Chain rule
y=f(g(x))
y´=(d f(gx)/d g)(d g/d x)
or
y=y(v) and v=v(x), then dy /dx=(dy/dv)(dv/dx)
in our case:
y=sin (v)
v=arcsin(x)
dy/dv=d sin (v)/dv=cos (v)=cos(arcsin(x)
dv/dx=d arcsin(x)/dx=1/√(1-x²)
dy/dx=[cos (arcsin(x))]/√(1-x²)
Answer: d sin(arcsin(x))/dx=[cos (arcsin(x))]/√(1-x²)
Answer:
-5
Step-by-step explanation:
We can find the slope between two points by using
m = (y2-y1)/(x2-x1)
= ( -9-6)/(-6 - -9)
=(-9-6)/( -6+9)
-15/3
-5
Thank you for the free points!!!
X=-0.61 and Y is 4 is I did my math right
We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05
Since the p-value is smaller than alpha, this means we <u>reject the null hypothesis</u>.
The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".
Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.
In short, the p-value being smaller than alpha = 0.05 means we reject the null.
In order to accept the null, the p-value must be 0.05 or larger.
