Roy bought a board game for $22. Then, he marked up the price of the board game and resold it for $25.78. What percentage of the original price was the markup rate?

General solution = CF + PS= c₁ cos 5x + c₂ sin 5x - (2/25) tan 5x= C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)), where C = c₂ and D = c₁.

Explanation:

The general solution of the given non-homogeneous differential equation: y"(x) + 25y(x) = 2tan 5x isy (x) = C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)).

First of all, we need to find the complementary function(CF) of the differential equation to find the general solution.To find the complementary function (CF),

we set the non-homogeneous term to 0.y" (x) + 25y (x) = 0T

his is a homogeneous differential equation with the characteristic equation: r² + 25 = 0Solving this quadratic equation gives:r = ± 5i

Hence, the complementary function is given by:CF = c₁ cos 5x + c₂ sin 5xwhere c₁ and c₂ are constants of integration.

Now, we find the particular solution (PS) of the given non-homogeneous differential equation using the method of undetermined coefficients.

Given, y" (x) + 25 y (x) = 2 tan 5x

For PS, we assume that y = A tan 5x + B

where A and B are constants to be determined.Substituting this in the given equation, we get:10A sec² 5x + 25(A tan 5x + B) = 2 tan 5x

Simplifying this equation, we get:10A sec² 5x + 25A tan 5x + 25B = 2 tan 5x⇒ 10A sec² 5x + 23A tan 5x + 25B = 0

Comparing the coefficients of tan 5x and sec² 5x on both sides, we get:A = -2/25 and B = 0

Hence, the particular solution is given by:PS = - (2/25) tan 5xNow, the general solution of the given non-homogeneous differential equation is given by

:GS = CF + PS= c₁ cos 5x + c₂ sin 5x - (2/25) tan 5x= C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)), where C = c₂ and D = c₁.

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Answer:

Step-by-step

To make 100 to 250, you need to multiply 100 by 2.5 to make 250. In the similar way you need to multiply 80 by 2.5 which equals 200 which is the answer

Answer:

Step-by-step explanation:

Its the 3rd one

The total cost of the items if they were not sold as a combo is R137.

Let's assume that the individual prices of the two items are X and Y. Here we have to use the concept of algebraic equation. We have two unknowns (X and Y), and we use the information given about their combined cost and the savings made when sold as a combo to form an equation in terms of X and Y

When the items are sold individually, the total cost would be X + Y.

When the items are sold together as a combo, the cost is R100, and this saves R37 compared to the individual prices. This means:

X + Y - 37 = 100

Simplifying the above equation, we get:

X + Y = 137

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The length of QR, considering the intersecting chords in the circle, is given as follows:

QR = 26.4.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

The product to obtain the length QR is given as follows:

37QR = 25 x 39

Then the length QR is given as follows:

QR = 25 x 39/37

QR = 26.4.

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Answer:

A= 2w^2 + 11w +12

Step-by-step explanation:

(w + 4)(2w + 3) = l x b = A

2w^2 + 3w +8w +12 = A

A= 2w^2 + 11w +12

Answer:

8x^(3)+10x^(2)-13x-15

Step-by-step explanation:

The area of the parallelogram above is 490 metres squared.

A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The area of a parallelogram can be calculated as follows:

area of a parallelogram = bh

where

Therefore,

b = 49 metres

h = 10 metres

Therefore,

area of a parallelogram = 10 × 49

area of a parallelogram = 490 metres squared

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Answer:The first table is linear.  The other are not linear.

Step-by-step explanation:

Step-by-step explanation:

p-grams have equal opposite side lengths

soooo  

 5x+7   =  27  

               x = 4

then 22x = 22(4) = 88  units      ( this is also AB length)

Factorization of the given polynomial is: (x - 15)(x - 15).

The length of a side is: x = 15

In the case of polynomials in mathematics, the factors of the polynomials are the polynomials which are multiplied to produce the original polynomial. For example, the factors of x² + 5x + 6 is (x + 2) (x + 3).

When we multiply both x + 2 and x  +3, then we will see that the original polynomial is generated.

We are given the polynomial as:

A = x² - 30x + 225

This can be broken down into:

A = x² - 15x - 15x + 225

A = x(x - 15) - 15(x - 15)

A = (x - 15)(x - 15)

Thus:

x = 15

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The radius of the sphere with a volume of 4,500π cubic inches is 15 inches, not 2,000 inches as the student had incorrectly calculated.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The volume of the sphere is given as 4,500π cubic inches.

The formula for volume of the sphere is -

V= 4/3πr³

Substituting the values in the equation -

4,500π = 4/3πr³

4,500 = 4/3r³

The mistake in the student's calculation is in the step where they simplified 4/3πr³ to 4,500.

