Fiona wants 6 red, 3 green and 3 yellow buttons on her dress. All buttons must be placed along a straight vertical line with no
2 answers:
Answer:
Total number of ways are
Step-by-step explanation:
Red balls can only be placed at alternate spots.
This can be done in two different ways, by starting at spot one and by starting at spot two.
Now, yellow
green balls can be placed in the intermediate spots.
It can be done in following ways:
So, total number of ways are=
Learn more about permutation:
The appropriate method to use in solving the given question is permutation. Then, the numbers of ways to arrange the buttons is 1320 ways.
In the given question, the order of arrangement is important, so that the number of ways that Fiona could order the buttons can be determined by permutation method.
i.e =
Red 6
Green 3
Yellow 3
Total 12
Since no two neighbouring buttons of the same colour is allowed, then 3 buttons would be arranged at a time.
Thus, n = 12 and r = 3;
=
=
=
= 12 x 11 x 10
= 1320
Therefore the buttons can be arranged in 1320 ways without two neighbors having the same colour.
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<h2>Hello!</h2>
The answers are:
a) The height of the ball after 3 seconds is 49 feet.
b) The maximum height of the ball is 66 feet.
c) That the ball hit the ground after 4 seconds.
d) The domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers.
<h2>Why?</h2>Since we are working with a quadratic function which describes the ball's motion in function of the time, we need to remember the following:
- The general equation of the parabola is:
- We can calculate the coordinates of the vertex of the parabola using the following formula:
- Evaluating a function means replacing the variable with the given value to evaluate.
The given function is:
Where,
Now, calculating we have:
a) What is the height of the ball after 3 seconds?
We need to evaluate the time of 3 seconds into the function, so:
So, the height of the ball after 3 seconds is 49 feet.
b) What is the maximum height of the ball?
Since the function is describing the motion of a ball thrown into the air, we can find the maximum height by finding the y-coordinate of the vertex. If the parabola opens downward or upward, the vertex will be always the highest or the lowest point of the parabola.
So, calculating the vertex we have:
Then, replacing "x" into the equation of the parabola, we find the y-coordinate of the vertex:
So, if the y-coordinate is 66.03, the maximum height of the ball is 66.03 feet, or 66 feet (rounded to the nearest foot).
c) When will the ball hit the ground?
We can find the time when the ball hit the ground by making equal to 0 the function and finding the roots (zeroes)
Since it's a quadratic function, we can find the zeroes using the quadratic equation:
Substituting a, b and c, we have:
Now, since negative time does not exists, we can conclude that the ball hit the ground after 4 seconds.
d) what domain makes sense for the function?
Since the function represents the motion of the thrown ball at "t" time, the domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers,
Note: I've attached the graph of the function.
Have a nice day!
Answer:
Now we can find the expected value with this formula:
And replacing we got:
Step-by-step explanation:
For this case we know the following probability mass function given:
For this case we need to satisfy the following condition in order to have a probability distribution function:
And we have this:
Now we can find the expected value with this formula:
And replacing we got: