In how many ways can four people with different heights line up single-file so that exactly two people are taller than the person immediately behind them?

If the expression be [tex]$\frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}$[/tex] then the equivalent expression exists [tex]$\frac{\sqrt[3]{16 y^4}}{\sqrt[3]{x^6}}$$[/tex].

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.

Expression is a term used in mathematics to describe a grouping of numbers, variables, and operators that illustrates the value of something. A mathematical statement that has two expressions that are equal is known as an equation. A phrase fragment can be used as an expression to represent a single numerical value.

An expression in mathematics is a sentence made up of terms and operations. Terms may be variables with coefficients or constant (numeric) values. Addition, subtraction, multiplication, and division are all possible operations.

Let the given expression be [tex]$\frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}$$[/tex]

Apply radical rule: [tex]$\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}, \quad$[/tex] assuming [tex]$a \geq 0, b \geq 0$[/tex]

[tex]$$\begin{aligned}& \frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}=\sqrt[3]{\frac{32 x^3 y^6}{2 x^9 y^2}} \\& =\sqrt[3]{\frac{32 x^3 y^6}{2 x^9 y^2}}\end{aligned}$$[/tex]

simplifying the above equation, we get

[tex]$\frac{32 x^3 y^6}{2 x^9 y^2}: \frac{16 y^4}{x^6}$[/tex]

[tex]$=\sqrt[3]{\frac{16 y^4}{x^6}}$$[/tex]

Apply radical rule: [tex]$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}, \quad$[/tex] assuming [tex]$a \geq 0, b \geq 0$[/tex]

[tex]$=\frac{\sqrt[3]{16 y^4}}{\sqrt[3]{x^6}}$$[/tex]

Therefore, the correct answer is option c.

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Answer:

option c

Step-by-step explanation:

edge 2023

Answer:

4th option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (8, 4 )

m = [tex]\frac{4-6}{8-3}[/tex] = [tex]\frac{-2}{5}[/tex] = - [tex]\frac{2}{5}[/tex] , then

y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (8, 4 ) , then

4 = - [tex]\frac{2}{5}[/tex] (8) + c = - [tex]\frac{16}{5}[/tex] + c ( add [tex]\frac{16}{5}[/tex] to both sides )

[tex]\frac{20}{5}[/tex] + [tex]\frac{16}{5}[/tex] = c , that is

c = [tex]\frac{36}{5}[/tex]

y = - [tex]\frac{2}{5}[/tex] x + [tex]\frac{36}{5}[/tex] ← equation of line

Using the laws of exponents to simplify the expression, we have; 5 1/3

When the power of one or more terms of an expression is greater than 1, then the expression is in an exponential form. Thus some laws can be require to simplify an exponential expression.

In the given question,

2^7/ 2^5 + (4^5)^0 + 3^-1

Thus applying the division law of indices to the first term, we have;

2^7/ 2^5 = 2^(7 - 5)

              = 2^2

In the second term, anything to the power of zero is 1. So that;

(4^5)^0 = (1024)^0

            = 1

In the third term, applying the inverse law of indices. We have;

3^-1 = 1/ 3

Therefore,

2^7/ 2^5 + (4^5)^0 + 3^-1 = 2^2 + 1 + 1/3

                                        = 4 + 1 + 1/3

                                        = 5 + 1/3

                                        = 16/ 3

                                        = 5 1/3

The value of the expression is 5 1/3.

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The equation of the line is 6x-5y = 25.

What is equation of line?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept equation.

Here in the given graph the points are [tex](x_1,y_1)=(0,-5)[/tex] and [tex](x_2,y_2)=(5,1)[/tex]

Now using slope formula  m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = [tex]\frac{1-(-5)}{5-0}[/tex]

=> m =  [tex]\frac{1+5}{5} = \frac{6}{5}[/tex]

Now using equation formula [tex]y-y_1 = m(x-x_1)[/tex] then

=> [tex]y - (-5) = \frac{6}{5}(x-0)[/tex]

=> y+5 = [tex]\frac{6}{5}[/tex]x

=> 5y+25 = 6x

=> 6x-5y = 25.

Hence the equation of line is 6x-5y = 25.

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Answer: (-45 , -25)

Step-by-step explanation:

Please mark brainliest!!

The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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The values of x from the given figures are 3 √29 and 24 respectively.

What is triangle ?

Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.

Given

In the figure,

The two given triangles are similar ,

So, in the first figure it is given that they are similar ,

√29 / 5  = x / 15

x  = √29 * 15  / 5

x =√29 * 3

x = 3 √29

And in the second figure , here also they gave they are similar

so we get,

12 / 13  =  x /  26

x = 12 * 26 / 13

x = 12 * 2

x = 24

Hence, The values of x from the given figures are 3 √29 and 24 respectively.

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The area of the polygon is 24 unit².

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

We have four coordinates of vertices given, K(-3,3), L(3,3), M(3,-1), N(-3,-1).

So the polygon must be a quadrilateral.

Length of KL = [tex]\sqrt{(3--3)^{2} + (3-3)^2 }[/tex] = [tex]\sqrt{6^2}[/tex] = 6

Length of LM = [tex]\sqrt{(3-3)^2+(-1-3)^2}[/tex] = [tex]\sqrt{(-4)^2}[/tex] = 4

Length of MN =[tex]\sqrt{(-3-3)^2+(-1--1)^2}[/tex] = [tex]\sqrt{(-6)^2}[/tex] = 6

Length of NK = [tex]\sqrt{(-3--3)^2+(3--1)^2}[/tex] = [tex]\sqrt{4^2}[/tex] = 4

So we get that, opposite sides are having equal length.

So the polygon must be a rectangle.

Area of the rectangle = Length × Width

                                    = 6 × 4

                                    = 24 units²

Hence the area of the polygon with the given vertices is 24 unit².

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The total monthly premium for all her insurance is 6249 .

What is percentage ?

Percentage can be defined as the product of ratio of given value , total value and hundred.

Given ,

Donna Wagner is a self-employed musician. She pays 100 percent of the PPO insurance premium of 5,824 annually.

She also has a dental plan that costs 600 annually and a vision plan that costs 365 annually.

The total monthly premium for all her insurance = 5284+600+365

= 6249.

So, The total total monthly premium for all her insurance is 6249 .

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Answer:

A

Step-by-step explanation:

Any equation with a single independant variable (often an 'X') that is not ( x2,x3 ) is linear.

Height is an example of a variable that uses the ratio scale.

Hence, option (a) is the correct choice.

Weight, height, and distance are all ratio variables. The ratio scale allows you to add, subtract, divide, and multiply data. Ratio scales are further distinguished from interval scales by the presence of a 'true zero'.

Height is an excellent example of a measuring scale based on a ratio. It is not nominal or ordinal since each change in the height unit (inches, metres, feet, etc.) has a standard distance between them, and it is not interval because height has a genuine zero.

Height, for example, is ratio data. There is no such thing as negative height. If the height of an item is 0, there is no object. This is not the same as talking about temperature.

The complete question should be:

Height is an example of a variable that uses the scale.

a. ratio b. interval c. nominal d. ordinal

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Answer:

Triangle ABC is being enlarged using a scale factor of 2 and the origin as the center to give triangle A'B'C'. To find the coordinates of A' and B', we will have to multiply each of the x and y coordinates of A and B by the scale factor of 2.

The coordinates of A are (-5, -6) and the coordinates of B are (2, 3)

The coordinates of A' will be (-52, -62) = (-10, -12)

The coordinates of B' will be (22, 32) = (4, 6)

So the coordinates of A' are (-10, -12) and the coordinates of B' are (4, 6).

The difference after the subtraction is: 2a³ +  10a² - 5a - 4

A polynomial is an expression which has one or more of its variables with a power of at least 2 degrees. It can be expressed in form of a term.

Therefore, a polynomial equation is a means of expressing an expression with terms and on variable with a degree of 2 or more.

To find the difference by subtracting the polynomials, we have:

4a³ + 6a² - 11a - 3 - (2a³ - 4a² - 6a + 1) = 4a³ + 6a² - 11a - 3 - 2a³ + 4a² + 6a - 1

collecting like terms,

4a³ - 2a³ +  6a² + 4a²  - 11a + 6a - 3 - 1 = 2a³ +  10a² - 5a - 4

Therefore, the difference by subtracting the two polynomials is:

2a³ +  10a² - 5a - 4

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Meters and seconds are the two units of measurement required to describe speed.

