Consider the point P where the gears meet. When the smaller gear rotates clockwise, the larger one will rotate counterclockwise.
Through one rotation of the smaller gear, P will have traveled the circumference of the smaller gear, which is 
in.
At the same time, a point P' on the larger gear traverses the same distance along the larger gear's circumference. This point traces out an arc that is subtended by some angle 
. The arc is as long as the smaller gear's circumference.
The measure of a circle's interior angle subtended by an arc is proportional to a complete revolution, i.e. an angular displacement of 
radians:
For part 2, we apply the same reasoning to the larger gear. In one full rotation of the larger gear, the point P' traverses the circumference 
in, and so does the point P on the smaller gear.
A full rotation is 360 degrees, so the smaller gear would have rotated 
times.
Answer:
Option A) 0.0074
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 110
Sample mean, 
= 20
Sample size, n = 100
Alpha, α = 0.05
Population standard deviation, σ = 115.35
First, we design the null and the alternate hypothesis
We use two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now, we calculate the p-value from the standard normal table.
P-value = 0.0074
Thus, the correct answer is
Option A) 0.0074
A percentage is a number that represents a ratio expressed as a fraction of 100. It means parts per 100. 1% would then mean 25 parts per 100. We solve the given statement above as follows:
1% (7) = (1/100) (7) = 0.07
Hope this answers the question.
Answer:
4(2x-3y+8)
Step-by-step explanation:
8x-12y+32
4(2x-3y+8)
