Yong is measuring two pyramids whose bases are rectangles.
Given the length and width of the base of the first pyramid, as well as its volume V, Yong uses the formula
h=3v/lxW
to compute its height h to be 7 centimeters.

The second pyramid has the same volume and base length, but its base's width is 2 times as long. What is its
height?

The beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

Given that, a lighthouse is located on a small island 4 km away from the nearest point P.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

\(\frac{d\theta}{dt}\) = 6 rev/min

= 6π rad/min

tan θ = x/6

\(\frac{d}{dt}tan\theta=\frac{d}{dt}(\frac{x}{6} )\)

\(sec^2\frac{d\theta}{dt} = \frac{1}{6}(\frac{dx}{dt} )\)

\(\frac{dx}{dt}=6sec^2\theta\frac{d\theta}{dt}\)

At x=1 km; tan θ= x/6 = 1/6

\(sec^2 \theta= 1+tan^2 \theta= 1 + (\frac{1}{6})^2\)

\(sec^2 \theta = \frac{10}{9}\)

\(\frac{dx}{dt} = 6 sec^2\theta \frac{d\theta}{dt}\)

dx/dt = 6 × 10/9 × 6π

dx/dt = 125.66 km/min

Therefore, the beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

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The slope of a line is m= rise / run .

The rise measures the vertical change and the run measures the horizontal change.

Slope of the straight line passing through the points (X1,y1) and ( x2 , y2 ) is given by :-

\(m = \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \)

Slope of the straight line passing through the points ( -3 .2 ) and (-1 , 0 ) is .

\(m = \frac{0 + 2} { - 3 - 1} = - \frac{3}{2} \)

The base is a square with side length 4, and the triangular faces have a base of 4 and a height of 3.So, the surface area of the square pyramid is 40 square units.



A square pyramid has a square base and four triangular faces that meet at a common vertex or apex. The net of the square pyramid with 3 at the top and 4 at the right side can be visualized as follows:  In this net, the square base has sides of length 4, and the height of the pyramid is 3. Each of the four triangular faces is a right triangle with legs of length 3 and 4.



For the triangular faces of the pyramid, the base and height are given by the legs of the right triangle. So, the area of each face is:Face area = 1/2 * 3 * 4 = 6
Since there are four triangular faces, the total area of all four faces  add the area of the base and the area of the four triangular faces to get the total surface area of the pyramid:
Total surface area = Base area + 4 * Face area
                  = 16 + 24
                  = 40
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The given Linear Programming (LP) problem is given below: Minimize f = 5x + 4x₂ - x²3 Subject to x + 2x₂ - x²1 2x + x₂ + x₃ ≥ 4 x₁, x₂ ≥ 0; x₃ is unrestricted in signTo solve the above LP problem in Excel Solver, we have to follow the following steps:

Step 1: Open a new Excel worksheet and enter the given data in a tabular form as shown below:  

Step 2: Go to the “Data” tab and click on the “Solver” button as shown below:

Step 3: In the “Solver Parameters” dialog box, choose the following options and click on the “OK” button: Set Objective: Minimize By Changing Variable Cells: B5 and C5 Subject to the Constraints: B3:C3 >=B4:C4 and B3:C3 >= 0 and C5 >= -1000 and C5 <= 1000.

Step 4: The Solver tool will find the optimal solution and display the result as shown below:  Thus, the optimal solution of the given LP problem is x₁ = 1.29, x₂ = 0.86, and x₃ = -0.86, and the minimum value of f is 3.57.

We can solve the given LP problem by using the Excel Solver tool, which is a built-in optimization tool in Microsoft Excel. Excel Solver tool is used to find the optimal solution of a linear programming problem by adjusting the values of the decision variables to minimize or maximize an objective function subject to certain constraints.

The given LP problem is a minimization problem, and the objective function is given by f = 5x + 4x₂ - x²3. The decision variables are x₁, x₂, and x₃, which represent the amounts of three products to be produced. The objective is to minimize the total cost of production subject to the production capacity and resource constraints.

To solve the given LP problem in Excel Solver, we need to enter the given data in a tabular form in an Excel worksheet. Then, we need to follow the following steps to find the optimal solution:

Step 1: Open a new Excel worksheet and enter the given data in a tabular form.

Step 2: Go to the “Data” tab and click on the “Solver” button.

Step 3: In the “Solver Parameters” dialog box, choose the following options and click on the “OK” button:Set Objective: MinimizeBy Changing Variable Cells: B5 and C5Subject to the Constraints: B3:C3 >=B4:C4 and B3:C3 >= 0 and C5 >= -1000 and C5 <= 1000.

