Use DeMoivre's Theorem to find the following. Write your answer in
standard form.
(3 - 3i)^3

Answer:

[tex]\large\boxed{\sf n^{th} \ term =3n}}[/tex]

Step-by-step explanation:

Find common difference from subtracting any term in the sequence with the previous term.

[tex]\large{\sf 6-3}=3[/tex]

Apply nth term formula.

[tex]\large{\sf a_n=a_1+(n-1)d[/tex]

[tex]\large{\sf d=3 \ \ a_1=3}[/tex]

[tex]\large{\sf a_n=3+(n-1)3[/tex]

[tex]\large{\sf a_n=3+3n-3[/tex]

[tex]\large{\sf a_n=3n}[/tex]

Answer:

a(n) = 3 + 3(n -1)

Step-by-step explanation:

Note that each new term is found by adding 3 to the previous term.  The first term is 3 and the common difference is 3.  Thus, the formula for the nth term is

a(n) = a(1)+d^(n - 1)

or, in this case,

a(n) = 3 + 3(n -1)

Answer:

288 cm^3

Step-by-step explanation:

First, you have to calculate the volume of your individual bar. To do this, you multiply the three given values, so it would look like 8*3*1=24. This means that your individual bar has a volume of 24 cm^3.

To hold 12 granola bars, this would mean that your volume of the individual granola bar would be multiplied by 12, because that is how many you want to fit inside the box. So your operation would looked like 24*12=288 cm^3

Answer:

12pi.

Step-by-step explanation:

The area of the circle is pi * r^2.

r = 4.

pi * 4^2 = pi * 16 = 16pi.

There is 3/4 of the circle. (3/4) * 16pi = 3 * 4pi = 12pi.

Hope this helps!

Answer:

37.68

Step-by-step explanation:

4^2=16

16x3.14=50.24

50.24/2=25.12

25.12/2=12.56

25.12+12.56=37.68

Answer:

3c-8

Step-by-step explanation:

Answer:

Step-by-step explanation:

expression for surface area = a² + a √(a²/4+h²)

=4² + 2(4) √(4²/4+5²)

=16 + 8  √(16/29)

= 24 √0.55

= 20.65

Answer:

The inverse of the function is

-2x-3

Step-by-step explanation:

The inverse of the function f(x) = -\dfrac{1}{2}(x+3) is f(x)⁻¹ = -2x - 3

The inverse of a function is a function that gives us the actual value for which the desired function has a given result.

The given function is:

[tex]\mathbf{ f(x)=-\dfrac{1}{2}(x+3)}[/tex]

To find the inverse, we need to follow the following steps

[tex]\mathbf{ y=-\dfrac{(x+3)}{2}}[/tex]

[tex]\mathbf{ x=-\dfrac{(y+3)}{2}}[/tex]

2x = - (y + 3)

2x = -y - 3

y = -2x - 3

Writing back in inverse notation, we have:

f(x)⁻¹ = -2x - 3

Learn more about the inverse of a function here:

https://brainly.com/question/2873333

#SPJ2

Answer:

[tex]\boxed{Option \ C}[/tex]

Step-by-step explanation:

Percentage means "out of hundred" So measuring the rate in percentage we've to find it using "per 100 units".

Answer:

c) per 100 unit

Step-by-step explanation:

a percent measures a rate:

per cent ⇒ per 100

The correct answer is option c.

Answer:

Data set A {41,19,29,12,49,30} = 30

Data set B {28,22,10,30,15} = 21

Data set C{49,24,18,53,38} = 36.4

Step-by-step explanation:

Data set A {41,19,29,12,49,30} =

Mean = Sum of terms/ number of terms

Number of term = 6

Mean = 41 + 19 + 29 + 12 + 49 + 30/ 6

= 180/6 = 30

Data set B {28,22,10,30,15} =

Mean = Sum of terms/ number of terms

Number of term = 5

Mean = 28 + 22 + 10 + 30 + 15/ 5

= 105/5 = 21

Data set C{49,24,18,53,38} =

Mean = Sum of terms/ number of terms

Number of term = 5

Mean =49 + 24 + 18 + 53 + 38/ 5

= 182/5 = 36.4

Answer:

440 blue cubes

Step-by-step explanation:

We can put it in a ratio of 9:5:11. Add those up we get 25. Then we do 1000/25 which if 40. So each number in the ratio equals 40. Then we do 11*40 and we get 440.

Answer:

440 times

Step-by-step explanation:

First, you need to find the total number of cubes each student receives (25)

Now you put it into a ratio of blue cubes to the total number of cubes

11 : 25

After that you make another ratio and solve for x

x : 1000

25x = 11000

x = 440

Answer:

$5 per ticket

Step-by-step explanation:

If you put it into a ratio of movie tickets to cost it will be 7 : 35

When you simplify it the ration will be 1 : 5

Answer:

$5 per ticket . # Unit rate.

Step-by-step explanation:

7 tickets costs =$35

therefore, 1 ticket cost = $35÷ 7

= $5

Answer:

  2x -y = 5

Step-by-step explanation:

The 2-point form of the equation of a line is a useful starting point.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (9 -3)/(7 -4)(x -4) +3

  y = 6/3(x -4) +3 = 2(x -4) +3 = 2x -8 +3

Adding 5-y, we get ...

