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grin007 [14]
3 years ago
8

What’s the answer and explain it please -

Mathematics
2 answers:
MariettaO [177]3 years ago
7 0

Answer:

2.6

Step-by-step explanation:

The Mean Absolute Deviation (MAD) is the average amount that each point is from the overall average of the data set.

So, first find the overall average (also called the mean):

avg = (1 + 1 + 2 + 3 + 5 + 7 + 9) / 7

= 28 / 7

= 4

The average (mean) is 4, so now you calculate how far each point is from 4 and average those numbers:

Note: Remember to use absolute values, since distance can't be negative.

4 - 1 = 3

4 - 1 = 3

4 - 2 = 2

4 - 3 = 1

4 - 5 = |-1| = 1

4 - 7 = |-3| = 3

4 - 9 = |-5| = 5

And finally, average (or find the mean) the new data set:

avg = (1 + 1 + 2 + 3 + 3 + 3 + 5) / 7

so 18 / 7 is the MAD of the data set.

Finally, round it to the nearest tenth:

18 ÷ 7 = 2.57142857143 ≈ 2.6

Nonamiya [84]3 years ago
5 0

Answer:

2.6

Step-by-step explanation:

average (or find the mean) the new data set:

avg = (1 + 1 + 2 + 3 + 3 + 3 + 5) / 7

so 18 / 7 is the MAD of the data set.

Finally, round it to the nearest tenth:

18 ÷ 7 = 2.57142857143 ≈ 2.6

hope this helps

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At a pumpkin patch, if Armando guesses the weight of his pumpkin within 0.3 pounds, he gets to take the pumpkin home for free. I
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Answer: last option

Step-by-step explanation:

You know that the weight of his pumpkin 4.9 pounds and that, if he guesses its weight within 0.3 pounds, he will get the pumpkin for free.

Then, to find the minimum weight he can guess  in order to get his pumpkin for free, it's necessary to write the expression:

x-0.3=4.9

Rewriting it:

x-4.9=0.3

To find the maximum weight he can guess  in order to get his pumpkin for free, it's necessary to write the expression:

x+0.3=4.9

Rewriting it:

x-4.9=-0.3

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An artist cuts 4 squares with side length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She bends
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Answer:

V=4x^3-60x^2+216x

Step-by-step explanation:

<u>Volume And Function s</u>

Geometry can usually be joined with algebra to express volumes as a function of some variable. The volume of a parallelepiped of dimensions a,b,c is

V=abc

Our problem consists in computing the volume of a box made with some sheet of metal 12 ft by 18 ft. The four corners are cut by a square distance x as shown in the image below .

If the four corners are to be lifted and a box formed, the base of the box will have dimensions (12-2x)(18-2x) and the height will be x. The volume of the box is

V=x(12-2x)(18-2x)

Operating and simplifying

V=4x^3-60x^2+216x

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Which of the following tables represents the rule, y equals seven less than four times a number
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EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =
Taya2010 [7]

Answer:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

\bigtriangledown  f=\lambda \bigtriangledown  g

for some scalar \lambda called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

\bigtriangledown  f=\lambda \bigtriangledown  g+\mu \bigtriangledown  h

The gradient of f is

\bigtriangledown  f=

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in x,y,z,\lambda,\mu.

We have

f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0

Let's compute the partial derivatives

f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0

The Lagrange condition leads to

1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)

Operating and simplifying

1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11

Replacing the value of \lambda in the two first equations, we get

1=11+2x\mu\\2=-11 +2y\mu

From the first equation

\displaystyle 2\mu=\frac{-10}{x}

Replacing into the second

\displaystyle 13=y\frac{-10}{x}

Or, equivalently

13x=-10y

Squaring

169x^2=100y^2

To solve, we use the restriction h

x^2 + y^2 = 1

Multiplying by 100

100x^2 + 100y^2 = 100

Replacing the above condition

100x^2 + 169x^2 = 100

Solving for x

\displaystyle x=\pm \frac{10}{\sqrt{269}}

We compute the values of y by solving

13x=-10y

\displaystyle y=-\frac{13x}{10}

For

\displaystyle x= \frac{10}{\sqrt{269}}

\displaystyle y= -\frac{13}{\sqrt{269}}

And for

\displaystyle x= -\frac{10}{\sqrt{269}}

\displaystyle y= \frac{13}{\sqrt{269}}

Finally, we get z using the other restriction

x - y + z = 1

Or:

z = 1-x+y

The first solution yields to

\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}

\displaystyle z = \frac{-23\sqrt{269}+269}{269}

And the second solution gives us

\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}

\displaystyle z = \frac{23\sqrt{269}+269}{269}

Complete first solution:

\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0
3 years ago
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