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

3.11. QUESTIONNAIRE DESIGN

1.Roles of questionnaires: Primary purpose: facilitate the extraction of data from a respondent. Secondly: It serves as an ‘aide memoire’ to the interviewer.Thirdly: It provides consistency in the way the interview is conducted. Without a questionnaire: questions would be asked in a haphazard way at the discretion of the individual.

2.Types of questionnaires: Structured questionnairesconsist of closed or prompted questions (with predefined answers) that require the designer to anticipate all possible answers. Semi-structured questionnaires comprise a mixture of closed and open questions used in B2B market research where there is a need to accommodate a large range of different responses from companies.Unstructured...

Golden circle:

This relates to the innovation. If a company is able to attract those who share its beliefs, it is also able to connect easier with innovators.

This is a graph made up of three circles, each inside the other. Each circle has a meaning and a way to apply it to our business efficiently.

We can explain the operation of the Golden Circle in such a way that while most companies ask themselves the answers to the question 'what' as their starting point, they are fully aware of the 'how', but very few companies are clear about the 'why'.

The 'what' responds to what we do and what we want to do. The 'how' responds to the processes through which we carry out our actions, and the 'why' would respond to the reason why we develop our business....

Polygon Interior Angles Theorem

The sum of the measures of interior angles of an n-gon is (n-2)x180

Interior angles of a quadrilateral:

The sum of the measures of the interior angles of a quadrilateral is 360^o

Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.

Angles have to measure up to 360. 360/n (n=#of sides)

Theorems

If a quadrilateral is a parallelogram, then its opposite sides are congruent

If a quadrilateral is a parallelogram, then its opposite angles are congruent

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary

If a quadrilateral is a parallelogram, then its diagonal bisects each other

If both pairs of opposite sides of a quadrilateral

Axiom

Statement that is considered to be self evident and assumed to be true without any proof or demonstration.

Theorem

Statement that has been proved on the basis of previously established statements, such as other theorems and generally accepted statements such axioms.

Corollary

Statement that follows with little or no proof required from an already proven statement.

Lemma

Mathematical result that is useful in establishing the truth values of some other results.

Trivial proof

The statement on the proof is trivial if we can prove that Q(x) is true for all x in S, then for all x in S, p(x) => q(X) is true regardless of the truth value of p(x).

Vacuous proof

The statement on the proof is vacuous if we can prove that P(x) is true for all x in S, then...

Bond Price Sensitivity

7.7 Interest rate sensitivity. An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase date. Immediately after the investor purchased them, interest rates fell, and each of them had a new YTM of 7%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table:

N=10 Y=8 or 7 PV=? FV=1000 PTM=0 except coupon=100

Default Risk Premium

6.4 Default risk premium. A treasury bond that...

Chapter 3: Key Concepts

Missing Variable

x = given Median * 2 - ((1 of 2) median numbers if even): ascending order

Unreadable Score

(U * N of unreadable) - (U * N of readable)

Degrees of Freedom

1 # of freedom is lost

Chebyshev's Theorem

K = Deviation

Calculate time % within K Dev of mean - (1 - 1/k^2) * 100 = %

Finding Values

Find x K devs from mean - (mean - K * given standard dev) = XLow...(mean + k * given standard dev) = XHigh

Finding % Within Times Xlow-Xhigh

K = (XHigh - Mean) / Given Standard dev....then do Chebyshev's - (1 - 1/k^2) * 100 = %

Z-Score Simplified

(Mean - Given Mean) / Given Standard Dev = ZScore

Finding Minimum Score Accepted

(Min devs) * (Given Devs) + (Mean) = Min Score

Weighted Mean

Chart Xi / Wi /XiWi

Use Empirical Rule if distribution

The Architecture of Basilica San Lorenzo

The Basilica San Lorenzo was built during the Quattrocento by the architect Filippo Brunelleschi, with construction conducted between 1422 and 1470. It is inspired by the Church of the Holy Cross (Gothic). The structure is divided into three naves and lateral chapels. In the middle of the transept is a cupola, which is surrounded by chapels. Opposite the middle of the transept is the main chapel.

Geometric and Mathematical Design

Its plan is a Latin cross with three naves and side chapels, forming a basilica that is almost extremely longitudinal. In the transept, which has little development, he set a dome with a lantern. The space was mathematically and geometrically modulated by the circle inscribed in

Qualitative and Quantitative Variables

Qualitative: variables that are not numerical. They represent categories or groups that the data can fall into. Nominal: the categories do not have a natural order or ranking. The key characteristic of nominal variables is that the different categories are mutually exclusive and there is no inherent order to the categories. Ordinal: the categories have a logical or natural order. However, the distances between the categories are not necessarily meaningful.

Quantitative: variables that represent quantities and can be measured numerically. Discrete: a type of quantitative variable that can take on a countable number of distinct values. These are typically values that you can list or count. They often represent...

SQL Date Format Cheat Sheet

This reference provides a comprehensive list of SQL Server CONVERT styles for formatting date and time values. Use these codes to transform your data into the desired output format.

Common Date and Time Conversion Styles

Chapter 6 Review: Bond Valuation Problems

1. Coupon Rate Calculation

   A $1,000 face value bond is currently quoted at 100.8. The bond pays semiannual payments of $22.50 each and matures in six years. What is the coupon rate?

   Coupon rate = ($22.50 × 2) / $1,000 = 0.0450, or 4.50 percent

2. Current Price of a Bond

   A $1,000 face value bond currently has a yield to maturity of 8.22 percent. The bond matures in five years and pays interest semiannually. The coupon rate is 7.5 percent. What is the current price of this bond?

   FV = 1000; PMT = 75/2 = 37.5; N = 5 x 2 = 10; I/Y = 8.22 / 2 = 4.11 => PV = 970.96

3. Determining Coupon Rate

   A six-year, semiannual coupon bond is selling for $991.38. The bond has a face value of $1,000 and a yield to maturity of 9.19