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3 years ago

PLEASE HELP ASAP Which equation BEST models the data shown in the scatterplot below?

Mathematics

1 answer:

cricket20 [7]3 years ago

8 0

Answer:

Option D. y=4x+35

Step-by-step explanation:

From the graph take the points (5,50) and (50,250)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{250-50}{50-5}$

$m=\frac{200}{45}=4.4$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=4.4\\point\ (5,50)$

substitute

$50=4.4(5)+b$

solve for b

$b=50-22\\b=28$

substitute

$y=4.4x+28$

therefore

The equation that BEST models the data is

$y=4x+35$

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Law Incorporation [45]

Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by $\nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}$

- (Gauss' theorem)Given a closed surface S, the following applies

$\int_{S} F\cdot \vec{n} dS = \int_{V} \nabla \cdot F dV$

where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

$\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8$

Hence, by the Gauss theorem we have that

$\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}$

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

$\sqrt[]{(1-1)^2+(1-1)^2+(1-(-1)^2} = \sqrt[]{4} = 2$ .

Hence, the volume of V is $2\cdot 2 \cdot 2 = 8$ . Then, the final answer is

$\int_{S} F\cdot \vec{n} dS =8\cdot 8 = 64$

5 0

3 years ago

Is the answer right?

son4ous [18]

Almost. Where you put -(-5) and then later on you say it’s -5. It’s not. It would be +5 or just 5 because - and - makes a plus :)

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2 years ago

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Katen [24]

Answer:

50%

Step-by-step explanation:

As you can see there is only two options for crust, sesame crust, and plain crust. 100/2 = 50 so the probability of getting a plain crust pizza would be 50%

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

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zhannawk [14.2K]

Answer:

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Andre45 [30]

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