Step 4: The Solver tool will find the optimal solution and display the result.Thus, we have found that the optimal solution of the given LP problem is x₁ = 1.29, x₂ = 0.86, and x₃ = -0.86, and the minimum value of f is 3.57. Hence, we can conclude that to minimize the total cost of production, the company should produce 1.29 units of product 1, 0.86 units of product 2, and should not produce product 3.

Thus, we have solved the given LP problem using Excel Solver tool and found the optimal solution to minimize the total cost of production.

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1) to find the area of the figure, all we need to do is to find the distance between all the coordinates.

2) The area of the quadrilateral is given as approximately 151

The formula for finding the distance between two coordinates is given as:

d = √((x2-x1)2 + (y2-y1)2)

Where:

(x1, y1) are the coordinates for the first point; and

(x2 y2) are the coordinates for the second point.

Let A be the first Point with coordinates (7, 17); (18,12)

To compute the distance between the two coordinates, we insert the values into the formula:

(x2-x1) = (18 - 7) = 11

(y2-y1) = (12 - 17) = -5

Square the results and sum them up:

(11)2 + (-5)2 = 121 + 25 = 146

Now Find the square root and that's your result:

A = √146

Segment A = 12.083

Repeat the same process for B, C and D, to get:

Segment B = 18.02776

Line segment C = 12.08305

Line segment D = 21.4709

Now that we have the sides (line segments) of the quadrilateral, to compute it's area, we must use Brahmagupta's formula which states:

Area = √((s-a) * (s-b) * (s-c) * (s-d))

where s is the semiperimeter of the quadrilateral and is calculated as:

s = (a + b + c + d) / 2

Given the lengths of the line segments:

Segment A = 12.083

Segment B = 18.02776

Line segment C = 12.08305

Line segment D = 21.4709

we can calculate the semi perimeter as:

s = (12.083 + 18.02776 + 12.08305 + 21.4709) / 2

s = 31.341355

Substituting the values of a, b, c, and d into Brahmagupta's formula, we get:

Area = √((31.341355 - 12.083) * (31.341355 - 18.02776) * (31.341355 - 12.08305) * (31.341355 - 21.4709))

Area = √(9.43292 * 13.31159536 * 19.25867225 * 9.87087725)

Area = √(22781.771082368)

Thus, Area = 150.936314657
Rounded to the nearest whole unit, we have:

Area \(\approx\) 151

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Answer:

-3=v

Step-by-step explanation:

-12=9+7v

-9 from both sides

-21=7v

Divide both sides by 7

-3=v

Hope this helps:) Have a good day!

Answer:

v = - 3

Step-by-step explanation:

- 12 = 9 + 5v + 2v , that is

- 12 = 9 + 7v ( subtract 9 from both sides )

- 21 = 7v ( divide both sides by 7 )

- 3 = v

The product ((4√3) - 4i)((√2) + √2i) in polar form is 8√3 * cis(-π/4).

To find the product of ((4√3) - 4i)((√2) + √2i) in polar form, we can first multiply the two complex numbers using the distributive property: ((4√3) - 4i)((√2) + √2i) = (4√3)(√2) + (4√3)(√2i) - (4i)(√2) - (4i)(√2i)

Simplifying each term, we get:

(4√3)(√2) = 8√6

(4√3)(√2i) = 8√6i

(4i)(√2) = 4√2i

(4i)(√2i) = -4√2

Combining the terms, we have: 8√6 + 8√6i - 4√2i - 4√2

To express the result in polar form, we convert the complex number to its magnitude and argument form. The magnitude (r) can be calculated as the square root of the sum of the squares of the real and imaginary parts: r = √((8√6)^2 + (8√6)^2) = √(384 + 384) = √768 = 8√3

The argument (θ) can be determined as the arctan of the imaginary part divided by the real part: θ = arctan((-4√2 - 4√6) / (8√6 + 8√6)) = arctan(-√2/√3) = -π/4

Therefore, the product ((4√3) - 4i)((√2) + √2i) in polar form is 8√3 * cis(-π/4). The argument -π/4 corresponds to the fourth quadrant of the complex plane, as it is negative and lies between -π/2 and -π.

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The second hand moves 6 degrees in one second, it will take it: 294/6 = 49 seconds to move from halfway between 1 and 2 to 4/5 of the way from 1 to 2.

The measure of the arc is 144 degrees.

When the second hand of the clock moves from halfway between the 1 and the 2 to 4/5 of the way from the 1 to the 2, it moves a total of 144 degrees.

This can be calculated as follows: The second hand of a clock completes one full revolution every 60 seconds or 1 minute.

This means that in 1 second, it moves 360/60

= 6 degrees.

To find the measure of the arc when the second hand moves from halfway between the 1 and the 2 to 4/5 of the way from the 1 to the 2, we need to find the difference between the two positions in degrees.

The position halfway between the 1 and the 2 is 1.5 on the clock face.

