Please see the attached file for the fully formatted problem(s).

Note the similarities in the following parallel treatments of a frequency distribution and a probability distribution.

Frequency Distribution
Complete the table below for the following data. (Recall that x is the midpoint for the interval.)
14,7,1,11,2,3,11,6,10,13,11,11,16,12,9,11,9,10,7,12,9,6,4,5,9,16,12,12, 11,10,14,9,13,10,15,11,11,1,12,12,6,7,8,2,9,12,10,15,9,3
Interval x Tally f x*f f*x2
1-3 2 |||| | 6 12 24
4-6
7-9
10-12
13-15
16-18
Totals
Probability Distribution
A binomial distribution has n = 10 and p = .5. Complete the following table.
x P(x) x*P(x)
0 .001
1 .010
2 .044
3 .117
4
5
6
7
8
9
10
Totals

a. Find the mean (or expected value) for each distribution.
b. Find the standard deviation for each distribution.
c. (Extra credit) Use the normal approximation of the binomial probability distribution to find the interval that contains 95.44% of that distribution.

An AAA bond yielding a 10% return and a BB bond yielding a 15% return. Invest as much in AAA bond as in the BB bond, at least $5000 in the AAA bond and no more than $8000 in the BB bond. How much should she invest in each to maximize her return.

Solve this problem two different ways:
Mensa is an association for people with high IQs. An advertisement for the organization
offers the following challenge: "Take the instant test to see if you are a genius."
PUT THE APPROPRIATE PLUS OR MINUS SIGNS BETWEEN THE NUMBERS, IN THE CORRECT PLACES, SO THAT THE SUM TOTAL WIL

(a)For each of the following languages over the unary alphabet {a}, construct a finite automaton accepting it.
i. {a^2}
ii. {a^2, a^3, a^4}
(b) Let A be any finite nonempty subset of {a, a^2, a^3, a^4,...}. Is there always a finite automaton that accepts A?

Calculate the ratio of the area to the volume for a unit cube, a unit sphere inscribed inside the cube, and a right cylinder inscribed inside the cube.
Next, for each having a unit volume (i.e., all three solids have the same volume) calculate the area-to-volume ratios for a sphere, cube, and cylinder.

Sweet Delight Candies, Inc., sells boxes of candy consisting of creams and caramels. Each box sells for $4 and holds 50 pieces of candy (all pieces are the same size). If the caramels cost $0.05 to produce and the creams cost $0.10 to produce, how many caramels and creams should be in each box for no profit and no loss? Would

Math 212 FiniteMathematics
1. (4) Construct the augmented matrix for the following system of three equations in three
unknowns. Do not solve the system.
2x - y + z = 10
4x + 2y - 3z = 10
x - 3y + 2z = 8
2. (4) Use the Gauss-Jordan method to solve the following system of equations.

Two movie theaters, UAI and UAII, start their movies at 7:00 p.m. The movie at UAI takes 75 minutes and the movie at UAII takes 90 minutes. If the shows run continuously, when will they again start at the same time?

1. Determine without graphing whether the given quadratic function has minimum value or maximum value. Then find the coordinates ...
2. Solve the Triangle. Round lengths ...
3. Solve the problem: One number is 6 less than a second number. Twice the second number is ...
4. Find the standard form of the equation of the el

Suppose that we wished to develop a base three number system to be used in place of either a decimal system or a base two binary system
a-- How many separate symbols would we need in this system? In the binary system, we can get away with only two, 0 and 1. Will this work in a base three system? How would you write the decim

A study was taken at a certain university to determine what relationship, if any, exists between mathematics ability and interest in mathematics. The ability and interest for 150 students were determined, and the results are presented in the following table:
INTEREST
Ability Low Average High Total
Low 40 8 12