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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.
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.
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.
BAT Industries is a manufacturer of orange juice in Jamaica. In 2022 it sold a bottle of orange juice to wholesalers for $100 and its variable costs is $40 and fixed costs is $100,000 monthly:
Using the information provided.
i. How many bottles of orange juice must the company sell in order to break even and what is the breakeven revenue?
ii. If the company sold 1,500,000 bottles of orange juice for the year 2022, what was its profit?
iii. Due to inflation, in 2023 fixed costs are expected to rise to $175,000 monthly. What will be the NEW break-even quantity and revenue?
iiii. If the company will sell the same number of orange juice as it did in 2022 and it wants to make the same profit as in 20222, what price should they sell each bottle of orange Juice for in 2023?
Each time Caroline goes shopping she decides whether or not to buy fruit.
The probability that she does buy fruit is 0.6.
Independently, she then decides whether or not to buy a CD, with a probability of 0.2 that she does buy a CD.
Work out the probability that she buys fruit or buys a CD or both.
.4 If Universal Set U = {90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100} (10)
A = {90, 92, 94, 96, 98, 100}, B= {91, 93, 95, 97, 99},
C = {90, 94, 98}
1.4.1 What is (A ∩ C)c 1.4.2 What is (B ∪ C
give steps please