To correct this, we need to isolate r³ by dividing both sides by 4/3 -

4,500 = (4/3)r³

4,500 ÷ (4/3) = r³

4,500 × 3/4 = r³

3,375 = r³

Then, we can take the cube root of both sides to find r -

r = ∛3,375 = 15

Therefore, the radius of the sphere is 15 inches.

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Answer:

The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.

The rectangular prism in question has the following dimensions:

Length (l) = 3 cm

Width (w) = 5 cm

Height (h) = 4 cm

Using the formula for volume, we get:

V = l x w x h

= 3 cm x 5 cm x 4 cm

= 60 cm³

Therefore, the volume of the rectangular prism is 60 cm³.

The answer is (d) 60 cm³.

I Hope This Helps!

we need to buy at least 694 tickets to have a probability of winning at least 50%.

We can use the binomial distribution formula to solve this problem. Let X be the number of tickets we need to buy to have a probability of winning at least 50%. Then:

P(X ≥ 1) ≥ 0.5

This means that the probability of winning with at least one ticket is at least 50%. We can find this probability using the complement rule:

P(X ≥ 1) = 1 - P(X = 0)

The probability of not winning with any ticket is:

P(X = 0) = (999/1000)^n

where n is the number of tickets we buy. Therefore:

1 - (999/1000)^n ≥ 0.5

Simplifying this inequality, we get:

(999/1000)^n ≤ 0.5

Taking the logarithm of both sides, we get:

n log(999/1000) ≤ log(0.5)

n ≥ log(0.5) / log(999/1000)

n ≥ 693.15

Therefore, we need to buy at least 694 tickets to have a probability of winning at least 50%.

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The Polynomials that are listed in the question are the options labelled;

B, C, E

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents.

The variables represent unknown values, while the coefficients are constants that multiply the variables or their exponents. The exponents indicate the power to which the variables are raised.

Polynomials can be added, subtracted, multiplied, and divided to create more complex expressions, and they are used in a wide range of mathematical applications, including algebra, calculus, and geometry.

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As per the given triangle, the scale factor is 24/5

To identify the scale factor, we can choose two corresponding sides of the triangles and set up a proportion. Let's choose the legs of the triangles. We know that the length of the left leg is 5, and the length of the right leg is 25/4. Therefore, we can write:

5/x = 25/4/12

Here, x represents the length of the corresponding leg of the right triangle. We can simplify this proportion by cross-multiplying:

5 x 12 = (25/4) x (x)

Multiplying both sides by 4/25, we get:

(4/25) x 5 x 12 = x

Simplifying, we get:

x = 24/5

Therefore, the scale factor is 24/5. This means that if we multiply the lengths of any side of the left triangle by 24/5, we will get the corresponding length of the right triangle.

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Complete Question:

The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.

5 and 12, 25/4 and 15

Answer:

,,,

Step-by-step explanation:

Answer:

Scientifically proven that there is a 60% chance you will get an odd number and a 40% chance you will get an even number.

I hope this helps!!

The conditions does the function f(x) to meet in order to be able to use the integral test to verify convergence or divergence is

1) f(x) must be continuous, positive, and decreasing for all x greater than some fixed value N.

2) The series to be tested must have non-negative terms.

3) The integral of f(x) from N to infinity must converge or diverge.

To use the integral test to verify the convergence or divergence of an infinite series, the following conditions must be met for the function f(x)

1) f(x) must be continuous, positive, and decreasing for all x greater than some fixed value N.

2) The series to be tested must have non-negative terms.

3) The integral of f(x) from N to infinity must converge or diverge.

If these conditions are met, then the integral test can be used to determine whether the series converges or diverges. Specifically, if the integral of f(x) converges, then the series converges. On the other hand, if the integral of f(x) diverges, then the series also diverges.

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One of the advantages of buying a franchise is that the purchaser has access to a proven business system is true.

Explanation:

A franchise is a company's business model and brand name that it allows to be used by third parties in exchange for a fee. The individual or entity who pays the fee is referred to as the franchisee. The purchaser of the franchise receives a licence to use the franchisor's trade name, business systems, operational procedures, goods, and other intellectual property, among other things. The franchisee is also required to follow certain operational protocols and sales/marketing strategies, as well as purchase products from the franchisor. For various reasons, a franchise is often viewed as a low-risk business opportunity for a potential business owner. Among the numerous advantages of buying a franchise, the ability to access a proven business system is one of the most important.

                         A proven business system is a set of guidelines, operational procedures, marketing and sales strategies, and other tools that have been shown to be effective for a particular franchise. By using a proven business system, the franchisee is less likely to fail and more likely to succeed. As a result, a franchisee's revenue stream will be more stable, allowing for long-term growth and success.

