Show all work and any explanations so that I will understand how to work the problems.

See attached...

Math 212 Finite Mathematics

Show all work and any explanations:

1) An unprepared student takes a three-question, true/false quiz in which he guesses the
answers to all three questions, so each answer is equally likely to be correct or wrong.

a) (4) The student gets three answers wrong.

b) (4) The student gets exactly two answers correct.

c) (4) The student gets only the first answer correct

2) (4) An automobile manufacturer produces 7 models, each available in 6 different exterior
colors, with 4 different upholstery fabrics and 5 interior colors. How many varieties of
automobile are available?

3. (8) Construct a frequency distribution and construct a histogram for the following data
Use seven intervals, starting with 30-39.

4. The number of unemployed workers (in millions) from 1992 to 2001 are recorded below.
9.61 8.94 8.00 7.40 7.24 6.74 6.21 5.88 5.66 6.74

a) (8) Compute the median and mode number of unemployed workers

b) (2) Is there a mode?

c) (6) Compute the standard deviation of the number of unemployed works.

5. (4) Below is the simplex tableau for a linear programming problem.
x y s1 s2 z C
5 3 1 0 0 34
3 5 0 1 0 30
-2 -14 0 0 1 0
The pivot column is the y column and the pivot element is five in the middle row. Use this information to make the entry 0 in the first row, second column.

Attached are my FINITEMATH 106 short problems that I need completed and DONE.
PLEASE make sure to DO ALL OF THE PROBLEMS. Do not make the EXPLANATIONS complicated on how the ANSWERS were found.
I need something short and sweet and to the point to INCLUDE the ANSWER to ALL OF THE PROBLEMS. Of Course all of the answers nee

1.For the given sets, answer the following questions
A={1, 2, 3, 4}
B={1, 2, 5, 7}
C={3, 4, 5, 7}
A.B U C
B.A'
C.A U C(wasn't able to upside down the U)
D.A U(rotate the U) A'
e.A U (rotate the U) B

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.

If the probability that a woman is rich is 0.4, the probability that she is beautiful is 0.3 and the probability that she is either rich or beautiful is 0.5, what is the probability that she is both rich AND beautiful?
Please show "all" steps to solution.

A craft store sells small flags for $6 and large flags for $8. Recently, they sold a total of 70 flags in a single day. If flag receipts for the day totaled $520, how many of each type of flag were sold?

Hi,
I'm looking for a FSA (Finite State Acceptor) for all binary strings containing an odd number of 0's. A state diagram is the easiest for me to understand. A valid regular expression to describe the language (I've verified this) is 1*0(1+01*0)*
Thanks!

(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?

Proposition 10.2.1: (the addition principle)
Suppose that X and Y are disjoint finite sets. Then X U Y is finite and |X UY| = |X| + |Y|.
Corollary 10.2.2:
For a positive integer n, suppose that X1, X2....,Xn is a collection of n pairwise disjoint finite sets (i.e. i does not = j => Xi Xj = empty set)
Then X1 U X2

In 1866, a sixteen-year-old Italian student, Nicolo Paganini, discovered the second smallest amicable pair: 1184 = 2^5 x 11^2. Confirm that this pair is indeed amicable, but is not found by Thabit's rule.
The second smallest amicable pair is (1184, 1210).