(3^3*6^6)^-3
what is a simplified version of this

Answer:

Step-by-step explanation:

a) The amount of money in the account at the beginning is $222,222.222.

b) The total amount of money withdrawn from the account is $400,000.

c) The amount of interest earned is $177,777.778.

It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".

A = $20,000*20 = $400,000

Let the amount of money in the account at the beginning be represented by the variable "P".

A = P*R*T

400,000 = P*0.09*20

400,000 = P*1.8

P = 222,222.222

The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".

I = A - P = $400,000 - $222,222.222 = $177,777.778

To learn more about interest, visit :

https://brainly.com/question/22621039

#SPJ1

Line AD and line EG are parallel line, Transversal CH < ABC and EFH  are same side exterior angles

The presence of two parallel lines and a transversal line leads to some important theorem used in geometry

Some of the theorems include

The exterior angles refers to angles above line AD and below line EG, which are the parallel lines. These angles according to the figure are 4 and they include

The exterior angles to the left of the transversal line forms a pair of same side exterior, similarly, to the right of the transversal line forms another pair of same side exterior angles.

The question is asking  of same side exterior angles to < ABC, which is to the left of the transversal line. The pair that are same side exterior angles to the left of the transversal line are

Hence < EFH and < ABC are same side exterior angles

Learn more about same side exterior angles here:

https://brainly.com/question/14027512

#SPJ1

The solutions to the financial ratio requirements based on the supplied facts are:

A. Current ratio is 1.125.

B. Acid test is 1.

C. Average days' collection is 26.7 days.

D. Asset turnover is 1.4x.

E. Profit margin on sales is 14.63%.

Financial ratios are ratios that show the relative magnitude of one financial account to another.

Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.

Current Ratio = Current Assets ÷ Current Liabilities

= $18,000 ÷ $16,000

= 1.125

Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities

= ($18,000 - 2,000) ÷ $16,000

= $16,000 ÷ $16,000

= 1

Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days

= $3,000 ÷ $41,000 x 365

= 26.7 days

Asset Turnover = Net Sales ÷ Total Assets

= $41,000 ÷ $29,000

= 1.4x

Profit Margin on Sales = Net Income ÷ Net Sales x 100

= $6,000 ÷ $41,000 x 100

= 14.63%

Current Assets = $18,000

Accounts Receivable = $3,000

Current Liabilities = $16,000

Inventory = $2,000

Net Sales = $41,000

Total Assets = $29,000

Net Income = $6,000

Learn more about financial ratios at https://brainly.com/question/9091091

#SPJ1

Answer:B

Step-by-step explanation:

Becauee it already says the first night how many tickets were sold also on the second and the third night. And if someone read the equation they would have known that the play went in for three nights.

Answer:

6x=24-12y

x=24-12y/6

x=4-12y

The function that represents the graph f(x) = -3|x| is f(x) = -3|x| - 5

How to find the function of the graph ?

To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

As it is already given in the question that the function

f(x) = -3|x|

We will use transformation rules to solve the given question

f(x)→f(x-a) ⇒ Graph shifted to right by a units

f(x)→f(x+a) ⇒ Graph shifted to left by a units

f(x)→f(x) - a ⇒ Graph shifted downwards by a units

f(x)→f(x) + a ⇒ Graph shifted upwards by a units

When it is translated 5 units down

Then we subtract 5 outside of the given function

∴ f(x) = -3 |x| - 5

To learn more about finding the function of the graph from the given link  

https://brainly.com/question/7224793

#SPJ1

Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

f(x) = x³ - 4x² - 5x + 14

-2    |    1    -4     -5     14

                -2      12   -14

           1    -6       7     0

x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)

x²-6x+7=0

x²-6x+9-2=0

(x²-6x+9)-2=0

x²-6x+9=2

x²-3x-3x+9=2

x(x-3)-3(x-3)=2

(x-3)²=2

x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]

x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

our first "suspicion" for a factoring is an integer factor of the constant term : 14.

14 = 2 × 7 or -2 × -7

I started to try 2 or -2 and found that -2 is indeed a zero solution.

so, the first factors are

f(x) = (x + 2)(x² + ...)

let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.

x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7

- x³ + 2x²

--------------

0 -6x² - 5x

- -6x² - 12x

----------------

0 7x + 14

- 7x + 14

------------

0 0

f(x) = (x + 2)(x² - 6x + 7)

the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation

ax² + bx + c = 0

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =

= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =

= 3 ± sqrt(8/4) = 3 ± sqrt(2)

x1 = 3 + sqrt(2)

x2 = 3 - sqrt(2)

so, the zeros are

-2, 3 - sqrt(2), 3 + sqrt(2)

The rectangular equation for the plane curve defined by the parametric equation x = t + 4, y = t² is; y = x² - 8x + 16

We are given the parametric equations as;

x = t + 4

y = t²

Now, for us to convert parametric equations to a rectangular equation (cartesian equation) means that we are solving for t in terms of x and then plugging it back into the y equation.  Therefore, we have;

x = t + 4

t = x - 4

Thus;

y = (x - 4)²

Expanding this gives;

y = x² -4x - 4x + 16

y = x² - 8x + 16

Read more about Rectangular Equation at; https://brainly.com/question/27115097

#SPJ1

Answer:

i can help but first what the questions and where are the options?

Step-by-step explanation:

The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.

Let

x + y = 48

29x + 51y = 50*48

x + y = 48

29x + 51y = 2400

Solve simultaneously

From (1)

x = 48 - y

Substitute into (2)

29x + 51y = 2400

29(48 - y) + 51y = 2400

1392 - 29y + 51y = 2400

- 29y + 51y = 2400 - 1392

22y = 1008

y = 1008/22

y = 45.82 pounds

Substitute y = 45.82 pounds into (1)

x + y = 48

x + 45.82 = 48

x = 48 - 45.82

x = 2.18 pounds

So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.

Read more on simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

The slope of given line is 43

The slope of the line is the rate of change of y with respect to xSlope of a line gives the steepness of line.

The formula of finding the slope of line with two given points is as follows,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thewith[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]TheThe[tex]Hdb\pi[/tex]TheThelinem=y2-yy2-y1/xw-xq
x2-x1
x2-x1
x2-x1

It can be seen from the given image thatthat the line moves 3unit in x direct and 4unit in y direction.So the slope will be
be m=43

Hence,the slope of the give line is 43

To learn more about slope of line visit the be

brainly.com/question/3493733

#SPJ1

Answer:

(1,3)

(4,-3)

Step-by-step explanation:

To find y, replace x with 1 in the equation and solve for y

6x + 3y = 15

6(1) + 3y = 15

6 + 3y = 15  Subtract 6 from both sides

3y = 9  Divide both sides by 3

y = 3

(1,3)

To find x, replace y with -3 in the equation and solve for x

6x + 3y = 15

6x + 3(-3) = 15

6x - 9 = 15  Add 9 to both sides

6x = 24  Divide both sides by 6

x = 4

(4, -3)

Answer:

$66

Explanation:

Sam earns a 5.5% commission on everything he sells. He sells a television for $1200. What is 5.5% of $1200?

Convert 5.5% to decimal form: 0.055. Now, multiply 1200 by 0.055.

Sam will earn $66 because 5.5% of 1200 is 66.

Probability of drawing a card below a 6 (count an ace as high) is 4/13

Total number of outcome : n(S) = 52

(a) In a deck number of card below a 6 (counting ace as high) is {5 , 4 , 3, 2}

so , n(E) = 4 × 4 = 16

The probability of drawing a card below a 6 (count an ace as high) = P(E)

[tex]P(E) =\frac{n(E)}{n(s)}[/tex] =16/52

P(E) = 4/13

(b) Probability of drawing a card below a 6 (count an ace as high) is 4/13

Hence , the odds of drawing a card below a 6 (count an ace as high). is 0.308

(c) we should expect to draw a card below a 6 about four times out of every 13 attempts .Also, we should expect to draw a card below or 6 four times for every nine times we draw a 6 or above is the law of large number to interpret both the probability and odds of drawing a card below 6

To know more about Deck of card here ,

https://brainly.com/question/9627169

#SPJ1

Explanation:

Technically you could isolate any variable you wanted, from either equation. However, convention is to pick the variable in which isolating it is easiest, and most efficient.

The key thing to look for is if there's a coefficient of 1. This is found in the second equation for the y term. Think of -4x+y = -13 as -4x+1y = -13. Due to the coefficient of 1, when solving for y we won't involve messy fractions.

If you were to solve for y, then you'd get y = 4x-13, which is then plugged in (aka substituted) into the first equation. That allows you to solve for x. Once you know x, you can determine y.

Answer: Integers less than 4 will make the inequality true.

Step-by-step explanation:

1) subtract both sides by 4 to isolate 2x so we are now left with 8 > 2x.

2) divide both sides by 2 so we are left with just x, leaving us now with 4 > x.

Integers must be less than 4 because if you substitute x as 4, we have 12 > 12, which is not true. But, if we substitute x as 3, we are left with 12 > 10, which makes the inequality true.

The expected mean for a sample of 150 women is 168.5 pounds.

Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.

The formula for expected mean is :

E ( X ) = μ = ∑ x P ( x )

Where:

x = values of the random variable X

P(x) = Corresponding probability

∑ =Sum of all products xP(x)

μ = mean

Therefore the expected mean is 168.5 pounds.

Learn more about expected mean here: https://brainly.com/question/10675141

#SPJ1

Answer:

Step-by-step explanation:

A=60

B=75

C=45

D=60

E=75

F=45

G=90

The equation for the value of x will be 11/C.

According to the question,

We have the following equation:

Cx — 4 = 7

Now, we can easily find the value of x from this equation by following the given steps.

We will first add 4 on both sides of the equation:

Cx = 7+4

Adding the two numbers on the right hand side:

Cx = 11

Dividing by C on both sides of the equation:

x = 11/C

(More to know: we can now find the value of x if the value of C is given.)

