find the product 2 1/3 • 3 1/2 write the answer as a mixed number​

Answer:

I think 3 have more, but I am not 100 percent

Mean=23

Median=21.5 its a hard one to do so yeah

Modes=28

Range=22

Step-by-step explanation:

average means the sum of all values divided by a number of values

Answer:

15 kg, 22.5 kg, 52.5 kg

Step-by-step explanation:

Let the common multiplier of the given ratios be x. Therefore, weights of each bag would be 2x, 3x and 7x

According to the given information:

\(2x + 3x + 7x = 90 \\ 12x = 90 \\ x = \frac{90}{12} \\ x = 7.5 \: \\ \implies \\ 2x = 2 \times 7.5 = 15 \: kg \\ 3x = 3 \times 7.5 = 22.5 \: kg \\ 7x = 7 \times 7.5 = 52.5 \: kg\)

Hence the weight of sand in bag would be 15 kg, 22.5 kg and 52.5 kg

The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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The answer would be D.) 29.8 units

Hope this helps have a great day :)

1. The length is 14 inches and the width is 8 inches. 2. The two consecutive odd integers with a sum of squares equal to 74 are 5 and 7. 3. The two real numbers with a sum of 10 and a product of 22 are 2 and 8. 4. The solution to the inequality -x² + 6x + 7 ≥ 0 is x ≤ -1 or x ≥ 7.

1. To find the length and width of the rectangle, we can set up two equations. Let L be the length and W be the width. We know that 2L + 2W = 44 (perimeter) and L * W = 112 (area). Solving these equations simultaneously, we find L = 14 inches and W = 8 inches.

2. Let the two consecutive odd integers be x and x + 2. The sum of their squares is x² + (x + 2)². Setting this equal to 74, we get x² + (x + 2)² = 74. Expanding and simplifying the equation gives x² + x² + 4x + 4 = 74. Combining like terms, we have 2x² + 4x - 70 = 0. Factoring this quadratic equation, we get (x - 5)(x + 7) = 0. Therefore, the possible values for x are -7 and 5, but since we need consecutive odd integers, the solution is x = 5. So the two consecutive odd integers are 5 and 7.

3. Let the two real numbers be x and y. We know that x + y = 10 (sum) and xy = 22 (product). From the first equation, we can express y as y = 10 - x. Substituting this into the second equation, we get x(10 - x) = 22. Expanding and rearranging terms, we have -x² + 10x - 22 = 0. Solving this quadratic equation, we find x ≈ 2.28 and x ≈ 7.72. Therefore, the two real numbers are approximately 2.28 and 7.72.

4. To solve the inequality -x² + 6x + 7 ≥ 0, we can first find the roots of the corresponding quadratic equation -x² + 6x + 7 = 0. Using factoring or the quadratic formula, we find the roots to be x = -1 and x = 7. These roots divide the number line into three intervals: (-∞, -1), (-1, 7), and (7, ∞). We can then test a point from each interval to determine if it satisfies the inequality. For example, plugging in x = -2 gives us -(-2)² + 6(-2) + 7 = 3, which is greater than or equal to 0. Therefore, the solution to the inequality is x ≤ -1 or x ≥ 7.

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Answer:

-8 and 7 is the answer

-8*7 is -56

and -8+7 is -1

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer: True.  A sample is a subset of a population

Step-by-step explanation:

Answer:

1.11 is the answer

Best of luck

Step-by-step explanation:

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

Given

r= 2cost and theta = 9t

To Find

the velocity and acceleration vector

Solution

We can start by expressing the position vector r in terms of the Cartesian coordinates x and y:

x = r cos(theta) = 2cos(t)

y = r sin(theta) = 2sin(t)

To find the velocity vector, we can take the time derivative of the position vector:

v = (dx/dt) i + (dy/dt) j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the derivatives:

dx/dt = -2sin(t)

dy/dt = 2cos(t)

Substituting these back into the velocity vector equation:

v = (-2sin(t)) i + (2cos(t)) j

To find the acceleration vector, we can take the time derivative of the velocity vector:

a = (d^2x/dt^2) i + (d^2y/dt^2) j

Taking the derivatives:

d^2x/dt^2 = -2cos(t)

d^2y/dt^2 = -2sin(t)

Substituting these back into the acceleration vector equation:

a = (-2cos(t)) i + (-2sin(t)) j

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

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Answer:

B

Step-by-step explanation:

Just answer it nznnznkskosoaksns

Answer:

L={∅}

Step-by-step explanation:

