Howard sells used helicopters, and he receives a 3% commission on all that he sells. If Howard received $42,000 in commissions last year, how many dollars worth of used helicopters did he Sell?

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

Complex numbers are numbers of the form z = x + iy

Complex numbers in polar form z = r(cosθ + isinθ) where

Given that z = (2 - 2i√3)⁴ =

So,

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

The complex number z =  r(cosθ + isinθ) in rectangular form is z = x + iy where

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y =  rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

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The exponent for the expression, 5 × 5 × 5 × 5 × 5, would be expressed as: [tex]5^5[/tex].

An exponent can be defined as the power to which the base is to b e raised.

For example, a × a × a can be expressed in  exponent form as a³.

In the same vein, given the expression, 5 × 5 × 5 × 5 × 5, we would expressed this in exponent form as: [tex]5^5[/tex].

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Answer:

75 on mathematics and 55 on English!

Step-by-step explanation:

Answer:

English test score: 55

Mathematics test score: 75

Step-by-step explanation:

Let [tex]e[/tex] be Mary's score on the English test.

We can say that [tex]e + 20[/tex] is her score on the Mathematics test, as the score for the Mathematics test is just the English test score but 20 higher.

Since both scores add up to 130, we can set up an equation to solve for the English test score. Since we said [tex]e + 20[/tex] is Mary's score on the Mathematics test, [tex]e + e + 20[/tex] is the total of her 2 test scores.

[tex]e + e + 20 = 130\\2e + 20 = 130\\2e = 110\\\boxed{e = 55}[/tex]

This means that Mary got a 55 on her English test score.

To solve for the Mathematics test score we can substitute 55 for [tex]e[/tex] in [tex]e + 20[/tex].

[tex]e + 20 = 55 + 20 \rightarrow \boxed{75}[/tex]

This means Mary got a 75 on her Mathematics test.

Those are the answers

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Answer:

[tex] - 3x( - 4x + x) - x( - x - 2x) - 4x(4x + 3x) \\ \\ = 12 {x}^{2} - 3 {x}^{2} + {x}^{2} + 2 {x}^{2} - 16 {x}^{2} - 12 {x}^{2} \\ \\ = - 16{x}^{2} [/tex]

Answer:

Answer:

Graph C shows the solution for the inequality

Step-by-step explanation:

y - 4 > 2(x + 2)

y > 2x + 4 + 4

y > 2x + 8

Let y = 2x + 8, Then

X-intercept (0, 8)

Y-intercept (-4, 0)

Since the inequality sign is > we use broken line.

Put,  (0, 0)

y > 2x + 8

0 > 0+ 8

0 > 8 Which is false

so, the answer will be above the broken line

Hence , Graph C shows inequality

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Answer:

75 mL.

Step-by-step explanation:

3/(3+2) = 3/5 of the solution is concentrate.

So the answer is 125 * 3/5

= 3*25

= 75 mL.

Answer:

Length of the side of the square is 12 cm.

Step-by-step explanation:

Given information:

[tex]\text{side}_1 = 8a \text{ cm (side of a rectangle)}\\\text{side}_2 = 7a \text{ cm (side of a rectangle)}\\P_\text{rec} = 42 + P_\text{sq} \text{ cm } (P_\text{rec} \text{ is perimeter of the rectangle and } \\P_\text{sq} \text{ is the perimeter of the square)}\\\text{side}_\text{sq} = 4a \text{ cm (side of a square)}[/tex]

Our mission is to find the length of the side of the square. We know that the side of the square is 4a cm, so to be able to answer we have to find the value of a first.

Step 1: Finding the value of a

Key to finding the value of a is the perimeter of the rectangle. Notice that we can calculate the perimeter of the rectangle in two different ways.

One way was given in the question:
[tex]P_\text{rec} = 42 + P_\text{sq}[/tex]

We want equations in terms of a, so we can calculate a. Perimeter of the square can be calculated as:

[tex]\text{perimeter}_\text{square} = 4 \times \text{side}[/tex]

Substituting the values in equation:

[tex]P_\text{sq} = 4 \times 4a\\P_\text{sq} = 16a[/tex]

Therefore the first equation for perimeter of the rectangle becomes:

[tex]P_\text{rec} = 42 + P_\text{sq}\\\fbox{\begin{test}P_\text{rec} = 42 + 16a\end{test}}[/tex]

For the second way we use formula for the perimeter of rectangle which is:
[tex]\text{perimeter}_\text{rectangle} = 2 \times \text{width} + 2 \times \text{length}[/tex]

Substituting the values in equation:
[tex]P_\text{rec} = 2 \times 7a + 2 \times 8a\\P_\text{rec} = 14a + 16a\\\fbox{\begin{test}P_\text{rec} = 30a\end{test}}[/tex]

Now let's equate both perimeters of the rectangle.

