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3 years ago

Shaunee won 79 tickets at Chuck e' Cheese's. She

Mathematics

2 answers:

Harlamova29_29 [7]3 years ago

3 0

Answer:

Step-by-step explanation:

From the problem statement, we can set up the following equation:

$3N + S = 79$

where $N$ is the number of tickets each friend got, and $S$ is the number of tickets that Shaunee got. We know that Shaunee got 25, so we know $S = 25$ and can plug that into the equation:

$3N + 25 = 79$

Subtracting 25 from each side gives us the following:

$3N = 54$

Dividing both sides by 3 gives us the answer:

$N = 18$

amid [387]3 years ago

3 0

79 tickets minus 25 is 54

Shawnee has 54 tickets to split between her friends.

54 divided by 3 friends equals 18 tickets.

You can check the answer by multiplying: 18x3 equals 54.

Hence, her friends each got 18 tickets...

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Step-by-step explanation:

For this case we have the following data given:

Demand (x): 10,20,30,40,50,60,70,80,90,100

Price (y): 141 , 133,126, 128,113,97, 90, 82,79,53

We want to construct a linear model like this:

$y = mx +b$

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =550$

$\sum_{i=1}^n y_i =1042$

$\sum_{i=1}^n x^2_i =38500$

$\sum_{i=1}^n y^2_i =115882$

$\sum_{i=1}^n x_i y_i =49710$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=38500-\frac{550^2}{10}=8250$

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And the slope would be:

$m=-\frac{7600}{8250}=-0.921$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{550}{10}=55$

$\bar y= \frac{\sum y_i}{n}=\frac{1042}{10}=104.2$

And we can find the intercept using this:

$b=\bar y -m \bar x=104.2-(-0.921*55)=104.707$

So the line would be given by:

$p(x)=-0.921 x +104.707$

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