What is the next fraction in this sequence? Simplify your answer.<br> 6/7, 29/35, 4/5, 27/35......?

Use the given data to find a regression line that best fits the price-demand data for price p in dollars as a function of the de

Rufina [12.5K]

Answer:

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

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:

$y=-0.921 x +104.707$

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:

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

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=49710-\frac{550*1042}{10}=-7600$

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:

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

4 0

3 years ago

Gail and 3 of her friends all share half of a pie. All the pieces in the pie put together make up 180 degrees. Gail and her frie

Pachacha [2.7K]

No the angle of each piece should be 60 degrees, if the three pieces were to be 25 each that would only add to 75

8 0

3 years ago

5+1/2(14b-8)=-6 5+__b-4=-6 7b+__=-6 7b=__ b=__ ANSWERS 7-7-1 1

Lunna [17]

Answer:

7, 1, -7, -1.

Step-by-step explanation:

5+1/2(14b-8) = -6

5 + 7b - 4 = -6

7b + 1 = -6

7b = -7

b = -1

So, your answer will be 7, 1, -7, -1.

Hope this helps!

3 0

4 years ago

Determine the equation of the line with slope 3 that passes through the point (2, 0).

Aleonysh [2.5K]

Hello there! :)

If we are given the slope of the line and a point that the line passes through, we can write its equation in point-slope form:

y-y1=m(x-x1)

y-0=3(x-2)

y-0=3x-6

y=3x-6

Therefore, that's the equation. The right option is Option C.

I hope this helps you.

Please let me know if you have any doubts.

Good luck on your assignment.

~GracefulGirlie :-)

4 0

2 years ago

A guitar string vibrates back and forth 88 times in 1 minute. Round your answers to the following questions to the nearest tenth

ICE Princess25 [194]

<h2>Answer:</h2><h2>The frequency of the guitar string vibrates back and forth 88 times in 1 minute = 1.5 Hz</h2>

Step-by-step explanation:

A hertz is used to measure one cycle (complete wave) of a vibration.

The number of cycles per second is the frequency, measured in hertz.

A guitar string vibrates back and forth 88 times in 1 minute

The vibrations in 1 second = $\frac{88}{60}$ = 1.466 Hz ≈1.5 Hz

The frequency of the guitar string vibrates back and forth 88 times in 1 minute = 1.5 Hz

6 0

3 years ago

What is the next fraction in this sequence? Simplify your answer. 6/7, 29/35, 4/5, 27/35......?