[tex]P_\text{rec} = P_\text{rec}\\42+16a = 30a\\42 =14a\\3 = a[/tex]

Step 2: Find the length of the side of the square

It's given that side of the square is 4a cm. All we have to do is substituting a with its value, which we got in the previous step.

[tex]\text{side}_\text{sq} = 4a\\\text{side}_\text{sq} = 4(3)\\\text{side}_\text{sq} = 12 \text{ cm}[/tex]

Answer:

86%

Step-by-step explanation:

each shaped area represent 1% so you divide or subtract the unshaped area with the shaped area.

Answer:

y=21

Step-by-step explanation:

y= 9 cos x =3 so y=3 when x=1 on the base level so if x=7 would be x=1 on the base level * 7 then y=3 on the base level * 7 would be y = 21

Answer:

Solve v + 6 = 5v − 2 to find the value of v.

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

The correct method to find Meg's and Victor's ages is to equate the equations for their ages.

Hence. the answer is :

Solve v + 6 = 5v − 2 to find the value of v.

Answer:

Triangle D.

Step-by-step explanation:

A scalene triangle has different sides.

Answer: 1/216

Step-by-step explanation: please mark me brainly

Answer:

f(3)=0.005

Step-by-step explanation:

Plug in 3 for x

f(3)=(1/6)^3

f(3)=0.005

Hope this helps!

If not, I am sorry.

So, there are 3 fourths in 3 fourths

Answer:

$50 interest

Step-by-step explanation:

Simple interest formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for I:

⇒ I = 500 · 0.02 · 5

⇒ I = 50

Therefore, Frank will earn $50 interest in 5 years.

The inequality expression f(4) > g(4) is true when x = 4

The functions are given as:

[tex]f(x) = 2^x - 7[/tex]

g(x) = 1.5x - 3

See attachment for the graph of both functions.

From the graph, we have:

f(4) = 9

g(4) = 3

This means that:

f(4) > g(4) when x = 4

Hence, the inequality f(4) > g(4) is true when x = 4

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The number of 15-year old students that took part in the survey is 300 students and 20 "15-year old" students spent between 35 and 45 minutes on social media.

A frequency polygon can be defined as a type of line graph that is used to plot a class frequency against the class midpoint.

For the 15-year old students, the total number of students would be calculated by adding all the data points at each frequency:

Total students = 30 + 30 + 50 + 60 + 40 + 50 + 40

Total students = 300 students.

In order to determine the number of 15-year old students than 11-year old that spent between 35 and 45 minutes on social media, we would calculate the average and then read it from the frequency polygon.

Average = (35 + 45)/2

Average = 80/2

Average = 40.

For the 11-year old, we have:

Frequency (40) = 40

For the 15-year old, we have:

Frequency (40) = 60

Now, we can calculate the difference as follows:

Difference = 60 - 20

Difference = 20 students.

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The equation that could be used to determine the volume of Box B is (B = 14.325cm³ - 5.61cm³) and the volume of Box B is 8.715cm³.

This question is incomplete, the complete question is:

The sum of the volume of two rectangular prisms, box a and box b are 14.325cm cubed. Box a has a volume of 5.61cm.

a. Let B represent the volume of Box B in cubic centimeters. Write an equation that could be used to determine the volume of Box B.

b. Solve the equation to determine the volume of Box B

Volume is simply the amount of space that is enclosed within a container.

Given that;

a)

Let B represent the volume of Box B in cubic centimeters. The equation that could be used to determine the volume of Box B will be;

Sum of the volume of two rectangular prisms A&B = Volume of Box A + Volume of Box B

14.325cm³ = 5.61cm³ + B

B = 14.325cm³ - 5.61cm³

Hence, The equation that could be used to determine the volume of Box B is B = 14.325cm³ - 5.61cm³

b)

To determine the volume of Box B, we solve the equation.

B = 14.325cm³ - 5.61cm³

B = 8.715cm³

Hence, the volume of Box B is 8.715cm³.

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The conclusion is there is likely an association between the categorical variables because the sum of the relative frequencies is 1. 0.

Categorical variables are variables that can only take on a fixed number of values. An example of categorical variables is gender. One can either be a male or a female.

