SKIP (2)
First try was incorrect
What is the value of x? Your answer may be exact or rounded to the
nearest tenth.
-3x
96"
31"

Sorry about the blurry pic

Answer:

41

Step-by-step explanation:

All the values are as follows

27 28 31 38 41 43 50 52 56

If we go to the middle value (9 total values so #5), it's 41.

The requried, value is less than 8.5, as Imran claimed. Therefore, he is correct and not wrong.

To verify this, we can use the formula given:

Petrol consumption = 100 × litres of petrol used / kilometres travelled

Substituting the given values, we get:

Petrol consumption = 100 × 21.3 / 250 = 8.52

Rounding this value to three significant figures, we get:

Petrol consumption = 8.52

This value is indeed less than 8.5, as Imran claimed. Therefore, he is correct and not wrong.

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The value of the iterated integral  ∫85∫√x12ye−xdydx is

-[tex]4e^(-5) + 7e^(-8)[/tex] where the inner integral is first integrated with respect to y.

We are inquiring to assess the iterated integral:

[tex]∫85∫√x12ye−xdydx[/tex]

We are able to coordinate the internal integral, to begin with regard to y:

[tex]∫√x12ye−xdy = (-1/2)e^(-x) y√x1/2 | from y = to y = √x^1/2[/tex]

[tex]= (-1/2)e^(-x) (√x^1/2)^2 - (-1/2)e^(-x) (0)[/tex]

[tex]= (-1/2)x e^(-x)[/tex]

Substituting this into the first necessity, we get:

[tex]∫85∫√x12ye−xdydx = ∫85(-1/2)x e^(-x)dx[/tex]

To assess this necessarily, we utilize integration by parts with u = x and [tex]dv = e^(-x) dx, so that du/dx = 1 and v = -e^(-x):[/tex]

[tex]∫85(-1/2)x e^(-x)dx = (-1/2)xe^(-x) + ∫85(1/2)e^(-x)dx[/tex]

[tex]= (-1/2)xe^(-x) - (1/2)e^(-x) | from x = 8 to x = 5[/tex]

[tex]= (-1/2)(8e^(-8) - 5e^(-5)) - (1/2)(e^(-8) - e^(-5))[/tex]

[tex]= -4e^(-5) + 7e^(-8)[/tex]

therefore, the value of the iterated integral is [tex]-4e^(-5) + 7e^(-8).[/tex]

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Chaneece did not find the correct solution

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

x and y are the integers

So, we have

x + y ≤ 40

x - y ≥ 20

Add the equations

So, we have

2x = 60

Divide

x = 30

Next, we have

30 + y ≤ 40

So, we have

y ≤ 10

This means that

x = 30 or between 20 and 30

y = 10 or between 0 and 10

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1. MULTIPLE-CHOICE CONSTRAINT - c.; 2. COREQUISITE CONSTRAINT - e.; 3. K OUT OF N ALTERNATIVES CONSTRAINT - b.; 4. CONDITIONAL CONSTRAINT - a.; 5. MUTUALLY EXCLUSIVE CONSTRAINT - d.

1. MULTIPLE-CHOICE CONSTRAINT - an example of the this is c. A constraint requiring that the sum of two or more binary variables equals one. Thus, any feasible solution makes a choice of which variable to set equal to one.

2. COREQUISITE CONSTRAINT - This is associated with e. A constraint requiring that two binary variables be equal and that they are both either in or out of the solution.

3. K OUT OF N ALTERNATIVES CONSTRAINT - This corresponds to b. A constraint requiring that the sum of n binary variables equals k.

4. CONDITIONAL CONSTRAINT - This matches with a. A constraint involving binary variables that does not allow certain variables to equal one unless certain other variables are equal to one.

5. MUTUALLY EXCLUSIVE CONSTRAINT - This fits the description of d. A constraint requiring that the sum of two or more binary variables be less than or equal to one. Thus, if one of the variables equals one, the others must equal zero. However, all variables could equal zero.

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The effective interest method of amortization is a method used to allocate the cost of a bond over the bond's life, in order to determine the amount of interest expense to be recorded each period.

In the case of Bentley Corporation, since they issued $1,000,000 of 10-year, 8% bonds at 105, this means that they received $1,050,000 in cash from investors.

Since the market rate of interest was 7%, the bonds were sold at a premium, which means that the effective interest rate is less than the stated interest rate of 8%. The effective interest rate is the rate at which the present value of the bond's future cash flows equals the amount of cash received at the time of issuance.

