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find the truth value "1\\land 1 \\to 1 \\lor 1"
show that
"(p\\leftrightarrow q) (p\\land q) \\lor (\\neg p \\land \\neg q)"are logically equivalent
A survey of the National Capital Region finds the average commute time of employees on one way is 45 minutes. The Makati Chamber of Commerce feels that in their city it is greater and want to publicize this. They randomly selected 28 commuters and found the average is 50 minutes with a standard deviation of 6 minutes. At 0.05 level of significance.
The optimal solution for an LPP always lies on at least two vertices of the feasible region.
The country’s capital city of Kathmandu is located in the center of Province 3. You decide to visit Nepal and want to drive through all provinces, trying to avoid as much as possible to visit one province twice. You arrive at Kathmandu Airport and take a rental car. The trip can begin. But wait – let’s plan things a little bit first. You open your map and your laptop.
As an abstract thinker, you may decide to first formalize the map as a graph and use it to plan the trip.
1) Formalize the map of Nepal as a graph , where the vertices are the provinces and edges connect vertices that represent different provinces with a common border. For example, {1,3} is in E because Provinces 1 and 3 share a border.
2) What degree does each vertex of G have?
3) Determine which province is adjacent to the most other provinces.
4) Is G planar? If yes, provide a drawing as a justification, that is, draw G so that edges meet only at vertices. If the graph is planar, how many faces does it have?
Draw a graph which has an Euler circuit but is not planar. Formalize the graph in the form
Draw a graph which does not have an Euler path and is also not planar. Formalize the graph in the form
Note: If you cannot draw the graph due to technical reasons, it is OK to just use formal notation and describe the graph textually.
What is the lowest value of the sample mean in this sampling distribution? A.0 B.1.5 C.2 D.2.5
A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider samples of size 3 that can be drawn from this population. List all the possible samples and the corresponding mean. Sample Mean
In statistical thinking, why P (-2<z<1) is the same as P (-2≤z≤1)?
Question 2: Discrete Random Variable
The BRIT Sports Bar sells a large quantity of Guinness every Saturday. From past records, the pub has determined the following probabilities for sales:
Number of Crates (X)
P(x)
18-0.15
19-0.10
20-0.32
21-0.05
22-0.13
23-0.25
a. Verify that this [P(x)] is a probability distribution. (2 marks)
b. Find the probability that the number of crates sold will be at least 22. (3 marks)
c. Find the probability that the number of crates sold will be at most 20. (3 marks)
d. What is the expected value for the number of crates sold for any given Saturday?
(4 marks)
e. Calculate the variance of the distribution? (6 marks)
f. Determine the standard deviation of the distribution? (2 marks)
can workout be shown please.
#339914 on Dec 2023