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Marizza181 [45]
3 years ago
12

In 1984 a locally-owned car company sold 2,743 cars. In 2003, the car sales rose to 4,069. What was the average rate of change f

or the total number of cars sold?
Mathematics
1 answer:
tatiyna3 years ago
7 0

Answer:

70 cars  per year.

Step-by-step explanation:

Given:

In 1984 a locally-owned car company sold 2,743 cars.

In 2003, the car sales rose to 4,069.

Question asked:

What was the average rate of change for the total number of cars sold?

Solution:

In 2003 number of cars sold = 4069

In 1984 number of cars sold = 2743

Change in the number of car sold = 4069 - 2743

                                                         = 1326

Now, time interval between 2003 and 1984 = 19

The\ average\ rate\ of\ change=\frac{Change\ in\ the\ number\ of\ car\ sold}{Time \ interval}

                                             =\frac{1326}{19} \\=69.789\\\\=70\ cars\ per\ year\  (approx)

Thus, the average rate of change for the total number of cars sold is 70 cars  per year.

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Suppose you want to learn more about the heights of the buildings in New York City. How would you choose a sample of the buildin
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Assume you have noted the following prices for books and the number of pages that each book contains. Book Pages (x) Price (y) A
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Answer:

a) y=0.00991 x +1.042  

b) r^2 = 0.7503^2 = 0.563

c) r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

y = mx +b

Wehre

m=\frac{S_{xy}}{S_{xx}}  

And:  

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}  

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}=2595100-\frac{4210^2}{7}=63085.714  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625  

And the slope would be:  

m=\frac{625}{63085.714}=0.00991  

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

\bar x= \frac{\sum x_i}{n}=\frac{4210}{7}=601.429  

\bar y= \frac{\sum y_i}{n}=\frac{49}{7}=7  

And we can find the intercept using this:  

b=\bar y -m \bar x=7-(0.00991*601.429)=1.042  

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y=0.00991 x +1.042  

Part b

The correlation coefficient is given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=7 \sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354  

r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

The determination coefficient is given by:

r^2 = 0.7503^2 = 0.563

Part c

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