When we express the equation 2x - y = 12 in slope intercept form, the result obtained is y = 2x - 12 (2nd option)

The slope intercept form for an equation is written as illustrated below:

y = mx + c

Where

With the above information, we can obtain the slope intercept form of the equation. Details below:

2x - y = 12

Rearrange to make y the subject of the expression, we have

2x = 12 + y

y = 2x - 12

Thus, we can conclude that the equation in the slope intercept form is

y = 2x - 12 (2nd option)

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Complete question:

Given the equation 2x - y = 12, which equation is written in slope intercept form?

y = -2x + 12

y = 2x - 12

y = 2x + 12

y = -2x - 12

The inequality 4(x – 3) + 4 < 10 + 6x is solved as x > -9. Then the variable x is greater than the negative 9. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign.

The inequality equation is given below.

4(x – 3) + 4 < 10 + 6x

Then the steps of solving are given below.

1. The distributive property: 4x – 12 + 4 < 10 + 6x

2. Combine like terms: 4x – 8 < 10 + 6x

3. The addition property of inequality: 4x < 18 + 6x

4. The subtraction property of inequality: –2x < 18

5. The division property of inequality: x > –9

Then x is greater than the negative 9.

Then the correct option is B.

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The eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

An eigenvector is a non-zero vector that, when multiplied by a matrix, results in a scalar multiple of itself. In other words, if A is a square matrix and v is an eigenvector of A, then Av = λv, where λ is the eigenvalue associated with v.

Given the eigenvalues and eigenvectors for matrix A as λ1 = 2, v1 = [-5 1]ᵀ and λ2 = 6, v2 = [5 4]ᵀ, we can say that:

- Av1 = λ1v1 = 2[-5 1]ᵀ = [-10 2]ᵀ
- Av2 = λ2v2 = 6[5 4]ᵀ = [30 24]ᵀ

Therefore, the eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

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The coordinates of the image of point D are (- 6, - 4) and a representation  of the rigid transformation is shown in the picture attached below.

Herein we find the location of point D, which is set on Cartesian plane and must be modified by the use of a rigid transformation known as dilation. The general definition of the dilation rule is defined below:

D'(x, y) = O(x, y) + k · [D(x, y) - O(x, y)]

Where:

If we know that O(x, y) = (0, 0), D(x, y) = (- 3, - 2) and k = 2, then the coordinates of the image are:

D'(x, y) = (0, 0) + 2 · [(- 3, - 2) - (0, 0)]

D'(x, y) = (- 6, - 4)

Now we proceed to present the location of the image on the Cartesian plane.

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Answer:

Step-by-step explanation:

Answer: 84

Step-by-step explanation:

ratio of 7:1

one dozen is 12 cookies

two dozen is 24 cookies (12 x 2)

7:1
x:12

cross multiply

7 x 12= 84

84/1= 84

Answer: 168

Step-by-step explanation: If it's wrong sorry.

you first set up a proportion with the given information, chocolate chips on top and the cookie number of bottom. For the second fraction in the proportion you put x/24 because we're assuming x is the number of cookies and we get 24 on the bottom because it says two dozen cookies. the proporiton will then look like this: 7/1=x/24 you then cross multiply and get, x=168. The answer is 168

The interpretation of -600 is (a) the slope of the function and the change in distance remaining, in meters per minute, of riding the bus

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

f(t) = -600t + 12000

A linear equation is represented as

y = mx + c

Where

Slope = m

When the equations are compared, we have

m = -600

This means that

Slope = -600

So, the interpretation of -600 is the slope

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Mathematical modeling of surfaces is the representation of two-dimensional manifolds using mathematical techniques, particularly in the context of Digital Terrain Modeling (DTM) where surfaces refer to the Earth's terrain or physical objects.

Mathematical modeling of surfaces plays a crucial role in various fields, including computer graphics, engineering, and geosciences. Surfaces are fundamental objects that can be represented and analyzed using mathematical techniques.

In this section, we will delve into the concept of surfaces, particularly in the context of Digital Terrain Modeling (DTM). Additionally, we will explore the distinction between 3D and 2D DTM.

1. The Concept of Surfaces:

In the realm of mathematics, a surface is defined as a two-dimensional manifold, meaning it is a topological space that locally resembles Euclidean space.

In simpler terms, a surface is a geometrical entity that can be thought of as a continuous collection of points, forming a boundary between a solid and its surrounding space. In the context of DTM, surfaces typically refer to the representation of the Earth's terrain or any other physical object using mathematical models.