Using the effective interest method of amortization, the premium of $50,000 will be amortized over the life of the bond, reducing the effective interest rate each year. The interest expense recorded on December 31, 2021, the first interest payment date, will be calculated as follows:

$1,050,000 x 7% = $73,500 (effective interest)
$73,500 - $80,000 (stated interest) = -$6,500 (amortization of premium)
$80,000 - $6,500 = $73,500 (interest expense)

The premium of $50,000 will be reduced by $6,500, leaving a balance of $43,500 at the end of the first year. This process will continue each year until the bond matures in 2031.

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The Fourier transform of x(t) is zero for all frequencies.

(a) x(t) = δ(t-1)

Using the time-shifting property of the Fourier transform, we have:

F{δ(t-a)} = e^{-j2πf a}

Therefore,

F{x(t)} = F{δ(t-1)} = e^{-j2πf (1)}

The Fourier transform of x(t) is a complex exponential at frequency f = 1:

F{x(t)} = e^{-j2π} = cos(2π) - j sin(2π) = -1

(b) x(t) = δ(t-1) + δ(t+1)

Using the linearity property of the Fourier transform and the time-shifting property, we have:

F{x(t)} = F{δ(t-1)} + F{δ(t+1)} = e^{-j2πf (1)} + e^{j2πf (1)}

The Fourier transform of x(t) is a sum of two complex exponentials at frequencies f = ±1:

F{x(t)} = e^{-j2π} + e^{j2π} = cos(2π) - j sin(2π) + cos(2π) + j sin(2π) = 0

Therefore, the Fourier transform of x(t) is zero for all frequencies.

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The equivalent form of expression 15(p+ 4) - 12(2q + 4) is,

⇒ 15p - 24q + 12

We have to given that;

The value of expression is,

⇒ 15(p+ 4) - 12(2q + 4)

Now, We can simplify as;

⇒ 15(p+ 4) - 12(2q + 4)

⇒ 15p + 60 - 24q - 48

⇒ 15p - 24q + 12

Thus, The equivalent form of expression 15(p+ 4) - 12(2q + 4) is,

⇒ 15p - 24q + 12

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We need to find the inverse of the function f(x) = 1/x. Therefore, h'(3) = -1/[tex]3^2[/tex] = -1/9. So, h'(3) = -1/9.

In the equation expressing the function, swap out f(x) with y. Swap out x and y. To put it another way, swap out every x for a y and vice versa.

An inverse in mathematics is a function that is used to another function.

Calculate y using a solution.

To find the inverse, we switch the x and y variables and solve for y:

x = 1/y

y = 1/x

So the inverse function of f(x) = 1/x is h(x) = 1/x.

Now, we need to find h'(3), the derivative of h(x) at x = 3.

h(x) = 1/x, so using the power rule of differentiation, we get:

h'(x) = -1/[tex]x^2[/tex]

Therefore, h'(3) = -[tex]1/3^2[/tex] = -1/9.

So, h'(3) = -1/9.

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Correct Question:

If h is the inverse function of f and if f(x) = 1/x, then h'(3) =

Answer:

Step-by-step explanation:

First, organize the numbers; 1,1,1,2,2,3,4,5,5,6. The median is the middle number, in this case, 2 and 3 are in the middle. You'd add 2+3 which equals 5, then divide by 2 to get 2.5. The median is 2.5, to find the mode you need to see how many times one number appears. The mode is 1, the range is the largest number minus the smallest number. The range is 5, to find the mean you add all numbers up, then divide by how many numbers there are. All the numbers added up are 30, now divide that by 10 to get 3. The mean is 3. The standard deviation is 1.7 x 6.5 = 20.8

I'm only an algebra student so I may not be entirely correct.

0 is a single digit whole number for y that supports Doni's claim.

2 is a single digit whole number for y that does not supports Doni's claim.

Doni claims that [tex]\frac{3^y}{2^y} \leq 1[/tex]

We have to find a single digit whole number for y that supports Doni's claim.

Let 0 be the single digit whole number for y that supports Doni's claim.

1/1≤1

Now let us find  single digit whole number for y that does not support Doni's claim.

2 be the whole number

9/4≤1

2.25≤1

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The three main techniques of measuring quantitative data are surveys, experiments, and observational studies.

