Rewrite in simplest rational exponent form (square root of x times the fourth root of x). Show each step of your process.

The solutions to the simplification of the following surds are:[tex]-12\sqrt[3]{3}+4\sqrt[3]{2}[/tex] and [tex]-5x^2 y^2\sqrt[3]{3x^2y^2}[/tex]

A number without a root is simply referred to as a surd. These surds illustration comprises fractions as powers if presented in exponential form. There are three main forms of surds, according to the definition of surds.

The simplification of the given surds is carried out as follows:
[tex]-2\sqrt[3]{81} +2\sqrt[3]{16}-2\sqrt[3]{81}[/tex]

Factor 27 out of 81

[tex]-2\sqrt[3]{27*3} +2\sqrt[3]{16}-2\sqrt[3]{27*3}[/tex]

Rewrite it as 3³*3

[tex]-2\sqrt[3]{3^3*3} +2\sqrt[3]{16}-2\sqrt[3]{3^3*3}[/tex]

Rearrange and simplify

[tex]-2\sqrt[3]{3^3*3} -2\sqrt[3]{3^3*3}+2\sqrt[3]{16}[/tex]

Pull term out from the radical

[tex]-2*3\sqrt[3]{3} -2*3\sqrt[3]{3}+2\sqrt[3]{16}[/tex]

[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2\sqrt[3]{16}[/tex]

Rewrite 16 as 2³*2

[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2\sqrt[3]{2^3*2}[/tex]

Pull term out of the radical

[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2*2\sqrt[3]{2}[/tex]

[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+4\sqrt[3]{2}[/tex]

Simplify altogether;

[tex]-12\sqrt[3]{3}+4\sqrt[3]{2}[/tex]

In [tex]\sqrt[3]{-375x^8y^8}[/tex]; simplify the radical by breaking the radicand up into a product of known factors, assuming real numbers.

[tex]\sqrt[3]{(-5) ^3(x^2)^3 (y^2)^3*3x^2y^2}[/tex]

[tex]\sqrt[3]{(-5x^2y^2) ^3*3(x^2y^2)}[/tex]

[tex]-5x^2 y^2\sqrt[3]{3x^2y^2}[/tex]

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Answer:

41.  (-∞, -1] ∪ [2, 3)

42.  (2, 5) ∪ (5, ∞)

Step-by-step explanation:

Given rational inequality:

[tex]\dfrac{x^2-x-2}{x-3} \leq 0[/tex]

Factor the numerator:

[tex]\dfrac{(x-2)(x+1)}{x-3} \leq 0[/tex]

Find the roots by solving f(x) = 0  (set the numerator to zero):

[tex]\implies (x-2)(x+1)=0[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

[tex]\implies x+1=0 \implies x=-1[/tex]

Find the restrictions by solving f(x) = undefined  (set the denominator to zero):

[tex]\implies x-3=0 \implies x=3[/tex]

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attachment 1).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

For each test value, determine if the function is positive or negative:

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

[tex]f(0)=\dfrac{(0)^2-(0)-2}{(0)-3} =\dfrac{-}{-}=+[/tex]

[tex]f(2.5)=\dfrac{(2.5)^2-(2.5)-2}{(2.5)-3} =\dfrac{+}{-}=-[/tex]

[tex]f(4)=\dfrac{(4)^2-(4)-2}{(4)-3} =\dfrac{+}{+}=+[/tex]

Record the results on the sign chart for each region (see attachment 1).

As we need to find the values for which f(x) ≤ 0, shade the appropriate regions (zero or negative) on the sign chart (see attached).

Therefore, the solution set is:

As interval notation:

Given rational inequality:

[tex]\dfrac{\sqrt{x}}{(x-2)|x-5|} > 0[/tex]

Find the roots by solving f(x) = 0  (set the numerator to zero):

[tex]\implies \sqrt{x}=0 \implies x=0[/tex]

Find the restrictions by solving f(x) = undefined  (set the denominator to zero):

[tex]\implies (x-2)|x-5|=0[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

[tex]\implies |x-5|=0 \implies x=5[/tex]

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attachment 1).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

For each test value, determine if the function is positive or negative:

[tex]f(-1)=\dfrac{\sqrt{-1}}{(-1-2)|-1-5|}=\dfrac{\sf unde\:\!fined}{-}=\sf unde\:\!fined[/tex]

[tex]f(1)=\dfrac{\sqrt{1}}{(1-2)|1-5|}=\dfrac{+}{-}=-[/tex]

[tex]f(3)=\dfrac{\sqrt{3}}{(3-2)|3-5|}=\dfrac{+}{+}=+[/tex]

[tex]f(6)=\dfrac{\sqrt{6}}{(6-2)|6-5|}=\dfrac{+}{+}=+[/tex]

Record the results on the sign chart for each region (see attachment 2).

