Answer:
The common difference (or common ratio) = 0.75
Step-by-step explanation:
i) let the first term be 
= 80
ii) let the second term be 
= . r = 80 × r = 60 ∴ r = 
= 0.75
iii) let the third term be 
= . r = 60 × r = 45 ∴ r = 
= 0.75
iv) let the fourth term be 
= . r = 45 × r = 33.75 ∴ r = 
= 0.75
Therefore we can see that the series of numbers are part of a geometric progression and the first term is 80 and the common ratio = 0.75.
Answer:
We conclude that cheddar popcorn weighed less than 5.5 ounces.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ =5.5 ounces
Sample mean, 
= 5.23 ounces
Sample size, n = 64
Alpha, α = 0.05
Sample standard deviation, σ = 0.24 ounce.
First, we design the null and the alternate hypothesis
We use One-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now, 
Since,
We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that cheddar popcorn weighed less than 5.5 ounces.
Answer:
yes,
Step-by-step explanation:
because of them being quadrilaterals
Answer:
M=v^2r / 2G
Step-by-step explanation:
Open the file, it is solved for you, your welcome.
Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.
A) The midpoint C' of AB is
.. (A +B)/2 = ((0, 0) +(m, n))/2 = ((0 +m)/2, (0 +n)/2) = (m/2, n/2) = C'
The midpoint B' is
.. (A +C)/2 = ((0, 0) +(p, 0))/2 = (p/2, 0) = B'
The midpoint A' is
.. (B +C)/2 = ((m, n) +(p, 0))/2 = ((m+p)/2, n/2) = A'
B) The slope of the line between (x1, y1) and (x2, y2) is given by
.. slope = (y2 -y1)/(x2 -x1)
Using the values for A and A', we have
.. slope = (n/2 -0)/((m+p)/2 -0) = n/(m+p)
C) We know the line goes through A = (0, 0), so we can write the point-slope form of the equation for AA' as
.. y -0 = (n/(m+p))*(x -0)
.. y = n*x/(m+p)
D) To show the point lies on the line, we can substitute its coordinates for x and y and see if we get something that looks true.
.. (x, y) = ((m+p)/3, n/3)
Putting these into our equation, we have
.. n/3 = n*((m+p)/3)/(m+p)
The expression on the right has factors of (m+p) that cancel*, so we end up with
.. n/3 = n/3 . . . . . . . true for any n
_____
* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.
The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