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Step-by-step explanation:

A negative divided by a negative gives a positive

If we put the biggest negative divided by the smallest negative, that gives our best chance

[tex] \frac{ - 10}{ - (\frac{2}{5} )} = 25[/tex]

this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.

a) The equation that represents this situation is:

2x + 2y = 175

where x is the length of the short sides (in feet) and y is the length of the long sides (in feet).

b) The equation in terms of y is:

2(6) + 2y = 175

which simplifies to:

12 + 2y = 175

2y = 163

y = 81.5

However, this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.

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The expression that could result in a final unit measure of dollars is given by (mnk²) dollars.

To write an expression that could result in a final unit measure of dollars, we need to consider the units given.

We have three units, i.e., m feet, n feet, and k dollars per square foot.

To convert these units to dollars, we need to multiply the given units with appropriate conversion factors.

The conversion factor for the given units is as follows:

Unit 1: 1 foot = k dollars (Conversion factor)

Unit 2: 1 foot = k dollars (Conversion factor)

Unit 3: 1 square foot = 1 x k dollars = k dollars (Conversion factor)

Now, let us write the expression that results in a final unit measure of dollars.

The expression should be written in HTML format.

Let us begin: Final Unit Measure = (Unit 1) x (Unit 2) x (Unit 3)

Final Unit Measure = (m feet) x (n feet) x (k dollars per square foot)

Final Unit Measure = m x k dollars x n x k dollars per square foot

Final Unit Measure = (m x k x n x k) dollars

Final Unit Measure = (mnk²) dollars.

Thus, the expression that could result in a final unit measure of dollars is given by (mnk²) dollars.

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The expression (5/7)^-1  can be written without an exponent as 8/5.

Exponents have a number of important properties, such as the product rule (a^m × a^n = a^(m+n)) and the power rule ((a^m)^n = a^(m*n)). They are used in a wide range of mathematical contexts, including algebra, calculus, and geometry.

Given that (5/8)^-1, then we can deduced that the  negative exponent is the samething as putting it in the denominator, which can be exprtessed as;

=[1/ (5/8)]

=[1 ÷ (5/8)]

[1 * 8/5]

=8/5

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the correct answer is either (c) or (d), depending on the size of the object. If the object is small, the base is likely to be a triangle with an area of 6in2. If the object is larger, the base is likely to be a triangle with an area of 12in2.

The question asks about the shape and area of the base of an object. The possible answers are a rectangle with an area of 60in2, a rectangle with an area of 32in2, a triangle with an area of 6in2, and a triangle with an area of 12in2.

To determine the correct answer, it is important to understand what the base of an object is. The base is the surface upon which the object rests, and it is often a flat, two-dimensional shape. The area of the base is the measure of the surface area of that shape.  

Answer (a) is a rectangle with an area of 60in2. This means that the length and width of the rectangle multiply to give a product of 60. However, we are not given any measurements of the object, so we cannot determine if this is correct.

Answer (b) is a rectangle with an area of 32in2. Again, we are not given any measurements of the object, so we cannot determine if this is correct.

Answer (c) is a triangle with an area of 6in2. This means that the base and height of the triangle multiply to give a product of 12, and then divide by 2 to get an area of 6.

Answer (d) is a triangle with an area of 12in2. This means that the base and height of the triangle multiply to give a product of 24, and then divide by 2 to get an area of 12.

Based on this information, we can see that the correct answer is either (c) or (d), depending on the size of the object. If the object is small, the base is likely to be a triangle with an area of 6in2. If the object is larger, the base is likely to be a triangle with an area of 12in2.

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If a sample of 50 items are chosen at random.  the probability that the sample mean length is greater than 9.1 inches is 0.0571, or 5.71%.

The sample mean of the 50 items follows a normal distribution with mean equal to the population mean (μ), and standard deviation  equal to σ/√n, where n is the sample size.

Substituting the given values, we have:

= μ = 9 inches

= σ/√n = 1/√50 inches

Now, we need to standardize the sample mean distribution to find the corresponding z-score using the formula:

z = (X- μX) / σX

Substituting the given values, we have:

z = (9.1 - 9) / (1/√50) = 1.58

The probability of getting a z-score of 1.58 or less is 0.9429. Therefore, the probability of getting a z-score of 1.58 or greater is:

P(z > 1.58) = 1 - P(z ≤ 1.58) = 1 - 0.9429 = 0.051

Therefore the probability that the sample mean length is greater than 9.1 inches is 0.0571.

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As a result, 37.6 is the number of x in the provided diagram as The fact that angles x and z are opposite angles in a parallelogram.