As we need to find the values for which f(x) > 0, shade the appropriate regions (positive) on the sign chart (see attached).

Therefore, the solution set is:

As interval notation:

The two points on the line y = − 54x − 3 will be (1, −57) and (−1, 51).

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

y = − 56x − 4

Let x = 1, the value of y will be

y = − 54 (1) − 3

y = − 54 − 3

y = − 57

Let x = − 1, the value of y will be

y = − 54(−1) − 3

y = 54 − 3

y = 51

The two points on the line y = − 56x − 4 will be (1, −57) and (−1, 51). Then the diagram of the line is given below.

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The client should invest $8889 in AAA bonds, $4444 in A bonds, and $5667 in B bonds.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x + 4 = 8 is an equation.

We have,

Amount invested in AAA bond = 2x

Amount invested in A bond = y

Amount invested in B bond = x

Now,

Average yield:

AAA bond = 4%

A bond = 5%

B bond = 8%

Now,

Total amount = $19,000

Total yield = $990

Now,

Two equations can be made:

2x + y + x = 19000

3x + y = 19000 _____(1)

0.04 x (2x) + 0.05 x y + 0.08x = 990

0.08x + 0.05y + 0.08x = 990

0.16x + 0.05y = 990 ______(2)

From (1) and (2),

3x = 19000 - y

x = (19000 - y)/3

Substituting in (2)

0.16 x (19000 - y)/3 + 0.05y = 990

0.053 x 19000 - 0.053y + 0.05y = 990

1007 - 0.003y = 990

1007 - 990 = 0.003y

y = 17/0.003

y = 5666.6

y = 5667

Now,

x = (19000 - y)/3

x = (19000 - 5667)/3

x = 4444.333

x = 4444

Now,

x = $4444

y = $5667

2x = $8889

Thus,

Amount invested in AAA bond = $8889

Amount invested in A bond = $5667

Amount invested in B bond = $4444

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Answer: 4x + 4y - 8

Step-by-step explanation:

4(x−2+y)

4x -8 +4y

4x + 4y - 8

According to the information there are 76 numbers in the sequence between 10 and 238.

To calculate how many  terms there are in the sequence we have to perform the following mathematical operation:

According to the above, there are 76 numbers in the sequence between 10 and 238. Also, we can prove this calculating each number:

10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100...

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To model the division of -24 by -4 on a number line, we can start at -24 and move to the left by -4 units at a time, counting the number of times we move until we reach 0.

A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that each real number and each point on a number line correspond to one another.

Since -24 divided by -4 is 6, we would move to the left 6 times and end at 0 on the number line. The negative signs of the dividend and divisor indicate that the quotient will be a negative number.

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The cost for the flooring of the rectangular room is $864.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Dimension of each time = 1 foot

Length of the room = 18 feet

Width of the room = 12 feet

Number of tiles needed for the room = 18 × 12 = 216

Cost of one tile = $4

Total cost for the tile = 216 × $4 = $864

Hence the total cost for the tiles is $864.

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As per the elimination method, in order to solve a system of equations when multiplication is necessary to eliminate a variable.

The term equation is known as algebra is a statement of equality that contains one or more unknown quantities or variables.

Here we have given that When using the multiplication method, it is important to multiply all the terms on both sides of the equation, then here we do not just the one term you are trying to eliminate.

According to the rule of elimination method we all know while solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation.

So in order to multiplying to solve linear systems is to find a number to multiply to one or both of the equations so that the x or y terms in one of the equations will have opposite coefficients from the x or y in the other equation.

