Discrete Math
How long will it take for the sample to contain 500 million counts of bacteria, given it triples every 15 minutes?
Write an exponential function to model each situation and find the amount after the specified time. For example, given a population of 1,236,000 that grows at an interest rate of 1.3% over 10 years, find the final population.
Find a Hamiltonian circuit for the given graph, ensuring that each vertex is visited exactly once, and return to the starting vertex.
Determine if a Hamiltonian path or circuit exists for the given graph, considering the structure and connections of its vertices.
Given a graph where the edges have weights, find the optimal Hamiltonian circuit with the lowest total weight. This brings us to the Traveling Salesman Problem, where a salesperson needs to visit each city once and return home at the lowest cost, examining airfare costs between cities.
Given a graph G, determine its vertex connectivity by identifying the minimum number of vertices that can be deleted to disconnect the graph or make it trivial.
For example, in specific cases, identify if deleting certain vertices (e.g., or ) disconnects the graph or reduces it to a trivial graph.
Given a non-trivial graph G, identify an edge cut set X such that G-X is disconnected. Additionally, determine if X is a minimal or minimum edge cut, and calculate the edge connectivity of G.
How many ways can you select one student from a class with 18 girls and 15 boys?
How many total possible pairs are there if you need to select one boy and one girl from a class with 18 girls and 15 boys?
If you have a bag with 5 purple balls, 4 green balls, and 6 red balls, how many choices do you have to select one ball?
How many choices do you have if you want to select one purple ball and one red ball from a bag containing 5 purple balls and 6 red balls?
If you want to select one purple, one green, and one red ball from a bag containing 5 purple balls, 4 green balls, and 6 red balls, how many total choices do you have?
How many ways can you roll an even number on a six-sided die?
How many ways can you draw a face card in a standard 52-card deck?
How many ways can you roll an even number on a die or draw a face card?
How many different sandwiches can you make when choosing from different types of bread, meat, and vegetables?
How many license plates can be made with specific restrictions on numbers and letters?
How many license plates can be made with six letters, where no letters are repeated?
Find a spanning tree for a graph with eight vertices, nine edges, and two circuits by removing two edges to break the circuits.
Find all the spanning trees for a graph with seven vertices, seven edges, and one circuit, by removing one edge to break the circuit.