1. Surveys: Surveys involve collecting data by asking a sample of individuals to respond to a set of questions. This method can be done through various formats such as questionnaires, interviews, or online polls. Surveys are useful for gathering information on opinions, attitudes, or preferences and can help determine relationships between variables.
2. Experiments: Experiments involve manipulating one or more variables to observe the effect on a dependent variable. Participants are typically randomly assigned to different conditions, and the researcher measures the outcomes to determine cause-and-effect relationships. Experiments can provide strong evidence for causal relationships and are often used in scientific research.
3. Observational studies: Observational studies involve collecting data by observing and recording the natural behavior or characteristics of individuals or groups without any intervention. Researchers can observe the participants in their natural settings or use existing data sources such as records, databases, or archival data. Observational studies are useful for understanding patterns, trends, and relationships between variables, but they cannot establish causality.
These techniques can provide valuable insights into various aspects of quantitative data, allowing for informed decision-making and improved understanding of patterns and relationships.

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If the 5 cats in the pet store weigh (in pounds) 6, 8, 7, 16, and 9, respectively, the mean and median weights are:

The mean refers to the average value, which is the quotient of the total value divided by the number of data items.

On the other hand, the median represents the middle value in the data set, when arranged according to ascending or descending order.

The total number of cats in the pet store = 5

The weights of the cats (in pounds) = 6, 8, 7, 16, 9

The total weight = 46 pounds (6, 8, 7, 16, 9)

The average (mean) weight = 9.2 pounds (46 ÷ 5)

The median weight = 8 (6, 7, 8, 9, and 16)

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The radius of the cylinder is 2 feet.

The volume of this cylinder is 37. 68 cubic feet. Therefore, the radius of the cylinder can be found as follows:

Therefore,

volume of a cylinder = πr²h

where

Therefore,

volume of a cylinder = 3.14 × r² × 3

37.68 = 9.42r²

divide both sides by 9.42

r² = 37.68 / 9.42

r² = 4

square root both sides of the equation

r = √4

radius = 2 feet

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Answer:

c

Step-by-step explanation:

Substituting the point C in the given equation

[tex]= 2(4) + 3(-4)\\=-4[/tex]

(1) The two triangles are similar because they have equal angles.

(2)  Triangle QRS is similar to triangle QLM because they have equal angles.

(3) Both triangles are similar and the value of x is 21.

Two triangles are said to be similar if they have equal sides, equal angles or both.

The missing angles of the triangles for the question is calculated as;

Bigger triangle; missing angle = 180 - (44 + 46) = 90

Smaller triangle; missing angle = 90 - 46 = 44⁰

Both triangles are similar.

For the second question; triangle QRS is similar to triangle QLM  because angle R is equal to angle L, and also they have common angle Q, which implies that angle S must be equal to angle L.

For third question, the triangles are similar because their corresponding angles are equal.

The value of x is calculated as;

48 + 4x + (180 - (56 + 76)) = 180 (sum of angles on a straight line)

48 + 4x + 48 = 180

4x = 84

x = 84/4

x = 21

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By giving an explanation, we have shown that 2 + 6 + 2 · 3² +.... +2.3ⁿ = 3ⁿ⁺¹ - 1 holds true for all non-negative integers, and completed the proof by mathematical induction.

Mathematical induction is a method of mathematical proof that is used to establish the validity of an infinite number of statements. It involves two steps:

Base case: Prove that the statement holds true for a specific value of n, often n=0 or n=1.

Inductive step: Assume that the statement holds true for some arbitrary value k, and use this assumption to prove that it holds true for k+1.

By showing that the statement holds true for the base case and that it implies that the statement holds true for k+1, we can conclude that the statement holds true for all values of n.

Here we have

2 + 6 + 2 · 3² +.... +2.3ⁿ= 3ⁿ⁺¹ - 1

To prove the given equation using mathematical induction, first show that it holds true for the base case, n = 0.

Then we will assume that the equation holds true for an arbitrary non-negative integer 'a' and show that it implies that the equation also holds for (a + 1). This will complete the proof by mathematical induction.

Base case:

When n = 0, we have:

=> 2 = 3⁰⁺¹ - 1 = 3 - 1

So the base case holds true.

