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The height of a cabinet is twice the width. The depth is 1.5 times the width. The volume of the cabinet is 5.184 in^3. What are the dimensions of the cabinet?

Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. (2xy2 − 3xy3)(2xy2 + 3xy3). So, correct answer is A.

To multiply two binomials, we use the FOIL method which stands for First, Outer, Inner, Last. For option A, using the FOIL method, we get

(2xy² - 3xy³)(2xy² + 3xy³) = (2xy²)² - (3xy³)² = 4x²y⁴ - 9x²y⁶

This is the given polynomial, so option A is correct.

For other option, we have two identical binomials multiplied together, which would give us a trinomial with three terms, so it cannot be a product of two binomials.

Option C is also incorrect because when we multiply the two binomials, we do not get the given polynomial. Option D is incorrect as well because the signs are incorrect and we would get a different polynomial when we multiply the two binomials.

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--The given question is incomplete, the complete question is given

" Given the polynomial 4x²y⁴ − 9x²y⁶, rewrite as a product of polynomials. a. (2xy² − 3xy³)(2xy² + 3xy³) b. (2xy² − 3xy³)(2xy² − 3xy³) c. (4xy² + 9xy³)(xy² − xy³) d. (4xy² − 9xy³)(xy² − xy³)"--

The true statement is that An integer programming solution can be better than the linear programming solution to the same problem. So, option(b) is right one.

In integer linear programming is harder than linear programming, because the branch-and–bound method requires many iterations of the simplex method, integer programming problems, So, option(a) is false one.

Hence, required answer is option(b).

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Complete question :

which of the following statements is true? group of answer choices

a) in general, it is no more difficult to solve an integer programming model than a linear programming one.

b) an integer programming solution is better than the linear programming solution to the same problem rounding does not necessarily.

c) provide feasible solutions and feasible solutions from rounding are not necessarily optimal.

d) all of these answers

The best prediction of the number of times Maverick should spin a 4 is 3 times.

Assuming the spinner is fair and unbiased, the best guess for how many times Maverick should spin a 4 is three.

The expected number of times a 4 should appear can be calculated by calculating the probability of spinning a 4 (1/5, or 0.2) by the total number of spins (15):

Expected number of 4's = Probability of spinning a 4 x Total number of spins

Expected number of 4's = 0.2 x 15

Expected number of 4's = 3

Therefore, the best prediction of the number of times Maverick should spin a 4 is 3 times.

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The amount of juice that can be poured into 6 cups with a diameter of 4.4 inches and a height of 7 inches is 638.30 cubic inches (rounded to the nearest hundredth).

Solution:We can use the formula to find the volume of a cylinder,V = πr²hwhere V is the volume of the cylinder, r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant approximately equal to 3.14.To begin solving this problem, we must first find the radius of the base of the cylinder.

Since the diameter of each cup is given as 4.4 inches, the radius is half of this, or 2.2 inches.Now we can use the formula for the volume of a cylinder, with r = 2.2 inches and h = 7 inches.V = πr²hV = 3.14(2.2)²(7)V ≈ 106.38 cubic inches

This is the volume of juice that can be poured into a single cup. To find the total volume of juice that can be poured into 6 cups, we multiply this by 6.6(106.38) ≈ 638.30 cubic inches

Therefore, the answer is 638.30 cubic inches.

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It is not possible for a subset of A to contain elements of Ac

To answer the question, "Can a subset of A contain elements of Ac?" we must first understand what these terms mean.

A subset of A is a set that contains only elements that are also in A. On the other hand, Ac is the complement of A, which is the set of all elements that are not in A. Therefore, an element that is in Ac is not in A.

Now, let us consider the possibility of a subset of A containing elements of Ac. If an element is in Ac, it is not in A. Therefore, it cannot be in any subset of A, as all elements of a subset must be in A. This means that it is not possible for a subset of A to contain elements of Ac.

In summary, It is not possible for a subset of A to contain elements of Ac because the complement of A includes all the elements that are not in A. Therefore, any element that is in Ac cannot be in any subset of A

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Complete Question:

Can a subset of A contain elements of Ac? Give reason.

The assertion will be correct and the reason provided is also correct.

A rational number is termed as a number which can be represented as the ratio of the two integers, where the denominator (q) will be not equal to zero. In other words, a rational number can be expressed in the form of a p/q, where p and q are the integers and q ≠ 0.

In the given reason, 17/3 is cited as an example of a rational number. Since both 17 and 3 are integers, and 3 ≠ 0, 17/3 can be expressed as the ratio of two integers, making it a rational number.

