Answer:
The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time
Step-by-step explanation:
we have
![h=-16t^2+55t+4](https://tex.z-dn.net/?f=h%3D-16t%5E2%2B55t%2B4)
This is a vertical parabola open downward
The vertex represent a maximum
where
h is the height of the bird
t is the amount of time, in seconds, the bird had been in the air
For h=40 ft
substitute in the quadratic equation
![40=-16t^2+55t+4](https://tex.z-dn.net/?f=40%3D-16t%5E2%2B55t%2B4)
![-16t^2+55t+4-40=0](https://tex.z-dn.net/?f=-16t%5E2%2B55t%2B4-40%3D0)
![-16t^2+55t-36=0](https://tex.z-dn.net/?f=-16t%5E2%2B55t-36%3D0)
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
![-16t^2+55t-36=0](https://tex.z-dn.net/?f=-16t%5E2%2B55t-36%3D0)
so
substitute in the formula
therefore
The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time
Answer : ![P(\text{this group will speak both French and Spanish})=0.141666666](https://tex.z-dn.net/?f=P%28%5Ctext%7Bthis%20group%20will%20speak%20both%20French%20and%20Spanish%7D%29%3D0.141666666)
Explanation:
Since we have given that
n(U) = 120, where U denotes universal set ,
n(F) = 45, where F denotes who speak French,
n(S) = 42 , where S denotes who speak Spanish,
n(F∪S)' = 50
n(F∪S) = n(U)-n(F∪S) = 120-50 = 70
Now, we know the formula, i.e.
n(F∪s) = n(F)+n(S)-n(F∩S)
⇒ 70 = 45+42-n(F∩S)
⇒ 70 = 87- n(F∩S)
⇒ 70-87 = -n(F∩S)
⇒ -17 = -n( F∩S)
⇒ 17 = n(F∩S)
![P(\text{this group will speak both French and Spanish})= \frac{17}{120}\\P(\text{this group will speak both French and Spanish})=0.141666666](https://tex.z-dn.net/?f=P%28%5Ctext%7Bthis%20group%20will%20speak%20both%20French%20and%20Spanish%7D%29%3D%20%5Cfrac%7B17%7D%7B120%7D%5C%5CP%28%5Ctext%7Bthis%20group%20will%20speak%20both%20French%20and%20Spanish%7D%29%3D0.141666666)
Answer:
<u>After (3/2) months Tyler's gym would be a better deal.</u>
Step-by-step explanation:
Let x the number of months
Cody's Gym charges a $15 fee to join and $30 per month
y₁= 15 + 30x (1)
Tyler's Gym charges a $30 fee to join and $20 per month
y₂ = 15 + 30x (2)
See the attached figure which represent the graph of y₁ (with blue color) and y₂ (with red color)
The point of intersection between y₁ and y₂ is ( 3/2 , 60)
After 3/2 months Tyler's Gym charges will be less than Cody's Gym charges
So, the inequality will be:
<u>After (3/2) months Tyler's gym would be a better deal.</u>