This is equivalent to 45 degrees (since the clock face is divided into 12 hours, each hour marking is 30 degrees apart, so halfway between 1 and 2 is 30+15 = 45 degrees).

4/5 of the way from the 1 to the 2 is 4/5 x 30 = 24 degrees from the 1 mark.

Therefore, the total angle between halfway between 1 and 2 and 4/5 of the way from 1 to 2 is:

24 + (360 - 45)

= 339 degrees.

However, we need to find the difference between these two positions, not the total angle.

Therefore, we need to subtract the position of the second hand at halfway between 1 and 2 from the position at 4/5 of the way from 1 to 2:

339 - 45

= 294 degrees.

Since the second hand moves 6 degrees in one second, it will take it:

294/6 = 49 seconds to move from halfway between 1 and 2 to 4/5 of the way from 1 to 2.

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer: a prediction of the number of hot cocoas sold when the temperature is 0F

Step-by-step explanation: i did it on delta math

The line's y-intercept represent ''Number of hot cocoas sold''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Chloe has a part-time job at an ice skating rink selling hot cocoa.

She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Now,

Since, She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Hence, By the graph we have;

The line's x - intercept represent ''Temperature''.

And, The line's y-intercept represent ''Number of hot cocoas sold''.

Thus, The line's y-intercept represent ''Number of hot cocoas sold''.

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Answer:

Answer: X=12

Explanation: 180-72= 108. 108/9 = 12

Step-by-step explanation:

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

Answer:

I believe it's choice (3) because the exponent of x is 25 and it's the largest exponent of the choices.

Step-by-step explanation:

Answer:

C. 25x^10+3x-15

Step-by-step explanation:

The degree of 3x^8-2x^7+x^6 is 8

The degree of 5x-100 is 1

The degree of 25x^10+3x-15 is 10

The degree of 134x^2 is 2

Therefore the largest degree is 10

In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the error term come from a normal distribution.

In a simple linear regression model, the normal quantile plot of the residuals is a graphical tool used to assess the normality assumption of the error term (also known as the residual). The error term represents the difference between the actual value of the dependent variable and the predicted value by the model.

Assuming that the error term follows a normal distribution is important for various reasons. Firstly, the normal distribution is a very common assumption in statistics, and many statistical methods rely on it. Secondly, a normal distribution of the error term is essential for making reliable predictions and for computing valid confidence intervals.

The normal quantile plot of the residuals compares the distribution of the residuals against a theoretical normal distribution. The plot consists of a straight line if the residuals are normally distributed. However, if the plot shows deviations from the straight line, it indicates non-normality in the residuals.

If the normality assumption is not satisfied, we need to explore the reasons for the non-normality and consider alternative methods to analyze the data, such as non-parametric methods.

Therefore, the normal quantile plot of residuals is an essential diagnostic tool in simple linear regression, as it allows us to evaluate the assumption of normality and make appropriate adjustments to the model.

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The expression 2(w + 3z)² can be visualized using an area model as the total area of a rectangle that is divided into four smaller rectangles with dimensions w, 3z, w, and 3z, respectively.

An area model is a graphical representation of a mathematical expression or equation that uses rectangles to represent the different parts of the expression.

Each rectangle has a width and a height that correspond to the variables or coefficients in the expression. The area of each rectangle corresponds to the value of the term it represents.

To represent the expression 2(w + 3z)² using an area model, we can draw a rectangle with a width of 2(w + 3z) and a height of w + 3z, as shown below:

+-----------------------------+

|                             |

|                             |

|                             |

|         w + 3z              |

|                             |

|                             |

|                             |

+-----------------------------+

             2(w + 3z)

We can then divide the rectangle into four smaller rectangles, as shown below:

+-------+-------------+-------+

|       |             |       |

|       |             |       |

|       |             |       |

|  w    |      3z     |   w   |

|       |             |       |

|       |             |       |

|       |             |       |

+-------+-------------+-------+

   w           3zw           w

Each of the four smaller rectangles has an area of w(2w + 6z) or 2zw(2w + 6z), so the total area of the larger rectangle is:

Area = 2(w + 3z)²

    = 2(w² + 6wz + 9z²)

    = 2w² + 12wz + 18z²

We can interpret this area as the sum of the areas of the four smaller rectangles.

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The graph would show a line at the 10/40 mark or 25%.

A graph is a visual representation of data, usually in the form of a chart or diagram. It is used to illustrate relationships between different variables or to compare data points. Graphs can be used to explain a variety of topics, from economic trends and population growth to scientific data and statistical analysis. Graphs can help people better understand data and make informed decisions.

This would indicate that 25% of the sweets chosen in the first forty trials were blue.

(b) What is the theoretical probability of choosing a blue sweet.

