Write the standard form of the complex number

sqrt 108[cos(−30°) + i sin(−30°)]

Answer:

1,2,3,4,6,8,12,24 sub set

If your cost of money is 6.4 percent, what is the current value of the lease is equal to $820.0054.

In Economics, a lease can be defined as a contractual agreement between a lessor and lessee, which avails the lessee an opportunity to make use of an asset, while making payments in instalment to the lessor for a specific period of time.

Mathematically, the current (present) monetary value of a lease can be calculated by using this formula:

Current value, PV = [Annuity × (1 + r) × [1 - (1 + r)^{-n}]/r]

Where:

Note: r = 0.064/12 = 0.0053333

Substituting the given parameters into the formula, we have;

Current value, PV = [144 × (1 + 0.0053333) × [1 - (1 + 0.0053333)^{-36}]/0.0053333]

Current value, PV = [144 × (1.0053333) × [1 - (1.0053333)^{-36}]/0.0053333]

Current value, PV = [144 × (1.0053333) × [1 - 0.8257290]/0.0053333]

Current value, PV = [144 × (1.0053333) × [0.174271/0.0053333]

Current value, PV = 25.095024 × 32.6760167

Current value, PV = $820.0054.

Read more on current value on annuity here: https://brainly.com/question/27882683

#SPJ1

The number of tiles with the dimensions 3 cm x 3 cm are needed to cover the grid is 4.

Given that, a grid is 6 cm x 6 cm.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Here,

Area of a grid is 6×6 =36 cm²

a) Area of a tile with 1 cm x 1 cm is

1×1 =1 cm²

Number of tiles = 36/1 =36

b) Area of a tile with 2 cm x 2 cm is

2×2 =4 cm²

Number of tiles = 36/4 =9

a) Area of a tile with 3 cm x 3 cm is

3×3 =9 cm²

Number of tiles = 36/9 =4

Therefore, the number of tiles with the dimensions 3 cm x 3 cm are

needed to cover the grid is 4.

Learn more about the area here:

https://brainly.com/question/27683633.

#SPJ1

The value of the equation is 2² x A ²

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be D

D = 2 power 8 multiply by A power 5  /  4 power 3 multiply by a power 3​

So , on substituting the values in the equation , we get

D = 2⁸ x A⁵ / 4³ x A³

Now , 2⁸ /  4³ can be simplified as

4³ = 2⁶

So ,

2⁸ /  2⁶ = 2 ⁸⁻⁶

            = 2²

And , A⁵ / A³ can be simplified as

A⁵ / A³ = A⁵⁻³

           = A²

So , the equation becomes ,

D = 2⁸ x A⁵ / 4³ x A³

D = 2² x A²

D = ( 2A )²

Hence , the value of the equation is D = 2² x A²

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ1

Answer:

350:3=116.66666....

Step-by-step explanation:

so 1/3 is 116.6 (117)

Ratio of women in company is 117.

Good luck!

Thank me later.

Tadano

The correct representation of the solution to the inequality given; –3(2x – 5) < 5(2 – x) are;

It follows from the task content that the correct representation of the inequality given in the task content be determined.

The given inequality can be evaluated for the solution set as follows;

–3 (2x – 5) < 5 (2 – x)

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

By dividing both sides by -1; we have;

x > 5.

On this note, the required representation is; An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Read more on inequalities;

https://brainly.com/question/11613554

#SPJ1

An equation that represents the situation is 780/x and the initial number of participants is 95.

Equation:

An equation is the combination of number, variables and the mathematical operators such as addition, subtraction, multiplication and division etc.

Given,

The chess club plans to fundraise $780, which is to be divided evenly among the members. Initially there are x participants, but then 2 more participants come forward, causing each participant to fundraise $8 less.

Here we need to find the equation that represents the situation and then we have to find the initial number of participants.

According to the given question,

Total amount for fundraise = $780

Number of participants = x

Here we know that the amount is divided evenly among the members.

So, the equation is written as.

=> 780/x

And the other part of the condition is, 2 more participants come forward, causing each participant to fundraise $8,

So, it can be written as,

=> 780 / (x+2)  = 8

=> x + 2 = 780/8

=> x + 2 = 97

=> x = 95

Therefore, there are 95 initial number of participants.

To know more about Equation here.

https://brainly.com/question/10413253

#SPJ1

The surface area of the figure in square inches will be 17.5 inch².

It is defined as a six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.

It is given that, Rectangular prism with dimensions 0.5 feet by 1.5 feet by 4 inches.

