You should write of what parts of the text were the most difficult to read, and to identify how
many times a passage was read before some understanding was achieved. Mathematical writing
is often not immediately understood, and takes time and thought befo
Tasks
1. Apply the function "plot" to the formula that relates the response "frequency" to the explanatory variable
"march2007" in order to produce the two box-plots of the response. Redo the plotting with "frequency" replaced
by "log(frequency)". The dis
The principles of estimating parameters.
Estimating the expectation.
Estimating the variance and the standard deviation.
Estimating other parameters.
The bias, variance, and mean-square error of an estimator.
Comparing between estimators.
Using simulatio
First of all, we have to know what a statistic is before we can even talk about
it. A statistic is a numerical characteristic of the data, which estimates the
corresponding population parameter (Yakir, 2011, p.13). It is important to note
the difference b
Topics:
Confidence interval and confidence level
Confidence interval for the mean, proportion, Normal mean and variance
The t and the chi-square distributions
Selecting the sample size
Learning Objectives:
Define confidence intervals and confidence levels
Learning Objectives:
Formulate statistical hypothesis for testing.
Identify the test statistic and the rejection region.
Identify the two types of error associated with the testing of hypothesis.
Compute the p-value.
Test hypotheses on the expectation and
This week we focused on Newtons Method from chapter 3 of the text. Newtons Method is an
application of Taylor Polynomials for finding roots of functions. In general solving an equation f(x) = 0 is
not easy, though we can do it in simple cases like find ro
In this weeks lesson, we learned about graphs, quadratic functions and linear functions. Graphs
were the most difficult to read because if a function is graphed and you are asked questions based
on the graph without the function, it can be a hassle. Norma
Chapter 10.5 discuses the graphs of trigonometric functions. First we looked at the graphs of the cosine
and sine functions. We identified the properties associated with both the cosine and sine functions and
we could see how they relate to each other and
If f(x) = 2x + 1 and g(x) = x2, what is f g? What is g f?
f g = f(g(x)
= 2(x2) +1
= 2x2 + 1
g f = g(f(x)
= (2x +1) 2
= (2x+1) (2x+1)
= (2x2x) + (2x1) + (12x) + (11)
= 4x2 +2x + 2x +1
= 4x2 +4x
+1
2. Consider f(x) = 2x + 3. Find the inverse of this functio
What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given
that at least one root is a complex number?
If the equation is 7th degree then it has 7 roots.
Complex roots always come in pairs, so if it has at least one, then it
This week we studied three topics:
1. Graphs of Polynomial Functions
2. The Factor Theorem and the Remainder Theorem
3. Complex Zeroes and the Fundamental Theorem of Algebra
The first problem I had was trying to understand the polynomial function form (f(
First I would like to define velocity, which is the speed an object in a given direction or the rate of change
in its position (Velocity, 2016). Speed is scalar which means it states how fast the object is moving,
however, velocity is vector which means i
This week we focused on Systems of linear and non-linear equations. I understand the definition of
a system of equation as one when both solutions for x and y are of interest.
The questions we're pretty simple for me because I remember how to work them fr
Let
Let
Let
be the set of all calendar dates from 4/30/1789 to 9/25/2014.
be the set of names of U.S. presidents.
be the set of names of first ladies of the U.S.
Consider the following two functions
where
is the name of the
president of the U.S. on date (
This week we focused on Trigonometry. In Chapter 10.1, we looked at Angles and their measures. We
started off by defining a ray, which is described as a half line and the initial
point which is self-explanatory (the point where the ray originates). When t
1.
What is the equation of the line through (1,2) and (3, -1)?
m= y2y1
x2x1
= -1-(2) = -3
3-(1)
2
Substitution into point-slope form of the line, we get
y - y0 = m(x x0)
y 2 = -3 (x 1)
2
y 2 = -3 x + 3
2
2
y
= -3 x + 3 + 4
2
2 2
y
= -3 x + 7
2
2
ANS: y= -
.What must be invested today, to be worth $20,000 in 10 years, if it is compounded yearly at 8%?
2. Write as a sum or difference of simple (single symbol argument) logs: Log [(AB)/(CD)]
3. The half-life of carbon 14 is 5730 years. How old is a bone contai
1. If the terminal side of a 330 degree angle intersects a unit circle, what would the
coordinates at the point of intersection?
For any point on a unit circle, x=cos( ) and y=sin( ).
The coordinates would be
,
2. Solve for x: 3 + cos 2x = 7/2; only inclu
One of the largest issues in ancient mathematics was accuracynobody had calculators that went out
ten decimal places, and accuracy generally got worse as the numbers got larger. Why did trigonometry
allow for some questions to be answered very accurately,
The perception of sound is probably logarithmic. The inventor of the telephone,
Alexander G. Bell, noticed that the difference in sound intensity between two soft
tones and two loud tones, were completely different. Therefore, if you were
comparing two so
Mathematical writing can be difficult to understand and it is for this reason that I
came up with a strategy to fully understand any given concept. I used to read lineby-line and sentence by sentence in order to understand, but I realized that I could
not
This week we looked at the derivative of a function. Derivative seemed very confusing at first and I had
to reread a paragraph at least four times before any understanding was achieved. I understand that the
derivative is what we call velocity in chapter
Discuss how the limit allows a way to "divide by 0.
In basic math, it is impossible to divide any number by 0. 12/3 = 4 because 4 x 3
= 12
3/0 =x Let's suppose. Does 0(x) = 3?
By the way - 0/0 can have any answer you want !
0/0 = 6 Sure! 6(0) = 0
0/0 = 12
1.
What is the equation of the line through (1,2) and (3, -1)?
m= y2y1
x2x1
= -1-(2) = -3
3-(1)
2
Substitution into point-slope form of the line, we get
y - y0 = m(x x0)
y 2 = -3 (x 1)
2
y 2 = -3 x + 3
2
2
y
= -3 x + 3 + 4
2
2 2
y
= -3 x + 7
2
2
ANS: y= -
1. Give an example of a function, f(x), with a domain of (0,5] and a range of [0,)
f(k)=
2.
f(t+h) =
If f(t) = 2t t2, what is (f(t + h) f(t) / h?
2t+2h(t+h)2
2t+2h(t+h)(t+h)
2t+2h(tt+th+ht+hh)
2t+2h(t2+2ht+h2)
2t+2h+(t2(2ht)h2)
2t+2h+(t22(ht)h2)
2t+2h+(t2
20
Lines can be used to approximate a wide variety of functions; often a function can be described using many lines.
If a stock price goes from $10 to $12 from January 1st to January 31, and from $12 to $9 from February 1st to February 28th, is the
price
WRITTEN ASSIGNMENT UNIT 1
1. Give an example of a function, f(x), with a domain of (0,5] and a range of [0,)
ANSWER:
f(x) = cfw_x+1 , if 0 > x 5
2. If f(t) = 2t t2, what is (f(t + h) f(t) / h?
ANSWER:
[f(t+h) f(t)] / h = [2(t+h) (t+h)2 (2t t2)] / h
= [2t
1.
What is the equation of the line through (1,2) and (3, -1)?
m=
y (12) 3
=
=
x (31)
2
y y 0 =m(xx 0)
y2=
3
3
x+
2
2
y2=
y=
3
( x1)
2
3 7
x+ =1.5 x +3.5
2
2
f ( x )=1.5 x+3.5
2.
What is the vertex of f(x) = x2 6x + 3?
A) Find axis of symmetry:
x=
b
6
6