Inductive step:

Let's assume that the equation holds true for some arbitrary non-negative integer 'a'. That is,

=> 2 + 6 + 2·3² + ... + 2·3ᵃ = 3ᵃ⁺¹- 1 --- Equation (1)

Now show that it implies that the equation also holds for k+1, that is,

=> 2 + 6 + 2·3² + ... + 2·3ᵃ+ 2·3ᵃ⁺¹ = 3ᵃ⁺¹⁺¹ - 1 --- Equation (2)

To do this, we start by adding 2·3⁽ᵃ⁺¹⁾ to both sides of Equation (1):

=> 2 + 6 + 2·3² + ... + 2·3ᵃ + 2·3ᵃ⁺¹ = (2 + 6 + 2·3² + ... + 2·3ᵃ) + 2·3ᵃ⁺¹

Using Equation (1) in the right-hand side of the above equation, we get:

=> 2 + 6 + 2·3² + ... + 2·3ᵃ + 2·3ᵃ⁺¹ = (3ᵃ⁺¹ - 1) + 2·3ᵃ⁺¹

Simplifying the right-hand side, we get:

=> 2 + 6 + 2·3² + ... + 2·3ᵃ + 2·3⁽ᵃ⁺¹⁾= 3ᵃ⁺¹ + 2·3⁽ᵃ⁺¹⁾ - 1

Using the laws of exponents, we can simplify the right-hand side further:

=> 2 + 6 + 2·3² + ... + 2·3ᵃ + 2·3⁽ᵃ⁺¹⁾= 3⁽ᵃ⁺¹⁾ ·3 - 1

=> 2 + 6 + 2·3² + ... + 2·3ᵃ + 2·3⁽ᵃ⁺¹⁾ = 3⁽ᵃ⁺¹⁾ - 1

This is precisely the right-hand side of Equation (2).

Therefore, Equation (2) holds true if Equation (1) holds true.

By giving an explanation, we have shown that 2 + 6 + 2 · 3² +.... +2.3ⁿ = 3ⁿ⁺¹ - 1 holds true for all non-negative integers, and completed the proof by mathematical induction.

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Complete Question:

Use mathematical induction to prove that for every nonnegative integer, it holds 2 + 6 + 2 · 3² +.... +2.3ⁿ = 3ⁿ⁺¹ - 1

a)the median of the random variable X is approximately 0.1386.

b) This equation has no solutions,

a. To find the median, we need to solve for x in the equation F(x) = 0.5:

1 - e^(-5x) = 0.5

e^(-5x) = 0.5

Taking the natural logarithm of both sides:

ln(e^(-5x)) = ln(0.5)

-5x = ln(0.5)

x = -ln(0.5)/5 ≈ 0.1386

Therefore, the median of the random variable X is approximately 0.1386.

b. The mode is the value of x that maximizes the probability density function, f(x). To find the density function, we take the derivative of the cumulative distribution function:

f(x) = F'(x) = 5e^(-5x)

Setting f'(x) = 0 to find the maximum, we get:

f'(x) = -25e^(-5x) = 0

e^(-5x) = 0

This equation has no solutions, which means that the density function does not have a maximum value. Therefore, the random variable X has no mode.

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Answer:

Area of the semi-circle:

(1/2)π(2^2) = 2π = 6.28 square centimeters

Area of the triangle:

(1/2)(4)(5.7) = 11.4 square centimeters

Total area:

6.28 + 11.4 = 17.68 square centimeters

a) No, f is not injective.

b) Yes, g is injective.

c) No, f is not surjective.

d) Yes, g is surjective.

(a) Is f injective?
No, f is not injective. A counterexample is f(1,2) = 2 * (1 - 1) = 0 and f(2,2) = 2 * (2 - 1) = 0. Since f(1,2) = f(2,2), the function is not injective.

(b) Is g injective?
Yes, g is injective. To prove this, let's assume g(a1, b1) = g(a2, b2). This means (a1, b1) = (a2, b2), which implies a1 = a2 and b1 = b2. Therefore, g is injective.

(c) Is f surjective?
No, f is not surjective. For example, consider the number 1 in the codomain R. There is no pair (a, b) in the domain such that f(a, b) = 1 because 2 * (a - b) must be an even number.

(d) Is g surjective?
Yes, g is surjective. To prove this, let (c, d) be any element in the codomain. Then g(c, d) = (c, d), so there exists an element in the domain for every element in the codomain. Thus, g is surjective.

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The real speed of the vessel, adjusted to the closest tenth, is 20.4 hitches.

