Given:
Eighteen 2.5 gallon buckets are needed to fill a cistern with water.
To find:
The constant of variation.
Solution:
If y is directly proportional to x, then
Where, k is constant of variation.
In the given problem, water in cistern (w) is directly proportional to number of buckets (n).
(Capacity of each bucket is 2.5 gallons)
Therefore, the constant of variation is 2.5.
Answer:
a.
b.
c.
Attached file
d.
Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.
Step-by-step explanation:
a, b) For the group of smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:
a, b) For the group of non-smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:
c. In the attached file you can see the diagram of points for the times, in the smoking and non-smoking groups.
d. Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.
Answer:
Step-by-step explanation:
The equation that models the height of the ball in feet as a function of time is
Where is the initial height,
is the initial velocity and t is the time in seconds.
We know that the initial height is:
The initial speed is:
So the equation is:
The ball hits the ground when when
So
We use the quadratic formula to solve the equation for t
For a quadratic equation of the form
The quadratic formula is:
In this case
Therefore
We take the positive solution.
Finally the ball takes 2.47 seconds to touch the ground