What is the length of one side of a cube that has a surface area of 2400 square mm?
a. 20.00 mm
b. 24.29 mm
c. 17.32 mm
d. 8.16 mm

32 km/h

Step-by-step explanation:

Davit's Train travels at 108 km/h

Mila's train travels at 140 km/h

140-108=32

Therefore the difference in their average speed is 32 km/h

Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

\(\lambda = \frac{1500}{30}\)

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

\(P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}\)

So, in this case

\(P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}\)

\(P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}\)

\(P(x=0)={1.9287 \times 10^{-22}\)

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

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The price of a rake and a shovel is $22 and $25 respectively.

Let's assume the price of a rake is x and the cost of a shovel is y.

Now, Theresa purchased 10 rakes and 15 shovels for $595.

10x + 15y = $595                                                                      -------------------(1)

Taking 5 common out from each side of the equation,

5( 2x + 3y) = 5( 119)

2x + 3y = 119                                                                             ------------------(2)

Brett purchased 8 rakes and 20 shovels for $676.

8x + 20y = $676                                                                       ------------------(3)

Multiply equation (2) by 4 and subtract from equation (3),

8x + 20y - ( 8x + 12y ) = 676 - 476

8x + 20y - 8x - 12y = 200

8y = 200

y = $25

Therefore,

10x + 15y = 595

10x + 15(25) = 595

10x + 375 = 595

10x = 595 - 375

10x = 220

x = $22

Hence, the price of a rake and shovel is $22 and $25 respectively.

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Answer:

160 servings

Step-by-step explanation:

32 cups = 2 gallons

4 * 8 = 32

20 * 8 = 160 servings

Your welcome!

Kayden Kohl

8th Grade Student

Answer:

Step-by-step explanation:

x² + y²

x = - 3 , y = - 2

Substitute the values of x and y into the above expression and solve

That's

( - 3)² + (-2)²

= 9 + 4

We have the final answer as

Hope this helps you

The correct option is C, the slope is −4 throughout the line.

We can see that the same linear equation is the hypotenuse of both triangles.

So, if there is a single line, there is a single slope, then the slopes that we can make with both triangles are equal.

To get the slope we need to take the quotient between the y-side and x-side of any of the triangles, using the smaller one we will get:

slope = -4/1 = -4

Then the true statment is C, the slope is -4 throughout the line.

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Answer:

For the first question the answer is 50(0.2 + 1)^2 = 72

For the second question it is y = 32

Step-by-step explanation:

In case you need to see how i got it...it's below

For number 1, y is proportional to (x + 1)^2

The equation would be y(x +1)^2 = k(the constant). Then I substituted numbers you gave me in the equation which was : 50(0.2 + 1)^2 = k(72)

For number 2 I used this equation: y (x + 1)^2 = 72. I substituted x for 0.5. The equation will be: y(0.5 + 1)^2 = 72. Then I got 32 for y.

Hope this helps:)

Answer:

For the first question the answer is 50(0.2 + 1)^2 = 72

For the second question it is y = 32

Step-by-step explanation:

In case you need to see how i got it...it's below

For number 1, y is proportional to (x + 1)^2

The equation would be y(x +1)^2 = k(the constant). Then I substituted numbers you gave me in the equation which was : 50(0.2 + 1)^2 = k(72)

For number 2 I used this equation: y (x + 1)^2 = 72. I substituted x for 0.5. The equation will be: y(0.5 + 1)^2 = 72. Then I got 32 for y.

Hope this helps:)

Step-by-step explanation:

The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

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Answer:

6

Step-by-step explanation:

2 x 3

let's call that point C, thus we get the splits of AC and CB

\(\textit{internal division of a line segment using ratios} \\\\\\ A(0,0)\qquad B(6,9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{2:1} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{1}\implies \cfrac{A}{B} = \cfrac{2}{1}\implies 1A=2B\implies 1(0,0)=2(6,9)\)

\((\stackrel{x}{0}~~,~~ \stackrel{y}{0})=(\stackrel{x}{12}~~,~~ \stackrel{y}{18}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{0 +12}}{2+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{0 +18}}{2+1} \right)} \\\\\\ C=\left( \cfrac{ 12 }{ 3 }~~,~~\cfrac{ 18}{ 3 } \right)\implies C=(4~~,~~6)\)

