SALES DIGESTS (2013 2014)
ATTY. RAY PAOLO SANTIAGO
properties for the aggregate amount of P1,8000,000 with the following
CARCELLER vs. COURT OF APPEALS and SIHI
February 10, 1999
Jose Ramon Carceller
Neuroevolution in Mario Kart
February 7, 2017
North Carolina School of Science and Math
We have neither given nor received unauthorized assistance on this investigation assignments
* image evolution
* -* see http:/parasec.net/transmission/image-evolution/
* genetic algorithm configuration.
var conf = cfw_
crossOverRate: 0, / probability of crossover
mutationRate: 1, / probability of a mutation
The Art Gallery
Magd Bayoumi, James Boyd, Rohan Reddy
October 6, 2016
The curator of a watercolor exhibit has 50 paintings that theyd like to showcase in
their gallery. The challenge is changing the layout of the gallery with portable walls
MATH355 Discrete Math / Quiz 6 / 2 Mar 2015
Name KE. 2 12 points
1. Base b numeration systems. Convert (2035),ight to base ten. Show work.
2.33+ o-gzv 392W 5.2 s was + o -+ m + 5 = 6053)
2. Integer division
a. Prove: Let a, b, and c be integers with a at
MATH355 Discrete Math / Quiz 8 / 1 Apr 2015
Name K E"? 12 points Box
This is a take-home quiz.
0 It is due at the beginning of class on Monday, April 6.
oYou'may use your own class-notes, textbook, other books, and previous quizzes.
0 Do not get help from
MATH355 Discrete Math / Quiz 41/ 11 Feb 2015
Name - K5 Y 12 points Box
1. (7 points) Congruence modulo m
a. List three positive integers and three negative integers that are congruent to 5 modulo 8.
we-27,*fi-).II 3.? .5) /3) 2:) 26) 37J .,
7 b. According
MATH355 Discrete Math / Quiz 1 / 12 Jan 2015
Name x_< g 2 12 points
1. (4 points) Write the converse and contrapositive of the following conditional proposition:
If n2 is even, then H is even.
converse: Of ,4 M W) W n1 ML. oemh
. . _ .z m n 2-. (4; o"
MATH355 Discrete Math / Quiz 9 / 13 Apr 2015
Name K E 2 12 points
1. (8 points) Complete the denitions, where A and B are sets.
a.Afunctionf:A > Bis one-to-one ifand only if. . V15) e A) 430g) :5?th A X, we.
b.AfunctionF:A ~+BmapsAontoBifandonlyif. V L B
MATH355 Discrete Math / Quiz 3 / 28 Jan 2015
Name 5 E z 12 points Box
1. (3 points) Write the negation of each proposition.
a.p>q P A?-
b. All prime integers are odd. meal/e 15 at. Prime ~Hmi [5 even .
c. Vx e R (x is rational > x2 is rational)
3956 R (x
MATH355 Discrete Math / Quiz 7 f/ 25 Mar 2015
Name K as; 12 points Box
1. Complete the denitions, where A and B are sets.
a. A is a subset of B, denoted A 5 8 , if and only if . . .
For sevw-y %, iva/Jc my: xe; 8*.
b. The Cartesian product of A andB is th
MATH355 Discrete Math / Quiz 2 / 14 Jan 2015
Name &5 z 12 points
1. (2 points) Write the contrapositive of the following conditional proposition:
If a matrix A is invertible, then det(A) = 1.
Di ,6; any a. Mm Mme, alarmw 1,
2. (4 points) Complete the
1. Choose Method
a. Let x be a element with a certain property something is true.
a. Assume p then q.
a. We will use the contrapositive so assume not q then not p.
Finite: If there are exactly n distinct elements in S where n is non negative
Same cardinality: one to one corr
Countable: finite or same cardinality as set of positive int
UAi = for some i
Div & Mod
Divides (Divisor): Let a&b be integers where a=/= 0. We say a divides b iff b=ak for
some integer k.
Modulo: Let a&b be integers and let m be a positive integer. We say a is congruent to
Worksheet # 1: Review
1. (MA 113 Exam 1, Problem 1, Spring 2007). Find the equation of the line that passes through (1, 2) and is parallel to the line 4x + 2y = 11. Put your answer in y = mx + b form. 2. Find the slope, x-intercept, and y-intercept of the
CHAPTER 2: METHODS OF PROOF Section 2.1: BASIC PROOFS WITH QUANTIFIERS Existence Proofs Our first goal is to prove a statement of the form (x) P (x). There are two types of existence proofs: Constructive Proofs of Existence: (a) One type of constructive p
4 out of 4 points
taken and are:
59.8". Find the
likely size of the
chance error in a
That is cor
die is tossed 5 times. Find the probability that none of the rolls show 4 or more spots.
4 out of 4 points
Find the chance
that if you toss a
pair of dice, you
get 6 for the sum.
a certain town, there are 40,000 registered voters, of whom 15,000 are Republicans. A survey
organization is about to take a simple random sample of 1,200 registered voters. Find the
expected value for the percentage of Republicans in the sample.
Math 170 Test #2 Review
DIRECTIONS: Show all steps leading to your answers, including any intermediate results obtained
using a graphing utility.
f ( x + h) f ( x )
1) Use the definition of a derivative f ( x) = lim
to find the derivative of f ( x) = 2 x