The sum of the categorical variables is 1. This indicates that the two variables are negatively correlated. It means that someone would be either pick one of the variables.

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Answer:

c

Step-by-step explanation:

Answer:

It depends on what way the line is facing, if it starts out vertical(meaning up or down), the answer is yes.

Answer:

First,

the age of the son: s

the age of the father is 2 less than 7 times the age of his son: 7s - 2

In 3 years, the sum of their ages will be 52, In 3 years, the age of the sun will

increase 3, so s+3. Also, the age of his

father also increase 3, (7s-2)+3

(s+3)+ [(7s-2)+3] = 52 is the equation.

The correct answer is :

( 7s - 2 ) +3+ ( s + 3 ) = 52 , or 8s + 4 = 52 .

Since s is the son's age , " two less than seven times " the son's age would be represented by 7s - 2 .

To represent this in 3 years , we would add 3 : ( 7s - 2 ) +3 .

In 3 years , the son's age , s , would be represented by s + 3 . We are told that the sum of these ages will be 52 ; this gives us ( 7s - 2 ) +3+ ( s + 3 ) = 52 .

To simplify this , combine like terms .

7s + s = 8s ; -2 + 3 + 3 = 4 .

This gives us 8s + 4 = 52 .

The profit earned by the gift shop owner on fifty vases will be $ 91.07.

The amount of money earned by any seller on the cost price is called the profit. It is given that A gift shop owner bought fifty vases for $210. she sells seven vases for what she paid for ten originally.

The profit will be calculated as we will create the expressions for all the selling and purchasing given in the question.

The total cost price of vases:-

50 vases = $210

1 Vase = 210 / 50 = 4.25

So 10 vases will be purchased at the price of:-

10 Vase = 4.25 x 10 = 42.5

Now from the question of the amount he paid for 10 vases, he gained it by selling 7 vases.

7 Vase = 42.5

1 Vase = 42.5 / 7 = 6.07

So he sold one vase for $6.07 and purchased it at $4.25.

The profit will be = 6.07 - 4.25 = 1.821

So profit for selling 50 vases will be:-

Profit = 50 x 1.821 = $91.07

Therefore profit earned by the gift shop owner on fifty vases will be $ 91.07.

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Answer:

60 ft

Step-by-step explanation:

a = 90

b = 108ft

the base angle can be found by using sin(x) = 120/108x2

=> x = 33.7 degrees

To find height, use tan(33.7) = Opp/ Adjacent = x / 90

=> x = 60.02 or 60 ft

Answer:

18 1/8

Step-by-step explanation:

4 7/8 x 4 = 23 1/2

23 1/2 - 5 3/8 = 18 1/8

A phrase that 18c can represent is the product of 18 and a number c

The expression is given as:

18c

Rewrite as:

18c = 18 * c

The above represents the product of two factors; 18 and c

Hence, a phrase that 18c can represent is the product of 18 and a number c

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Answer:

See below

Step-by-step explanation:

To get the fraction from mixed number you just need to take the number standing alone, multiply with the denominator and add with the numerator and keep it on top with the denominator in place to turn it into a fraction.

For example, [2]3/4 = 2*4 + 3 = 11 => the fraction is 11/4.

Using the probability concept, it is found that since the number of red sweets would be a decimal number, the probability cannot be [tex]\dfrac{7}{10}[/tex]

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

In this problem:

The probability of red is:

[tex]p=\dfrac{n}{n+8}[/tex]

Supposing, we solve for n:

[tex]\dfrac{n}{n+8} = \dfrac{7}{10}[/tex]

10n = 7n + 56

3n = 56

n  =  56 / 3

n  =  18.67

Since the number of red sweets would be a decimal number, the probability cannot be 7 / 10

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Step-by-step explanation:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{6 - 2}{19 - 3} \\ = \frac{4}{16} \\ \boxed{slope = \frac{1}{4} }[/tex]

Answer: 18

Step-by-step explanation:

By the angle bisector theorem, [tex]\frac{x}{48} =\frac{12}{32} \longrightarrow x=\boxed{18}[/tex]

Answer:

88

Step-by-step explanation:

All of the numbers are in the thirties (30's) except for 88, so that is the outlier

[tex]~~~~125x^9+64\\\\=(5x^3)^3+4^3\\\\=(5x^3 +4)[(5x^3)^2 - (5x^3)(4) + 4^2]\\\\=(5x^3 +4)(25x^6-20x^3+16)[/tex]