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A branch of mathematics that deals with separable and distinct numbers with graph and logical statements are included, and numbers can be finite or infinite.
Suppose inflation decreases the value of money by 3% per year? Which formula describes an = the value (in dollars) of $1000 after n years?
How many leaves does it have?
Which of is a formula for the sequence 3, 6, 12, 24, 48, ...? Assume that the first term in the sequence is called a0?
What is the probability that more than 600 cars will enter the airport tunnel during a peak hour? Round to three decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
Two finite state machines are said to be equivalent if they
How many terms does the binomial expansion of (2x+3)99 has?
A terminal node in a binary tree is called _______________.
How many edges does a tree with V vertices have?
How many nonisomorphic simple graphs are there with five vertices and three edges?
The following breakdown of a total of 18,686 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT). Mode of Transportation Car Train Bicycle Plane Number of Fatalities 16,525 842 698 538 What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a train or a plane accident? Round answer to two decimal places.
Which is not an invariant when determining if graphs are isomorphic?
Determine the event that the number that falls uppermost on the second die is double that of the number that falls on the first die.
What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?
How may isomorphic graphs are there for a graph with n number vertices?
Which rule states that if (k + 1) or more objects are placed into k boxes, then there is at least one box containing two or more of the objects?
Logic is a system based on __________.
"A simple graph with 15 vertices with each having a degree of 5 can exist." This statement is ________.
A binary tree of depth "d" is an almost complete binary tree if. A. Each leaf in the tree is either at level "d" or at level "d– 1" B. For any node "n" in the tree with a right descendant at level "d" all the left descendants of "n" that are leaves, are also at level "d"
Which of the following statements about binary trees is NOT true?
The number of different directed trees with 3 nodes is
You have 12 balls, numbered 1 through 12, which you want to place into 4 boxes, numbered 1 through 4. If boxes can remain empty, in how many ways can the 12 balls be disturbed among the 4 boxes?
Every tree with at least two nodes has at least two nodes of what degree?
How many different passwords are possible if each password consists of six characters where each character is either an uppercase letter, a lowercase letter, or a digit, and at least one digit must be included in the password? (Note: There are 26 letters and 10 digits)
A dormitory has 40 students: 12 sophomores, 8 juniors, and 20 seniors. Which of the following is equal to the number of ways to put all 40 in a row for a picture, with all 12 sophomores on the left, all 8 juniors in the middle, and all 20 seniors on the right?
The preorder and post order traversal of a Binary Tree generates the same output. The tree can have maximum
Which concept considers the arrangement of objects / elements in a set?
Which of the following graphs is not a characteristics of isomorphic graphs?
What is the maximum possible number of nodes in a binary tree at level 6
Translate the expression to predicate logic: “No students are allowed to carry guns.”
Consider the statement, “If n is divisible by 30 then n is divisible by 2 and by 3 and by 5.” Which of the following statements is equivalent to this statement?
A Finite State Automaton can have more than one initial state.
Suppose you want to use the principle of mathematical induction to prove that 1 + 2 + 22 + 23 + 23 + ... + 2n = + 2n+1 - 1 for all non-negative integers n. Which of theses is the correct statement P(k) in the inductive step?
How many different license plates are available if the license plate pattern consists of four letters that cannot be repeated and followed by three digits that can be repeated? (Assume that all letters are uppercase and the digits are 0, 1, ... 9)
The basic limitation of finite automata is that
What is the coefficient of x101 y99 in the expansion of (2x-3y)200?
Suppose you want to use the principle of mathematical induction to prove that 1 + 2 + 22 + 23 + 23 + ... + 2n = + 2n+1 - 1 for all positive integers n. Which of these is the correct implication p(k) -> P(k+1) to be used in the inductive step?
Suppose you want to prove that every product of integers of the form k(k+1)(k+2) is divisible by 6. If you want to prove this by cases, which of the following is a set of cases you would use?
An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space
This is a statement that is always false.
How many nodes in a tree have no ancestors?
Which of the following is not a recurrence relation?
Are the events F and G complementary?
If two finite states machine M and N are isomorphic, then A. M can be transformed to N, merely re-labelling its states B. M can be transformed to N, merely re-labelling its edges Which is true?
It is impossible for a valid argument to have a true premise and
A class consists of 12 women and 10 men. How many ways are there to form a committee of size six if the committee has equal numbers of women and men?
Consider the following finite automaton A over Σ = {a,b,c}:
Suppose you are hired by a company at an initial salary of $30,000. At the end of each year you receive a 3% raise, plus an addition of $1000 on your base salary. Let an equal your salary at the end of n years with the company. Find a recurrence relation for an.
Suppose you wish to prove this statement "If n is an integer, then n ≤ n3." Which of the following is correct?
Which logical operator represents the statement “if and only if”?
What type of graph is depicted below?
The number of leaf nodes in a complete binary tree of depth d is
What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 35 sec, the yellow signal for 5 sec, and the green signal for 60 sec? Round to two decimal places, if necessary, and be sure to express answer in decimal form, not as a percentage.
When inorder traversing a tree resulted e a c k f h d b g; the preorder traversal would return.
What is the 8th term in the binomial expansion of (2x+y)16?
Refer to the graphs below:
How many of the nodes have at least one sibling?
One light bulb is selected at random from a lot of 110 light bulbs, of which 2% are defective. What is the probability that the light bulb selected is defective?
Finite automata requires minimum _______ number of stacks.
If you give a proof by mathematical induction of the statement that 2n &ge= n2, for all integers n ≥ 4, the basis step requires you to prove that which of the following is true?
What is the negation of a tautology?
What is the coefficient of aby98 in the binomial expansion of (ab+y)99?
What is the probability that a person in the survey selected at random favors using cameras to identify red-light runners?
Are the two graphs isomorphic?
Assume that you have an ordinary deck of 52 playing cards. How many possible 7-card poker hands are there that contain at least one face card (J, Q, K)?
A full binary tree with 2n+1 nodes contain
How many different choices of winners can you have if the draw is limited to first year and second year students and you only have one grand prize? Note: Given that the population of the school is as follows: 1st year = 100 students, 2nd year = 98 students, 3rd year = 102 students, 4th year = 50 students.
In order to get the contents of a binary search tree in ascending order, one has to traverse it in.
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