Step 1: Let's recall what is SAS:

"SAS" means "Side, Angle, Side"

Step 2: Let's use The Law of Cosines to calculate the unknown side of the triangles given:

Formula of The Law of Cosines is:

In the triangle ABC, we have:

b = 15, c = 21 and angle A is 75 degrees

Step 3: Substitute the values given in the formula

Step 4: Let's use The Law of Sines to find the smaller of the other two angles

Step 5: Find the last angle, recalling that the interior angles of a triangle add up to 180 degrees

Now, we have the sides and the angles of triangle ABC:

Sides = 15,21, 22.43

Angles = 75, 64.74, 40.26

The derivative of the function y = (x²+3)(x-1)² x⁴(x³+5)³ without using the Quotient Rule is calculated by applying the Product Rule and the Chain Rule.
The derivative involves multiple steps, combining the derivatives of each term while considering the chain rule for the nested functions.

To find the derivative of the given function, we can apply the Product Rule and the Chain Rule. Let's break down the function into its individual terms: (x²+3), (x-1)², x⁴, and (x³+5)³.

Using the Product Rule, we can calculate the derivative of the product of two functions. Let's denote the derivative of a function f(x) as f'(x).

The derivative of (x²+3) with respect to x is 2x, and the derivative of (x-1)² is 2(x-1). Applying the Product Rule, we get:

[(x²+3)(2(x-1)) + (x-1)²(2x)] x⁴(x³+5)³

Next, we differentiate x⁴ using the power rule, which states that the derivative of xⁿ is nxⁿ⁻¹. Hence, the derivative of x⁴ is 4x³.

For the term (x³+5)³, we need to use the Chain Rule. The derivative of the outer function (u³) with respect to u is 3u². The derivative of the inner function (x³+5) with respect to x is 3x². Therefore, applying the Chain Rule, the derivative of (x³+5)³ is 3(x³+5)² * 3x².

Combining all the derivatives, we get the final result:

[2x(x²+3)(x-1)² + 2(x-1)²(2x)] x⁴(x³+5)³ + 4x³(x²+3)(x-1)² x³(x³+5)² * 3x².

This expression represents the derivative of the function y = (x²+3)(x-1)² x⁴(x³+5)³ without using the Quotient Rule.

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We can represent 0.614 using only 5 tenths as \(\mathbf{\dfrac{6.14}{10}}\)

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

The accepted method for representing both integer and non-integer numbers is the decimal number system.

From the given information, we are to represent 0.614 by using only 5 tenths.

Representing 0.614 in the same form, we have:

\(\mathbf{=\dfrac{0.614\times 1000}{1\times 1000}}\)

\(\mathbf{=\dfrac{614}{1000}}\)

\(\mathbf{=\dfrac{6.14}{10}}\)

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Answer: 6.14/10

Step-by-step explanation:

ANSWER

m∠D = 50º

EXPLANATION

Triangle DEF is:

We want to know the measure of angle D, knowing the side lengths DE (the hypotenuse of the triangle) and FD (the adjacent side to angle D). We can use the cosine of D:

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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Answer:

1:3

Step-by-step explanation:

Answer:

1:3 is the correct answer

Answer:

False

Step-by-step explanation:

If two angles are right angles, then they are congruent.

Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

Answer:

Step-by-step explanation:

The answer is 175 miles per day. I guessed on it and it was right :D

The number of miles per day that will have to be driven for the total cost of of a car from the first agency to equal the total cost of a car from the second agency is 175.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A rental car agency charges $16 per day plus 14 cents per mile to rent a certain car. Therefore, we can write,

Total charge for x miles = $16 + $0.14(x)

Another agency charges $23 per day plus 10 cents per mile to rent the same car. Therefore, we can write,

Total charge for x miles = $23 + $0.10(x)

Since it is needed to be found the number of miles that the car should be traveling so that the total cost from both the agencies is the same. Thus, equate the equation together,

$16 + $0.14(x) = $23 + $0.10(x)

16 + 0.14x = 23 + 0.10x

0.14x - 0.10x = 23 - 16

0.04x = 7

x = 7 / 0.04

x = 175 miles per day

Hence, the number of miles per day that will have to be driven for the total cost of of a car from the first agency to equal the total cost of a car from the second agency is 175.

