10 boys share 7 bars equally.What fraction of a bar does each boy get?
2 answers:
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Answer:
0.2514 = 25.14% probability that the diameter of a selected bearing is greater than 85 millimeters.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
Find the probability that the diameter of a selected bearing is greater than 85 millimeters.
This is 1 subtracted by the pvalue of Z when X = 85. Then
has a pvalue of 0.7486.
1 - 0.7486 = 0.2514
0.2514 = 25.14% probability that the diameter of a selected bearing is greater than 85 millimeters.
Answer:
We assume that the orange is dropped at t = 0s.
Once the orange is on the air, the only force acting on it is the gravitational force, then the acceleration of the orange is the gravitational acceleration.
A(t) = -32.17 ft/s^2
Where the negative sign is because this acceleration points downwards.
For the velocity equation, we need to integrate over time, we will get:
V(t) = (-32.17 ft/s^2)*t + V0
Where V0 is the initial vertical velocity of the orange, because the orange is accidentally dropped, this initial velocity is equal to zero.
V(t) = (-32.17 ft/s^2)*t
For the position equation we need to integrate again, this time we get:
P(t) = (1/2)*(-32.17 ft/s^2)*t^2 + P0
Where P0 is the initial height of the orange, we know that it is 40ft, then the position equation is:
P(t) = (1/2)*(-32.17 ft/s^2)*t^2 + 40 ft
Now that we know the equation, we can graph it. (you can see the graph below)
Now we also want to find at what time does the orange hit the water.
This happens when:
P(t) = 0 ft = (1/2)*(-32.17 ft/s^2)*t^2 + 40 ft
We just need to solve that equation for t.
0 ft = (1/2)*(-32.17 ft/s^2)*t^2 + 40 ft
(1/2)*(32.17 ft/s^2)*t^2 = 40 ft
t^2 = (40ft)/( (1/2)*(32.17 ft/s^2))
t = √( (40ft)/( (1/2)*(32.17 ft/s^2)) ) = 1.58 s
The orange hits the water 1.58 seconds after it is dropped.
