What is the probability of the spinner stopping on an even number?

By using the De Moivre's formula, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).

Complex numbers are numbers of the form a + i b, where a and b are the real and imaginary component, respectively. In other words, complex numbers are an expansion from real numbers. The n-th root of a complex number is found by using the De Moivre's formula:

[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n} \right) + i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for i = {0, 1, 2, ...,  n - 1}.

Where:

The norm of the complex number is found by Pythagorean theorem:

[tex]r = \sqrt{(2\sqrt{3})^{2}+(-2)^{2}}[/tex]

r = 4

And the direction is determined below:

[tex]\theta = \tan^{-1} \left(\frac{2\sqrt{3}}{-2} \right)[/tex]

θ = 2π/3 rad

Then, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).

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Answer:

see explanation

Step-by-step explanation:

PQRS is a cyclic quadrilateral.

the opposite angles in a cyclic quadrilateral sum to 180° then

∠ Q + ∠ S = 180 ( substitute values )

3x - 8 + 3x + 8 = 180

6x = 180 ( divide both sides by 6 )

x = 30

Then

∠ Q = 3x - 8 = 3(30) - 8 = 90 - 8 = 82°

∠ S = 3x + 8 = 3(30) + 8 = 90 + 8 = 98°

∠ P = x + 15 = 30 + 15 = 45°

∠ R = 180° - ∠ P = 180° - 45° = 135°

Answer:

dont now the answer but air math app will help you just take photo of problems

Answer:

4.08

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

Since she used only 1/2 of the recipe and the full recipe uses 1 cup, divide 1 by 2. The equation is 1/2=0.5.

For the lemon juice, the equation is 1/4 divided by 2. On the number line, make a dot at 1/4, and then travel backwards halfway. 1/4 divided by 2 is 1/8, or 0.125.

Hope this helps!

Answer:

36

Step-by-step explanation:

[tex]-2[-6(-4+7)]\\\\=(-2)(-6)(3)\\\\=12(3)\\\\=36[/tex]

The bearing of R from P is 019 and the distance |PR| is 8.75

A cyclist set out from a town P on a bearing of 060 to a town Q, 5 km away. He then moves on a bearing of 345 to a town R, 6km from Q.

See attachment

Start by calculating the distance PR using the following cosine ratio

PR² = PQ² + QR² - 2 * PQ * PR cos(Q)

Substitute known values

PR² = 5² + 6² - 2 * 5 * 6 cos(105)

Evaluate

PR² = 76.53

Take the square root of both sides

PR = 8.75

Next, calculate angle R using the following sine ratio

PQ/sin(R) = PR/sin(Q)

Substitute known values

5/sin(R) = 8.75/sin(105)

Evaluate the quotient

5/sin(R) = 9.06

Multiply both sides by sin(R)

9.06 * sin(R) = 5

Divide both sides by 9.06

sin(R) = 0.5519

Take the arc sin of both sides

R = sin⁻¹(0.5519)

Evaluate

R = 34

Calculate angle P using:

P = 180 - 34 - 105

P = 41

The bearing of R from P is then calculated as:

Bearing = 060 - 41

Evaluate

Bearing =  019

Hence, the bearing of R from P is 019

In (b), we have:

PR = 8.75

Hence, the distance |PR| is 8.75

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Answer:

x ≈ 0.67

Step-by-step explanation:

[tex]15(3)^2x = 90\\\\15(9)x = 90\\\\135x = 90\\\\x = 90/135\\\\ x = 2/3\\\\x = 0.666...\\\\x = 0.67 \ (rounded \ to \ nearest \ hundredth )[/tex]

The experimental probability that in a group of 4 students, at least one of them has brown eyes is 95%.

Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial. The experiment is conducted to find the chance of an event to occur or not to occur.

Here , Favorable Outcome = 19

          Total outcomes = 20

Probability = Favorable Outcome/ Total Outcome

                   = 19 / 20

                   = 95%

Thus, the experimental probability that in a group of 4 students, at least one of them has brown eyes is 95%.

