Reflect the point ( 7, 1) on the line y=x.

We can approximate the values of y₁ and y₂ at each step within the specified range. The resulting solution will provide an approximation of the behavior of the system of ODEs over the given interval.

To solve the system of ODEs ý₁ = -y₁ + 0.999y₂ and ý₂ = -0.001y using Implicit Euler method, we start with the initial conditions y₁ = y₂ = 1 at x=0. We will consider three different step sizes: h=0.1, 1, and 5, and solve the system for 1≤x≤200.

Implicit Euler method approximates the values at the next step by using a backward difference approximation. It involves solving a system of equations iteratively. For each step, we update the values of y₁ and y₂ using the equations:

y₁ₙ₊₁ = y₁ₙ + h*(-y₁ₙ + 0.999*y₂ₙ₊₁)

y₂ₙ₊₁ = y₂ₙ + h*(-0.001*y₂ₙ₊₁)

Starting with the initial conditions, we apply the above equations repeatedly for each step, where n represents the current step and n+1 represents the next step. We continue this process until we reach the desired range of x values.

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Answer:

"certain"

Step-by-step explanation:

by definition, any event with a probably of 1 is defined as certain (i.e certain to happen)

by contract any even with a probably of 0 is defined as impossible (i.e impossible to happen)

Answer:

Step-by-step explanation:

1. (X=3, y=7)

Use the elimination method and multiply the top row by 3 to eliminate your x's.  

3x+24=177

-3x+10y=61

34y=238 ( y=7), plug 7 into the original equation x + 8 (7)=59 solve x+56=59. Subtract 56 from both sides and (x=3)

2. (x=-4, y=10)

Problem 2 you would use the substitution method

Step 1 = -4x-6=6x+34.

Step 2= Solve for X. 10x=-40 therefore, x=-4

Step 3. Once you have x plug it back in to any of the original equations and get Y

Step 4: y=-4 (-4) -6. Y=16-6, therefore y=-0

3. (x=-4, y=3)

Use the substitution method:

Step 1: Plug y=-3x-9 into 4x +4y=-4

Step 2: 4x+ 4(-3x-9)=-4

Step 3: 4x-12x-36=-4

Step 4: Combine like terms -8x-36=4, add 36 to the right side

Step 5: -8x=32. Therefore when you divide by -8 (x=-4)

Step 6: Plug x=-4 into y=-3x-9

y=-3 (-4)-9 y=12-9. Therefore (y=3)

Answer:

StartFraction 5 Over 136 EndFraction

Step-by-step explanation:

The total number of books in Nadia's bookshelf is 10 + 2 + 5 = 17.

To calculate the probability, we multiply the probability of picking up a reference book (2 out of 17) by the probability of picking up a nonfiction book (5 out of 16, since one reference book has already been picked).

Probability = (2/17) * (5/16) = 10/272 = 5/136

Therefore, the correct answer is StartFraction 5 Over 136 EndFraction.

i hope i helped!

Answer:

Step-by-step explanation:

my answer is  3 1/9 gallons

Given: a container with 3 1/2 gallons of weed killer can spray 2 1/4 lawns.

No. of gallons required to spray 2 lawns = x

So, first of all we should divide 3 1/2 with 2 1/4

now this division we should equalise with  x/3

(3 1/2 ÷ 2 1/4)  = x ÷ 2

after doing this we have got the value of x = 28/9  or 3 1/9

hence, 3 1/9 gallons is required to spray 2  lawns.

So . this question is related to capacity.

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Sexagesimal representation of 1; 12 15: To represent 1; 12 15 in sexagesimal, we consider the whole part and the fractional part separately.

(a) Representing 1364 in hieroglyphics:

Hieroglyphics do not have a direct representation for numbers as we use in our decimal system. However, we can approximate the number 1364 in hieroglyphics by combining the symbols for 1000 (which is represented by a lotus flower), 300 (which is represented by a coil of rope), 60 (which is represented by a tadpole), and 4 (which is represented by four vertical lines). These symbols would be combined to visually represent the number 1364 in hieroglyphics.

(b) Decimal representation of sexagesimal numbers:

In the sexagesimal system, which is based on multiples of 60, the numbers 2, 15, 0, 30, and 5 can be converted to decimal representation as follows:

2 in sexagesimal is equivalent to 2 in decimal.

