Conclusion
a.) There is no relationship between the speed and friction of a box. Surface area does not effect friction. Tension angle has no effect on friction. Mass is directly proportional to static and kinetic friction. Surface type has an effect on friction because aluminum has the highest friction followed by paper, wax paper, wood, and felt with the lowest. Static friction tended to be higher than kinetic friction in all cases.

b.) The mathematical equation that is derived is f = (u)(Fn). This means that friction is equal to the coefficient of friction multiplied with the force normal of an object. The coefficient of friction represents the ratio of the force of friction between two surfaces and the force pressing them together. When two substances rub together there is a resistance, the coefficient of friction is a measure meant of this force. The force normal is the force of a surface acting on an object and is perpendicular to the plane of contact. The meaning of the slope is the force applied per kilogram on the object. The y-intercept is not significant because the five percent rule excludes it. However, since the y-intercept is zero, its means that at no force pulling on the mass, there is no friction.

c.) Newton’s third law of motion: for every force, there is an equal and opposite force. Static friction: frictional force is sufficient to prevent relative motion between surfaces. Kinetic friction: occurs when there is relative sliding motion at the interface of the surfaces in contact. Normal force: acts perpendicular to and away from the surface. Coefficient of friction: measure of force of friction between two surfaces.

d.) Errors include not finding the exact point on the graph at the end of the jerk for static friction, being off a little on the kinetic friction because the slope was not exactly zero, changing the speed by which the box was pulled across the table during one trial which can throw off the average kinetic...

...1. Which equation below represents the quadratic formula?
*a. -b±b2-4ac2a = x
b. a2+b2=c2
c. fx=a0+n=1∞ancosnπxL+bnsinnπxL
2. Which of the following represents a set of parallel lines?
a. Option one
b. Option two
*c. Option three
3. What is the definition of an obtuse angle?
*a. an angle greater than 90°
b. an angle equal to 90°
c. an angle less than 90°
4. Which formula below represents the area of a circle?
a. A=2πr
*b. A=πr2
c. A=π2r
d. A= √π
5.
What geometric term is represented by the image below?
a. a corner
*b. a cross-section
c. the circumference
d. the perimeter
11. Using the data in the table below, calculate the mean, or average, number of points scored by Player B.
| Game 1 | Game 2 | Game 3 | Game 4 | Game 5 |
Player A | 13 | 12 | 9 | 11 | 13 |
Player B | 12 | 11 | 15 | 20 | 12 |
*a. 14
b. 11.5
c. 13
d. 13.67
6. This instrument is commonly used by surveyors. It measures horizontal and vertical angles to determine the location of a point from other known points at either end of a fixed baseline, rather than measuring distances to the point directly. What is it called?
a. triangulator
b. binocular
c. tripod
*d. theodolite
7. What is the name of the missing shape in the flowchart below?
a. Acute
b. Obtuse
*c. Isosceles
d. Right
8. What category includes all of the items on the list below?
* Square
* Rectangle
*...

...Critiquing the Mathematical Literacy Assessment Taxonomy: Where is the Reasoning and the Problem Solving?
Hamsa Venkat 1 Mellony Graven 2 Erna Lampen 1 Patricia Nalube 1
1 Marang Centre for Mathematics and Science Education, Wits University hamsa.venkatakrishnan@wits.ac.za; christine.lampen@wits.ac.za; patricia.nalube@wits.ac.za
2 Rhodes University
m.graven@ru.ac.za
In this paper we consider the ways in which the Mathematical Literacy (ML) assessment taxonomy provides spaces for the problem solving and reasoning identified as critical to mathematical literacy competence. We do this through an analysis of the taxonomy structure within which Mathematical Literacy competences are assessed. We argue that shortcomings in this structure in relation to the support and development of reasoning and problem solving feed through into the kinds of questions that are asked within the assessment of Mathematical Literacy. Some of these shortcomings are exemplified through the questions that appeared in the 2008 Mathematical Literacy examinations. We conclude the paper with a brief discussion of the implications of this taxonomy structure for the development of the reasoning and problem‐solving competences that align with curricular aims. This paper refers to the assessment taxonomy in the ...

...Function
p(y) =
n
y
p y (1 − p)n−y ;
Mean
Variance
MomentGenerating
Function
np
np(1 − p)
[ pet + (1 − p)]n
1
p
1− p
pet
1 − (1 − p)et
y = 0, 1, . . . , n
Geometric
p(y) = p(1 − p) y−1 ;
p
y = 1, 2, . . .
Hypergeometric
p(y) =
r
y
N−r
n−y
N
n
;
nr
N
n
r
N
2
N −r
N
N −n
N −1
y = 0, 1, . . . , n if n ≤ r,
y = 0, 1, . . . , r if n > r
Poisson
Negative binomial
λ y e−λ
;
y!
y = 0, 1, 2, . . .
p(y) =
p(y) =
y−1
r−1
p r (1 − p) y−r ;
y = r, r + 1, . . .
λ
λ
exp[λ(et − 1)]
r
p
r(1 − p)
pet
1 − (1 − p)et
p
2
r
MATHEMATICAL STATISTICS WITH APPLICATIONS
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SEVENTH EDITION
Mathematical
Statistics with
Applications
Dennis D. Wackerly
University of Florida
William Mendenhall III
University of Florida, Emeritus
Richard L. Scheaffer
University of Florida, Emeritus
Australia • Brazil • Canada • Mexico • Singapore • Spain
United Kingdom • United States
Mathematical Statistics with Applications, Seventh Edition
Dennis D. Wackerly, William Mendenhall III, Richard L. Scheaffer
Statistics Editor: Carolyn Crockett
Assistant Editors: Beth Gershman, Catie Ronquillo
Editorial Assistant: Ashley Summers
Technology Project Manager: Jennifer Liang
Marketing Manager: Mandy Jellerichs
Marketing Assistant: Ashley Pickering
Marketing Communications Manager: Darlene
Amidon-Brent
Project Manager, Editorial Production: Hal Humphrey
Art Director: Vernon Boes
Print Buyer: Karen...