A triangle is a two-dimensional polygon with three straight edges and three angles in geometry. The most basic polygon, it serves as the foundation for more complicated shapes. Triangles can be categorized based on the lengths of their sides and the angles in their angles. Triangles can be categorized as either equilateral (all three sides are equal) or isosceles (two sides are equal) or scalene (three sides are equal) (all three sides are different lengths). Triangles can be categorized as acute, right, or oblique based on how many angles they have. Acute triangles have three angles that are all less than 90 degrees (one angle is greater than 90 degrees).

given

x + y + z = 180

By replacing y = 3x - 8 we obtain:

x + (3x - 8) + z = 180

When we simplify this solution, we obtain:

4x - 8 + z = 180

8 is added to both parts to arrive at:

4x + z = 188

The fact that angles x and z are opposite angles in a parallelogram, indicating that they are identical, can be used to determine the value of x. As a result, we have:

x = z

The result of adding x = z to the formula 4x + z = 188 is:

5x = 188

When we multiply both sides by 5, we get:

x = 37.6

As a result, 37.6 is the number of x in the provided diagram as The fact that angles x and z are opposite angles in a parallelogram.

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The altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.

Altitude refers to the height of an object or location above a specific reference point, usually the Earth's sea level. In aviation, altitude is often used to describe the height of an aircraft above sea level, and is measured in feet or meters.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which are functions of an angle, and are used to relate the angles and sides of a right triangle.

In the given question,

To solve this problem, we need to use trigonometry and the fact that the plane descended at a 2° angle. Let's assume that the altitude of the plane at the George Washington Bridge is h feet.

Using trigonometry, we know that the tangent of the angle of descent is equal to the difference in altitude divided by the horizontal distance traveled. In this case, we have:

tan(2°) = (h - e) / 6

To solve for h, we need to isolate it on one side of the equation. Multiplying both sides by 6, we get:

6 tan(2°) = h - e

Adding e to both sides, we get:

h = 6 tan(2°) + e

We can use a calculator to find the tangent of 2°, which is approximately 0.03492. Substituting this value and the given distance of 6 miles into the equation, we get:

h = 6(0.03492) + e

h = 0.2095 + e

Therefore, the altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.

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Answer:

Step-by-step explanation:

We can use the simple interest formula to solve this problem. The formula is:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial amount of money)

r = Interest rate per year (as a decimal)

t = Time (in years)

From the problem statement, we know that:

I = $80.00

r = 0.04 (4% as a decimal)

t = 8 years

Substituting these values into the formula, we get:

$80.00 = P * 0.04 * 8

Simplifying:

$80.00 = 0.32P

Dividing both sides by 0.32, we get:

P = $250.00

Therefore, the principal is $250.00.

The statement "Cleanups may be carried out by the Environmental Protection Agency or private parties" is true of the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), also known as Superfund.

What is the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA)?

The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), commonly known as Superfund, is a United States federal law aimed at cleaning up sites contaminated with hazardous substances as well as preventing future hazardous waste site contamination.

CERCLA was passed by the United States Congress in December 1980 as a means of counteracting the increasing risk of hazardous waste sites in the United States.

What does CERCLA cover?

CERCLA was enacted to offer a federal "Superfund" to clean up uncontrolled or abandoned hazardous waste sites, as well as responding to oil spills, chemical disasters, and other emergencies that present a threat to the public health and the environment.

Cleanups may be carried out by the Environmental Protection Agency or private parties.

When it comes to financing these cleanups, the law mandates that those responsible for the contamination pay for the cleanup or those who do not take responsibility for the pollution.

The legislation was enacted to provide for the cleanup of the country's most hazardous waste sites and to ensure that businesses that generate hazardous waste are held responsible for their toxic contributions to the environment.

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The probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460 is very low, almost zero.

To calculate the probability of obtaining a sample result of a mean of $470 or more, we need to use the sampling distribution of the mean.

Assuming that the sample size is large enough and that the sample means are normally distributed, we can use the central limit theorem to approximate the sampling distribution of the mean to a normal distribution. We can standardize the sample mean using the formula

z = (x - μ) / σ,

where x is the sample mean, μ is the population mean, and σ is the standard error of the mean.

In our case, we want to find the probability of obtaining a sample mean of $470 or more. We can convert this to a z-score by standardizing it using the formula

z = (470 - 460) / (σ / √n),

where n is the sample size.

If the sample size is 100 and the population standard deviation is 10, then the standard error of the mean is 1. We can then calculate the z-score as

=> z = (470 - 460) / (1 / √100) = 10.

We can look up the probability of obtaining a z-score of 10 or greater in a standard normal distribution table, which is almost zero.

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