15 in sexagesimal is equivalent to (1 × 60) + 15 in decimal, which is 75.

0 in sexagesimal is equivalent to 0 in decimal.

30 in sexagesimal is equivalent to 30 in decimal.

5 in sexagesimal is equivalent to 5 in decimal.

Therefore, the decimal representation of the sexagesimal numbers 2, 15, 0, 30, and 5 is 2, 75, 0, 30, and 5 respectively.

(c) Sexagesimal representation of 1; 12 15:

To represent 1; 12 15 in sexagesimal, we consider the whole part and the fractional part separately. The whole part, 1, remains the same. For the fractional part, we convert 12 and 15 to their decimal equivalents. 12 in decimal is (12/60) = 0.2, and 15 in decimal is (15/60) = 0.25. Therefore, the sexagesimal representation of 1; 12 15 would be 1.20.25.

(d) Expressing as the sum of distinct unit fractions:

To express a number as the sum of distinct unit fractions, we find fractions with a numerator of 1 and distinct denominators that add up to the desired number. For example, to express the number 1 as the sum of distinct unit fractions, we can use the Egyptian Fraction representation. One possible representation is 1 = 1/2 + 1/3 + 1/6, where each fraction has a distinct denominator. The denominators are chosen in a way that they don't repeat, and the sum of the fractions equals 1. The unit fractions 1/2, 1/3, and 1/6 have distinct denominators and add up to 1.

In general, expressing a number as the sum of distinct unit fractions can be done using various methods, such as the greedy algorithm or the harmonic series. These methods involve finding a sequence of unit fractions that converges to the desired number. Egyptian mathematicians extensively used such methods to represent numbers as the sum of unit fractions.

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Answer:

Mark me As Brainlist

Step-by-step explanation:

The mass of the salt grain is 0.0006 grams, which can be written in scientific notation as 6 x 10^-4 grams.

To compare the masses of the salt and sand grains, we need to express the mass of the sand grain in scientific notation as well.

The mass of the sand grain is 0.009 grams, which can be written in scientific notation as 9 x 10^-3 grams.

Comparing the two masses in scientific notation, we can see that:

6 x 10^-4 < 9 x 10^-3

Therefore, the sand grain is heavier than the salt grain

Answer:

Step 1. Move the decimal place to the right to create a new number between 1 and 10.This gives N=3.Step 2. Count the number of times you moved the decimal.You moved the decimal 8 places to the right.That means the exponent a=-8.Step 3. Write the number in scientific notation.0.000 000 03 g=3×10-8lg

Step-by-step explanation:

Answer: y+8=m(x+8)

Step-by-step explanation: because you follow the form y-y1=m(x-x1)

Answer:

Step-by-step explanation:

Find the unit rate of Sugar. Then find the cost of  2.5 Kg sugar

1 kg sugar =36 ÷ 4.5

                \(= \frac{36*10}{4.5*10}= \frac{360}{45}\\\\= 8\)

2.5 kg of sugar= 2.5 * 8 = 20.0 = R 20

Answer:

Kg Rupee

4.5 = 36

2.5 = ?

Therefore, 2.5*36/4.5

Therefore, 25*36*10/45*10

Therefore, 25*36/45

Therefore, 5*5*36/9*5

Therefore, 5*36/9

Therefore, 5*3*2*3*2/3*3

Therefore, 5*2*2

Therefore, 10*2

Therefore, 20

2.5 kg =20 Rupees

The Laplace transform of sin(πt) can be found using the table of Laplace transforms, which is  π / (s²+ π²).

Applying these transformations to the differential equation y'' - 4y = sin(πt), we get the following equation in terms of the Laplace transform Y(s):

s²Y(s) - s(0) - (0) - 4Y(s) = π / (s²+ π²).

Simplifying this equation, we have:

(s² - 4)Y(s) = π / (s ²+ π²).

Now, we can solve for Y(s):

Y(s) = π / [(s² - 4)(s² + π²)].

To find y(t), we need to take the inverse Laplace transform of Y(s). However, the given equation is missing the initial conditions y(0) and y'(0). Without these initial conditions, we cannot determine the complete solution for y(t) and hence cannot provide a specific answer.

In summary, the Laplace transform of the given initial value problem is Y(s) = π / [(s² - 4)(s² + π²)], but the solution for y(t) cannot be determined without the initial conditions y(0) and y'(0).