  2x -y = 5

Answer:

$252

Step-by-step explanation:

Let the initial amount of money Ami, Jan and Toy have initially be A, J and T respectively.

Please see attached picture for full solution.

Answer:

$252

Step-by-step explanation:

Toy has $36 and gets $36 from Ami. Now he has $36*2= $72

Toy gets $72 from Jan to double his money and now has $72*2= $144

Toy gives enough money to Ami and Jan to double their money

Toy has $36 at the end, so he has given $144 - $36= $108 to Ami and Jan

Since he doubles their money by giving $108, they now have

Now we add the amount Toy has at the end to the amount Ami and Jan have at the end to get final amount:

The three lines drawn are at 90 degree angles, so are drawn perpendicular to the vertex.

This means point T is the orthocenter.

The answer is A

The correct answer is the last one, 7.5 x 104. (the sum is 772.5)

if you multiply it the sum is 772.5, and all the other ones sum is less than 772.5

I hope this helped (:

Answer:

The operating symbol is divide (/) and the exponent is 5

[tex]7,320 / \ 10^5 = 0.07320[/tex]

Step-by-step explanation:

Given

[tex]7,320 \ \_\ 10^{\_} = 0.07320[/tex]

Required

Fill in the gap

[tex]7,320 \ \_\ 10^{\_} = 0.07320[/tex]

Multiply the right hand side by 1

[tex]7,320 \ \_\ 10^{\_} = 0.07320 * 1[/tex]

Express 1 as 100000/100000 because 100000/100000 = 1

[tex]7,320 \ \_\ 10^{\_} = 0.07320 * \frac{100000}{100000}[/tex]

Split the fraction

[tex]7,320 \ \_\ 10^{\_} = 0.07320 * 100000 * \frac{1}{100000}[/tex]

Multiply 0.7320 and 10000

[tex]7,320 \ \_\ 10^{\_} = 7,320 * \frac{1}{100000}[/tex]

Express [tex]\frac{1}{100000}[/tex] as an exponent

[tex]7,320 \ \_\ 10^{\_} = 7,320 * \frac{1}{10^5}[/tex]

Change the * sign to /

[tex]7,320 \ \_\ 10^{\_} = 7,320 / \frac{10^5}{1}[/tex]

[tex]7,320 \ \_\ 10^{\_} = 7,320 / \ 10^5[/tex]

Compare the expression on the right hand side with the left hand side base on the order of appearance;

[tex]7,320 = 7,320[/tex]

[tex]The first\ \ _ = \ /[/tex]

[tex]10 = 10[/tex]

[tex]The second\ \_ = 5[/tex]

Hence, the operating symbol is / and the exponent is 5

Answer:

  see below for a table; see second attachment for a graph

Step-by-step explanation:

Each of the distance values in km in the table will be 3 times the time value in hours.

The slope of the line on the graph is 3. The practical domain of the distance function is 0 to 5 hours.

Answer:

32 ounces

Step-by-step explanation:

18+14=32

32 is the total

Answer:

32 ounces

Step-by-step explanation:

She already drank 18 ounces and 14 ounces was left which means that If she didn't drink anything it would have been 32 ounces as 18 + 14 = 32

Hope this helps and pls mark as brainliest : )

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Explanation:

Ignore the values 3000 and 1000 as they are simply labels for the printer names (or brand models). I'll call the two printers A and B for simplicity.

Printer A can produce a large document in 1/4th the time printer B can do the same job. So we can say x = (1/4)y where x and y are the times it takes for both printers to do the job if they work alone. Solving for y gets us y = 4x.

Printer A can do the full job, on its own, taking x hours. It's rate is 1/x jobs per hour. Printer B's rate is 1/y = 1/(4x) jobs per hour for similar reasons.

Their combined rate is

1/x + 1/(4x) = 4/(4x) + 1/(4x) = 5/(4x)

Set this equal to 1/6 and solve for x. The 1/6 represents the combined rate based on how they can work together to get the job done in 6 hours.

-----------

5/(4x) = 1/6

5*6 = 4x*1 .... cross multiply

30 = 4x

4x = 30

x = 30/4 ... divide both sides by 4

x = 7.5

Printer A takes 7.5 hours to do the job alone

y = 4x

y = 4*7.5

y = 30

Printer B takes 30 hours to get the job done if it worked alone

-----------

Note how

1/x + 1/y = 1/7.5 + 1/30 = 4/30 + 1/30 = 5/30 = 1/6

so this confirms we have the right answer.

