Escenario 1: Proyección Inicial

Pragmatic Analysis of Academic Discourse

When we analyze a text from a pragmatic point of view, we should consider several key elements: the purpose, the channel, the genre, the sender, and the receiver.

Characteristics of Academic Discourse

The primary purpose of academic discourse is to inform. In this context, the issuer acts as a transmitter, while the receiver is positioned at either a specialized level (scientific, such as a nurse) or a declarative level for general dissemination (divulgation).

Linguistic Markers and Procedures

Key markers of academic discourse include:

• Absence of deictics and an emphasis on impersonality.
• Use of the third-person axis.
• Predominance of the indicative mode and declarative statements.
• Absence of modalization procedures.

Fundamental Concepts in Algebra

Numerical Language

Expressing mathematical information using only numbers.

Algebraic Language

Expressing mathematical information using both numbers and letters.

Algebraic Expression

A set of numbers and letters combined with mathematical operation signs.

Numerical Value of an Algebraic Expression

The number obtained by replacing the letters with their corresponding values and performing the indicated operations.

Monomial

A monomial consists of a number and one or more letters:

• The number (including its sign) is called the coefficient.
• The letter or letters that accompany it are called the literal part.

Degree of a Monomial

The sum of the exponents of the letters that form it.

Similar Monomials

Two or more monomials are similar...

Ratio and Proportion Word Problems

1. Pablo and Sebastian won a lottery prize. Sebastian received $140,000 less than Pablo. What was the total prize they received? (Note: This problem may be missing information to be solved.)
2. A secretary can complete a job in 40 days by working 9 hours per day. How many hours per day must the secretary work to complete the same job in 30 days?
3. A zoo has enough food to feed 52 animals for 250 days. If the number of animals decreases by 12, for how many days will the food last?
4. A car uses 40 liters of gasoline to travel 510 kilometers. How many liters will it use to travel 204 kilometers?
5. A contractor estimates that 6 workers can finish a job in 15 days. How many workers are needed to finish the same job in 9 days?
6. Two

Algebra and Trigonometry Problem Set

1. y = -6x³ + 4x² - x + 2
2. Vertical shrink by 1/2, horizontal translation 2 to the left, vertical translation 1 down
3. 4x⁴ - 11x³ + 7x² + 5x - 3
4. $713,476.20
5. Brian is designing a handrail for a staircase and needs to determine the length: 12
6. A meteorologist predicts a 42% chance of rain on Saturday and a 54% chance of rain on Sunday: 27%
7. a_n = 3n - 11
8. (-2, 6) lies on the terminal side of an angle θ in standard position: Sinθ = 3√10 is False, True, True
9. y = log(x - 2)
10. Find the sum of the series: 12
11. The table shows enrollment by gender as an undergraduate or graduate student: 515/2463 = 0.209

Zeros of Functions

12. Find the zeros of the function shown below:
f(x) = x² + 3x - 10: x = 2 and -5

Statistical Distributions

13. Normal...

1. Operations with Integers

Addition Rules

• Same signs: Add the numbers and keep the original sign.
  Example: -4 + (-6) = -10
• Different signs: Subtract the smaller number from the larger number and keep the sign of the larger number.
  Example: 7 + (-3) = 4

Subtraction Rules

To subtract, turn the operation into addition by changing the sign of the second number:

a - b = a + (-b)

Step-by-Step Example:
Solve: 5 - 8
Step 1: Rewrite as addition → 5 + (-8)
Step 2: Different signs, so subtract → 8 - 5 = 3
Step 3: Keep the sign of the larger number → -3

Multiplication and Division Sign Rules

Step-by-Step Example:
Solve: -3 × -4
Step 1: Same signs result in a positive product.
Step 2: 3 ×...

1. Emilie's 3-Year Payment Plan

Answer: 12.4%

Formula: Interest = P × r × t

• Total payment: 36 months × $33.70 = $1,213.20
• Total interest paid: $1,213.20 - $884.92 = $328.28
• Rate calculation: $328.28 = $884.92 × r × 3; r = 0.1236 or 12.4%

2. 312 Sq Ft Family Room Flooring

Answer: 22.7%

• Total cost: $1.37 × 312 = $427.44
• Tax amount: $427.44 × 0.068 = $29.07
• Total purchase: $427.44 + $29.07 = $456.51
• Total repayment: 24 × $27.66 = $663.84
• Total interest: $663.84 - $456.51 = $207.33
• Interest rate: $207.33 / ($456.51 × 2) = 0.227 or 22.7%

3. Sea Drift Motel Loan

Answer: 0.44%

Using the simple interest formula I = P × r × t:

• Interest (I): $97,000
• Principal (P): $1,000,000
• Time (t): 22 years
• Rate (r): 0.0044 or 0.44%

4. Effective Interest Rate Calculation

Using...

Statistics Problems and Solutions

Great! Let's continue with providing solutions to the questions:

Question 1: Empirical Rule Name

The Empirical Rule is also known as:

• E. The 68–95–99.7 Rule

Question 2: Normal Distribution Interval (95%)

For a normally distributed data set with a mean of 70 and a standard deviation of 13, approximately 95% of the data lie within about two standard deviations of the mean.

• Calculate: 70 ± 2 × 13 = 70 ± 26
• Result: 44 and 96

Question 3: Mean and Median for the Set

For the set of numbers: 27, 83, 55, 61, 102, 17:

• a) Mean — Add all the numbers together and divide by the count (6):
• Sum = 27 + 83 + 55 + 61 + 102 + 17 = 345
• Mean = 345 / 6 = 57.5
• b) Median — Arrange in ascending order and take the middle value (or average