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Dafna1 [17]
3 years ago
14

What is the simplified form of the expression 8x + 3 – 4x – 5?

Mathematics
1 answer:
SVEN [57.7K]3 years ago
8 0

Answer:

4x-2

Step-by-step explanation:

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3 hours* (460 dives/ 12 hours)= 115 dives.
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3 (x - 4) = 5 + 3x + 2
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What is the equation of the line of best fit for the following data? Round the
Svet_ta [14]

Answer:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=438-\frac{44^2}{5}=50.8

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4

And the slope would be:

m=\frac{45.4}{50.8}=0.8937 \approx 0.894

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

\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8

\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4

And we can find the intercept using this:

b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535

So the line would be given by:

y=0.894 x +0.535

And the best option is:

A. y = 0.894x + 0.535

Step-by-step explanation:

We have the following dataset given

x: 5,6,9,10,14

y: 4,6,9,11,12

We want to find the least-squares line appropriate for this data given by this general expresion:

y = mx +b

Where m is the slope and b the intercept

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 = 44

\sum_{i=1}^n y_i =42

\sum_{i=1}^n x^2_i =438

\sum_{i=1}^n y^2_i =398

\sum_{i=1}^n x_i y_i =415

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}=438-\frac{44^2}{5}=50.8

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4

And the slope would be:

m=\frac{45.4}{50.8}=0.8937 \approx 0.894

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

\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8

\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4

And we can find the intercept using this:

b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535

So the line would be given by:

y=0.894 x +0.535

And the best option is:

A. y = 0.894x + 0.535

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