Answer:

a) 6x²/2x³-4

b)  [tex]2ln (2x^3-4)+ C[/tex]

Step-by-step explanation:

a) Given the ln(2x³-4). We will use the chain rule in differentiating the function

If y = ln(2x³-4);

u = 2x³-4; du/dx = 3(2)x³⁻¹

du/dx = 6x²

y = ln u; dy/du = 1/u

According to chain rule, dy/dx = dy/dy*du/dx

dy/dx = 1/u * 6x²

dy/dx = 1/2x³-4 * 6x²

dy/dx = 6x²/2x³-4

Hence, the derivative of the given function is 6x²/2x³-4

b) Given an integral function [tex]\int\limits {\frac{12x^2}{2x^3-4} } \, dx[/tex], the integral problem can be solved using integration by substitution method as shown below;

From the question, let y = 2x³-4... 1, dy/dx = 6x²

dx = dy/6x² ... 2

Substituting equation 1 and 2 into the question given;

[tex]\int\limits {\frac{12x^2}{y} } \,\frac{dy}{6x^2} \\\\= \int\limits {\frac{2dy}{y} } \\\\= 2 \int\limits {\frac{dy}{y} }\\\\= 2lny + C\\substituting\ y = 2x^3-4\ into\ the \ resulting\ function\\\\= 2ln (2x^3-4)+ C[/tex]

Answer

2/15 or 0.13

Step By Step

2/3 ÷ 5

Rewrite the division as a fraction.

Rewrite the division as a fraction.2/3/5

Multiply the numerator by the reciprocal of the denominator.

2/3 x 1/5

= 2/15

The result can be shown in multiple forms.

The result can be shown in multiple forms.Exact Form:

2/15

Decimal Form:

Decimal Form:0.13

Answer:

Step-by-step explanation:

This is a decaying exponential function whose initial value is (0, 2).

Answer:

96 minutes in the whole game or 1 hour and 36 minutes and 1/8 of the game is left.

Step-by-step explanation:

So we know that there are 4 quarters in a game. So if they're halfway through the 3rd quarter with 12 minutes left in the game, that means half a quarter equals 12 minutes. That means a full quarter equals 24 minutes. Then we do 24 *4 which is 96. So there are 96 minutes in the whole game and there 1/8 of the game left since 96/8=12.

Hope this helped

Answer:

zephyr

Step-by-step explanation:

ez i am god of thunder

Answer:

This question contains some errors; the correct question is:

You pack sandwiches for a mountain hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich. How many slices of bread are used for n hikers? Write your answer as an expression.

The answer is:

(2n) slices of bread for n hikers

Step-by-step explanation:

According to the question, sandwiches packed for a mountain hike with friends is made of two (2) slices of bread.

Each hiker gets one sandwich

This, n hikers will get n× 1 sandwich

= (n) sandwiches.

If 1 sandwich contains 2 slices of bread, then (n) sandwiches for n hikers will contain:

(2 × n) slices of bread

That is, (2n) slices of bread.

The expression is (2n).

Answer:

The slope is 1

Step-by-step explanation:

there's actually a trick you can do to find the slope. if you go from where the y-intercept is and go over to the x- intercept it will give you the slope hope this helps you

Answer:

a) 2.5% b) 50%

Step-by-step explanation:

1300 is two standard deviations higher than the mean. Since 95% of the data is covered within two standard deviations to the left and right of the mean, 5% is not covered. So, we have 2.5% leftover on the left side of the curve, under 900, and 2.5% leftover on the right side of the graph that is above 1300.

The mean is 1100, so anything above or below the mean is exactly 50% in a normal distribution.

Answer:

Step-by-step explanation:

This is the Empirical Rule.

68% of the data lies within 1 standard deviation of the mean, and so on.

If the mean is 1100 and the standard deviation is 100, 1300 represents two standard deviations above the mean.  Using a calculator with distribution functions, we type in normcdf(2,10000), obtaining 0.023.  This tells us that 2.3 percent of test scores are more than 1300.

Less than 1100:  Since the mean is 1100, the area under the standard normal curve is exactly 0.5 (corresponding to 50% of data are less than 1100).

Answer:

You have to invest  $6,250

Step-by-step explanation:

very simple applying the simple interest formula which is

[tex]A = P (1 + rt)[/tex]

Given data

A, final amount =  $10,000

P, initial principal balance=  ?

r, annual interest rate = 7.5%

t, time (in years)= 8 years

we can substitute our given data to find the principal needed.

[tex]10000= P(1+0.075*8)\\\10000= P(1.6)\\\[/tex]

Divide both sides by 1.6 we have

[tex]P= \frac{10000}{1.6} \\\P= 6250[/tex]

P= $6,250

Answer:

80

Step-by-step explanation:

16 people =7

7*5= 16*5

35=80 people

Answer:

80 people are required to run 35 machines

Step-by-step explanation:

Write and solve an equation of ratios:

  p       35

------- = -----

 16         7

where p is the number of people needed to run 35 machines.

Cross-multiplying yields 7p = 16(35), or p = 16(5), or p = 80

80 people are required to run 35 machines.

Answer:

It is not linear.

Step-by-step explanation:

If you plug in the coordinates into a graphing calculator, you'll see that after the point (7,2), the line starts to increase. A linear function on a graph is going to be a straight line, not increasing or decreasing. It's consistent. I hope this was helpful.  

Answer:

Misleading?

Step-by-step explanation:

Graphs can have mislabeled axes or different values on the axes, making them hard to understand.

I think this is the right answer, but the question was way too vague. Next time, put some options or at least explain the problem better.