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Answer:

[tex]f(x)=x^3 +4x^2 +16x +64[/tex]

Step by step explanation:

[tex]\text{Given that, two roots are}~ -4~ \text{and}~ 4i.\\\\\text{Let,}\\\\~~~~~~~x = 4i\\\\\implies x^2 = 16i^2~~~~~~~;[\text{Square on both sides}]\\\\\implies x^2 = -16~~~~~~~~;[i^2 = -1]\\\\\implies x^2 +16 = 0\\\\\text{So,}~ x^2 +16~ \text{ is a factor of the 3 degree polynomial}.\\ \\ \text{The polynomial is ,}\\\\ f(x) = (x+4)(x^2 +16)\\\\~~~~~~~=x^3 +16x +4x^2 +64\\\\~~~~~~~=x^3 +4x^2 +16x +64[/tex]

Answer:

D1×D2/2sq

445×5= 225

225/2

=112.5

Answer: they can conclude the distributions are different at the 95% confidence interval. Compute the z test statistic to solve this.

Step-by-step explanation: to get the 95% confidence interval on the mean take the mean value (984) +/- (2*standard deviation divided by the square root of the number of samples) (I.e. 984 +/- (2*267/sqrt(501)))

Answer:

t would be steeper

Step-by-step explanation:

Answer:

Compound interest, or 'interest on interest', is calculated using the compound interest formula.

The formula for compound interest is A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.

Step-by-step explanation:

If the volume of each brick will be 64 cubic centimeters. Then the mass of each brick will be 192 grams.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

mass = density × volume

A construction company needs to transport 500 bricks. The dimensions of each brick are 2 cm by 4 cm by 8 cm.

The density of each brick is 3 g/cm³.

Then the mass of each brick will be

The volume of each brick will be

V = 2 x 4 x 8

V = 64 cm³

Then the mass will be

m = 3 x 64

m = 192 gram

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see the attachment for solution

hope it helps...!!!

Answer:

  $5.83

Step-by-step explanation:

The total amount of money is the sum of the values of the various denomination coins.

__

Let p, n, d, q represent the numbers of pennies, nickels, dimes, and quarters, respectively.

  p + n + d + q = 50 . . . . . . there are 50 coins in all

  16% × 50 = p . . . . . . . . . . 16% are pennies

  34% × 50 = d . . . . . . . . . . 34% are dimes

  n = p +3 . . . . . . . . . . . . . . there are 3 more nickels than dimes

The total value is ...

  v = 0.01p +0.05n +0.10d + 0.25q

__

The numbers of pennies and dimes are found easily:

  0.16 × 50 = p = 8

  0.34 × 50 = d = 17

Then the number of nickels can be found:

  n = p +3 = 8 +3 = 11

Finally, the number of quarters is found from the total number of coins:

  p + n + d + q = 50

  8 + 11 + 17 + q = 50 . . . substitute known values

  q = 14 . . . . . . . . . . . . . subtract 36 from both sides

The total value is then ...

  v = 0.01(8) +0.05(11) +0.10(17) +0.25(14) = 0.08 +0.55 +1.70 +3.50

  v = 5.83

The bag contains $5.83.

Answer:

[tex] \frac{1}{24} miles \\ [/tex]

Step-by-step explanation:

[tex] \frac{7}{8} - \frac{5}{6} = \frac{1}{24} [/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angle sum theorem tells you the sum of angles of a triangle is 180°. Angles of a linear pair are supplementary, so total 180°. These facts can be used to write a relation that can be solved for x.

__

The interior angle at the right end of the line is the supplement of 4x:

  180° -4x

The interior angle at the left end of the line is the supplement of 2x:

  180° -2x

  86° +(180° -4x) +(180° -2x) = 180°

Then the solution to the triangle is ...

  266° = 6x . . . . . . . . . add 6x-180°

  x = 266°/6 = 44 1/3° . . . . . divide by 6

Answer: 0.000000009085

Step-by-step explanation: This expression is rewritten like this because it is multiplied by a negative power of ten. Therefore, applying this principle to scientific notation, the answer would have to be less than 0. That would be your answer. Hope this helps!

