The probability of getting a total that is a factor of 21 is 0.22
<u>Explanation:</u>
Factor of 21 is = 1, 3, 7, 21
Out of all the factors of 21, we cannot get 21 when the two die are rolled as the maximum sum that can be obtained is 12
The possible combinations are:
(1,2) (1,6)
(2,1) (2,5)
(3,4)
(4,3)
(5,2)
(6,1)
Total outcome = 6 X 6
= 36
Number of outcomes that is the factor of 21 is 8
The probability of getting a total that is a factor of 21 is ![\frac{8}{36}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B36%7D)
p(21) = 0.22
Therefore, the probability of getting a total that is a factor of 21 is 0.22
Answer:
a
Step-by-step explanation:
about 4000 meters tall
Answer:
Is none a answer?
Step-by-step explanation:
They dont have a relashionship
Answer:
part 1) 0.78 seconds
part 2) 1.74 seconds
Step-by-step explanation:
step 1
At about what time did the ball reach the maximum?
Let
h ----> the height of a ball in feet
t ---> the time in seconds
we have
![h(t)=-16t^{2}+25t+5](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E%7B2%7D%2B25t%2B5)
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
so
The x-coordinate of the vertex represent the time when the ball reach the maximum
Find the vertex
Convert the equation in vertex form
Factor -16
![h(t)=-16(t^{2}-\frac{25}{16}t)+5](https://tex.z-dn.net/?f=h%28t%29%3D-16%28t%5E%7B2%7D-%5Cfrac%7B25%7D%7B16%7Dt%29%2B5)
Complete the square
![h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}](https://tex.z-dn.net/?f=h%28t%29%3D-16%28t%5E%7B2%7D-%5Cfrac%7B25%7D%7B16%7Dt%2B%5Cfrac%7B625%7D%7B1%2C024%7D%29%2B5%2B%5Cfrac%7B625%7D%7B64%7D)
![h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}](https://tex.z-dn.net/?f=h%28t%29%3D-16%28t%5E%7B2%7D-%5Cfrac%7B25%7D%7B16%7Dt%2B%5Cfrac%7B625%7D%7B1%2C024%7D%29%2B%5Cfrac%7B945%7D%7B64%7D%5C%5Ch%28t%29%3D-16%28t%5E%7B2%7D-%5Cfrac%7B25%7D%7B16%7Dt%2B%5Cfrac%7B625%7D%7B1%2C024%7D%29%2B%5Cfrac%7B945%7D%7B64%7D)
Rewrite as perfect squares
![h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}](https://tex.z-dn.net/?f=h%28t%29%3D-16%28t-%5Cfrac%7B25%7D%7B32%7D%29%5E%7B2%7D%2B%5Cfrac%7B945%7D%7B64%7D)
The vertex is the point ![(\frac{25}{32},\frac{945}{64})](https://tex.z-dn.net/?f=%28%5Cfrac%7B25%7D%7B32%7D%2C%5Cfrac%7B945%7D%7B64%7D%29)
therefore
The time when the ball reach the maximum is 25/32 sec or 0.78 sec
step 2
At about what time did the ball reach the minimum?
we know that
The ball reach the minimum when the the ball reach the ground (h=0)
For h=0
![0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}](https://tex.z-dn.net/?f=0%3D-16%28t-%5Cfrac%7B25%7D%7B32%7D%29%5E%7B2%7D%2B%5Cfrac%7B945%7D%7B64%7D)
![16(t-\frac{25}{32})^{2}=\frac{945}{64}](https://tex.z-dn.net/?f=16%28t-%5Cfrac%7B25%7D%7B32%7D%29%5E%7B2%7D%3D%5Cfrac%7B945%7D%7B64%7D)
![(t-\frac{25}{32})^{2}=\frac{945}{1,024}](https://tex.z-dn.net/?f=%28t-%5Cfrac%7B25%7D%7B32%7D%29%5E%7B2%7D%3D%5Cfrac%7B945%7D%7B1%2C024%7D)
square root both sides
![(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}](https://tex.z-dn.net/?f=%28t-%5Cfrac%7B25%7D%7B32%7D%29%3D%5Cpm%5Cfrac%7B%5Csqrt%7B945%7D%7D%7B32%7D)
![t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}](https://tex.z-dn.net/?f=t%3D%5Cpm%5Cfrac%7B%5Csqrt%7B945%7D%7D%7B32%7D%2B%5Cfrac%7B25%7D%7B32%7D)
the positive value is
![t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5Csqrt%7B945%7D%7D%7B32%7D%2B%5Cfrac%7B25%7D%7B32%7D%3D1.74%5C%20sec)