The theoretical probability of choosing a blue sweet is 1/5 or 20%. This is because there are five different colors of sweets in the jar, and one of them is blue. Therefore, the probability of choosing a blue sweet is 1 out of 5, which is 20%.

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Answer:

\(\huge \boxed{\sf \bf x^2+10x+24}\)

Step-by-step explanation:

Hello,

This is the same logic as your other question

-6 and -4 are roots and the leading coefficient is 1 so the quadratic equation is

\((x+4)(x+6)=x^2+10x+24\)

Thanks

Answer:

m = - 1/4

Step-by-step explanation:

When two line is perpendicular to each other the product of them is - 1

So let the other line be B

Gradient of B = t

Gradient of A = 4

\(t \times 4 = - 1 \\ t = - \frac{1}{4} \)

therefore m = - 1/4

The correct answer is B. y = e4x is a solution of y' = -(1/4)y2 that is not a member of the family in part (b).

An equation is a mathematical statement that contains an equal sign. A solution is a value or set of values that make the equation true. A member refers to a specific solution within a family of solutions.

In this question, we are given a differential equation y' = -(1/4)y and asked to find a solution that is not a member of a given family of solutions. The family of solutions is not provided in the question, but it is implied that it is a set of solutions that have the form y = Ce^(-x/4), where C is a constant.

To find a solution that is not a member of this family, we need to find a different function that satisfies the differential equation y' = -(1/4)y. Option B, y = e4x, is such a function. We can verify that it is a solution by taking its derivative and plugging it into the differential equation:

y = e4x
y' = 4e4x

y' = -(1/4)y
4e4x = -(1/4)e4x

This equation is true, so y = e4x is indeed a solution of y' = -(1/4)y that is not a member of the given family.

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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The solution of expression is,

⇒ (6 + a⁴b) / a²b²

We have to given that,

An expression to solve is,

⇒ 6/a²b² + a²/b

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, WE can simplify the expression as,

⇒ 6/a²b² + a²/b

Take LCM;

⇒ (6 + a² × a²b)  / a²b²

⇒ (6 + a⁴b) / a²b²

Therefore, The solution of expression is,

⇒ (6 + a⁴b) / a²b²

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Answer:

\(x=-2\)

Step-by-step explanation:

\(x-x(3x-5)=x-2(x^2+x)-x^2-14\)

\(x-3x^2+5x=x-2x^2-2x-x^2-14\)

\(-x\)                 \(-x\)  

\(-3x^2+5x=-2x^2-2x-x^2-14\)

\(-3x^2+5x=-3x^2-2x-14\)

\(+3x^2\)             \(+3x^2\)

\(5x=-2x-14\)

\(+2x\)   \(+2x\)

\(7x=-14\)

\(\frac{7x}{7} =\frac{14}{7}\)

\(x=-2\)

Hope this helps!

Answer:

just find it then multiply it by 0.50 because 0.50 is 1/2 converted to a decimal and thats the scale factor

Step-by-step explanation:

Answer:

25\(\pi\)

Step-by-step explanation:

Use the area formula, A = \(\pi\)r²

Plug in 10 as the radius:

A = \(\pi\)(10²)

A = 100\(\pi\)

Since it is a 1/4 circle, divide this by 4:

100\(\pi\)/4

= 25\(\pi\)

So, the area is 25\(\pi\) or approximately 78.54

Answer: 25pi

Step-by-step explanation:

Give the person above me brainliest!

After solving the cost function, the cost of each small van is $8,500 and the cost of each large van is $15,000.

Let's use the variables x and y to represent the cost of a small van and a large van, respectively.

From the information given, we can set up a system of two equations:

5x + 2y = 72500

2x + 6y = 107000

We can solve for x and y by using any method of linear equations, such as substitution or elimination. Here, we'll use elimination:

Multiplying the first equation by 3 and the second equation by -1, we get:

15x + 6y = 217500

-2x - 6y = -107000

Adding these two equations, we eliminate the y variable:

13x = 110500

Dividing both sides by 13, we get:

x = 8500

Now we can use this value to find y:

5x + 2y = 72500

5(8500) + 2y = 72500

42500 + 2y = 72500

2y = 30000

y = 15000

Therefore, the cost of each small van is $8,500 and the cost of each large van is $15,000.

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Answer:

The cost of the 5 t-shirts would be of 564.83 Kronas.

Step-by-step explanation:

For this problem, we have that 7 t-shirts cost $90.93, hence the cost of a t-shirt in U.S. dollars is given applying the proportion to find the unit rate as follows:

$90.93/7 = $12.99.

The cost of 5 t-shirts will be given by:

5 x 12.99 = $64.95.

Applying the proportion 1 U.S. Dollar = 8.6964 Krona, the cost in Kronas is:

64.95 x 8.6964 = 564.83 Kronas.

The cost of the 5 t-shirts would be of 564.83 Kronas.