Length(l) = 0.5 ft = 6 inch

Width(w) = 1.5 ft = 18 inches

Height(h) = 4 inches

The surface area of the figure in square inches is found as,

S = 2(lw + lh + wh)

S=2(6×8 + 8×4 +4×6)

A = 17.5 inch²

Thus, the surface area of the figure in square inches will be 17.5 inch².

Learn more about the rectangular prism here:

brainly.com/question/21308574

#SPJ1

Answer:

√32

Step-by-step explanation:

c = [tex]\sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]

The algebraic expression of raise t to the 10th power then add the result to 3 is t¹⁰ + 3

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

Given: raise t to the 10th power then add the result to 3

Note: t is the variable here

Let's write algebraic expression now:

raise t to the 10th power => t¹⁰

then add the result to 3 => t¹⁰ + 3

Therefore, the algebraic expression is t¹⁰ + 3

Learn more about algebraic expression on:

https://brainly.com/question/4344214

#SPJ1

During 30 days of summer, Val will spend $ 73.5 on electricity from the use of his air conditioner.

Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left side, then move all of the other values to the right side to determine the value of x. For the outcome, simplify the values.

Since Val's air conditioner uses 3,500 watts when running, and that Val Utilizes it for 7 hours during summer days, spending 10 cents per kilowatt hour, estimating how much money Val will spend during a 30-day summer must be done the following calculation:

3,500 watts = 3.5 kilowatts

3.5 kilowatts per hour = 35 cents

35 cents × 7 hours = 245 cents per day

245 cents per day × 30 days = 7,350 cents per month

7,350/100 = X

73.5 = X

Therefore, during 30 days of summer, Val will spend $ 73.5 on electricity from the use of his air conditioner.

To learn more about the value of x refer to:

https://brainly.com/question/27944341

#SPJ1

Answer:

A bar notation

Step-by-step explanation:

the line is called a bar notation

Answer:

If you have a line over a number (let's say there is a line over 0.2):

0.2, then it means that it is a repeating number.

So, a line over 0.2 would mean it is actually 0.2222222222 etc. They just don't want to right it out because it is way to long, and it is infinite.

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 14 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

22m+16

Step-by-step explanation:

4(6m+4)-2m

4(6m)+4(4)-2m

24m+16-2m

24m-2m+16

22m+16

Hopes this helps please mark brainliest

The rate for the balance to triple in 46 years is  2.42% .

$500 is compounded annually for 46 years. No other deposits are made.

The rate needed for the balance to triple in that time can be calculated as follows:

The interest rate as a percent can be calculated as follows:

For the principal to be tripled, the amount will be 500(3) = 1500 dollars

[tex]r = n((\frac{A}{P} )^{\frac{1}{nt} } -1)[/tex]

where

P = 500

A = 1500

n = 1

t = 46 years

r[tex]r = 1((\frac{1500}{500})^{\frac{1}{1(46)} } - 1 )[/tex]

[tex]r = 1((\frac{1500}{500})^{\frac{1}{46} } - 1 )[/tex]

r = 0.0241704

Then convert r to R as a percentage

R = r * 100

R = 0.0241704 * 100

R = 2.42% per year

learn more on compound interest here:https://brainly.com/question/12840579

#SPJ1

The volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 48π

Volume of the Solid:

Volume refers the measure of how much space an object takes up and it is measured by the number of unit cubes it takes to fill up the solid.

Given,

Here we have to use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

xy = 6, x = 0, y = 6, y = 8.

Here we know that,

xy = 6

Then the value of x is obtained as,

=> x = 6/y

Now, the volume of the solid is calculated with the given interval [6,8] as.

=> V = 2π ∫₆⁸ y x (6/y)/dy

=>  2π∫₆⁸ 6/dy

When we differentiate the equation, then we get,

=> 24π[y]₆⁸

=> 24π [8 - 6]

=> 24π [2]

=> 48π

Therefore, the volume of the solid is 48π.

To know more about Volume of Solid here.

https://brainly.com/question/12649605

#SPJ1

Given equation to us is , [tex](m-3)r^2+9r-2=0[/tex] .

The given equation is a quadratic equation and it has two real solutions if it's discriminant is greater than or equal to 0 .

For a quadratic equation in standard form of

[tex]ax ^{2} + bx + c = 0[/tex]

the discriminant is given by b² - 4ac .

