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# Discrete Structures

### Discrete structures

.Derive the statement as corollaries of other theorems from the text or of statement you have proved true in the exercise. Prove that if one solution to a quadratic equation of the form x^2+bx+c=0 is rational (where b and c are rational), then the other solutions is also rational. (Use the fact that if the solutions of the e

### Write each equation in standard form using only integers.

Write each equation in standard form using only integers. x/2=3y/5

### Equations in Standard Form : Hyperbola and Parabola

Write this equation in standard form: xsquared-4(ysquared)-2x+16y-19=0 Write this equation in standard form: 6x-xsquared=8y+1

### Palindromes Range Values

What are the palindromes between 100 & 200? Find the range, mode, and median.

### Discrete Mathematics-Properties of Lattices

Order Relations and Structures Properties of Lattices Theorem Let L be a Lattice. Then for every a and b in L

### Equivalence Relations and Classes

Let L be a subset of {a,b}* Define a relation R (R sub L) on S* as follows: L for All of x, y is a member of S*, (x,y) are members of R if for all of z, xz are members of L iff yz are members of L A) Show that R is an equivalence relation B) Suppose L={a^i b^i where i >= 0} What can you say about the inde

### Find the length difference of two moving objects.

L1=Lo*sqrt(1-(v/c)^2) where Lo is length of an obiect at rest, c is velosity of light, v is velocity of the object. If L2=Lo*(c^2-v^2)/c^2, what is L1-L2?

### Proving a Summation using an Identity

Please see the attached file for the fully formatted problems. I'm trying to prove the following: using the following identity:

### Domination Number Proof

Determine (without proof) a formula for the domination number of path Pn.

### Discrete Structures

11) Use generating functions to determine the number of different ways 12 identical action figures can be given to five children so that each child receives at most three action figures. 12) Use generating functions to find the number of ways to select 10 balls from an urn containing red, white and blue balls if: a. The

### Discrete structures

6. A string that contains only 0s 1s and 2s is called a ternary string a) find a recurrence relation for the number of ternary strings that contain two consecutive 0s b) what are the initial conditions c) how many ternary strings of length six contain two consecutive 0s The next 3 problems deal with a variation of the

### Calculating the standard deviation from a set of data.

Find the standard deviation. Round to one more place than the data. 20, 18, 12, 8, 7, 5, 12, 11, 9

### Calculating the standard deviation from a frequency table.

Find the standard deviation of the data in the given frequency table. A company had 80 employees whose salaries are summarized in the frequency table below. Find the standard deviation. Salary / Employees 5001-10000 / 17 10001-15000 / 16 15001-20000 / 20 20001-25000 /15 25001-30000 /12

### Standard deviation calculation by frequency table

Find the standard deviation of the data in the given frequency table. A company had 80 employees whose salaries are summarized in the frequency table below. Find the standard deviation. Salary Employees 5001-10000 17 10001-15000 16 15001-20000 20 20001-25000 15 25001-30000 12