Answer:
max height = 7.5 ft
1.3 ft far
Please check below for the detailed answer
Step-by-step explanation:
<u>Given: </u>
f(x) = −0.3x^2 + 2.1x + 7
a) To obtain the maximum height , find f'(x)
f'(x) = - 0.6x + 0.8 = 0
=> x = 0.8 / 0.6 = 1.33 feet
So f(x) is maximum at a horizontal distance of 1.33 ft
To find the max height , find f(1.33)
f(x) = −0.3x^2 + 2.1x + 7, plug in 1.33 for x
=> f(1.33) = −0.3(1.77) + 0.8(1.33) + 7 = 7.5 ft
So the answer is
Maximum height = 7.5 ft , and 1.3 ft far from where it was thrown.
Answer:
k=8192
Step-by-step explanation:
The number of teams,t remaining after each round, r, can be expressed as:
- 8 Teams will advance to the quarterfinals.
First, we determine the round,r at which there will be 8 teams left.
Using this value of r
Answer:
probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)
=194/285 or 0.6807.
Step-by-step explanation:
The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.
The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.
Hence
|E'| = C(14,3)
= 14×13×12/3!.
Therefore probability P(E')
= |E'|/|S|
= (14×13×12)/(20×19×18)
= (14×13×2)/(20×19×3)
=(7×13)/(5×19×3)
= 91/285.
Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.
Answer:
I think d = 6 because 24 + 6 = 30
Answer:
Step-by-step explanation:
we know that
The function of the graph is a vertical parabola open upward
The vertex is a minimum
The equation of a vertical parabola in vertex form is equal to
where
a is a coefficient
(h,k) is the vertex
In this problem
Looking at the graph
The vertex is the point (0,-4)
substitute
To determine the value of "a" take a point in the graph
I take the point (3,5)
substitute the value of x and the value of y and solve for a
therefore
The equation of the quadratic function is