To unravel this issue, we got to break down the boat's speed into its components. We will use trigonometry to discover the eastbound and northward components of the boat's speed.

First, let's draw a diagram:

              N

                |

                |

     NW 5 |   E15

                |

--------------|---------------> E

                |

                |

                |

               S

From the chart, we will see that the northward component of the boat's speed is:

16 hitches * sin(15°) = 4.16 knots

And the eastbound component of the boat's speed is:

16 ties * cos(15°) = 15.38 knots

Next, we ought to discover the whole northward and eastbound speed of the vessel by including the boat's speed components to the current's speed components. We are able moreover utilize trigonometry to discover the northward and eastbound components of the current's speed:

5 hitches * sin(45°) = 3.54 ties northward

5 hitches * cos(45°) = 3.54 ties eastbound

So, the overall northward speed of the pontoon is:

4.16 ties + 3.54 hitches = 7.7 hitches northward

And the full eastbound speed of the pontoon is:

15.38 ties + 3.54 ties = 18.9 ties eastbound

Presently, we will utilize the Pythagorean hypothesis to discover the greatness of the boat's speed vector:

sqrt((7.7 knots)^2 + (18.9 knots)^2) = 20.4 ties

In this manner, the real speed of the vessel, adjusted to the closest tenth, is 20.4 hitches.

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Answer :x^15

Step-by-step explanation:

You would combine components so it would be x^10x^5 you would add 5+10 and then you would get your answer

BRAINLIEST PLS:)

Answer:

Step-by-step explanation:

1. Make an equation. To stay balanced the sum of everything on the left must equal the value on the right.

2 + x + 2 + x + 2 + x + 2 + x + 2 + x = 11

2. Add all like terms. We have 2+2+2+2+2 = 10 and x+x+x+x+x=5x so the equation simplifies to

10 + 5x = 11

3. Substract 10 from both sides

10 - 10 + 5x = 11 - 10

0 + 5x = 1

5x = 1

4. Divide the number being multiplied by x from both sides

5x/5 = 1/5

x = 1/5  or x = 0.2

Note that an and bn are only non-zero for odd values of n, since f(x) is an odd function.

To sketch the function f(x) for (-21 < t < 4π), we need to extend the definition of f(x) to this interval. Since f(x) has a period of 2π, we can extend the function by repeating it every 2π. Thus, for (-21 < t < 0), we have:

f(x) = f(x + 2π) = f(x - 2π)

For (0 ≤ t < 2π), we use the original definition of f(x).

For (2π ≤ t < 4π), we have:

f(x) = f(x - 2π)

With  this extension, we can now sketch the function f(x) as follows:

              |\

              | \

              |  \

              |   \

              |    \

              |     \______

              |           /\

              |          /  \

              |         /    \

_______________|________/______\____________

             -21       0      2π     4π

Now let's find the Fourier series of f(x). The Fourier series is given by:

f(x) = a0/2 + Σ[an cos(nωx) + bn sin(nωx)]

where ω = 2π/T is the fundamental frequency, T is the period, and an and bn are the Fourier coefficients, given by:

an = (2/T) ∫[f(x) cos(nωx)] dx

bn = (2/T) ∫[f(x) sin(nωx)] dx

In this case, T = 2π, so ω = 1. The Fourier coefficients can be calculated as follows:

a0 = (1/π) ∫[f(x)] dx

= (1/π) [∫[x dx] from 0 to π/2 + ∫[½π(½π -½π(π x-2x(½π≤x≤2π)) dx] from π/2 to 2π]

= (1/π) [π²/4 + ½π²/3 - π³/8]

= (π/4) - (π²/24)

an = (2/π) ∫[f(x) cos(nωx)] dx

= (2/π) ∫[x cos(nωx)] dx from 0 to π/2 + (2/π) ∫[½π(½π -½π(π x-2x(½π≤x≤2π))) cos(nωx)] dx from π/2 to 2π

= [2/(nπ)] [(-1)^n - 1] + [2/(nπ)] [(-1)^n - 1/3]

bn = (2/π) ∫[f(x) sin(nωx)] dx

= (2/π) ∫[x sin(nωx)] dx from 0 to π/2 + (2/π) ∫[½π(½π -½π(π x-2x(½π≤x≤2π))) sin(nωx)] dx from π/2 to 2π

= [2/(nπ)] [1 - (-1)^n] + [2/(nπ)] [2/π - (1/π)cos(nπ) + (1/3π)cos(3nπ)]

Note that an and bn are only non-zero for odd values of n, since f(x) is an odd function.

