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3 years ago

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nathan smiled at 50 people one day and recorded that 36 people smiled back at him.Based on his observations how many people shou

ld nathan expect to return a smile if he smiles at 650 people over a period of time

1 answer:

Olegator [25]3 years ago

4 0

Given :

Nathan smiled at 50 people one day and recorded that 36 people smiled back at him.

To Find :

How many people should Nathan expect to return a smile if he smiles at 650 people over a period of time.

Solution :

Ratio of people smiled by total number of people is :

$R = \dfrac{36}{50}$

Now, it is given that we have to use the given conditions.

Therefore, ratio will be same :

$\dfrac{s}{650}=\dfrac{36}{50}\\\\s = \dfrac{36}{50}\times 650\\\\s = 468$

Therefore, number of smiles Nathan expect to return is 468.

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3 years ago

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2 years ago

Given the set points K+1:(-1,8),(1,0) and (2,5), find the quadratic polynomial interpolate

Sauron [17]

Answer:

The interpolating polynomial is $p(x) = 1-4x+3x^2$ .

Step-by-step explanation:

We want to find a quadratic polynomial $p(x)$ such that $p(-1)=8$ , $p(1)=0$ and $p(2)=5$ . In order to do this let us write $p(x) = a_0+a_1x+a_3x^2$ .

Now, evaluating the polynomial in the points -1, 1 and 2 we get

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This relations give us a linear system of equations:

$\begin{cases} 8 &= a_0-a_1+a_2\\ 0 &= a_0+a_1+a_2\\ 5&= a_0+2a_1+4a_2\end{cases}$

where the $a_0$ , $a_1$ and $a_2$ are the unknowns.

The augmented matrix of the system is

$\begin{pmatrix}1 & -1 & 1 & 8\\ 1 & 1 & 1 & 0\\ 1 & 2 & 4 & 5\end{pmatrix}$

In this matrix it is easy to eliminate the 1's of the first column and get

$\begin{pmatrix} 1 & -1 & 1 & 8\\ 0 & 2 & 0 & -8\\ 0 & 3 & 3 & -3\end{pmatrix}$

From this matrix we can find the values of each unknown. Notice that the second row gives us $2a_2=-8$ that yields $a_1=-4$ .

Then, the third row means $3a_1+3a_2=-3$ that gives $-12+3a_2=-3$ . So, $a_2=3$ .

Finally, the first row is $a_0-a_1+a_2=8$ and substituting is $a_0+7=8$ that yields $a_0=1$ .

Therefore, the interpolating polynomial is

$p(x) = 1-4x+3x^2$ .

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3 years ago

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AlexFokin [52]

Answer:

A. x= 3, y= -2

Step-by-step explanation:

[2] 2x= 4y+14

[1] 3y+5x=9

Solve equation [2] for the variable x

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[2] x = 2y + 7

// Plug this in for variable x in equation [1]

[1] 5•(2y+7) + 3y = 9

[1] 13y = -26

// Solve equation [1] for the variable y

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[1] y = - 2

// By now we know this much :

x = 2y+7

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good luck, I hope this helps!!!

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2 years ago

when solving the equation 5x-3=5, MaReeco rewrote the equation as 5x =2.Did MaReeco perform an acceptable move to this equation?

aliina [53]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equation

$5x-3=5$

MaReeco's rewrote equation is given by

$5x = 2$

As MaReeco subtracted 3 to the right side of the equation, which imbalanced the equation. Hence, it is not correct.

Correction:

For the next step, MaReeco should have added 3 to both sides

i.e.

$5x-3+3=5+3$

$5x=8$

Therefore, the acceptable move would have been:

$5x=8$

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2 years ago