The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviatio
1 answer:
Answer:
2.25 %
Explanation:
65-95-99.7 is a rule to remember the precentages that lies around the mean.
at the range of mean () plus or minus one standard deviation (
),
at the range of mean plus or minus two standard deviation,
at the range of mean plus or minus three standard deviation,
So, note that they are asking about the probability that it is greater than 0.32, that is the mean (0.3) plus two times the standard deviation (0.1) ()
So we know that the 95.5% is between and
, hence approximately the 4.5% (100%-95.5%) is greater than 0.32 or less than 0.28. But half (4.5%/2=2.25%) is greater than 0.32 and the other half is less than 0.28.
So
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Answer:
a) the mug hits the floor 0.7425m away from the end of the bar. b) |V|=5.08m/s θ= -72.82°
Explanation:
In order to solve this problem, we must first start by doing a drawing of the situation. (see attached picture).
a)
From the drawing we can see that we are dealing with a two dimensions movement problem. So in order to find out how far away from the bar the mug will fall, we need to start by finding how long it will take the mug to be in the air, so we analyze the vertical movement of the mug.
In order to find the time we need to use the following formula, which contains the data we know:
we know that and that
as well, so the formula is simplified to:
we can now solve this for t, so we get:
we know that and that
the acceleration of gravity is negative because the mug is moving downwards. So we substitute them into the given formula:
which yields:
t=0.495s
we can now use this to find the horizontal distance the mug travels. We know that:
so we can solve this for x, so we get:
and we can now substitute the values we know:
x=(1.5m/s)(0.495s)
which yields:
x=0.7425m
b) Now that we know the time it takes the mug to hit the floor, we can use it to find the final velocity in the y-direction by using the following formula:
we know the initial velocity in the vertical direction is zero, so we can simplify the formula:
so we can solve this for the final velocity:
in this case the acceleration is the same as the acceleration of gravity (which is negative) so we can substitute that and the time we found on the previous part to get:
which yields:
so now we know the components of the final velocity, which are:
and
so now we can find the speed by determining the magnitude of the vector, like this:
so we get:
which yields:
|V|=5.08m/s
now, to find the direction of the impact, we can use the following equation:
so we get:
which yields:
