How are changes in energy and matter related
1 answer:
Answer:
According to Einstein's famous equation, matter can convert into energy (and viceversa) as follows:
where
E is the energy
m is the mass
c is the speed of light ()
Given the huge value of , we see that even a tiny amount of matter is able to release a huge amount of energy, when the whole mass is converted into energy. This is precisely what happens in nuclear reactions. For example, in the process of nuclear fusion (that occurs in the core of the stars), two light nuclei fuse together into a heavier nucleus. The mass of the final nucleus is lower than the total mass of the initial nuclei, so part of the mass has been converted into energy according to the equation above: this is why the amount of energy produced by stars is so big.
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Given Information:
Mean length of aluminum rods = μ = 10 cm
Standard deviation of length of aluminum rods = σ = 0.02 cm
Required Information:
a) P(9.98 < X < 10.02) = ?
b) P(9.90 < X < 10.1) = ?
Answer:
a) P(9.98 < X < 10.02) = 68.27%
b) P(9.90 < X < 10.1) = 100%
Explanation:
What is Normal Distribution?
Normal Distribution or also known as Gaussian Distribution, is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability
a) We want to find out the probability that the length of aluminum rods is between 9.98 and 10.02 cm.
The z-score corresponding to -1 is 0.15866 and 1 is 0.84134
Therefore, the probability that the length of aluminum rods is between 9.98 and 10.02 cm is 68.27%
b) We want to find out the probability that the length of aluminum rods is between 9.90 and 10.1 cm.
The z-score corresponding to -5 is 0 and 5 is 1
Therefore, the probability that the length of aluminum rods is between 9.90 and 10.1 cm is 100%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.0, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.00 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.