Notes, summaries, assignments, exams, and problems for Mathematics

Chapter 1

- Information systems today are ubiquitous

Unit 1: Geometric Vectors

A ship heading of 143° at 18 Knots. 10 Knot current at bearing 112°. Ground Velocity?

x²=18²+10²-2(18)(10)cos149

=27.1 Knots

SinΘ = Sin149 Bearing

10 27.1 149-11= 132°

SinΘ=Sin149(10)

27.1

Θ=11°

Unit 2: Cartesian Vectors

Vectors a=[3,-7,8], b=[-6,3,4], c=[2,5,7] evaluate:

A) a + 2b B) B * C

=[3,-7,8]+2[-6,3,4] =[3,-7,8]+[-12,6,8] =[-9,-1,16] =31

C) a x c

=[-7(7)-5(8),8(2)-7(3),3(5)-2(-7)] [-89,-5,29] 5 7 2 5

Ex 2) A(2,3,5) B(5,10,-3) Determine:

A) ab B) |ab|

=[5-2,10-3,-3-5] =√3²+7²+8²

=[3,7,-8] =√122

Ex 3) Determine a x b

a x b= |a| |b| sinΘ n

=20(30)sin32 n

= 317.95 n

n is into the page

In my opinion, if we remove the cars in the center of the cities it will be a great change of adaptation, since it would cost us more to move, in addition almost all of us have a job far where we have to move through the center of the cities.
It is true that today we have a very high level of pollution and we must reduce it as much as possible, and on the other hand it has already prohibited a good part of the traffic in certain cities, for example, as in the case of Madrid or Oslo that they plan to center of their cities are completely pedestrian and only circulate taxis and buses.
I think we should not remove the cars from the city center, there are other solutions such as putting only electric cars or cars that do not pollute much.
We also

1) If a toy company is planning to introduce 3 new toys next Christmas. The toys sales can be a success or a failure, what is the probability that at least 2 of the toys are a success?

FFF FFS FSF FSS 4/8 = ½ = 0.5

S SFF SFS SSF SSS

For problems 2 and 3: a guitar manufacturer has an average daily production of 60 units, with a standard deviation of 7 units per day. If the guitar production distribution is mound shape:

2) What percentage of days in a month will have a daily production between 53 and 74 units?

53

3) What percentage of days in a month will have a daily production of more than 67 units?

x>67 = 16%

4) A combination lock system has three ten-digit (0 to 9) number wheels side by side. How many four-digit opening numbers are possible if... Continue reading "Probability and Statistics Problems with Solutions" »

unit 14.WORKING WITH THE TEXT

1.‐ Niamh is the student participating in the Erasmus pro

2.‐ a.‐ “we should all apply for it.” Recommendation that

all students apply for the Erasmus project b.‐ “we all

were still grateful” they were grateful despite not getting

what they wanted. C.‐ “After filling out papers and

forms” Completing the paperwork for the project

d.‐ “I would like to set up” she wants to begin the

creation of something. E.‐ “regardless of studying

Spanish for a year.” Despite studying Spanish during one

year she knew none. 3.‐ a.‐ It was good to know

someone spoke English. B.‐ They took him to the local

farm. C.‐ Because she gained experience and that would

be useful in the future.

VOCABULARY a.‐ English... Continue reading "Concept of education" »

Write your tLecture 1

Descriptive statistics: Describe and summarize the data from the sample.

Probability models describe a model For the population which can be used to make probability statements about what Can be seen in the sample.

Statistical Inference goes in the Other direction. It uses the data in the sample to make inference about Features of  the population with Associated confidence and/or error bounds.

SPSS: Rows are subjects/units which are also Referred to as cases.

Columns are Things which are being measured on the cases. These are called variables.

Examples:

Obtaining Frequency tables:

Analyze -> Descriptive Stats -> Frequencies

Bar Graph: Graphs -> Legacy Dialog -> Bars -> Simple -> Category Axis (zyg)

Pie Chart:... Continue reading "Blood test "solt" »

Statistics: The Science of Organizing Data

Statistics is the science of organizing data to draw conclusions or answer questions.

Descriptive Statistics

Descriptive statistics describe data through numerical summaries and graphs.

Variables

Variables are characteristics of individuals within the population.

Discrete and Continuous Variables

Discrete variables are counted, while continuous variables are measured.

Nominal and Ordinal Variables

Nominal variables are named, while ordinal variables are ranked or ordered.

Interval and Ratio Variables

Interval variables have no meaningful zero and equal intervals between values, while ratio variables have a meaningful zero.

Types of Variables in a Study

The response variable is what is being studied, the explanatory... Continue reading "Introduction to Statistics" »

Vocabulary Builder: 35 Essential Words

A

1. Agonized

Manifesting, suffering, or characterized by great physical or mental pain.

2. Ample

Large and accommodating.

3. Assent

The expression of approval or agreement.

B

4. Befall

(Of something bad) happen to someone.

C

5. Chariots

A two-wheeled horse-drawn vehicle used in ancient warfare and racing.

6. Conceive

Become pregnant with (a child). Form or devise (a plan or idea) in the mind.

7. Cordial

Friendly, warm.

D

8. Dews

Moisture condensed from the atmosphere, especially at night, and deposited in the form of small drops upon any cool surface.

9. Divine

Of, from, or like God or a god.

10. Doe

Female deer.

F

11. Foe

An enemy or opponent.

G

12. Gossamer

Used to refer to something very light, thin, and insubstantial or delicate.... Continue reading "Vocabulary Builder: 35 Essential Words with Definitions" »