2. Digital Terrain Modeling:

Digital Terrain Modeling involves the creation of digital representations of the Earth's surface or any specific region using computer algorithms. It serves as a crucial tool in various applications, such as urban planning, environmental analysis, and military simulations. DTM utilizes mathematical models to represent the terrain accurately, allowing for detailed analysis and visualization.

3. 3D Digital Terrain Models:

A 3D Digital Terrain Model (DTM) is a representation of the Earth's surface that captures three-dimensional information. It provides a detailed depiction of the terrain, including elevation data, contours, and topographical features.

3D DTMs are typically generated using techniques such as LiDAR (Light Detection and Ranging) or photogrammetry. These models enable precise analysis of the landscape, volumetric calculations, and visualization from different perspectives.

4. 2D Digital Terrain Models:

In contrast to 3D DTMs, 2D Digital Terrain Models represent the Earth's surface in two dimensions. They provide a simplified view of the terrain, focusing primarily on elevation data and contour lines. 2D DTMs are commonly used in cartography, where the terrain is represented on a flat surface, such as a map or a computer screen. While they lack the depth information of 3D DTMs, 2D models are still valuable for many applications, including geographic information systems (GIS) and land surveying.

5. Differences between 3D and 2D Digital Terrain Models:

The main distinction between 3D and 2D DTMs lies in the level of detail and the dimensionality of the representation. 3D DTMs provide a more comprehensive and realistic view of the terrain, capturing not only the elevation but also the shape, slopes, and other three-dimensional features. These models are highly suitable for applications that require a precise understanding of the terrain's topography, such as hydrological analysis or landscape design.

On the other hand, 2D DTMs offer a simplified representation of the terrain, primarily focusing on elevation data and contour lines. They are more commonly used for general visualization and analysis purposes where the third dimension is not critical. 2D DTMs are easier to create and process, making them more accessible for applications that do not require intricate three-dimensional modeling.

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(E) "Increase the sample size to 200 children"

To increase the statistical power in this context, where the program sponsors believe the program is effective, we need to consider methods that would increase the likelihood of detecting a statistically significant improvement in mathematics skills.

Statistical power is the probability of correctly rejecting the null hypothesis when it is false (i.e., detecting a true effect). In this case, the null hypothesis would be that there is no improvement in mathematics skills due to the program.

Among the options provided, the most appropriate method for increasing power would be to increase the sample size.

By increasing the sample size, we can reduce sampling variability and increase the precision of our estimates. This would lead to narrower confidence intervals and a higher likelihood of detecting a statistically significant improvement in mathematics skills if the program is indeed effective.

The other options, (A) "Use a two-sided test instead of a one-sided test," (B) "Use a one-sided test instead of a two-sided test," (C) "Use a = 0.01 instead of a = 0.05," and (D) "Decrease the sample size to 50 children," do not directly address the issue of increasing statistical power and may not necessarily improve the ability to detect a true effect.

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Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as

Line slope is a measure of the steepness or direction of a line in the coordinate plane.  

m = Δy/Δx

where,m is the slope

Given,

equations of the line

3x - 5y = 2

Moving 3x to RHS
-5y = -3x + 2

y = (3/5)x - 2/5

comparing with slope intercept equation of the line y = mx + c

slope m₁ = 3/5

Now, equation

3x + 5y = -2

moving 3x to RHS

5y = -3x - 2

y = (-3/5)x - 2

comparing with slope intercept equation of the line y = mx + c

slope m₂ = -3/5

Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.

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Answer:

sqrt 23,  180%, 1 2/7, (sqrt49)/7, pi-5

Step-by-step explanation:

sqrt 23 is between the integers 4 and 5 and closer to 5 and we can use these two reference points to base off the rest of our numbers

180% is essentially 180/100 which again is equal to 1.8 and is far less than sqrt 23s rough estimation of 4

1 2/7 is roughly 1.3 when they are made into decimal form and so that is rounded up and is closer to something around 1.28 but for our purposes, we shouldn't need to use this and 1.3 is just an easier number to work with.

sqrt49 is essentially a question asking what times itself becomes 49. That is 7 and 7/7 is just 1.

pi - 5 is like asking what is 3.14159 -5 and we dont even need to use this complex decimal. We can turn it to 3.5 rounding far up and still get a negative number which is far less than any other number on the list

Yes, Set K is a function.

To determine if Set K is a function, we need to check if for every x-value in Set K, there is a unique corresponding y-value.

