Answer:
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Answer:
The standard deviation is of 8.586.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have a genetic mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
About 9% of the population has a particular genetic mutation.
This means that 
900 people are randomly selected.
This means that 
Find the standard deviation for the number of people with the genetic mutation in such groups of 900.
The standard deviation is of 8.586.
We are choosing 2
2
r
shoes. How many ways are there to avoid a pair? The pairs represented in our sample can be chosen in (2)
(
n
2
r
)
ways. From each chosen pair, we can choose the left shoe or the right shoe. There are 22
2
2
r
ways to do this. So of the (22)
(
2
n
2
r
)
equally likely ways to choose 2
2
r
shoes, (2)22
(
n
2
r
)
2
2
r
are "favourable."
Another way: A perhaps more natural way to attack the problem is to imagine choosing the shoes one at a time. The probability that the second shoe chosen does not match the first is 2−22−1
2
n
−
2
2
n
−
1
. Given that this has happened, the probability the next shoe does not match either of the first two is 2−42−2
2
n
−
4
2
n
−
2
. Given that there is no match so far, the probability the next shoe does not match any of the first three is 2−62−3
2
n
−
6
2
n
−
3
. Continue. We get a product, which looks a little nicer if we start it with the term 22
2
n
2
n
. So an answer is
22⋅2−22−1⋅2−42−2⋅2−62−3⋯2−4+22−2+1.
2
n
2
n
⋅
2
n
−
2
2
n
−
1
⋅
2
n
−
4
2
n
−
2
⋅
2
n
−
6
2
n
−
3
⋯
2
n
−
4
r
+
2
2
n
−
2
r
+
1
.
This can be expressed more compactly in various ways.
Answer: the third angle is 106 degrees.
The base angles are 37 degrees each.
Step-by-step explanation:
In an isosceles triangle, the base angles are equal.
Let x represent the measure of each of the base angles.
The third angle in an isosceles triangle is 32 more than 2 times as large as each of the two base angles. It means that the measure of the third angle would be
(2x + 32) degrees
The sum of the angles inna triangle is 180 degrees. It means that
x + x + 2x + 32 = 180
4x = 180 - 32
4x = 148
x = 37
The third angle is
2x = 32 = (2 × 37) + 32
= 74 + 32 = 106