Therefore, the assertion will be true, and the reason provided is correct.

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An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.

From the given information, we have the following equations:

[tex]x = 2(y+z) - 40[/tex] (the largest angle is 40 degrees less than twice the sum of the other two angles)

[tex]x = 2z + 10[/tex] (the largest angle is twice the smallest angle plus 10 degrees)

[tex]x + y + z = 180[/tex] (the sum of the angles of a triangle is 180 degrees)

To simplify the system of equations, we can use the second equation to substitute for x in the first equation:

[tex]2z + 10 = 2(y+z) - 40[/tex]

Simplifying this equation, we get:

[tex]y = z + 25[/tex]

Now we can substitute x and y in terms of z into the third equation:

[tex]x + (z+25) + z = 180[/tex]

Simplifying this equation, we get:

[tex]x + 2z = 155[/tex]

Finally, we can substitute x in terms of z from the first equation into this last equation:

[tex]2(y+z) - 40 + 2z = 155[/tex]

Simplifying this equation, we get:

[tex]y + 3z = 97[/tex]

Therefore, the equations that represent this system are:

[tex]x = 2(y+z) - 40\\y = z + 25\\x + 2z = 155\\y + 3z = 97[/tex]

So the correct answers are:

[tex]a.) x=2y+10\\d.) x=2z+y-40\\e.) 2(y+z)-40[/tex]

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The equations that represent this system are:

a.) x=2y+10

d.) x=2z+y-40

e.) 2(y+z)-40

What is angles ?

An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.

From the given information, we have the following equations:

=> x=2(y+z)-40 (the largest angle is 40 degrees less than twice the sum of the other two angles)

=> x=2z+10 (the largest angle is twice the smallest angle plus 10 degrees)

=> x+y+z=180  (the sum of the angles of a triangle is 180 degrees)

To simplify the system of equations, we can use the second equation to substitute for x in the first equation:

=> 2z+10=2(y+z)-40

Simplifying this equation, we get:

y=z+45

Now we can substitute x and y in terms of z into the third equation:

x+z+25+z=180

Simplifying this equation, we get:

=> x+2z=155

Finally, we can substitute x in terms of z from the first equation into this last equation:

2(y+z)-40+2z=155

Simplifying this equation, we get:

y+3z=97

Therefore, the equations that represent this system are:

a.) x=2y+10

d.) x=2z+y-40

e.) 2(y+z)-40

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Answer:

A. 2

Step-by-step explanation:

Let's interpret the function.

First, let's look at the top section:

[tex]f(x)=x+2[/tex] if [tex]x < 1[/tex]

So, if the value of x is less than 1, to find f(x), we should add 2 to x.

Let's check if x is less than 1:

[tex]x=3\\x < 1\\3 < 1[/tex]

3 is not less than one, so to find f(x), we cannot add 2 to x.

The second part of the function is:

[tex]f(x)=x-1[/tex] if [tex]x\geq 1[/tex]

So, if the value of x is greater than or equal to 1, to find f(x), we should subtract 1 from x.

Let's check if x is greater than or equal to 1:

[tex]x=3\\x\geq 1=\\3\geq 1[/tex]

3 is greater than or equal to 1, so to find f(x), we should use x-1.

[tex]x-1=\\3-1=\\2[/tex]

Thus, f(3) = 2; the answer is A.

The equation for the proportional relationship between the number of hours Corrie works, h, and her total pay, P, can be represented as [tex]P = Ph[/tex].

If we assume that Corrie's pay rate is P dollars per hour, then the equation for the proportional relationship between the number of hours Corrie works, h, and her total pay, P, can be represented as P = Ph, which simplifies to:

P = hP

Here, the P is the pay rate in dollars per hour, and h is the number of hours worked. Note that this equation is similar to the original equation e = 23h, except that the constant of proportionality has been replaced with the pay rate, P.

Full question "The proportional relationship between the number of hours Corrie works, h, and his total earnings in dollars and cents, e, can be represented by the equation e = 23h. Write an equation for the proportional relationship between the number of hours Corrie works, h, and her total pay, P."

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Answer:

0.2 oz

Step-by-step explanation:

We Know

1g ≈ 0.035oz

5 gram = ? oz

We Take

0.035 x 5 ≈ 0.175 oz

So, 5 grams ≈ 0.2 oz

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:       This is called percent error this is how i solve.

                    8     20%

                    3     100%

          800. 60 =               48000          

To solve problems related to quadratic relations and conic sections, use the following formulae, respectively:

1. ax^2 + bx + c = 0

2. (x - h)^2 + (y - k)^2 = r^2

A quadratic relation is a type of equation in which the highest power of the variable is two. The general form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants and x is the variable.

