# Various Mathematics Problems

Please show the work on the answers asked.

1 - If during an election there were 6372 registered voters and 3560 registered voters voted, what percentage of the registered voters actually cast a vote? If there were 10,000 people in the district, what percent of the population voted in the election? What percent of the population registered to vote?

2 - A certain ball, when dropped from any height, bounces one-half the original height. If it were dropped from 80 feet and allowed to bounce freely, what was the total distance it traveled when it hit the ground for the third time?

3 - The number of cows owned by farmer Smith is the number of cows owned by farmer Thompson divided by the number of cows owned by farmer Jones. If Farmer Thompson, who owns 42 cows, had 14 cows, he would own 8 times as many cows as farmer Jones .How many cows does each farmer own?

4 - Tonya sold 160 sandwiches for $2.00 each. Each sandwich consisted of 4 ounces of ham, two slices of bread, and mustard. She paid $3.00/lb for the ham, $0.60/loaf for the bread (20 slices/ loaf) and used 8 jars of mustard at 50 cents each. How much profit did Latoya make (no partial Credit0?

5 - A typical children's aspirin contains 81 milligrams (mg) of acetylsalicylic acid as the active ingredient. Let's say you needed to give your daughter an 81 mg dosage, but you only had adult strength (500 mg) aspirin tablets available. You fully dissolved the adult strength aspiring tablet in 8 fluids ounces of water. How many ounces of the aspirin solution should you give your daughter to safely deliver the correct 81 mg dosage she needs?

6 - If you filled a 300-gallon tank to 80% of its capacity with water, how many gallons of water would be present in the tank? How many tons of water is in the tank if the water has a density of 2.20x 10e-3 pounds per 2.64 x 10e-4 gallons? If the bottom of the tank was five foot by five foot square, what would be the pressure exerted by the water on the bottom of the tank( assume that the entire mass of the water is pressing only on the bottom of the tank) in pounds per square inch psi)?

7 - The purchase price for a house you want is $200,000.00.The bank requires you to make a down payment on the house equal to 20% of the purchase price.

a. How much money do you need for a down payment?

b. How much money is the bank lending you to purchase the house?

c. Assume you take out what is called an interest only loan that requires you to pay 6% of the bank-financed amount each year for 5 years. If you interest only payment are spread out evenly over the 5 years, how much will your monthly payment be?

d. How much interest will you pay the bank over the 5 - year period?

e. How much will you still owe the bank, on the original amount financed after 5 years?

8 - Write the name of the noble gas that does not have 8 valance electrons.

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#### Solution Summary

The following posting discusses various mathematical problems.

Various Problems in Discrete Mathematics

Prove Each Directly.

1. The product of any two even integers is even.

Prove by cases, where n is an arbitrary integer and Ixl denotes the absolute

value of x.

2. [-x]=[x] (*Brackets are the x's is the absolute value symbol)

Give a counterexample to disprove each statement, where P(x) denotes an

arbitrary predicate.

3. Every month has exactly 30 days.

Let a, b, and c be any real numbers. Then a < b if and only if there

is a positive real number x such that a + x - b. Use this fact to prove

each.

4. If a+c is less than b+c, then a is less than b

Determine if the given sets are equal.

5. {x, {y}}, {{x},y}

Let A = {a, e, f, g,i}, B = {b, d, e, g, h}, C = {d, e, f, h, i}, and U= {a,b,... ,k}.

Find each set.

6. (A U B)'

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