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Answer:

Step-by-step explanation:

To start off we can subtract 27 from both sides

That gives us : 4(25-3y) = 23

We can then divide both sides by 4

That gives us: 25-3y = 23/4 (or 5.75)

We can then add 3y to both sides, and subtract 5.75

That gives us: 3y = 19.25

We can then divide 19.25 by 3

That gives us: 6.4

Using what you gave, that should be the correct answer? If there was an x-variable to substitute you did not include that.

Answer:

0

Step-by-step explanation:

If you replace y with 0 (which you do since you are given y = 0 and you are trying to find x from the (_,0) point), you get \(2x = 5x\). The only way for x to satisfy this is x = 0.

Step-by-step explanation:

Use one of them to solve for x the plug in to get the number for all of them, subtract from360 then there's your answer

Answer:

\( \cos(75 \degree) = \cos(45 \degree + 30\degree) \\ \\ = \cos(45\degree) \cos(30\degree) - \sin(45\degree) \sin(30\degree) \\ \\ = ( \frac{1}{ \sqrt{2} } ).( \frac{ \sqrt{3} }{2} ) - ( \frac{1}{ \sqrt{2} } ).( \frac{1}{2} ) \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } - \frac{1}{2 \sqrt{2} } \\ \\ = \frac{ \sqrt{3} - 1}{2 \sqrt{2} } \\ \\ = \frac{0.73205}{2.828427} \\ \\ = 0.2588\)

You can use the cosine addition formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find the exact value of cos(75°) and the exact value of cos(75°) is (√3 - 1)/(2√2).

The cosine addition formula states that cos(A + B) = cos(A)cos(B) - sin(A)sin(B).

In this case, we can rewrite 75° as 30° + 45°.

So, we have cos(75°) = cos(30° + 45°).

Using the cosine addition formula, cos(30° + 45°) = cos(30°)cos(45°) - sin(30°)sin(45°).

Now, we know the exact values of cos(30°) =  √3/2 and sin(30°) = 1/2 from the unit circle.

To find the exact value of cos(45°), we can use the fact that it is equal to sin(45°) because both angles are present in the same right-angled isosceles triangle.

Therefore, cos(45°) = sin(45°) = 1/√2.

Substituting these values;

(75°) = (√3/2)(1/√2) - (1/2)(1/√2)

Simplifying;

cos(75°) = (√3/2√2) - (1/2√2).

cos(75°) = (√3 - 1)/(2√2).

So, the exact value of cos(75°) is (√3 - 1)/(2√2).

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You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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The change in the amount of liquid in the vat after 1/2 minutes is 91/40 gallons .

In the question ,

it is given that

in 1 minute the amount of water that is allowed to enter the vat = \(40\frac{1}{5}\) gallons = (40*5 +1)/5 = 201/5 gallons

and

in 1 minute the amount of water that is allowed to leave the vat = \(44\frac{3}{4}\) gallons = (44*4 + 3)/4 = 179/4 galloons

so , the change in 1 minute can be written by the formula

change in 1 minute in the amount of liquid = (amount of water leave in 1 minute) - ( amount of water enter in 1 minute)

on substituting the values,

we get

change in 1 minute in the amount of liquid = 179/4 - 201/5

taking LCM as 20 and solving further ,

we get

= 895/ 20 - 804/20

= 91/20

So , in 1/2 minute the change in amount of liquid will be = 91/40 gallons

Therefore , The change in the amount of liquid in the vat after 1/2 minutes is 91/40 gallons .

The given question  is incomplete , the complete question is

A large vat has a faucet to allow liquid to enter the vat and a drain to allow liquid to leave the vat. each minute, the faucet allows \(40\frac{1}{5}\) gallons of liquid to enter the vat, and the drain allows \(44\frac{3}{4}\) gallons to leave the vat. what is the change in the amount of liquid in the vat after 1/2 minutes?

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Answer:

2,323. 13 dollars

Answer:

f (g (pi / 2)) = 0

Step-by-step explanation:

We have the following functions:

f (x) = sin x

g (x) = cos x

The first thing we must do in this case is the composition of functions:

f (g (x))

By making the composition we have:

f (g (x)) = sin (cos x)

We evaluate for x = pi / 2:

f (g (pi / 2)) = sin (cos (pi / 2))

f (g (pi / 2)) = sin (0)

f (g (pi / 2)) = 0

Answer:

y = 4x

Step-by-step explanation:

2(3y + 6x) = 2(5y - 2x)

Divide both sides by 2.