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Bar models can be used to represent the quotient and the product of numbers or expressions that are; y = x + 2 and x = m/4

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the expression as;

y - 2

LEt the expression Represent  y - 2 with x.

y - 2 = x

Add 2 on both sides we get;

y = x + 2

Similalry,

Represent the 4x with m.

4x = m

Divide by 4 on both sides we get;

x = m/4

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.56\%\to \frac{2.56}{100}\dotfill &0.0256\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000[1+(0.0256)(4)] \implies A=3000(1.1024)\implies A = 3307.2[/tex]

Only setup A places the mouse on the bottom right square and the cat there.

The pattern is continued, so we have to define where the cat and mouse would be after the 247th move.

Divide the issue into two parts: the location of the mouse and the location of the cat after the 247th move.

Every cycle, which consists of four different positions for the cat, is repeated once every four movements. When 247 is divided by 4, the remainder is 3. This matches the bottom right corner, where the cat is located after the third move.

Similar to the mouse, which repeats every eight moves, the mouse has eight possible places in a single cycle. When 247 is divided by 8, the remainder is 7. This matches the rat's bottom left corner position after the seventh motion.

The only configuration with the cat in the bottom right square and the mouse in that position is A.

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The complete question is given below:

The force with respect to the x and y axes can be calculated as follows:

F_x = 100N cos(30) = 86.6N

F_y = 100N sin(60) = 50N

Let F be the magnitude of the force, (theta) be the angle between the force and the x-axis, and (gamma) be the angle between the force and the y-axis. The components of the force with respect to the x and y axes can be calculated using the following formulas:

F_x = F cos(theta)

F_y = F sin(gamma)

For example, if the magnitude of the force is 100N and (theta) = 30 degrees and (gamma) = 60 degrees, then the components of the force with respect to the x and y axes can be calculated as follows:

F_x = 100N cos(30) = 86.6N

F_y = 100N sin(60) = 50N

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The inequality for the number of lawns he needs to mow is: $50 < $20 + $5n

The correct answer is an option (b)

Let n represents the number of lawns he needs to mow.

Here, Billy needs to make more than $50 between his allowance and the lawns that he mows. This means that an inequality should include 50 <

As Billy will make $5  for each lawn that he mows, for 'n' number of lawns the cost would be = 5n

Based on the mentioned conditions we formulate an inequality,

50 < 20 + 5n

20 + 5n > 50

20 + 5n - 20 > 50 - 20             ...........(subtract 20 from each side)

5n/5 > 30/5                      .............(divide each side by 5)

n > 6

This means, he needs to mow more that 6 lawns.

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The complete question is:

Billy makes $20 a week in allowance plus $5 for each lawn that he mows. this week billy wants to make over $50. select the inequality for the number of lawns he needs to mow.

a) $50 < $20+$5

b) $50 > $20+$5n

c) $50 < $20n+$5

d) $50 > $20n+$5

e) $50 < $20+$5n

The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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An equation is said to be linear if each term has a maximum of one degree.The system of linear equations is solved by (2,6).

An equation is said to be linear if each term has a maximum of one degree.

It is possible to formulate linear equations in the form y=mx+c.

A straight line results from a linear equation with two variables when its axes are plotted on the cartesian plane.

When the second equation for x is solved,

x + 5y = 32

x = 32 - 5y

Add the value of x to the first equation now,

2(32 - 5y) + 5y = 34

64 - 10y + 5y = 34

-5y = -30

y = 6

the value of y should be replaced in any one of the equations,

x + 5y = 32

x + 5(6) = 32

x = 2

Consequently, the system of linear equations' solution is (2,6).

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The standard deviation, in dollars, of the probability distribution of p is √(1.50 × 3.6) dollars.

We are given the following parameters -

Expected value = 2.6

Variance = 3.6

Price per doughnut = $1.50

Now we can write the price for the variance of the distribution as -

Price per doughnut × Variance

Variance = $1.50 × 3.6

The formula for the standard deviation of the distribution D in relation to the variance is given by -

Standard deviation = √variance

Standard deviation = √(1.50 × 3.6)

Therefore, the standard deviation of P in dollars will be √(1.50 × 3.6).

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11.69 is the exact length needed for the mid-segment of the trapezoid with STUV vertices.

The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.

We have,

vertices S(-2,4) ,T(-2,-4) ,U(3,-2) ,V(13,10).

