Answer: range= 26, variance= 80 and standard deviation= 8.94
Step-by-step explanation:
Range = highest - lowest
Range = 146 - 120
Range= 26
Let m be mean
M=mean=sum/n
Mean=(120+134+146+127+138+133) / 6
M=798/6
M=133
The standard deviation sample formula:
S.D = sqrt( Summation of |x-m|^2 / n-1)
Let start finding:
|x-m|^2
For 1st: |120-133|^2=169
For 2nd: |134-133|^2=1
For 3rd: |146-133|^2=169
For 4th: |127-133|^2=36
For 5th: |138-133|^2=25
For 6th: |133-133|^2=0
Summation of |x-m|^2 = 400
The standard deviation formula is :
S.D = sqrt( Summation of |x-m|^2 / n-1)
S.D= sqrt(400 / 5)
S.D=sqrt(80)
S.D= 8.94
Variance = (Summation of |x-m|^2 / n-1)
Variance= 400/5
Variance= 80
You can let the sides be a and b. You can then use the Law of Sines to create an equation relating the two sides and the angles opposite them, and finally isolate a/b.
Ok, so remember that the derivitive of the position function is the velocty function and the derivitive of the velocity function is the accceleration function
x(t) is the positon function
so just take the derivitive of 3t/π +cos(t) twice
first derivitive is 3/π-sin(t)
2nd derivitive is -cos(t)
a(t)=-cos(t)
on the interval [π/2,5π/2) where does -cos(t)=1? or where does cos(t)=-1?
at t=π
so now plug that in for t in the position function to find the position at time t=π
x(π)=3(π)/π+cos(π)
x(π)=3-1
x(π)=2
so the position is 2
ok, that graph is the first derivitive of f(x)
the function f(x) is increaseing when the slope is positive
it is concave up when the 2nd derivitive of f(x) is positive
we are given f'(x), the derivitive of f(x)
we want to find where it is increasing AND where it is concave down
it is increasing when the derivitive is positive, so just find where the graph is positive (that's about from -2 to 4)
it is concave down when the second derivitive (aka derivitive of the first derivitive aka slope of the first derivitive) is negative
where is the slope negative?
from about x=0 to x=2
and that's in our range of being increasing
so the interval is (0,2)
Answer:
Dude, where's the picture?