3y + 6x = 5y - 2x

Subtract 5y from both sides. Add 2x to both sides.

-2y = -8x

Divide both sides by -2.

y = 4x

Answer: We can find this by finding how many odd numbers are in one row since each row is numbered 1 to 11 so by counting we find:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...

That there are exactly 6 odd numbers in one row, So 6 time's how many rows there are will equal our product, which equals our answer.

The coordinates of the centroid for the region bounded by the curves y = x, y = 1/x, y = 0, and x = 2 are (1, ln(2)).

To find the centroid of a region, we need to determine the x-coordinate and y-coordinate of the centroid separately.

The x-coordinate of the centroid (bar x) can be found using the formula:

bar x = (1/A) ∫[a to b] x*f(x) dx,

where A is the area of the region and f(x) represents the function that defines the boundary of the region.

In this case, the region is bounded by the curves y = x, y = 1/x, y = 0, and x = 2. To find the x-coordinate of the centroid, we need to calculate the integral ∫[a to b] x*f(x) dx.

Since the curves y = x and y = 1/x intersect at x = 1, we can set up the integral as follows:

¯x = (1/A) ∫[1 to 2] x*(x - 1/x) dx,

where A is the area of the region bounded by the curves.

Simplifying the integral, we have:

¯x = (1/A) ∫[1 to 2] (x^2 - 1) dx.

Integrating, we get:

¯x = (1/A) [(1/3)x^3 - x] evaluated from 1 to 2.

Evaluating this expression, we find ¯x = (1/A) [(8/3) - 2/3] = (6/A).

To find the y-coordinate of the centroid (¯y), we can use a similar formula:

¯y = (1/A) ∫[a to b] (1/2)*[f(x)]^2 dx.

In this case, the integral becomes:

¯y = (1/A) ∫[1 to 2] (1/2)*[x - (1/x)]^2 dx.

Simplifying the integral, we have:

¯y = (1/A) ∫[1 to 2] (1/2)*[(x^2 - 2 + 1/x^2)] dx.

Integrating, we get:

¯y = (1/A) [(1/6)x^3 - 2x + (1/2)x^(-1)] evaluated from 1 to 2.

Evaluating this expression, we find ¯y = (1/A) [2/3 - 4 + 1/4] = (3/A).

Therefore, the coordinates of the centroid (¯x, ¯y) for the given region are (6/A, 3/A).

To find the exact coordinates, we need to calculate the area A of the region.

The region is bounded by the curves y = x, y = 1/x, y = 0, and x = 2.

To find the area A, we need to calculate the definite integral of the difference between the two curves.

A = ∫[1 to 2] (x - 1/x) dx.

Simplifying the integral, we have:

A = ∫[1 to 2] (x^2 - 1) / x dx.

Integrating, we get:

A = ∫[1 to 2] (x - 1) dx = [(1/2)x^2 - x] evaluated from 1 to 2 = (3/2).

Therefore, the area of the region is A = 3/2.

Substituting this value into the coordinates of the centroid, we have:

¯x = 6/(3/2) = 4,

¯y = 3/(3/2) = 2.

Hence, the exact coordinates of the centroid for the region bounded by the curves y = x, y = 1/x, y = 0, and x = 2 are (4, 2).

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Answer:

Step-by-step explanation:

15x+5y=8-3x

18x+5y=8⇒eqn 1

15x+5y=20y

15x-15y=0⇒eqn 2

eqn 1 * 3

 54x + 15y=24⇒eqn 3

eqn 3 + eqn 2

69x=24

x=24/69=0.3478

eqn  1⇒

    5y=8-18(24/69)

     y=1.7391/5

     y=0.3478

The solution to the system of equations is (10/3, -2).

Two or more expressions with an equal sign are defined as an equation.

The given equations are 15x + 5y = 20 and y = 8-3x.

15x + 15y = 20

Substitute y = 8-3x into the above equation:

15x + 15(8-3x) = 20

15x + 120 - 45x = 20

45x - 15x = 120 - 20

30x = 100

x = 10/3

Substitute x = 10/3 in y = 8 - 3x:

y = 8 - 3 (10/3)

y = 8 - 10

y = -2

Hence, the solution to the system of equations is (10/3, -2).