On comparing wrt to Standard form, we have ;

Now we have,

[tex]\longrightarrow b^2-4ac \geq 0\\\\\longrightarrow 9^2-4(m-3)(-2)\geq 0\\\\\longrightarrow 81 +8(m-3)\geq 0 \\\\\longrightarrow 81 +8m-24\geq 0 \\\\\longrightarrow 8m \geq 24-81 \\\\\longrightarrow 8m \geq -57 \\\\\longrightarrow \underline{\underline{ m \geq \dfrac{-57}{8}}}[/tex]

Therefore for all values greater than or equal to -57/8 the equation will have a real solution .

And we are done!

The equation (m-3)r² + 9r -2 = 0 will have two real solution for the value of m, greater than or equal to -57/8.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The standard form of equation of power two is ax²+bx+c =0 .

The given equation,

(m-3)r² + 9r -2 = 0

Compare the given equation with standard equation ax²+bx+c =0,

The value of a=m-3, b=9 and c=-2

An equation has two real solutions if a discriminant of the equation is greater than or equal to zero.

⇒D ≥ 0

⇒b²-4ac ≥ 0

Substitute the value of a, b and c,

⇒9² - 4×(m-3)(-2) ≥ 0

⇒81 +8m - 24 ≥ 0

⇒8m ≥ -57

⇒ m ≥ -57/8

For the values of m greater than or equal to -57/8, the equation have two real solutions.

To know more about Equation on:

https://brainly.com/question/187506

#SPJ1

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

Learn more about solutions to the system of inequalities here:

https://brainly.com/question/16339562

#SPJ1

Answer: C

Step-by-step explanation:

[tex]A=\pi (17)^2 \approx 908[/tex]

Answer:

Answer C is correct

Step-by-step explanation:

The formula to find the area of a circle is:

A = πr²

Here,

r => radius = 17cm

Let us find the area of the circle.

A = πr²

A = 3.14 × 17 × 17

A = 907.46 cm²

Approx. = 908 cm²

The probability that a student chosen at random is in the choir or band or both is 0.911

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In mathematics terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain.

Total number of students in the school = 450

number of students in choir = 110

number of students in band = 240

number of students in both = 60

Probability a student chosen at random is in the choir or band or both is

110/450 + 60/450 + 240/450

= 410/450 which is 0.911

In conclusion, the probability of a student being in music, or band or both is 0.911

Learn more about probability: htps://brainly.com/question/25870256

#SPJ1

The number of point on this graph that represent a relative minimum is one, which is point b.

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair (x, y)on a graph.

A relative minimum can be defined as the lowest point or valley point on the graph of a function. Additionally, all of the points that are located to the left and right of the lowest point (valley point) on a graph must be larger than the relative minimum.

By critically observing the graph of function f(x), we can reasonably and logically deduce the following information:

Read more on relative minimum here: https://brainly.com/question/9180672

#SPJ1

The values of the addition given will be:

6 + 9 = 15

0 + 9 = 9

2 + 3 = 5

11 + 90876 = 90887

Addition simply means sum. It is one of the basic operations that are used in Mathematics. In this case, the addition of two whole numbers will bring about the total amount of the value combined.

Therefore the addition will be the sum of the numbers. This will be:

6 + 9 will be:

= 6 + 9

= 15

0+9 will be:

= 0 + 9

= 15

2+3 will be:

= 2 + 3

= 5

11+90876 will be:

= 11 + 90876

= 90887

Learn more about addition on:

brainly.com/question/24536701

#SPJ1

Answer:

The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.

Step-by-step explanation:

The end behavior of a function is what happens to the value of the function as x approaches negative infinity and as x approaches positive infinity.

Graphing the function is very helpful to visualize the end behavior.

Here, the graph has the shape of a V with the vertex on the x-axis going up in value on both sides forever.

The function here is f(x) = 3|x|.

Let's try a few values for x to get an idea.

We will deal with x approaching positive infinity first.

f(0) = 3|0| = 0

Let's get larger and larger values for x, approaching positive infinity.

f(10) = 3|10| = 30

f(10,000) = 3|10,000| = 30,000

f(1,000,000) = 3|1,000,000| = 3,000,000

As you can see, as x increases, the value of f(x) also increases. As x approaches positive infinity, f(x) also approaches positive infinity.

Now let's look at values of x approaching negative infinity.

f(0) = 3|0| = 0

Let's get smaller and smaller values for x, approaching negative infinity.

f(-10) = 3|-10| = 30

f(-10,000) = 3|-10,000| = 30,000

f(-1,000,000) = 3|-1,000,000| = 3,000,000

As you can see, as x decreases, the value of f(x) increases. As x approaches negative infinity, f(x) approaches positive infinity.

The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.

