Answer:
Step-by-step explanation:
Total number of kindergarten children in that region that were tested is 160
It is generally believed that nearsightedness affects about 12% of children in a certain region. Therefore,
The expected number of kindergarten children expected to be nearsighted is
12/100 × 160 = 19
Probability of success, p = 0.12
Probability of failure, q = 1 - p = 1 - 0.12 = 0.88
Standard deviation = √npq = √(160 × 0.12 × 0.88) = 4.11
Answer:
Step-by-step explanation:
<u>We know that:</u>
<u>Then </u>
- 810° = 810*π/180 = 4.5π radians
Answer:
a=-13/10
b=-5/2
Step-by-step explanation:
Complete Question:
Alejandro jumped from a cliff into the ocean in Acapulco while vacationing with some friends.
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
Where t is the time in seconds and h is the height in feet
(a) How long did it take for Alejandro to reach his maximum height
(b) What was the highest point Alejandro reached
(c) Alejandro hits the water after how many seconds
Answer:
(a) 0.5 seconds
(b) 484 feet
(c) 6 seconds
Step-by-step explanation:
Given
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
Solving (a): Time to reach maximum height
This is the maximum of the function and it is calculated using:
![t = -\frac{b}{2a}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
Where
![a = -16; b = 16; c =480](https://tex.z-dn.net/?f=a%20%3D%20-16%3B%20b%20%3D%2016%3B%20c%20%3D480)
So:
![t = -\frac{16}{2*-16}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B16%7D%7B2%2A-16%7D)
![t = \frac{16}{32}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B16%7D%7B32%7D)
![t = 0.5](https://tex.z-dn.net/?f=t%20%3D%200.5)
Solving (b): Highest point reached
Time to reach the highest point is 0.5.
So, the highest point is: h(0.5)
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
![h(0.5) = -16 * 0.5^2 + 16 * 0.5 + 480](https://tex.z-dn.net/?f=h%280.5%29%20%3D%20-16%20%2A%200.5%5E2%20%2B%2016%20%2A%200.5%20%2B%20480)
![h(0.5) = 484](https://tex.z-dn.net/?f=h%280.5%29%20%3D%20484)
Solving (c): Time he hits water.
At this point, h(t) = 0
So;
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
![-16t^2 + 16t + 480 = 0](https://tex.z-dn.net/?f=-16t%5E2%20%2B%2016t%20%2B%20480%20%3D%200)
Factorize
![-16(t^2 - t -30) = 0](https://tex.z-dn.net/?f=-16%28t%5E2%20-%20t%20-30%29%20%3D%200)
Divide both sides by -16
![t^2 - t -30 = 0](https://tex.z-dn.net/?f=t%5E2%20-%20t%20-30%20%3D%200)
Expand
![t^2 + 5t - 6t - 30 = 0](https://tex.z-dn.net/?f=t%5E2%20%2B%205t%20-%206t%20-%2030%20%3D%200)
Factorize
![t(t + 5)-6(t + 5) =0](https://tex.z-dn.net/?f=t%28t%20%2B%205%29-6%28t%20%2B%205%29%20%3D0)
![(t -6)(t + 5) =0](https://tex.z-dn.net/?f=%28t%20-6%29%28t%20%2B%205%29%20%3D0)
![t =6\ or\ t = -5](https://tex.z-dn.net/?f=t%20%3D6%5C%20or%5C%20t%20%3D%20-5)
Time can't be negative.
So:
![t = 6](https://tex.z-dn.net/?f=t%20%3D%206)
The domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+
] will be [
, -3 ] and [
,3].
<h3>What are domain and range?</h3>
Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
The range of the function we can see from the graph of the function will be from [
, -3 ] and [
,3]
The domain of the function will be all the values of the real numbers for the function ranges from ( 0, ∞ ).
Therefore the domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+
] will be [
, -3 ] and [
,3].
The complete question is given below:-
what is the domain and range of the function
F(x) = -3Cos[2x+
] .
To know more about Domain and Range follow
brainly.com/question/26098895
#SPJ1