Answer: Hope this helps you.

1,3

Step-by-step explanation:

(6, 4) and (0,2)

4-2/6-0 =2,6 (1,3)

Step-by-step explanation:

please mark me as brainlest

Answer:

Surface area is 288π cm² (exact solution), which is approximately 904.78 cm² (if you use pi on calculator) or 904.32 cm² (if you use 3.14 for pi).

Step-by-step explanation:

Surface area of cylinder

[tex]SA = 2 \times \text{area of base} + \text{lateral area}\\SA = 2 \pi r^2 + 2 \pi r h[/tex]

SA ... surface area

r ... radius

h ... height of cylinder

Given:

d = 12 cm

h = 18 cm

Since diameter d is 12 cm, that means that radius is half of that, so 6 cm.

r = 6 cm

Insert in formula:

[tex]SA = 2 \pi r^2 + 2 \pi r h\\SA = 2 \pi (6)^2 + 2 \pi (6)(18)\\SA = 72 \pi + 216 \pi\\SA = 288 \pi \text{ cm}^2 \approx 904.78 \text{ cm}^2[/tex]

                  [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

         [refer to attachment for question] ~

    [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

✫ First of all, Slope-intercept form is written as follows:-

                                        [tex]\longmapsto\Large\textbf{y=mx+b}[/tex]

Where:-

To find:-

Solving,

           Replace m with -1/5 And b with -3:-

                 [tex]\large\text{$y=-\displaystyle\frac{1}{5} x-3$}[/tex]

[tex]\Uparrow[/tex]  [tex]\sf{the\:equation}[/tex]

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[tex]\rule{300}{1}[/tex]

The distance around the perimeter would be 120 ft.

Perimeter is the distance around the edge of a shape.

The complete question is

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

A rhombus is shown. Lines are drawn from each point to the opposite point to form 4 right triangles. The other 2 angle measures are 30 and 60 degrees. The base length of each triangle is 15 feet.

What is the distance around the perimeter of the garden?

let AE is the half of the diagonal AC.

AC = 30 ft.

So, AE = ½ * 30

AE = 15 ft

Now, using trigonometry

sin 30 = 15/AD

0.5= 15/AD

AD= 30 ft

Hence, distance around the perimeter would be: AD+AD+AD+AD=

=30 ft + 30 ft + 30 ft + 30 ft

= 120 ft.

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Answer:A

Step-by-step explanation: just took it

Answer: it might be 8

Step-by-step explanation: Write a distance formula:  x^2  - x^1    

substituted -3.8, 4.2 into  x^2  - x^1   and u will get 4.2 + 3.8 and u will calculate and it gets 8

I hope its right

Answer:

4

Step-by-step explanation:

x = 7 - 3

x = 4

Answer:

x = 4

Step-by-step explanation:

3+x = 7

Subtract 3 from each side

3+x-3 = 7-3

x = 4

Answer:

Step-by-step explanation:

4x - 8 = 2x - 10

2x - 8 = -10

2x = -2

x = -1

y = 4(-1) - 8 = -4 -8 = -12

(-1, -12)

The equation represents a circle whose center is (-4, 1) and has a radius r = √2

We have the equation:

[tex]x^2 + y^2 + 8x - 2y + 15 = 0[/tex]

We can rewrite this as:

[tex](x^2 + 8x ) + (y^2 - 2y ) + 15 = 0\\\\\\\\(x^2 + 8x + 16) - 16 + (y^2 - 2y + 1) - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 - 16 - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 = 2[/tex]

Where we just completed squares.

Comparing this with the general circle equation, we can see that the center is the point (-4, 1) and the radius is √2.

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Step-by-step explanation:

In given, it's said that D is a midpoint, which mean DP == AD, DP is the same as DP because isosceles triangle properties said that two-length are equal when their base angle are equal. In a right triangle, the midpoint D, draws a line to the "90 degree" angle is always a isosceles