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3 years ago

Which graph is defined by the function given below? y= (x + 2)(x+7)

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

8 0

Answer:

A parabola

Step-by-step explanation:

It's a quadratic equation so the graph will be a parabola.

The solutions are -2 and -7

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The number of motor vehicles registered in millions in the US has grown as follows:

zysi [14]

Answer:

a) Figure attached

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

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:

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

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

4 0

3 years ago

Chester has less than $25 to spend at the county fair. The entrance fee is $5, and each ride costs $3. The number of rides, r, t

padilas [110]

Answer:

6 rides

Step-by-step explanation:

3r+5<25

3r<20

r<6.67

rides=6

check answer

3r+5<25

3(6)+5<25

18+5<25

23<25

4 0

3 years ago

Given the following functions f(x) and g(x), solve f over g(−4) and select the correct answer below:

marishachu [46]

$\left(\dfrac{f}{g}\right)(x)=\dfrac{f(x)}{g(x)}\\\\f(x)=4x-4;\ g(x)=x-1\\\\f(-4)=4\cdot(-4)-4=-16-4=-20\\\\g(-4)=-4-1=-5\\\\\left(\dfrac{f}{g}\right)(x)=\dfrac{-20}{-4}=4$

5 0

3 years ago

Read 2 more answers

What is the least common multiple of 15 and 6?<br><br> Take notes and show your work.

Mariulka [41]

Hello!

The least common multiple is 3

Hope this helps!

4 0

3 years ago

Really need help please! Brainliest to correct!

vovikov84 [41]

Let's say "m" is the manufactoring cost per drill (in dollars).

Then the manufactorer sells it for $4 more, so this would be:

m+4

Then the chain store sells it for 140% of the price is paid the manufactorer, so this would be "140% of (m+4)" which translates to "1.4•(m+4)" or more simply:

1.4(m+4)

P(m) = 1.4(m+4), where m is the initial manufactoring cost (in dollars).

Simplifying, you could rewrite this as:

P(m) = 1.4m + 5.6

7 0

3 years ago