Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. The princ
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The value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.
<h3>What is arithmetic mean?</h3>Arithmetic mean is the mean or average which is equal to the ratio of sum of all the group numbers to the total numbers.
The two arithmetic means between 3 and 24 are has to be inserted.
3, A₂, A₃, 24
All the four numbers are in arithmetic progression. The nth terms of AM can be found using the following formula:
t(n)=a(n-1)d
Here, d is the common difference a is the first terms and n is the total term. The first term, a=3 and t₄=24. Thus, the common difference is;
The second and 3rd term are:
Thus, the value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.
Learn more about the arithmetic mean here;
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Answer:
0.5 seconds (at 100 feet in the air).
Step-by-step explanation:
So, the height of the ball can be modeled by the function:
Where h(t) represents the height in feet after t seconds.
And we want to find its maximum height.
Notice that our function is a quadratic.
Therefore, the maximum height will occur at the vertex of our function.
The vertex of a quadratic function in standard form is given by the formula:
In our function, a=-16; b=16; and c=96.
Find the x-coordinate of the vertex:
So, the ball reaches its maximum height after 0.5 seconds of its projection.
Notes:
To find it’s maximum height, we can substitute 1/2 for our function and evaluate. So:
Evaluate:
So, the ball reaches its maximum height of 100 feet 0.5 seconds after its projection.