Half of the lengths of the two parallel sides, ST and UV, make up the length of the trapezoid's middle section.

The trapezoid's vertices are S(2, 4), T(2, 4), U(3, 2), and V. (13, 10).

The distance formula is then used to calculate the length of the ST and UV sides;

Length = [tex]\sqrt{x_{2}-x_{1}+y_{2}-y_{1}}[/tex]

Side ST's length is S(-2, 4), T(-2, -4).

ST = [tex]\sqrt{x_{2}-x_{1}+y_{2}-y_{1}}[/tex]

ST = [tex]\sqrt{(-2-(-2))^2+(-4-(4))^2[/tex]

ST = [tex]\sqrt{0 + 64}[/tex]

ST √64

ST = 8

Side UV's length is U(3, 2), V. (13, 10).

UV = [tex]\sqrt{(13-3)^2+(10-(-2))^2[/tex]

UV = [tex]\sqrt{(10)^2+(12)^2[/tex]

UV = √244

UV = 15.62

Therefore,

The mid-segment STUV's length is,

Length of mid-segment = (ST + UV)/2

Length of mid-segment = (8 + 15.62)/2

Length of mid-segment = (23.62)/2

Length of mid-segment = 11.81

Therefore, 11.69 is the exact length needed for the mid-segment of the trapezoid with STUV vertices.

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The cost of the flowers she bought for her mum alone would be = $18

The items purchased by Emma = flowers and a gift certificate.

The total cost of the flowers and a gift certificate = $68

But, cost of gift certificate= $14 +2x

cost of flower = X

That is 14 + 2x + X = 68

2x + X = 68 - 14

3X = 54

X = 54/3

X= $18

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Answer: B - 11

Step-by-step explanation:  Hello! How you can do this is by substituting A, B, C, and D for x.

D:

4(16)<45
64<45

64 is not less than 45, so this is false.  D is not the answer.

C:
4(13.5)<45
54<45

54 is not less than 45, so this is false.  C is not the answer.

A:
4(12)<45
48<45

48 is not less than 45, so this is false.  A is not the answer.

B:
4(11)<45
44<45

44 is less than 45 so this is true.

The answer is B - 11.

The types of solutes and their distribution between the ICF and ECF are not the same for the appropriate solute amounts to the ECF and ICF columns.

Intracellular fluids are fluids found inside the cell's cytoplasm while extracellular fluid are fluids the flow outside the cells which consist of plasma, interstitial and trancellular fluid

The types of solutes and their distribution between the ICF and ECF are not the same because intracellular fluid of the cystosol is composed of water, dissolved ions, small molecules, and large, water-soluble molecules while extracellular fluid consist of plasma, interstitial fluid and cytosol have high potassium concentration and low sodium Concentration.

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The total length of A+C will be 172 cm(unit).

What is a unit?

Units are the tools to measure and compare different things. Comparison becomes easy when all the units for the measurement are the same.  Different units can be classified depending on their use. A few of the units can be classified as:

The seven SI base units (The International System of Units (SI), commonly known as the metric system, is the international standard for measurement) which are comprised of:

Length - meter (m)

Time - second (s)

Amount of substance - mole (mole)

Electric current - ampere (A)

Temperature - kelvin (K)

Luminous intensity - candela (cd)

Mass - kilogram (kg)

Now,

Given B-A=120   -->1

B-C=84              -->2

A+B+C=360      -->3

Therefore, from equations 1,2 and 3

B-120+B+B-84=360

B=188

By putting B=188 in 1 and 2

A=68

C=104

A+C=172cm

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Answer:

5$ Per Lawn

Step-by-step explanation:

10$/2=5$

2/2=1

MARK ME BRAINLISIST

Answer: the rate she is earning is 5$ per lawn mowed

Step-by-step explanation:

if she earns 10$ after mowing 2 lawns then if you divide 10 and 2 you get 5

Please make me brainllest

ΔABD and ΔBCD are congruent by AAS congruence theorem.

The proof is given below.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure below,

ΔABD and ΔBCD are congruent.

