A piece of copper wire of length 200 m has a diameter of 1.2 mm.
1 answer:
The volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.
Given that, the length of copper wire=200 m=200000 mm and the diameter of the copper wire=1.2 mm.
We need to find the volume of the copper wire.
<h3>What is the formula to find the volume of the cylinder?</h3>The formula to find the volume of a cylinder is πr²h.
Now, the volume of the copper wire=πr²h= mm³=226.080 cm³
If the density of copper is 8.9 g/cm³, find the mass of the wire.
We know that .
⇒8.9 g/cm³=
⇒Mass=2,012.112 g/cm³
Therefore, the volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.
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a) Probability of both being males is 27%
b) Probability of both being females is 23%
c) Probability of having exactly one male and one female is 50%
Step-by-step explanation:
a)
The probability that the birth is a male can be written as
(which corresponds to 52%)
While the probability that the birth is a female can be written as
(which corresponds to 48%)
Here we want to calculate the probability that over 2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:
And substituting, we find
So, 27%.
b)
In this case, we want to find the probability that both children are female, so the probability
As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:
And substituting
We find:
Which means 23%.
c)
In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:
- The probability that 1st child is a male and 2nd child is a female, namely
- The probability that 1st child is a female and 2nd child is a male, namely
So, this probability is
We have:
Therefore, this probability is
So, 50%.
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Answer:
The price that is two standard deviations above the mean price is 4.90.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 3.22 and a standard deviation of 0.84.
This means that
Find the price that is two standard deviations above the mean price.
This is X when Z = 2. So
The price that is two standard deviations above the mean price is 4.90.