A ball freely falling at 20 m/s will in the next second have a speed of 30 m/s.This is because the speed of a freely falling item rises by 9.8 m/s per second owing to gravity's acceleration. The ball begins at a speed of 20 m/s and adds 9.8 m/s to its initial speed after one second, ending in a final speed of 20 + 9.8 = 29.8 m/s (approx. 30 m/s).

Meters and seconds are the two units of measurement required to describe speed. These units are used to calculate the distance travelled by an item as well as the time it takes to traverse that distance. In this scenario, the ball's speed is measured in metres per second (m/s), which is the distance the ball travels in one second.

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Answer:

450 cupcakes

Step-by-step explanation:

Let x be the number of cupcakes sold for John's total pay to be the same for both companies

For the first company

Salary = $800/week

Commission is $0.30 per cupcake

For sales of x cupcakes, total commission = 0.30x

Total pay = Weekly salary + Total commission from sales

Total Pay = 800+ 0.3x

For the second company
Salary = 350 /week

Commission: $1.30 per cupcake

For sales of x cupcakes, total commission = 1.30x

Total Pay = Weekly salary + Total commission from sales

Total Pay = 350 + 1.3x

If both pay must be he same,
800 + 0.3x = 350 + 1.3x

800-350 = 1.3x - 0.3x

450 = 1x

x = 450 cupcakes ANSWER

Answer: 450

Step-by-step explanation:

    If we let x and y represent the number of cupcakes John sells and his total weekly income, respectively, we get the following system of equations.

=0.35x+845

=1.4x+372.5

​

Since both equations are solved for y​, any substitution for y​ will result in the following

211.4 x+372.5&=0.35

x+845

1.4x+372.5

​

=0.35x+845

​

Solving for x will give us the number of cupcakes John needs to sell weekly for each paycheck to be the same. Doing so, we get

1.4 x+372.5&=0.35     x+845

1.05 x&=472.5x=450

1.4x+372.5

1.05x

x

=0.35x+845

=472.5

=450

Therefore, John needs to sell 450450​ cupcakes each week for both salaries to be the same.

The rate of change for the Carol with respect to time is 3/16 miles per minute.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line.

Given The table shows the distance Carol traveled after various numbers of minutes,

Input        Output

 2            1/6

 3          17/48

 4          13/24

 5          35/48

 6          11/12

Here, the output values from 1/6 to 11/12 indicate the distance in miles whereas the input values from 2 to 6 describe the time in minutes.

by utilizing the first two sets of input-output numbers, calculating the rate of change

Relative change = change in distance/change in time

(17/48 - 1/6)/(3-2) = (17/48 - 8/48) /1 = 9/48 = 3/16 miles per minute

Hence the rate of change is 3/16 miles per minute.

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The minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.

Domain of Y = -x³ + 2: A = {-2, -1, 0, 1, 2}. The equation is defined for all x in the set A.

Range of Y = -x³ + 2: To find the range, we need to find the minimum and maximum values of Y for x in the set A. Using the formula Y = -x³ + 2, we can substitute the values of x from the set A and find the corresponding values of Y:

x = -2, Y = -(-8) + 2 = 10

x = -1, Y = -(-1) + 2 = 3

x = 0, Y = -(0) + 2 = 2

x = 1, Y = -(1) + 2 = 1

x = 2, Y = -(8) + 2 = -6

Thus, the minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.

Relation Y = -x³ + 2 is a function: A relation is a function if every input x in the domain corresponds to only one output Y in the range. To check if the relation is a function, we need to ensure that no two different inputs in the domain result in the same output.

For this relation, every input x in the domain results in only one unique output Y, so the relation is a function.

Function Notation: If the relation is a function, we can write it in function notation as: f(x) = -x³ + 2, where f is the function name and x is the input.

Evaluating f(-5), f(0) and f(1):

f(-5) = -(-125) + 2 = 127

f(0) = -(0) + 2 = 2

f(1) = -(1) + 2 = 1

Thus, f(-5) = 127, f(0) = 2 and f(1) = 1.

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Total amount in Ruby's account after doing one time investment of $6200 for 12 years with rate of interest 4.3% is equal to $10,300 ( nearest hundreds dollars )

Principal 'P' amount in Ruby's account is equal to $6200

Rate of interest 'r' compounded continuously is 4.3%

Time 'N' = 12 years

Let 'A' be the final amount in Ruby's account after 12 years

Amount 'A' = P × ( 1 + (r/100) )ⁿ

Substitute the value in the formula we get,

⇒ A = 6200 × [ 1 + ( 4.3/100) ]¹²

⇒ A = 6200 × [ 1 + 0.043 ]¹²

⇒ A = 6200 × [ 1.043 ]¹²

⇒ A = $10,275.5

⇒ A = $10,300 ( nearest hundreds dollars )

Therefore , the total money in Ruby's account after depositing $6200 with rate of interest 4.3% compounded continuously for 12 years is equal to

$10,300 ( nearest hundreds dollars ).

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Answer:

370.1 [tex]units^{2}[/tex]

Step-by-step explanation:

Square

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

a = [tex]12^{2}[/tex] = 144

Semi - Circle:

a = 1/2([tex]\pi r^{2}[/tex])

a = 1/2(3.14)(36)     The radius is 1/2 the diameter of 12 (6) [tex]6^{2}[/tex] = 36

a = 1/2(113.04)

a = 56.52

144 + 4(56.52)

144 + 226.08

370.08  rounded to the nearest tenths place 370.1

Answer:

pls see attached

Step-by-step explanation:

Answer:ugy8f67

Step-by-step explanation: yessss

Answer:

equiangular triangle

Step-by-step explanation:

Answer:

462

Step-by-step explanation:

do 6x77 which is 462.       alternative forms: 4.62 x 10^2

The area for the given figure by using distributive property is 5y+35.

What is Area of rectangle?

Area of rectangle can be defined as the product of length and breadth .

From the Given figure,

We have to find the area of rectangle

so,

There is one small rectangle inside that,

So,

total area = area of small rectangle + area of larger rectangle

area = 5*y + 7*5

So by summing up the area of two rectangles

we get,

Total area = 5y+ 35

Therefore, The area for the given figure by using distributive property is 5y+35.

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The simplified form of the polynomial ( x + 6 )( x² - 3x - 4 ) is x³ + 3x² - 22x - 24

Given the polynomial in the question;

( x + 6 )( x² - 3x - 4 )

Apply distributive property.

x( x² - 3x - 4 ) + 6( x² - 3x - 4 )

x³ - 3x² - 4x + 6x² - 18x - 24

Collect like terms

x³ - 3x² + 6x² - 18x - 4x - 24

Add like terms

x³ - 3x² + 6x² - 18x - 4x - 24

Add -3x² and 6x²

x³ + 3x² - 18x - 4x - 24

Add -18x and -4x

x³ + 3x² - 22x - 24

Therefore, the simplified form is x³ + 3x² - 22x - 24.

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The amount of salt in the tank is decreasing exponentially with time.

At time t, the amount of salt in a tank containing oz of salt dissolved in gallons of water can be calculated using the following formula:

Salt in tank (oz) = 200 - 140e^(-t/25)

For example, at time t = 10 min, the amount of salt in the tank is 200 - 140e^(-10/25) = 200 - 140(0.7787) = 124.42 oz.

This calculation assumes that brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. Thus, the amount of salt in the tank is decreasing exponentially with time.

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Answer:

B

Step-by-step explanation:

Because all four packages of baseball cards added up together makes 76 cards, and since 6 is over 5 that makes it closer to 80.

Answer: 1st Package: 17 = 20

2nd Package: 21 = 20

3rd Package: 22 = 20

4th Package: 16 = 20

Total Amount of Cards: 20 + 20 + 20 + 20 = 80

I hope this helps! :)

Step-by-step explanation:

The angle ∠Y so that ∠Y ≅ ∠Z is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Construct ∠Y so that ∠Y ≅ ∠Z.

There are several ways to do this, some of them are:

The above statements are true because the base angles of an isosceles triangle are congruent and all angles in a rectangle/square are congruent

See attachment

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