Answer: D

Step-by-step explanation:

Using the formula for the volume of a rectangular prism,

[tex]x(8-2x)(11-2x)\\\\=x(88-38x+4x^2)\\\\=4x^3 -38x^2 +88x[/tex]

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

[tex]\frac{a}{b}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = [tex]\frac{5}{8}[/tex] a

also

[tex]\frac{b}{c}[/tex] = [tex]\frac{3}{4}[/tex] ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = [tex]\frac{4}{3}[/tex] b = [tex]\frac{4}{3}[/tex] × [tex]\frac{5}{8}[/tex] a = [tex]\frac{5}{6}[/tex] a

Then

a : b : c

= a : [tex]\frac{5}{8}[/tex] a : [tex]\frac{5}{6}[/tex] a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

120 cm² is the surface area of the right triangular prism

The surface area of a right triangular prism can be determined using the formula below:

A = (S₁ + S₂ + h)L + bh    (Check the attached image for the labeling)

Given: S₁ = 3 cm,  S₂ = 5 cm, h = 4 cm, L =  6cm and b = 3 cm

Substitute these values into the formula:

A = (S₁ + S₂ + h)L + bh

A = (3 + 5 + 4)6 + 3(4)

A = (18)6 + 12

A = 120 cm²

Therefore, the surface area of the right triangular prism is 120 cm²

Learn more right triangular prism on:

https://brainly.com/question/26979119

#SPJ1

Podras comprar un total de 8 docenas, y sobrara $1.30

Sabemos que una docena de bananos cuesta $2.65, y queremos ver cuantas docenas se peden comprar con $22.50, para ver esto, debemos tomar el cociente entre la cantidad de dinero que tenemos y el precio de una docena.

Obtendremos:

$22.50/$2.65 = 8.49

Redondenado al proximo numero entero obtenemos 8, es decir, se pueden comprar 8 docenas.

La cantidad que sobra es:

$22.50 - 8*$2.65 = $1.30

Aprende mas sobre cocientes:

https://brainly.com/question/3493733

#SPJ1

Step-by-step explanation:

[tex] \frac{dy}{dx} ( \sqrt{x} ) = \frac{1}{2 \sqrt{x} } [/tex]

The slope of the line at x=1 is

[tex] \frac{1}{2(1)} = \frac{1}{2} [/tex]

so our equation is

[tex]y - 1 = \frac{1}{2} (x - 1)[/tex]

[tex]y - 1 = \frac{1}{2} x - \frac{1}{2} [/tex]

[tex]y = \frac{1}{2} x + \frac{1}{2} [/tex]

Answer:

  d = 23 1/3

Step-by-step explanation:

You want to solve the proportion (0.3d -1)/(3 1/3) = (0.84)/(7/15).

  [tex]\dfrac{0.3d-1}{3\dfrac{1}{3}}=\dfrac{0.84}{\dfrac{7}{15}}\qquad\text{given}\\\\\\\dfrac{3(0.3d-1)}{10}=\dfrac{15(0.84)}{7}\qquad\text{invert and multiply}\\\\0.09d -0.3=1.8\qquad\text{simplify}\\\\0.09d = 2.1\qquad\text{add 0.1}\\\\d=\dfrac{2.10}{0.09}=\dfrac{70}{3}\qquad\text{divide by 0.09}\\\\\boxed{d=23\dfrac{1}{3}}[/tex]

__

Check

  (0.3·(70/3) -1)/(3 1/3) = 0.84/(7/15)

  (7 -1)/(10/3) = 1.8

  6(3/10) = 1.8 . . . . . . true

Answer: 23 1/3

Step-by-step explanation:

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

Read more about Perimeter of triangle at; https://brainly.com/question/24382052

#SPJ1

a. The hypothesis to be tested are given as follows:

b. The p-value is of: 0.0047.

c. The decision is of: Reject the null hypothesis.

d. The conclusion is of: There is enough evidence to conclude that the mean rate is less for people who exercise regularly.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the heart rate is less, than is, if the difference is not negative, hence:

[tex]H_0: \mu_d \leq 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the heart rate is less, that is, if the difference is negative, hence:

[tex]H_1: \mu_d > 0[/tex]

The parameters to the p-value are given as follows:

We have a left-tailed test, as we are testing if the mean is less than a value, hence, using a t-distribution calculator, the p-value is of:

0.0047.

Since the p-value is less than the critical value, the decision and the conclusion are given as follows:

More can be learned about the test of an hypothesis at https://brainly.com/question/13873630

#SPJ1