Answer:
33.4933333333, rounded, 
4/3x3.14x2x2x2=33.4933333333
Answer:
a) k = 5; (-10, -35)
Step-by-step explanation:
Given:
Co-ordinates:
Pre-Image = (-12,3)
After dilation
Image = (-60,15)
The dilation about the origin can be given as :
Pre-Image
where
represents the scalar factor.
We can find value of
for the given co-ordinates by finding the ratio of
or
co-ordinates of the image and pre-image.

For the given co-ordinates.
Pre-Image = (-12,3)
Image = (-60,15)
The value of 
or 
As we get
for both ratios i.e of
and
co-ordinates, so we can say the image has been dilated by a factor of 5 about the origin.
To find the image of (-2,-7), after same dilation, we will multiply the co-ordinates with the scalar factor.
Pre-Image
Image
Pre-Image
Image
(Answer)
Okay, so since both y values share the same number, let's add both equations so the y values cancel out leaving us to solve for x.
10x+(-5x)=5x
7y+(-7y)=0
1+24=25
Now we have 5x=25
divide both sides by 5 and we have x=5
Now that we know x=5, we can plug it into one of the problems to find y.
Let's do 10(5) +7y=1
50+7y=1 subtract 5 and we get 7y=-49
divide -7 from both sides and we get y=-7
so there you have it x=5 and y=-7
Answer:

And we can use the cumulative distribution function given by:

And for this case we can write the probability like this:

And then the final answer for this case would be 
Step-by-step explanation:
For this case we define our random variable X "price of gasoline for a city in the USA" and we know the distribution is given by:

And for this case the density function is given by:

And we want to calculate the following probability:

And we can use the cumulative distribution function given by:

And for this case we can write the probability like this:

And then the final answer for this case would be 