When and how do we use them? “Logic allows us to analyze a piece of reasoning, and determine whether it is correct or not. To use the technical terms, we determine whether the reasoning is valid or invalid”. We use logical arguments to support our beliefs and to persuade others to understand our belief. Logical arguments are a way for us to analyze information and decide whether it is valid or invalid.
Real World Applications of Number Theory A. Rounding and Truncation 1. Student 1 received a score of 299 out of a possible 334 points for a term in an unknown class. To find what percentage the student received, one must take the score received and divide it by the total amount of points possible, and then multiply the quotient by 100. In this particular case, the teacher chose to use rounding to attain the final grade of the student. To round to the nearest whole number, one must consider the value in the tenths place.
a. with 1 significant figure b. with 2 significant figures c. with 3 significant figures d. with 5 significant figures Question 5 Express 0.0003711 in scientific notation. a. with 1 significant figure b. with 2 significant figures c. with 3 significant figures d. with 4 significant figures Question 6 Perform the calculation with the correct number of significant digits. 22.81 + 2.2457 Question 7 Perform the calculation with the correct number of significant digits. 815.991 x 324.6 Question 8 Perform the calculation with the correct number of significant digits. 3.2215 + 1.67 + 2.3 Question 9 Perform the calculation with the correct number of significant digits.
Distinguish among a scientific fact, a hypothesis, a law and a theory. A Scientific fact is something that competent observers can observe and agree to be true. A Hypothesis is and educated guess or a reasonable explanation. A law is scientific hypothesis that has been tested over and over again and has not been contradicted. Also known as a principle.
It can be seen that 32 + 42 = 52 (9+16=25). I am going to investigate Pythagorean Triples where the shortest side is an odd number and all 3 sides are positive integers. I will then investigate other families of Pythagorean Triples to see if Pythagoras' theorem (a²+b²=c²) works. A Pythagorean triple consists of three positive integers, a, b, and c, such that a2 + b2= c2. A well-known example is 3, 4, and 5 because 32+ 42 = 9 + 16 = 25 =52.
There are no differences. C. We divide the sum of the observations by n - 1 instead of n D. The observations are ranked and select the middle value for the population mean. Ans: A 3) In a set of observations, which measure of central tendency reports the value that occurs most often? A. Mean B. Geometric mean C. Median D. Mode Ans: D 4) Which of the following is not a requirement of a binomial distribution?
The three endpoint values chosen were 15.84 mL, 15.91 mL, and 16.17 mL, leading to an average endpoint value 15.97 mL with a standard deviation of .17. The milimoles of Fe(III) titrated was .3289, corresponding to .01837g of Fe(III) in a total mass sample of .18417g. The salt sample was determined to be 9.976% Fe(III). Part Two: Since a well-trained technician is expected to perform a titration with a percent relative standard deviation below 1.0%, the performance of this titration would be deemed almost passable, but ultimately sub-par. The % RSD was 1.1% based on the three closest endpoint values.
Does the essay delve into the subtle nuances and complexities of the varied interpretations of the theories and the principles, and demonstrate their relevance to the issues at stake? ANALYSIS and ARGUMENTATION - Does the essay contain elements arising from the exercise of one own’s judgment and insight? Does the essay show evidence of careful and thoughtful interpretation, and critical evaluation, of competing claims and arguments? Does the essay provide analysis – not just description? Description reports what happened; analysis explores how and why.
In other words, these events seem to be related in some way. * The next step is to make a prediction on the basis of this observation, and the scientist formulates a hypothesis. A hypothesis is a tentative statement regarding the relationship between the variables. The hypothesis formulated must be testable, and the scientist conducts a research study during which empirical evidence is gathered through scientific observation. * The empirical evidence gathered is what scientists call data, and it is the analysis of the data at the end of an experiment that allows the scientist to conclude that the hypothesis has either been supported or not supported.
Not only is this because of the different types of data that the researcher is aiming for but also the process that leads to it. In both research techniques the researcher will identify an area of interest or come up with a question, however in quantitative research the researcher will then develop this research question into a hypothesis. This method can be referred to as theory verification. That is starting with a theory, developing it into a hypothesis and then designing a study or research plan to test the hypotheses (Punch, 2005). In quantitative research the researcher is not going in blind as they might in qualitative, they have an idea of what they want to achieve and the sort of information they need to find in order to do so.