Answer:
l = 6 inches
Step-by-step explanation:
We have,
The volume of a rectangular prism with a square base is .
Height of the prism is 5 in
It is required to find the length of the edge of the square base. Let it is l.
The formula of the volume of the rectangular prism is given by :
A is area of base of prism
It has a square base, l =b
So, the length of the edge of the square base is 6 inches.
The exercise says that the life variable is measured in days, that is, it is a discrete distribution, this because it takes finite and punctual values, 21, 22, 23 days, etc., not 21 and a half days or 23 and a quarter days.
Now, the discrete uniform distribution assumes that the probability of each value it takes is equal.
In this case the distribution takes 15 values, from 15 to 29 including the extremes, so the probability of each value is =
, so the probability mass function will be:
With this we can calculate the probability that an insect, selected at random, lives more than 24 days, like this:
On the other hand, the expected life or average life in this distribution is calculated as follows: that this case is
= 22
Answer
A) The awakened life of the insect is 22 days
B) The probability that an insect, selected at random, lives more than 24 days is 1/3 = 0.33 = 33.3%
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Answer:
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Given:
Find:
Solution: In order to determine the length of x we need to use some trigonometric functions. Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees. We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin. Plug in the values and solve for the unknown.
<u>Plug in the values</u>
<u>Multiply both sides by x</u>
<u>Divide both sides by sin(30)</u>
<u>Simplify</u>
Therefore, the value of the unknown variable x is 6 units.