frac{1}{5})[/tex] [Positive]

3). (3)(-3)(-3)(-3)(-3) = 3.(-1).3.(-1).3.(-1).3(-1).(3)

                              = (-1)⁴(3)⁵

                              = (3)⁵ [Positive]

4). [tex](-\frac{1}{6})(-2)(-\frac{3}{5})(-9)[/tex] = [tex](-1)(\frac{1}{6})(-1)(2)(-1)(\frac{3}{5})(-1)(9)[/tex]

                                   = [tex](-1)^4(\frac{1}{6})(2)(\frac{3}{5})(9)[/tex]

                                   = [tex](\frac{1}{6})(2)(\frac{3}{5})(9)[/tex] [Positive]

5). [tex](-\frac{4}{7})(-\frac{3}{5})(-9)=(-1)(\frac{4}{7})(-1)(\frac{3}{5})(-1)(9)[/tex]

                            [tex]=(-1)^3(\frac{4}{7})(\frac{3}{5})(9)[/tex]

                            [tex]=-(\frac{4}{7})(\frac{3}{5})(9)[/tex] [Negative]

6). [tex](-\frac{10}{7})(\frac{8}{3})=(-1)(\frac{10}{7})(\frac{8}{3})[/tex]

                    [tex]=-(\frac{10}{7})(\frac{8}{3})[/tex] [Negative]

Answer:

7/16.  

Step-by-step explanation:

The first triangle has no shading.

The second triangle has 1/4 shaded.

The third has 3/9.

The fourth has 6/16.

Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.

The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.

So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.

Hope this helps!

Answer:

Can 1 will contain more stew

Step-by-step explanation:

diameter= 8

radius=d/2=4

height=4

therefore volume= [tex]\pi[/tex] r2 h= 201.06

Diameter= 6

radius=d/2=3

height= 7

therefore volume= [tex]\pi[/tex] r2 h= 197.92

The cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

The more volume of a can is, the more stew it can store.

For first can:

Since radius = diameter/2, so radius of base = 8/2 = 4 inches.

Thus, volume of first can: [tex]V = \pi (4)^2 (4) = 64\pi \: \rm unit^3[/tex]

For second can:

Since radius = diameter/2, so radius of base = 6/2 = 3 inches.

Thus, volume of first can: [tex]V = \pi (3)^2 (7) = 63\pi \: \rm unit^3[/tex]

Thus, as π > 0, so first can can contain more stew.

Thus, the cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

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Answer:

b= 10.39

c = 20.79

Step-by-step explanation:

a = 60 °

b = 30°

c= 180-(60+30)

c = 180-(90)

c = 90°

Length facing angle a = 18

Let's look for length facing angle b

b/sinb = a/sin a

b/sin 30 = 18/sin 60

b =( 18 * sin30)/sin 60

b = (18*0.5)/0.8660

b = 9/0.8660

b= 10.39

Let's look for c

c/sin c = a/sin a

c/sin 90 = 18/sin 60

c = (18 * sin 90)/sin 60

c =18/0.8660

c = 20.79

The inverse of the given permutation matrix A is

                          [tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

To find the inverse of the given permutation matrix A:

[tex]\[ A = \begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\\end{bmatrix} \][/tex]

Utilize the concept that the inverse of a permutation matrix is its transpose.

Therefore, the inverse of matrix A is:

[tex]\[ A^{-1} = A^T \][/tex]

Taking the transpose of matrix A, gives

[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

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Answer:

The answer is explained below

Step-by-step explanation:

stiffness        frequency

2480             23

2440             35

2400             40

2360             33

2320             21

a) The mean for the population is calculated using the formula:

[tex]mean (\mu)=\frac{\Sigma f_ix_i}{\Sigma f_i} \\=\frac{x_1f_1+x_2f_2+.\ .\ .+x_nf_n}{x_1+x_2+.\ .\ . +x_n} \\=\frac{(2480*23)+(2440*35)+(2400*40)+(2360*33)+(2320*21)}{23+35+40+33+21} =\frac{365040}{152}=2401.6[/tex]

b) The standard deviation is given by:

[tex]\sigma=\sqrt{ \frac{\Sigma f_i(x_i-\mu)^2}{\Sigma f_1} } \\=\sqrt{ \frac{f_1(x_1-\mu)^2+f_2(x_2-\mu)^2+.\ .\ .+f_n(x_n-\mu)^2}{f_1+f_2+.\ .\ .+f_n} } \\=\sqrt{ \frac{23(2480-2401.6)^2+35(2440-2401.6)^2+40(2400-2401.6)^2+33(2360-2401.6)^2+21(2320-2401.6)^2}{23+35+40+33+21 }}\\=\sqrt{\frac{390021.12}{152} }= 50.7[/tex]

c) We have to find the z score for x = 2350. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2350-2401.6}{50.7}=-1.02[/tex]

From the z table:

The probability that stiffness would be less than 2350 for any given channel section = P(x < 2350) = P(z < -1.02) = 0.1539 = 15.39%

Answer:

Step-by-step explanation:

A "rate of change" is usually referring to ...

  "something" per "something else"

The "per" signifies division, as in a fraction, so this can also be written ...

  "something" / "something else"

When the "something else" is one of it (1 week, for example), the rate is called a "unit rate."

When you're dealing with a graph, the "rate of change" usually refers to the slope of the line or curve on the graph. That is why it is computed as ...

   rate of change = (vertical change)/(horizontal change)

So, you can find what the "something" is by looking at the chart label and the vertical axis label. You can find what the "something else" is by looking at the horizontal axis label.

__

1. The rates of change in this problem represent ...

  total savings $ per week

__

2. Alyssa's higher rate of change means Alyssa's savings per week are higher than Sarah's.

__

3. The "initial value" is the value of the curve or line where the number on the horizontal axis is zero (0). It is usually, but not always, at the left side of the graph. It is also often called the "y-intercept", because it it the value where the curve intercepts the vertical (y) axis. Here, you're asked for an ordered pair, so you want the (x, y) values at that point. We've already said the x-value is zero.

  Sarah's initial value: (0, 8)

  Alyssa's initial value: (0, 0)

The first ordered pair is   ( -4 , -3 )

The second ordered pair is   ( 8, 3 )

=================================================

Explanation:

The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x

x-2y = 2

x-2(-3) = 2 ... replace every y with -3; isolate x

x+6 = 2

x = 2-6

x = -4

The first point is (-4, -3)

---------------------------

We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y

x-2y = 2

8-2y = 2

-2y = 2-8

-2y = -6

y = -6/(-2)

y = 3

The second point is (8, 3)

Answer:

Step-by-step explanation:

y-|x|+3

y=|x|+3

vertex=(0,3)

y=|x-4|-7

vertex(4,-7)

Answer:

Group B is farther from the airport.

Step-by-step explanation:

To find the distance of each group to the airport we can use the law of cosines in the triangle created with the two movements done and the resulting total distance.

Law of cosines:

[tex]c^2 = a^2 + b^2 - 2ab*cos(angle)[/tex]

For group A, we have the sides of 200 miles and 75 miles, and the angle between the sides is (180-68) = 112°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(112)[/tex]

[tex]c^2 = 56863.198[/tex]

[tex]c = 238.46\ miles[/tex]

For group B, we also have the sides of 200 miles and 75 miles, and the angle between the sides is (180-51) = 129°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(129)[/tex]

[tex]c^2 = 64504.612[/tex]

[tex]c = 253.98\ miles[/tex]

The distance from group B to the airport is bigger, so group B is farther from the airport.

Answer:

y = (x - 4)² + 2 , x ≥ 4.

Step-by-step explanation:

Finding the inverse of

f(x) = 4 + √(x - 2)

Begin by swapping the x and y variables in the equation:

x = 4 + √(y - 2)

Subtract 4 from both sides:

x - 4 = √(y - 2)

Square both sides:

(x - 4)² = y - 2

Add 2 to both sides to get your equation:

y = (x - 4)² + 2

However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.

Answer:

24.95 kg

Step-by-step explanation:

one pound =0.45356 kg

55 lbs=55*45356 =24.95 kg

Answer:

180 degrees

Step-by-step explanation:

The sum of all the interior angles in a triangle is always equal to 180 degrees.

Answer:

The correct answer is TRUE.

Step-by-step explanation:

Find the measure of x.

Begin by setting up an equation of the five angles equal to 180°.

x + 37° + 41° + 29° + 51°  = 180° • The sum of the angles is 180°.

x + 158° = 180°       • Add the known values on the left side.

x = 22° • Subtract 158° from both sides.

The measure of angle x is 22°.

Answer:

[tex] \boxed{\sf x \degree = 62 \degree} [/tex]

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

[tex] \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree[/tex]

In the given figure, the value of x is 62°.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

The given angles are,

x°, 38° and 100°.

To find the value of angle x, use exterior angle property.

According to exterior angle property,

The  sum of two interior angles is equal to exterior angle.

Since, 100° is the exterior angle of x and 38.

x + 38 = 100

x = 100 - 38

x = 62.

The required value of angle x is 62°.

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Answer:

hello your question is incomplete here is the complete question

Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81

Answer : [tex]\frac{4 \pi }{3} [729 - 65\sqrt{65} ][/tex]

Step-by-step explanation:

The given data

cylinder  = x^2 + y^2 = 16

sphere = x^2 + y^2 +z^2 = 81

from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then  multiply the sesult by 2

Note : we are restricting our attention to the cylinder  x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well

the r parameter goes from 0 to 4

ATTACHED IS THE REMAINING PART OF THE SOLUTION

showing the integration

Answer:

The expected number of sales of this store from this sample of 30 is 6.

Step-by-step explanation:

For each prospect, there are only two possible outcomes. Either there is a trade, or there is not. Prospects are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability.

This means that [tex]p = 0.2[/tex]

Suppose 30 prospects are randomly selected from a city-wide mailing.

This means that [tex]n = 30[/tex]

What is the expected number (mean) of sales of this store from this sample of 30?

[tex]E(X) = np = 30*0.2 = 6[/tex]

The expected number of sales of this store from this sample of 30 is 6.

The expected number (mean) of sales of this store from this sample of 30 is 6.

Since A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.

So here the expected mean should be

= 20% of 20

= 6

Hence, The expected number (mean) of sales of this store from this sample of 30 is 6.

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Answer and Step-by-step explanation:

The rate of change of an area of a circle in respect to tis radius is given by:

ΔA / Δr = [tex]\frac{\pi(r_{1}^{2} - r_{2}^{2}) }{r_{1} - r_{2}}[/tex]

(i) 2 to 3:

ΔA / Δr = [tex]\frac{\pi(3^{2} - 2^{2}) }{3-2}[/tex] = 5π

(ii) 2 to 2.5

ΔA / Δr = [tex]\frac{\pi(2.5^{2} - 2^{2}) }{2.5-2}[/tex] = 4.5π

(iii) 2 to 2.1

ΔA / Δr = [tex]\frac{\pi(2.1^{2}-2^{2})}{2.1-2}[/tex] = 4.1π

Instantaneous rate of change is the change of a rate at a specific value. In this case, it wants at r = 2, so take the derivative of area and determine the area with the specific radius:

[tex]\frac{dA}{dr}[/tex] = π.r²

A'(r) = 2.π.r (1)

A'(2) = 4π

Note that expression (1) is the circumference of a circle, so it is shown that to determine the instantaneous rate of change of the are of a circle, is the circumference of any given radius.

The circles in the attachment shows a circle with radius r (light green) and a circle with radius r + Δr (darker green).

The rate of change between the two circles is the area shown by the arrow:

ΔA = π,[r² - (r+Δr)²]

ΔA = π.[r² - r² + 2rΔr + Δr²]

ΔA = π.(2rΔr + Δr²)

If Δr is too small, Δr² will be approximately zero, so

Δr²≈0

ΔA = π.(2rΔr)

The rate of change with respect to its radius will be:

ΔA / Δr = π.(2rΔr) / Δr

ΔA / Δr = 2.π.r

which is the circumference of a circle, so, this is the geometrical proof.

Answer:

350 mL of water

Step-by-step explanation:

Well she starts with 200mL of water and there is 800 mL of acid of water.

She drains 100 mL of acid and adds 100 mL of water so there is 300 mL of water.

And she stirs meaning the compounds have mixed.

Then she drains 100 mL and she they are mixed she drains half of acid and half of water so she has 250 mL of water.

The she adds 100 mL of water so now there’s 350 mL of water left.

Answer:

His final velocity is 48.03 m/s

Step-by-step explanation:

Using SI units  (m, kg, s)

a = 3.7

x0 = 25

x1 = 300

v0 = 16.5

Apply kinematics formula

v1^2 - v0^2 = 2a(x1-x0)

solve for v1

Final velocity

v1 = sqrt(2a(x1-x0)+v0^2)

= sqrt( 2(3.7)(300-25)+16.5^2) )

= 48.03 m/s

Given that,

ABC and ADC are triangles.

The area of ΔADC is 52 m².

Suppose , AD is the median.

According to figure,

We need to find the area of ΔABC

Using theorem of triangle

[tex]\bigtriangleup ADB +\bigtriangleup ADC=\bigtriangleup ABC[/tex]

Here, Δ ADB = Δ ADC

So, [tex]2 \bigtriangleup ADC=\bigtriangleup ABC[/tex]

Put the value of Δ ADC

[tex]\bigtriangleup ABC =2\times52[/tex]

[tex]\bigtriangleup ABC = 104\ m^2[/tex]

Hence, The area of ΔABC is 104 m².

Answer:

1:3

Step-by-step explanation:

10 red cards, 10 black cards, and 20 blue cards

We want the ratio of red to other cards

red : blue and black

10 : 10+20

10 : 30

Divide each side by 10

10/10 : 30/10

1:3

Hey there! :)

Answer:

D: [8, 12].

R: [-10, -6].

Step-by-step explanation:

Notice that the endpoints of the graph are closed circles. This means that square brackets will be used:

The graphed equation is from x = 8 to x = 12. Therefore, the domain of the function is:

D: [8, 12].

The range goes from y = -10 to -6. Therefore:

R: [-10, -6].

Answer:

D: [8 , 12]

R: [-10 , -6]

Step-by-step explanation:

Well for this parabola domain and rage are acttually limited because of the solid dots you see on the graph.

So first things first, what is range? Well range is the amount of y values on a line or anything in a graph.

And what’s domain? Domain is the amount of x values on a line or whatnot.

So let’s do domain first.

On the parabola the first x value is 8 and the last is 12 so we have to write this in interval notation which is  [8 , 12].

Now for range the lowest y value is -10 and the highest is -6 so in interval notation it is [-10 , -6].

Answer:

Combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation

Step-by-step explanation:

The first thing to keep in mind is the difference between combination and permutation.

The main difference is that in the combinations the order does not matter, whereas in the permutations the order does matter.

Combination example:

Choose 7 people for a project.

Example of permutation:

Choose 5 men for each specific role in a soccer team.

Therefore, "group of 5 senators is chosen to be part of a special committee" is a combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation.

Answer:

The valid point is (5/2, 5)

Step-by-step explanation:

In order to check which ones are valid we will apply all of them to the expression.

(5,15):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}5 - \frac{1}{5}15 \geq 0\\\\-1 \geq 0[/tex]

False.

(1/2, 5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{1}{2} - \frac{1}{5}5 \geq 0\\\\-\frac{4}{5} \geq 0[/tex]

False.

(5/2, 5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{5}{2} - \frac{1}{5}5 \geq 0\\\\0 \geq 0[/tex]

True.

(2,5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}2 - \frac{1}{5}5 \geq 0\\\\-\frac{1}{5} \geq 0[/tex]

False

(-1,0):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}(-1) - \frac{1}{5}0 \geq 0\\\\-\frac{2}{5} \geq 0[/tex]

False.

Step-by-step explanation:

Let's say the coordinates of Q are (h, k).

The slope of PQ is perpendicular to the tangent line.

(k − 2) / (h − 2) = -⅓

3(k − 2) = -(h − 2)

3(k − 2) = 2 − h

Solving for h:

h = 2 − 3(k − 2)

h = 2 − 3k + 6

h = 8 − 3k

(2, 2) is a point on the circle, so:

(2 − h)² + (2 − k)² = r²

Substituting:

9 (k − 2)² + (2 − k)² = r²

10 (k − 2)² = r²

The equation of the circle is:

(x − 8 + 3k)² + (y − k)² = 10 (k − 2)²

Without more information, there are an infinite number of possible solutions.  For example, if k = 1, the equation of the circle is:

(x − 5)² + (y − 1)² = 10

Answer:

Sqrt 3

Step-by-step explanation:

The value of tan(G) is √3

Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.

In ΔGYK

∠GYK = 90°

∠KGY = 60°

∠GYK = 30°

side GK = 27

Let side KY = x

tan(Y) = tan30° = GK/KY

1/√3 = 27/x

x = 27√3

So side KY = 27√3

tan(G) = KY/KG

tan(G) = 27√3/27

tan(G) = √3

Hence, the value of tan(G) is √3

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