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Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.

The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.

P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.

There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.

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1) For the polynomial \(P(x) = x^4 + 4x^2\):

The zeros of \(P\) are \(x = 0\) (with multiplicity 2) and \(x = \pm 2i\) (complex zeros). The polynomial can be factored as \(P(x) = x^2(x^2 + 4)\).

To find the zeros of \(P(x)\), we set \(P(x)\) equal to zero and solve for \(x\):

\[x^4 + 4x^2 = 0.\]

We can factor out a common term of \(x^2\) from both terms:

\[x^2(x^2 + 4) = 0.\]

Using the zero product property, we set each factor equal to zero:

\[x^2 = 0 \quad \text{and} \quad x^2 + 4 = 0.\]

For the first equation, \(x^2 = 0\), we find \(x = 0\) with multiplicity 2. For the second equation, \(x^2 + 4 = 0\), we subtract 4 from both sides and take the square root:

\[x^2 = -4 \quad \Rightarrow \quad x = \pm 2i.\]

Therefore, the zeros of \(P(x) = x^4 + 4x^2\) are \(x = 0\) (with multiplicity 2) and \(x = \pm 2i\). The polynomial can be factored as \(P(x) = x^2(x^2 + 4)\).

2) For the polynomial \(P(x) = x^3 - 2x^2 + 2x\):

The zeros of \(P\) are \(x = 0\) (with multiplicity 1) and \(x = \pm 1\) (real zeros). The polynomial can be factored as \(P(x) = x(x-1)(x+1)\).

To find the zeros of \(P(x)\), we set \(P(x)\) equal to zero and solve for \(x\):

\[x^3 - 2x^2 + 2x = 0.\]

We can factor out a common term of \(x\) from each term:

\[x(x^2 - 2x + 2) = 0.\]

Using the zero product property, we set each factor equal to zero:

\[x = 0, \quad x^2 - 2x + 2 = 0.\]

The quadratic equation \(x^2 - 2x + 2 = 0\) does not have real solutions, as its discriminant (\(-2^2 - 4(1)(2) = -4\)) is negative. Therefore, there are no additional real zeros.

Therefore, the zeros of \(P(x) = x^3 - 2x^2 + 2x\) are \(x = 0\) (with multiplicity 1) and \(x = \pm 1\). The polynomial can be factored as \(P(x) = x(x-1)(x+1)\).

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Answer:

B = -6

Step-by-step explanation:

so yes, you're correct.

Velocity of jet in still air is 647 miles per hour and velocity of wind is 70 miles per hour.

Given,

Jet's velocity against wind 1731 / 3 = 577  mile per hour

flying with wind it   2151 / 3 = 717 miles per hour.

Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x−y and with wind is x+y and therefore

x−y=577;

x+y=717

Adding the two

2x = 1294

x = 647

y= 717 − 647

y = 70

Hence velocity of jet in still air is 647 miles per hour and velocity of wind is 70 miles per hour.

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Answer:

An even function is symmetric about the y-axis. An odd function is symmetric about the origin. As the graphed function is neither symmetric about the origin, nor symmetric about the y-axis, it is neither even nor odd.

Step-by-step explanation:

Even and odd functions are special types of functions.

An even function is symmetric about the y-axis. An odd function is symmetric about the origin. As the graphed function is neither symmetric about the origin, nor symmetric about the y-axis, it is neither even nor odd.

Answer:

The answer is quadratic

Step-by-step explanation:

I just took the quiz and got this question correct, also it cant be linear because if it were linear, it would be more of a straight shape, but this is more of a u shape, if it were exponential, it would look more drawn out to the sides i believe, and if it were no pattern, there would just be dot points threwn at random spots. Therefore, the answer is Quadratic.

Answer:

5 hours

Step-by-step explanation:

$272 = 13h

/273      /273

$1=     0.4.......

*105    *105

105=  5

Answer:

5

Step-by-step explanation:

Answer:

hi uhm what am i supposed to figure out?

Step-by-step explanation:

Gina did not use the same ratio as her teacher. I know this because 4:3 is not a simplified version of 9:6. If her teacher were to use a 8:6 ratio then it would’ve been the same.