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Answer: Example 2: Solve the system of equations with augmented matrices using the Gauss-Jordan elimination method. x – 3z = – 2. 2x + 2y + z = 4. 3x + y – 2z = 5.

Step-by-step explanation:

Answer:

3x + 4y = 12; 2x – 3y = 6

Multiplying the first equation by 2 and the second equation by 3, we get:

6x + 8y = 24

6x - 9y = 18

Subtracting the second equation from the first, we get:

17y = 6

y = 6/17

Substituting y in the first equation, we get:

3x + 4(6/17) = 12

3x = 180/17 - 24/17

3x = 156/17

x = 52/17

Therefore, the solution of the given system is x = 52/17 and y = 6/17.

x + y = 3; x – y = 5

Adding the two equations, we get:

2x = 8

x = 4

Substituting x in the first equation, we get:

4 + y = 3

y = -1

Therefore, the solution of the given system is x = 4 and y = -1.

3x + 2y – z = 4; 2x – y + 3z = 4; x + y + 2z = 4

Adding the first and second equations, we get:

5x + y + 2z = 8

Subtracting the third equation from the above equation, we get:

4x + z = 4

Substituting z = 4 - 4x in the third equation, we get:

3x + 2y - (4 - 4x) = 4

7x + 2y = 8

Substituting y = (8 - 7x)/2 in the first equation, we get:

9x - z = 8

Substituting z = 4 - 4x, we get:

x = 4/5, y = 2/5, and z = 4/5

Therefore, the solution of the given system is x = 4/5, y = 2/5, and z = 4/5.

x – y + 5z = -4; 4x – 2y + 3z = 1; 3x – 2y + 6z = 6

Multiplying the first equation by -4 and adding it to the second equation, we get:

16x - 6z = 17

Multiplying the first equation by -3 and adding it to the third equation, we get:

9x + 4z = 18

Multiplying the second equation by 2 and subtracting it from the third equation, we get:

x + 6z = 8

Substituting z = (8 - x)/6 in the above equation, we get:

x = 10/3, y = 8/3, and z = 2/3

Therefore, the solution of the given system is x = 10/3, y = 8/3, and z = 2/3.

x2 + y2 = 13; 2x – 3y = -5

Squaring the second equation and simplifying, we get:

4x2 - 12xy + 9y2 = 25

Adding the above equation to the first equation, we get:

5x2 + 10y2 = 38

Sub

Step-by-step explanation:

For theoretical probability of each letter is 0.2, the experimental probability of drawing a card with the letter for which the experimental probability is closest to the theoretical probability is equals the 0.5.

Theoretical Probability: The theoretical probability of an event is the probability of a particular event based on mathematical calculations, assuming ideal conditions. The theoretical probabilities do not take into account the flaws of the system.

Experimental probability: The experimental probability of an event is the actual probability of an event occurring based on the results of facts rather than mathematical calculations

The theoretical probability of each letter = 0.2 = 2/10

We have to determine the experimental probability of drawing a card with the letter for which the experimental probability is near to the theoretical probability. Now, total possible outcomes = 10 and each letter comes two times

so, the experimental probability = 10/20

= 0.5

Hence, required value is 0.5.

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The larger can price is proportional to the price of

smaller can in relation to its volume.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

The volume of a cylinder is expressed as;

V = πr²h

Volume of the small cylinder = πr²h

= 3.14 × 2² × 3

= 3.14 × 4 × 3

= 37.68 in²

The volume of big cylinder

= πR²h

= 3.14 × 6² × 9

= 3.14 × 36 × 9

= 1017.36 in³.

price of the big can = 2 × price of small

Therefore the volume of the big can is thrice the volume of the small cylinder and the price of the

big can is twice of the price of the small can.

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The solution to the system of equations is given as follows:

(-1, 0.5).

The system of equations in the context of this problem is defined as follows:

At the solution, the two systems have the same x-coordinates and y-coordinates, hence the value of x of the solution is obtained as follows:

-0.5x = 0.75x + 1.25.

-1.25x = 1.25

1.25x = -1.25

x = -1.25/1.25

x = -1.

Then the y-coordinate of the solution is given as follows:

y = -0.5(-1)

y = 0.5.

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