Hence, the equation for the value of x will be 11/C.

To know more about equation here

https://brainly.com/question/3162971

#SPJ1

The value of the test statistic when the engineer has designed a valve is -2.83.

From the information, the following can be deduced:

Sample mean = 5.8

Population mean = 6.0

Population standard deviation = 1

Significance level = 0.02

(Sample mean - Population mean) /(Standard Deviation / ✓200)

= (5.8 - 6.0) / (1 / ✓200)

= -0.2 ✓200

= -2.83

The value is -2.83.

It's important to note that the test statistic is the z value. This will be:

=

Learn more about test statistic on:

brainly.com/question/15110538

#SPJ1

The total cost is $1.75

Given that we've done it:

The total price is shown by:

Now, let's display the following in a number line:

So, after seven hops, we arrive at 1.75, which is the correct response.

Hence, the total cost is $1.75

To learn more about Place value click on the link

brainly.com/question/25137147

#SPJ1

D after three rotations: 3 × 36° = 108°

F after five rotations: 5 × 36° = 180°

H after seven rotations: 7 × 36° = 252°

I after eight  rotations: 8 × 36° = 288°

Given,

In the question:

ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.

To find the each angle of rotation to the point A' coincides with after that rotation.

Now, According to the question:

let's know about Decagon:

A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.

Every regular polygon with n sides can be divided into n  congruent triangles. The angle with vertex the center of the polygon will measure

360 : n degrees.  We are given a regular decagon, therefore:

n = 10

α = 360 : n = 36°

We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.

A' will coincide with D after three rotations: 3 × 36° = 108°

A' will coincide with F after five rotations: 5 × 36° = 180°

A' will coincide with H after seven rotations: 7 × 36° = 252°

A' will coincide with I after eight  rotations: 8 × 36° = 288°

Learn more about Angle Rotation at:

https://brainly.com/question/14380185

#SPJ1

N × (-5/6) ≥ -1/2 is the inequality for the statement

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given the statement: negative one half is a minimum of the product of a number and negative five sixths.

This statement can also be written as the product of a number and negative five sixths is greater than or equal to negative one half

Let N represent the number. Thus, the inequality of the statement is:

N × (-5/6) ≥ -1/2    

Note: The symbol ≥ is pronounced as greater than or equal to

Therefore, the inequality for the statement is N × (-5/6) ≥ -1/2

Learn more about inequality on:

https://brainly.com/question/25275758

#SPJ1

Answer:

a = 41°

b = 57°

c = 82°

Step-by-step explanation:

all angles in a triangle must add up to equal 180°

The solution to the mathematical expression -(1/4x1/4x1/4x1/4) in exponent form is [tex]\mathbf{-4^{-4}}[/tex]

Number multiplication is a basic and common operation. However, the product of multiplication can be stated differently at times, whether to reduce the equation or to explain the mathematics required. Many numbers can be expressed exponentially.

The concept of exponential form is a method of expressing a number that has been multiplied by itself several times. The fundamental formula is [tex]\mathbf{y=b^x}[/tex]

Exponential expressions are simply a shorthand way of writing powers. The exponent specifies how many times the base has been utilized as a factor.

From the information given

:= -(1/4*1/4*1/4*1/4)[tex]

=-(4^{-1}\times4^{-1}\times4^{-1}\times4^{-1})[/tex][tex]=-(4^{(-1+(-1)+(-1)+(-1))})[/tex][tex]=-(4^{(-1-1-1-1)})[/tex][tex]=-(4^{(-4)})[/tex][tex]\mathbf{=-4^{-4}}[/tex]

Learn more about exponent on:

https://brainly.com/question/13669161

#SPJ1

The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.

In this question, we simply need to make the width (w) the subject of formula.

The equation given is

p = 2w + 2l

p = 2w + 2l

p = 2(w + l)

p / 2 = w + l

w = p/2 - l

learn more on perimeter of rectangle here;

https://brainly.com/question/19819849

#SPJ1

A. Yes, the data justifies a function because there is no repeating x values.

B. The relation f(x) = 2x + 13 has a greater value at x = 7

C. The value of x when f(x) = 75 is; 31

A) The general formula for equation of a line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Slope is;

m = (y₂ - y₁)/(x₂ - x₁)

m = (5 - 2)/(6 - 5)

m = 3

Let us test the first coordinate;

2 = 3(5) + b

2 = 15 + b

2 - 15 = b

-13 = b

so the equation is : y = 3x - 13

B) When x = 7, we have;

y = 3(7) - 13

y = 21 - 13

y = 8

Let us now test for when  f(x) = 2x + 13 to get;

f(x) = 2x + 13, when x = 7

f(7) = 2(7) + 13

f(7) = 14 + 13

f(7) = 27

the function has a greater value for f(x) = 2x + 13

C. f(x) = 2x + 13

when f(x) = 75

Thus;

75 = 2x + 13

75 - 13 = 2x

62 = 2x

62/2 = x

31 = x

Read more about Function Table at; https://brainly.com/question/3632175

#SPJ1