∠BCD = ∠BAD [ 90 degrees ]

∠CDB = ∠ABD [ alternate angles ]

BD = BD [ Common ]

ΔABD ≈ ΔBCD [ AAS ]

Thus,

ΔABD and ΔBCD are congruent by AAS congruence theorem.

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Answer:

480

Step-by-step explanation:

Lets break this down to make it even easier

(24x2)x10

=(48)x10

=480

Answer:

If you are looking for the simplest form of 24/20 it is basically 6/5.

because if you multiply 6/5 by 4/4 you could get the answer which is 24/20.

and the same thing if you divide

I hope that I helped

Answer:

Step-by-step explanation:

The answer is 42 MB.If it's round to nearest tenth than it's 40 MB

Answer:

-40F to 284F

Step-by-step explanation:

C = 5/9F -32

so F = 32+9/5*C

so the range is

F= 32+9/5*(-40) = 32-72 = -40F

F= 32+9/5*(140) = 32+252 = 284F

Answer:

x=-8

Brief explanation:

Well I simplify first

4x-(9-3x)=8x-1

4x-9+3x=8x-1

then you do this operation called collecting similar terms

4x+3x-9=8x-1

7x-9=8x-1

7x-8x=-1+9

7x-8x=8

-x=8

--

Answer:

[tex] \sf \: x = - 8[/tex]

Step-by-step explanation:

Given equation,

→ 4x - (9 - 3x) = 8x - 1

Now the value of x will be,

→ 4x - (9 - 3x) = 8x - 1

→ 4x - 9 + 3x = 8x - 1

→ (4x + 3x) - 9 = 8x - 1

→ 7x - 9 = 8x - 1

→ 7x - 8x = -1 + 9

→ -x = 8

→ [ x = -8 ]

Hence, the value of x is -8.

De acuerdo con lo anterior, la respuesta correcta serían 270,000 es el precio más bajo que obtuvo para comprar un motor generador de ondas estacionarias para cuerdas en el primer almacén.

¿Cómo calcular cuál almacén le ofrece el precio más bajo a Juan?

Para calcular cuál es el almacén que le ofrece el precio más bajo a Juan debemos identificar a cuanto equivale el descuento y restarlo del precio total. Cuando sepamos el precio final comparamos para saber cuál de todos es el menor.

300,000 / 100 = 3,000

3,000 * 10 = 30,000

300,000 - 30,000 = 270,000

400,000 / 100 = 4,000

4,000 * 14 = 56,000

400,000 - 56,000 = 344,000

500,000 / 100 = 5,000

5,000 * 20 = 100,000

500,000 - 100,000 = 400,000

700,000 / 100 = 7,000

7,000 * 22 = 154,000

700,000 - 154,000 = 546,000

750,000 / 100 = 7,500

7,500 * 12 = 90,000

750,000 - 90,000 = 660,000

800,000 / 100 = 8,000

8,000 * 10 = 80,000

800,000 - 80,000 = 720,000

1'000.0000 / 100 = 10,000

10,000 * 6 = 60,000

1'000.000 - 60,000 = 940,000

1'200.000 / 100 = 12,000

12,000 * 4 = 48,000

1'200,000 - 48,000 = 1'152.000

1'500.000 / 100 = 15,000

15,000 * 2 = 30,000

1'500,000 - 30,000 = 1'270,000

De acuerdo a lo anterior, el precio más bajo para comprar un motor generador de ondas estacionarias para cuerdas es 270,000 en el primer almacén.

Nota: Esta pregunta está incompleta y tiene errores en los valores. A continuación esta la información completa y correcta.

Pregunta

¿Cuál tienda le ofrece el precio más bajo a Juan?

Precios

Almacén 1: 300 mil pesos con el 10% de descuento.

Almacén 2: 400 mil pesos con el 14% de descuento.

Almacén 3: 500 mil pero con el 20% de descuento.

Almacén 4: 700 mil pesos con el 22% de descuento.

Almacén 5: 750 mil pesos con el 12% de descuento.

Almacén 6: 800 mil pesos con el 10% de descuento.

Almacén 7: 1'000.000 de pesos con el 6% de descuento.

Almacén 8: 1'200.000 de pesos con el 4% de descuento.

Almacén 9: 1'500.000 de pesos con el 2% de descuento.

Aprenda más sobre descuentos en: https://brainly.com/question/24130820

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