Answer:
A
Step-by-step explanation:
One complete turn is 1 perimeter (aka circumference).
We have to find the length it turned, hence, its circumference.
The formula for circumference (C) of a circle is:
Where r is the radius
The radius is HALF of diameter. Given diameter is 250, the radius is:
r = 250/2 = 125 feet
Now, substituting in formula we have:
So, it turned 785.4 feet with 1 rotation.
The correct answer is A
Answer:
(-2,-6)
-2
Step-by-step explanation:
To get the vertex take the number that's in the parathenses with the x and flip it's sign (in this case to a negative) which means we have
-2
this is the x coordinate of the vertex.
Next take the number that's being subtracted (or added) on the outside and leave that as is (-6)
This is the y coordinate
which means we have (-2,-6)
the axis of symmetry is just the x coordinate of the graph
which is -2
Answer:Your left hand side evaluates to:
m+(−1)mn+(−1)m+(−1)mnp
and your right hand side evaluates to:
m+(−1)mn+(−1)m+np
After eliminating the common terms:
m+(−1)mn from both sides, we are left with showing:
(−1)m+(−1)mnp=(−1)m+np
If p=0, both sides are clearly equal, so assume p≠0, and we can (by cancellation) simply prove:
(−1)(−1)mn=(−1)n.
It should be clear that if m is even, we have equality (both sides are (−1)n), so we are down to the case where m is odd. In this case:
(−1)(−1)mn=(−1)−n=1(−1)n
Multiplying both sides by (−1)n then yields:
1=(−1)2n=[(−1)n]2 which is always true, no matter what n is
Answer:
(a) Null Hypothesis (H₀) = Mean of x₁ > Mean of x₂
Alternative Hypothesis (H₁) = Mean of x₁ ≠ Mean of x₂
(b) We will use here t-test for two sample means which is given by,
![[tex]t = \frac{\bar_{x_{1}}-\bar_{x_{2}}}{\sqrt{s^2(\frac{1}{n_{1}}+\frac{1}{n_{2}} )}}](https://tex.z-dn.net/?f=%5Btex%5Dt%20%3D%20%5Cfrac%7B%5Cbar_%7Bx_%7B1%7D%7D-%5Cbar_%7Bx_%7B2%7D%7D%7D%7B%5Csqrt%7Bs%5E2%28%5Cfrac%7B1%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B1%7D%7Bn_%7B2%7D%7D%20%20%29%7D%7D)
[/tex]
Putting all values we get, t = 17.5 with 20 degree of freedom
At α = 0.05
p-value = 95% Confidence Interval for the Difference ( 6.6068 , 8.3932 )