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Answer:

3x-x+6=0

2x+6=0

2x=-6

x= -6/2

x=. -4

Answer:

could you upload a picture?

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

[] First we need to set up an equation

\(\frac{91 + 94 + 78 + 90 + x}{5}\) = 88

[] What does it mean? We want all of his scores plus the 5th test score (x) to equal an average of 88 so we must find the average of all of his test scores.

[] Now to solve!

First, let's multipy everything by 5 to remove the fraction.

91 + 94 + 78 + 90 + x = 440

Then, simplify

353 + x = 440

Now subtract the 353 from both sides

x = 87

Which results with our answer, he needs to get an 87!

Hope this helps, have a nice day :)

Answer:

The 5th score has to be 87.

Step-by-step explanation:

Equation

(91 + 94 + 78 + 90 + x)/5 = 88  Multiply both sides by 5

91 + 94 + 78 + 90 + x = 88*5    Combine like terms on both sides.

353 + x = 440                           Subtract 353 from both sides.

x = 440 - 353

x = 87

Answer:

g(1) = 1

Step-by-step explanation:

Since 1 ≠ -2  and  1 ≠ -1

Then we must use the expression:

g(x) = x³ - x² + 1  ,to calculate g(1).

Therefore

g(1) = (1)³ - (1)² + 1

     = 1 - 1 + 1

     = 0 + 1

     = 1

Answer:

Step-by-step explanation:
The problem is:

8x (6x + 8x) = 16 (12+16)

I will simplify and combine like terms
6x + 8x = 14x. 14x + 8x = 22x.

12 + 16 = 28. 28 + 16 = 44

New problem
22x = 44

22x divided by 22 is x

44 divided by 22 is 2

x = 2

Answer:

b 2/7

Step-by-step explanation:

Because there is a 6/21 chance and 2/7=6/21

Answer:

I do not think that this is a function, but I am not 100% sure

Step-by-step explanation:

The foci of the ellipse given by the equation 225x^2 + 144y^2 = 32400 can be found by identifying the major and minor axes of the ellipse and using the formula for the foci coordinates. The foci of the ellipse are located at (±c, 0). Therefore, the foci are approximately (±15.87, 0).

The equation of the ellipse can be rewritten in standard form:

(225x^2)/32400 + (144y^2)/32400 = 1

We can identify the major and minor axes of the ellipse by comparing the coefficients of x^2 and y^2. The square root of the denominator gives the lengths of the semi-major axis (a) and semi-minor axis (b) of the ellipse.

a = sqrt(32400/225) = 24

b = sqrt(32400/144) = 18

The foci of the ellipse can be calculated using the formula:

c = sqrt(a^2 - b^2)

c = sqrt(24^2 - 18^2)

c = sqrt(576 - 324)

c = sqrt(252)

c ≈ 15.87

The foci of the ellipse are located at (±c, 0). Therefore, the foci are approximately (±15.87, 0).

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Answer:

Yes, at positive x coordinates

Step-by-step explanation:

Find the equation of g(x)

Given ordered pairs of g(x):  (-1, -22)  (0, -20)  (1, -18)

\(\sf let\:(x_1,y_1)=(0,-20)\)

\(\sf let\:(x_2,y_2)=(1,-18)\)

\(\sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-18-(-20)}{1-0}=2\)

Point-slope form of linear function: \(\sf y-y_1=m(x-x_1)\)

\(\implies \sf y-(-20)=2(x-0)\)

\(\implies \sf y=2x-20\)

Substitute the equation of g(x) into the equation of the circle and solve for x

Given equation:  \(y^2+x^2=100\)

\(\implies (2x-20)^2+x^2=100\)

\(\implies 4x^2-80x+400+x^2=100\)

\(\implies 5x^2-80x+300=0\)

\(\implies x^2-16x+60=0\)

\(\implies x^2-10x-6x+60=0\)

\(\implies x(x-10)-6(x-10)=0\)

\(\implies (x-6)(x-10)=0\)

Therefore:

\((x-6)=0 \implies x=6\)

\((x-10)=0 \implies x=10\)

So the linear function g(x) will intersect the equation of the circle at positive x coordinates.