This is closely related to conic sections which are geometric shapes that can be obtained by intersecting a plane with a double-napped cone. If we assume the equation of a circle with center (h, k) and radius r is, a good equation that can be used to resolve this will be:

(x - h)^2 + (y - k)^2 = r^2.

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The equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

(x, y) represents any point on the circle

A circle is described as a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The properties of the circle are as follows:

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The geometric mean of the given number is √3.

Hence option C is correct.

Use the concept of geometric mean  defined as:

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.

In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

The given numbers are,

1/4 and 12

Take a = 1/4 and b = 12

Now since we know the geometric mean of a and b = √ab

geometric mean  = [tex]\sqrt{\frac{1}{4}\times 12[/tex]

geometric mean  = √3

Hence,

The geometric mean for the given numbers is √3.

So option C is correct.

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Answer:

90 km/h

Step-by-step explanation:

There are 3600 seconds in an hour. So, let's multiply the unit rate by 3600.

[tex]3600*25=90000[/tex]

So, after 3600 seconds (or an hour), the car will have traveled 90000 meters.

Or, the car's rate is 90000 meters per hour.

1 meter is 0.001 kilometer. Let's multiply 90000 by 0.001 to find how many kilometers the car travels after an hour.

[tex]90000*0.001=90[/tex]

So, the car's speed is 90 km/h.

Answer:

Step-by-step explanation:

One minute is equal to 60 seconds modeled by the ratio 1:60 one hour is equal to 60 minutes modeled by the ratio 1:60 therefore using substitution 1hour:60minutes(1):60seconds(60) therefore 1:[tex]60^{2}[/tex] or 3,600 so in this instance 25m/s = 25:1 and because a km is equal to 1,000 meters as denoted by the prefix kilo. One can understand that multiplying by 1,000 is the same as dividing by 1,000 less therefore instead of doing (25*3600)/1000 you can simply do 25*3.6 which yields 90.

Therefore 2.5m/s = 90km/h

PS. For future reference, you can reference a free conversion tool if you find that easier to use.

Answer:

Step-by-step explanation:

1 )

a) quotient of powers as dividing two powers with the same base, we subtract the exponents.

b) product of powers when you are multiplying two terms with the same base, you add their exponents

c) property of negative exponents. According to the rules of exponents, a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.

2)

Yes, when raising a fraction to a power with parentheses, the same principles apply as when raising a fraction to a power without parentheses. When evaluating expressions with fractions and exponents, the order of operations, including parentheses, is followed. To re-write the expressions (1/3)^2 is = (1/9) and (1/3)^-2 is equal to 9 9*(1/9) is 1 which is the rule of the product of powers. then the same applies to the second expression

3)

[tex](-2.3^{2})^{6}[/tex]  power to a power rule

[tex](\frac{1}{4}) ^{3}[/tex] power of a quotient

[tex]6^{4}[/tex] power to a power rule

[tex]7^{-1}[/tex] product of powers

ps: please grade me appropriately if you need more help with problems I am glad to help and these stars mean a lot to me. make sure you study your exponent laws and all the best!

Therefore, the simplified form of the given expression is 7/36.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve one or more operations or functions. Expressions are an important concept in mathematics and are used in a wide range of applications, from simple arithmetic calculations to advanced mathematical modeling and analysis.

Here,

To simplify this expression, we can multiply the numerators of the fractions and multiply the denominators of the fractions, and then simplify the resulting fraction:

7/8 x 1/3 x 2/3 = (7 x 1 x 2)/(8 x 3 x 3)

= 14/72

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

14/72 = (2 x 7)/(2 x 36)

= 7/36

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Answer:

[tex] {10}^{32} {10}^{6} = {10}^{38} [/tex]

The new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

To rotate a triangle 270 degrees clockwise with the origin as the centre of rotation, you can follow these steps:

Draw the coordinates of the vertices of the triangle. Let's assume that the coordinates of vertex A are (x₁, y₁), the coordinates of vertex B are (x₂, y₂), and the coordinates of vertex C are (x₃, y₃).

To rotate the triangle 270 degrees clockwise, you need to reflect it first over the x-axis, and then over the y-axis.

To reflect the triangle over the x-axis, you need to change the sign of the y-coordinates of each vertex. So the new coordinates of vertex A would be (x₁, -y₁), the new coordinates of vertex B would be (x₂, -y₂), and the new coordinates of vertex C would be (x₃, -y₃).

