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
*...

...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...

...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 ...

...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.
( (...

...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...

...
Mathematical Happenings
Rayne Charni
MTH 110
April 6, 2015
Prof. Charles Hobbs
Mathematical Happenings
Greek mathematicians from the 7th Century BC, such as Pythagoras and Euclid are the reasons for our fundamental understanding of mathematic science today. Adopting elements of mathematics from both the Egyptians and the Babylonians while researching and added their own works has lead to important theories and formulas used for all modern mathematics and science.
Pythagoras was born in Samon Greece approximately 569 BC and passed away between 500 - 475 BC in Metapontum, Italy. Pythagoras believed that all things are numbers. He also believed that mathematics was and is the core of everything mathematical. He also believed that geometry is the highest form of mathematics and that the physical world could always be understood through the science of mathematics.
Pythagoreans have and will continue to give recognition to Pythagoras for 1) the angles of a triangle equaling to two right angles. 2) The Pythagoras theorem, which is a right-angled triangle, and the square on the hypotenuse equaling to the sum of the squares on the other two sides. This theory was created and understood years earlier by the Babylonians, however, Pythagoras proved it to be correct. 3) Pythagoras constructed three of the five regular solids. The regular solids are called tetrahedron, cube, octahedron, icosahedron, and dodecahedron. 4) Proving and...

...FIRST-ORDER
DIFFERENTIAL EQUATIONS
OVERVIEW In Section 4.8 we introduced differential equations of the form dy>dx = ƒ(x),
where ƒ is given and y is an unknown function of x. When ƒ is continuous over some interval, we found the general solution y(x) by integration, y = 1 ƒ(x) dx. In Section 6.5 we
solved separable differential equations. Such equations arise when investigating exponential growth or decay, for example. In this chapter we study some other types of first-order
differential equations. They involve only first derivatives of the unknown function.
15.1
Solutions, Slope Fields, and Picard’s Theorem
We begin this section by defining general differential equations involving first derivatives.
We then look at slope fields, which give a geometric picture of the solutions to such equations. Finally we present Picard’s Theorem, which gives conditions under which first-order
differential equations have exactly one solution.
General First-Order Differential Equations and Solutions
A first-order differential equation is an equation
dy
= ƒsx, yd
dx
(1)
in which ƒ(x, y) is a function of two variables defined on a region in the xy-plane. The
equation is of first order because it involves only the first derivative dy> dx (and not
higher-order derivatives). We point out that the...