...REPORT
AIM
The aim of this experiment is to:
□ Explore the equations of uniform accelerated motion and investigate the relationship between displacement and time
□ Determine the magnitude of deceleration due to friction.
□ Assess the effect of mass on the car’s accelerated motion.
DESIGN
Hypothesis – A car moving in a straight line with a non-zero initial velocity will finally come to a rest as a result of friction, given that the car has no engine or external tractions. This motion can be considered as a uniform accelerated motion because:
1. The car is moving in a horizontal straight line so weight is cancelled by the normal reaction force from the ground. The only other force existed is the friction between the car and the surface therefore it will be equal to the net force
2. According to the formula Fr = μN, the amount of the friction depends on two factors: the friction coefficient and the normal reaction force, both of which are fixed. Therefore the amount of friction is constant throughout the motion
3. According to Newton’s Second Law F = ma, a constant net force will result in a uniform acceleration (deceleration). The acceleration is negative in this case as cars are slowing down to a rest.
For convenience, this decelerated motion can be inverted into an equivalent motion in which the car is acceleration from rest. It should follow the equation of
x = ut + 1/2 at2,
where x = distance traveled, u = 0 (seen as the...

...DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH, 2nd Edition
DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA, Gian Paulo A. ECE / 3, Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves a lot of integral calculus as well, so in general, differential equations straddle the specific parts of basic calculus or it can be considered part of advanced calculus. There are two general types of differential equations. An ordinary differential equation involves only two variables, whereas a partial differential equation involves more than two. A differential equation can have many variables. The independent variable is the variable of concern from which the terms are derived on, whereas if the same variable appears in its derivative, then it is a dependent variable. Variables are different from parameters, which are constants with no derivatives.
The given equation is the general differential equation for calorimetry. The variable q is dependent, t is dependent, and c and m are the parameters.
( (...

...Summer 2010-3 CLASS NOTES CHAPTER 1
Section 1.1: Linear Equations
Learning Objectives:
1. Solve a linear equation
2. Solve equations that lead to linear equations
3. Solve applied problems involving linear equations
Examples:
1. [pic]
[pic]
3. A total of $51,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment?
4. Shannon, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $608 for 56 hours worked. What is her regular hourly wage?
Answers: 1. [pic]
2. [pic]
3. $24,000 in CDs, $27,000 in bonds 4. $9.50/hour
Section 1.2: Quadratic Equations
Learning Objectives:
1. Solve a quadratic equation by (a) factoring, (b) completing the square, (c) the
quadratic formula
2. Solve applied problems involving quadratic equations
Examples:
1. Find the real solutions by factoring: [pic]
2. Find the real solutions by using the square root method: [pic]
3. Find the real solutions by completing the square: [pic]
4. Find the real solutions by using the quadratic formula: [pic]
5. A ball is thrown vertically upward from the top of a...

...Mathematical Models
Contents
Definition of Mathematical Model Types of Variables The Mathematical Modeling Cycle Classification of Models
2
Definitions of Mathematical Model
Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. It is a process that attempts to match observation with symbolic statement. A mathematical model uses mathematical language to describe a system. Building a model involves a trade-off between simplicity and accuracy. The success of a model depends on how easily it can be used and how accurate are its predictions.
3
Types of Variables
A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The variables represent some properties of the system. There are four basic groups of variables:
– – – – Input variables Parameters Random variables Decision variables (output variables)
4
The Mathematical Modeling Cycle
Simplify Real World Problem
Interpret
Mathematical Model
Program
Conclusions Simulate
Computer Software
5
The Mathematical Modeling Cycle
1. Identify and understand the problem, draw diagrams 2. Define the terms in your problem 3....

...MATHEMATICAL METHODS
1. Finding An Initial Basic Feasible Solution:
An initial basic feasible solution to a transportation problem can be found by any one of the three following methods:
I. North West Corner Rule
II. The Least Cost Method
III. Vogel’s Approximation Method
1. North West Corner Rule
The North West corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North-West Corner (i.e. top left corner).
The standard North West corner rule instructions are paraphrased below:
Steps:
Step 1. Select the north west (upper left hand) corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand.
Step 2. Adjust the supply and demand numbers in the respective rows and columns.
Step 3. If the demand for the first cell is satisfied, then move horizontally to the next cell in the second row.
Step 4. If the supply for the first row is exhausted, then move down to the first cell in the second row.
Step 5. If for any cell, supply equals demand, then the next allocation can be made in either in the next row or column.
Step 6. Continue the process until all supply and demand values are exhausted.
2. The Least-Cost Method
The least-Cost Method is a method for computing a basic feasible solution of a transportation problem, where the basic...