To reflect the triangle over the y-axis, you need to change the sign of the x-coordinates of each vertex. So the final coordinates of vertex A would be (-y₁, x₁), the final coordinates of vertex B would be (-y₂, x₂), and the final coordinates of vertex C would be (-y₃, x₃).

These final coordinates represent the vertices of the rotated triangle.

So, the new vertices of the rotated triangle ABC are (-y₁, x₁), (-y₂, x₂), and (-y₃, x₃).

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Answer:

  144 m²

Step-by-step explanation:

You want to know the surface area of a square base pyramid with a side length of 6 m and a slant height of 9 m.

The area of the given net is the sum of the areas of 4 congruent triangles and one square. The areas of these can be found using the relevant formulas.

  SA = square area + 4 × triangle area

  SA = 6² + 4 × 1/2(6)(9) = 36 +108

  SA = 144 . . . . square meters

__

Additional comment

The area of a square of side s is A = s².

The area of a triangle with base b and height h is A = 1/2bh.

In a regression equation, the estimated coefficients represent the change in the dependent variable for a one-unit increase in the corresponding independent variable, holding all other independent variables constant.

For example, if the estimated coefficient for television advertising is 0.5, then we can interpret it as a $0.5 increase in the dependent variable (such as sales) for every one-unit increase in television advertising expenditure, holding newspaper advertising constant.

Whether the interpretations of the estimated coefficients are reasonable depends on the data and the research question being investigated. It is important to examine the statistical significance, magnitude, and direction of the estimated coefficients, as well as their practical relevance and theoretical soundness, to evaluate the validity and usefulness of the regression model.

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The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principia Mathematica" in 1687. The three laws are:

According to the given information:

a) When input is 10.

   output= 10×4 - 15 =25

b) From the question output is 25

  Because input* 4 -15= output. So (output +15) / 4= input

  so input =[tex](25+15)/4[/tex] =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principal Mathematical" in 1687. The three laws are:

The Law of Inertia: An object at rest will remain at rest, and an object in motion will continue in a straight line with constant velocity, unless acted upon by an external force.

The Law of Acceleration: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.

The Law of Action-Reaction: For every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.

According to the given information:

a) When input is 10.

  output= 10×4 - 15 =25

b) From the question output is 25

 Because input* 4 -15= output. So (output +15) / 4= input

 so input = =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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The area of Pac-Man to the nearest tenth mm² is 11.4 mm².

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.

To find the area of Pac-Man, we need to calculate the area of the sector that corresponds to the angle of his open mouth and subtract the area of the isosceles triangle formed by the two radii of the sector and the chord that represents the straight edge of his mouth.

First, we need to calculate the angle in radians that corresponds to the 60° angle given:

angle in radians = (60/360) x 2π = π/3 radians

Next, we can use the formula for the area of a sector:

Area of sector = (angle in radians / 2π) x πr²

where r is the radius of the circle.

Area of sector = (π/3 / 2π) x π(13mm)² ≈ 84.95 mm²

Now, we need to calculate the area of the triangle. We can use the formula for the area of an isosceles triangle:

Area of triangle = (1/2) x base x height

where the base is the chord that represents the straight edge of Pac-Man's mouth, and the height is half the length of the chord times the sine of half the angle of the mouth opening.

The base of the triangle is given by the formula:

base = 2r x sin(angle/2)

base = 2(13mm) x sin(30°) ≈ 22.52 mm

The height of the triangle is given by the formula:

height = (base / 2) x sin(angle/2)

height = (22.52 mm / 2) x sin(30°) ≈ 6.53 mm

Therefore, the area of the triangle is:

Area of triangle = (1/2) x base x height ≈ 73.5 mm²

Finally, we can subtract the area of the triangle from the area of the sector to get the area of Pac-Man:

Area of Pac-Man ≈ 84.95 mm² - 73.5 mm² ≈ 11.4 mm²

Therefore, the area of Pac-Man to the nearest tenth mm² is 11.4 mm².

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An observed effect (the difference between the observed value and the claimed value) is statistically significant if it is unlikely to have occurred due to chance variation.

An observed effect is statistically significant if it is unlikely to be due to chance variation, which means that the probability of observing such a large difference between the observed value and the claimed value purely by chance is very small.

In statistical hypothesis testing, this probability is quantified by a p-value, which is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

If the p-value is less than a pre-specified significance level (e.g., 0.05), the null hypothesis is rejected, and the observed effect is deemed statistically significant.

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The graph of the data from the table is added as an attachment

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

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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