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[tex]\qquad \textit{power of two complex numbers} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ z=3[\cos(30^o)+i\sin(30^o)] \\\\\\ z^3=3^3[\cos(3[30^o])+i\sin(3[30^o])]\implies z^3=27[\cos(90^o)+i\sin(90^o)] \\\\\\ z^3=27(0~~ + ~~i1)\implies z^3=0+27i[/tex]

so that gives us the point (0 , 27) on the imaginary plane, and we also know the line goes through the origin, since it'd be a line in component form, and to get the equation of a line we only need two points off of it, let's use those two.

[tex]\stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{27}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{27}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{0}}}\implies \cfrac{27}{0}\implies und efined[/tex]

a line with an undefined slope is a vertical line, namely in this case x = 27.

207/5 is the simplest form of  [tex]1\frac{3}{10}[/tex] ×18

A number system is defined as a system of writing to express numbers.

We need to find the simplest form of [tex]1\frac{3}{10}[/tex] ×18

Convert the mixed fraction to improper fraction and simplify.

 [tex]1\frac{3}{10}[/tex]=23/10

Now multiply Twenty three divided by ten with eighteen.

23/10×18

Multiply 23 and 18

23×18=414

Now divide 414 by 10

414/10

Both numerator and denominator can be divided by 2 so

207/5

Hence 207/5 is the simplest form of  [tex]1\frac{3}{10}[/tex] ×18

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Answer:

Correct answer is the first one I think. hope this helps

Answer:

72

Step-by-step explanation:

Triangle area formula: A = 1/2 (B) (H)

This means the area of a triangle is half of the base times the height.

So we can plug the numbers into the formula:

A = 1/2 (16) (9)

16 x 9 is 144, divided by 1/2 is 72.

Final answer 72.

Answer:

8 is the ans because it is 8

Answer: The awnser is 48

Step-by-step explanation: I took the quiz

6.03 Quiz: Use Theoretical Probability to Predict

It is expected to take 48 spins for a multiple of 5 to be spun 8 times.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since there are 12 sectors, the probability of landing on a multiple of 5 is 2/12 or 1/6.

The probability of not landing on a multiple of 5 is 5/6.

We can use the geometric distribution formula to find the expected number of spins:

E(X) = 1/p, where p is the probability of success.

As per the question, the probability of success is 1/6.

Therefore, E(X) = 1/(1/6) = 6.

We need to spin a multiple of 5 8 times, so we multiply the expected number of spins by 8:

6 x 8 = 48.

Therefore, we can expect to spin a multiple of 5-8 times after 48 spins.

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Answer:

Step-by-step explanation:

Drinks:

Answer: 8

Answer:

Forty games

Step-by-step explanation:

80 ÷ 2 = 40

40 games are required

Answer:

118

Step-by-step explanation:

Because if you add 34 and 28 you get 62 then if you minus 62 from 180 you get 118. Then you get 180 because all of the angles have to equal 180 degrees.

Answer;

J(5,3) = x,y

rotated on 90;

J'(-3,5)

Therefore, the coordinates of the resulting point is J'(-3,5).

Step-by-step explanation:

1. feet/min

2. square feet/min

3. cubic feet/min

4. square feet/min

A)

Hence rate of walking should be measured in feet/minute

B)

Hence rate of painting should be in sqaure feet per minute

C)

Hence rate of paining is measured in cubic feet per minute

D)

Hence rate of mopping should be in sqaure feet per minute

Answer:

12 of 40=30 so if you do 4 percent of 40 its 1.4

Step-by-step explanation:

Answer:

when were they introduced?

Step-by-step explanation:

1.

(x+7)²

using (a+b)²=a²+b²+2ab

= x²+7²+ ( 2×x×7 )

= x²+49+14x

THEREFORE, x²+14x+49 is the answer

2.

4x²-1 = 0

= (2x)²-1² = 0

using a²-b² = (a+b) (a-b)

THEREFORE, (2x+1) (2x-1) is the answer

HOPE IT HELPS :)

Answer:

A

Step-by-step explanation:

From inspection of the graph, we can see that every time the x-value increases by 10, the y-value increases by 1000.

So, the employee earns an additional $1000 for every 10 units sold.

To calculate how much the employee earns for every 1 unit sold, divide $1000 by 10:

1000 ÷ 10 = 100

Therefore, the employee earns an additional $100 for every one unit sold.

Proof

This can be proved by calculating the slope (gradient) of the graph:

[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

where [tex]\sf (x_1,y_1)[/tex] and [tex]\sf (x_2,y_2)[/tex] are two points on the line

When picking the two points, remember that the y-values are in thousands of dollars.

Two points on the line:

(0, 30000) and (20, 32000)

Substituting these into the formula:

[tex]\sf \implies slope=\dfrac{32000-30000}{20-0}=\dfrac{2000}{20}=100[/tex]

Therefore, the employee earns an additional $100 for every one unit sold.

Answer:

-160 or in alternative form -1.6x10[tex]{2}[/tex]

Step-by-step explanation

1600 divide -10 equals to -160

Answer:

x=0

Step-by-step explanation:

add 3 to both sides

subtract 4 from both sides

[tex]\sqrt{x} +4-3=1\\\sqrt{x} +4=4\\\sqrt{x} =0[/tex]

Answer: x=12

√x+4 - 3 = 1

(√x+4 - 3) + 3 = 1 + 3

√x + 4 = 4

(√x+4)^2 = 4^2

√(x+4)^2 = 16

x+ 4 = 16 (cancels out the square root)

(x + 4) + (-4) = 16 + (-4)

x + 4 - 4 = 16 - 4

And then just solve it out

x = 12

Hope this helped in some way

Answer:

188 m²

Step-by-step explanation:

The formula to find the surface area of a rectangular prism/cuboid: [tex]A = 2(lw + lh + wh)[/tex], where [tex]l[/tex] is the length, [tex]w[/tex] is the width and [tex]h[/tex] is the height.

1) Plug the values into the formula.

[tex]A = 2((7(6)) + ((7)(4)) + ((4)(6)))[/tex]

2) Solve it.

[tex]A = 2(42 + 28 + 24)\\A = 2(94)[/tex]

A = 188 m²

Answer:

may not be exact

1- surveying every fifth student who walks in

2-randomly selected people of both genders

3-asking 8 random students from each second period

4-asking 4 girls and 4 boys from each~~

5-randomly choosing a page and counting the words

Step-by-step explanation:

1-explanation; the first one is skewed two 7th graders, the third one is skewed to volleyball players, the fourth one is skewed to eight graders

Answer:

[tex]someone \: needs \: to \: g et \: laid \\ [/tex]

Answer: a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold

Step-by-step explanation:

Answer:

Answer: a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.

Step-by-step explanation:

Answer:

M=33/8

Step-by-step explanation:

Answer:

M+4 7/8 =9

Step-by-step explanation:

Answer:

Area=length×width

11.4×11.4=129.96

so the area is 129.96

Hope this helps!

length= 11.4 in

the area of the given figure.

[tex]a = l \times l \: or \: l {}^{2} [/tex]

[tex]a = {11.4}^{2} [/tex]

[tex]a = 129.96 \: {in}^{2} [/tex]

therefore, the area of the square is 129.96 square inches.

The mass of cesium left afer 120 years if the original mass of cesium is 8640 with an half-life of 30 years,  is 540 grams.

This can be defined as the time taken for half the amount of a radioactive substance to decay.

To calculate the amount of cesium left after 120 years, we use the formua below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The mass of cesium left afer 120 years is 540 grams.

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