Set K is defined as {(x, y) | x - y = 5}.

This means that any pair (x, y) in Set K must satisfy the equation x - y = 5.

To test if it is a function, we can consider two scenarios:

If we fix a value for x, is there a unique value for y that satisfies the equation x - y = 5?

If we fix a value for x, say x = 7, we can substitute it into the equation and solve for y:

7 - y = 5

-y = 5 - 7

-y = -2

y = 2

In this case, there is a unique value of y (y = 2) that satisfies the equation x - y = 5 when x = 7.

If we fix a value for y, is there a unique value for x that satisfies the equation x - y = 5?

If we fix a value for y, say y = 3, we can substitute it into the equation and solve for x:

x - 3 = 5

x = 5 + 3

x = 8

In this case, there is a unique value of x (x = 8) that satisfies the equation x - y = 5 when y = 3.

Since for every x-value in Set K, there is a unique corresponding y-value, and vice versa, we can conclude that Set K is indeed a function.

Therefore, Set K is a function.

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer:

\(a=9\)

Step-by-step explanation:

In this problem, you can use the Pythagorean Theorem (\(a^{2} +b^{2} =c^{2}\)) to find what a is. The steps are shown below:

Steps (variables a, b, and c are in italics):

-You can rearrange the formula from the Pythagorean Theorem, which is\(a^{2} +b^{2} =c^{2}\) to only get a because we want to know what a is.

Rearranged: \(a=\sqrt{c^{2}-b^{2} }\) or \(a=-\sqrt{c^{2}-b^{2} }\)  It has to ways/options for a because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.

-Since we know what c and b are, you can plug them into the new formula:

\(a=\sqrt{15^{2}-12^{2} }\)

-Simplify it:

\(a=\sqrt{225-144}\)

-Subtract inside the radical:

\(a=\sqrt{81}\)  Then simplify it to get \(a=9\).

You can check your answer by putting a back into the original Pythagorean Theorem formula (\(a^{2} +b^{2} =c^{2}\)):

Steps

-Plug a, b, and c into the formula \(a^{2} +b^{2} =c^{2}\):

\((9)^{2} +(12)^{2} =(15)^{2}\)

-Simplify to get:

\(81+144=225\)

-Add:

\(225=225\)  This is very true. So our answer is correct.

ANSWER: \(a=9\)

Sorry for the long explanation, but I hope you understand and that this helps with your question! :)

Answer:

Step-by-step explanation:

lets make is short and simple

Pythagorean theorem: a² + b² = c²

a² + 12² = 15²

a² = 15² - 12²

a = √81

a = 9

The small manufacturing firm should produce 30 items per day to minimize the unit cost C(x) = \(x^2\)-60x+5500..

Given that, the unit cost C(x) in dollars of producing x units per day is given by C(x) =  \(x^2\) - 60x + 5500. The given equation can be written as, C(x) = x^2 - 60x + 5500. To minimize the unit cost, we need to find the minimum value of C(x).

For that we need to find the value of x for which C(x) is minimum. To find the value of x, we need to differentiate C(x) w.r.t. x. Let's differentiate C(x) w.r.t. x as shown below.:

C'(x) = 2x - 60

Now, equating C'(x) to 0, we get: 2x - 60 = 0 => 2x = 60 => x = 30

Hence, x = 30 is the value for which C(x) is minimum.

So, the manufacturing firm should produce 30 items per day to minimize the unit cost.

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Due to the fact that the figure is made up of a rectangle and a square, its overall dimension is 69 square centimeters.

A rectangle is a four-sided polygon with opposite sides that are identical in length and four right angles (90-degree angles). It is a particular kind of quadrilateral in which the opposing edges are parallel and of equal length. A rectangle's diagonals bisect one another and are of equal length, and its two sets of opposite sides are equal in length. A rectangle's area is calculated by increasing its length by its width (or breadth). The lengths of a rectangle's edges are added to determine its perimeter.

given

the figure consists of one rectangle and one square

length of rectangle = 11 cm

breadth = 4 cm

side of square = 5 cm

The rectangle's surface size is:

A rectangle is equal to 11 centimeter by 4 cm, which equals 44 cm2.

The square's surface size is:

A square = side * (5 * 2) * (25 * 2)

We combine the square's and rectangle's areas to get the figure's overall area:

Overall area is calculated as follows: A rectangle + A square = 44 cm2 + 25 cm2 = 69 cm2.

Due to the fact that the figure is made up of a rectangle and a square, its overall dimension is 69 square centimeters.

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