Problem 7)
The answer is choice B. Only graph 2 contains an Euler circuit.
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To have a Euler circuit, each vertex must have an even number of paths connecting to it. This does not happen with graph 1 since vertex A and vertex D have an odd number of vertices (3 each). The odd vertex count makes it impossible to travel back to the starting point, while making sure to only use each edge one time only.
With graph 2, each vertex has exactly two edges attached to it. So an Euler circuit is possible here.
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Problem 8)
The answer is choice B) 5
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Work Shown:
abc base 2 = (a*2^2 + b*2^1 + c*2^0) base 10
101 base 2 = (1*2^2 + 0*2^1 + 1*2^0) base 10
101 base 2 = (1*4 + 0*2 + 1*1) base 10
101 base 2 = (4 + 0 + 1) base 10
101 base 2 = 5 base 10
Answer:
(−1)(5x+2)
Step-by-step explanation:
I googled it
Answer:
0.1732 = 17.32% probability exactly 24 residents own a home.
Step-by-step explanation:
For each resident, there are only two possible outcomes. Either they own a home, or they do not. The probability of a resident owning a home is independent of any other resident. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
78% of residents in Summerville own a home.
This means that ![p = 0.78](https://tex.z-dn.net/?f=p%20%3D%200.78)
30 residents are randomly selected:
This means that ![n = 30](https://tex.z-dn.net/?f=n%20%3D%2030)
Find the probability exactly 24 residents own a home.
This is P(X = 24).
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 24) = C_{30,24}.(0.78)^{24}.(0.22)^{6} = 0.1732](https://tex.z-dn.net/?f=P%28X%20%3D%2024%29%20%3D%20C_%7B30%2C24%7D.%280.78%29%5E%7B24%7D.%280.22%29%5E%7B6%7D%20%3D%200.1732)
0.1732 = 17.32% probability exactly 24 residents own a home.