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1. Let ∼ be defined so that a ∼ b exactly when a · b is divisible by 3. Is this an equivalence relation? If not, which of the three properties (reflexive, symmetric, transitive) does not hold?
2. Encrypt the message we are all made of stars using the atbash cipher.
3. Prove that a ≡ b (mod n) if and only if n|(a - b); that is, check that the condition given in Definition 5.3.1 is correct.
In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability tha..
Inside a semicircular tunnel of diameter 20 feet, a vertical support beam is placed 6 feet from the side of the tunnel. How tall is the beam? (Round to one decimal place.)
suppose you deposit 2000 for 5 years at a rate of 8. calculate the return a if the bank compounds anually n1 round
A property retained whenever additional edges are added to a simple graph (without adding vertices) is called monotone increasing, and a property that is retained whenever edges are removed from a simple graph (without removing vertices) is called..
Last season a major league baseball player got 120 hits in 240 times at bat. If the player expects to bat 500 times in the entire season with the same ratio of hits to at bats, how many hits can the player expect to have?
Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20. Since they have not enough money to pay the custom duties, the first pays 5 casks of wine and 40 francs
The normal stress acting at the end of the bar varies according to s = E(x - x1)/x1 , where x is the position of the end of the bar, x1 is the initial length, and E is a material constant (Young's modulus). For E = 2 * 107 kPa, determine the work..
Develop a 2D plot for average cost versus the quantity.
Determine the order of each differential equation, and whether or not the given functions are solutions of that equation on some interval of x values.
A wooden artifact from an ancient tomb contains 55% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
Mr. Smith feels that each day his dog should have at least 8 units of protein, 5 units of carbohydrates, and 16 units of fat. How many cans of each dog food should he give to his dog each day to provide the minimum requirements at the least cost?
Use reference angles to find exact value - Provide an exact number using radicals as needed and rationalize all denominators.
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