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Leni [432]
3 years ago
5

What is the mean of the dot plot???​

Mathematics
1 answer:
vichka [17]3 years ago
7 0

Answer:

19.5 (Rounded: 20)

Step-by-step explanation:

In math, the mean is every number added together, then divided by the amount of numbers. For example, 1,2,5,4,8 would have a median of 4.

<em>(1 + 2 + 4 + 5 + 8 = 20 ÷ 5 = 4)</em>

Your dot plot has 14 total numbers, meaning that you add up all the numbers and divide by 14.

16 + 17 + 17 + 17 + 17 + 19 + 19 + 19 + 19 + 21 + 22 + 22 + 23 + 25 = 273

273 ÷ 14 = 19.5

If you don't need to round, 19.5 is correct. However, if you need to round my best guess is 20. Good luck!

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Let φ(x, y) = arctan (y/x) .
Alexandra [31]

Answer:

a) \large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})

b) \large \mathbb{R}^2-\{(0,0)\}

c) the points of the form (x, -x) for x≠0

Step-by-step explanation:

a)

If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be

\large F(x,y)=(\frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y})

On one hand we have,

\large \frac{\partial \phi}{\partial x}=\frac{\partial arctan(y/x)}{\partial x}=\frac{-y/x^2}{1+(y/x)^2}=-\frac{y/x^2}{1+y^2/x^2}=\\\\=-\frac{y/x^2}{(x^2+y^2)/x^2}=-\frac{y}{x^2+y^2}

On the other hand,

\large \frac{\partial \phi}{\partial y}=\frac{\partial arctan(y/x)}{\partial y}=\frac{1/x}{1+(y/x)^2}=\frac{1/x}{1+y^2/x^2}=\\\\=\frac{1/x}{(x^2+y^2)/x^2}=\frac{x}{x^2+y^2}

So

\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})

b)

The domain of definition of F is  

\large \mathbb{R}^2-\{(0,0)\}

i.e., all the plane X-Y except the (0,0)

c)

Here we want to find all the points such that

\large (-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})=(k,k)

where k is a real number other than 0.

But this means

\large -\frac{y}{x^2+y^2}=\frac{x}{x^2+y^2}\Rightarrow y=-x

So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0

8 0
2 years ago
Alyssa fed her dog 2/3 cup of dog food in the morning and another 5/8 cup in the evening. How much did her dog eat over the cour
kotegsom [21]
1 7/24 is the correct answer I will show you how to get it if needed.
8 0
2 years ago
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suter [353]
Is there a picture to go along with this??
4 0
3 years ago
Productive use of machinery on a farm made it possible to decrease the number of tractors by 12. How many tractors does the farm
frez [133]
1. the answer is 24. think of x as the original amount, and y as the new amount. y times 1.5 is x, and y+12 is x. reverse that to figure out y, which is what we need, and you have x/1.5 = y as well as x-12 = y. Use the equal values method and make an equation x/1.5=x-12. solve this equation to get x, which is 36. to figure out the new amount, y, you need to subtract 12, which would help you get 24 as your final answer. 

2. once again, create an equation. let's call team 1 x and team 2 y. team one has 1/4th as many as team 2, so that would be x=1/4y. An easier way to write that is 4x=y. after 6 people quit team two, that would be y-6. after the transfer, that would be y-6-12, and x+12 for the teams. they are equal after these, so y-6-12=x+12. solve this equation to get y-18= x+12. if you recall earlier, y was 4 times x, so substitute that into y to get 4x-18=x+12. Solve the equation to get 10 people on team one originally. your final answer is 10 people. 
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3 years ago
4. Find the solution of y = 2x + 5 for x = 1.<br> A (1, 7)<br> B (3, 1)<br> C (1, 12)<br> D (1, -2)
Sati [7]

Answer:

A

Step-by-step explanation:

4 0
2 years ago
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