# Project #3445 - Science and Mathematics

Show all of your work.  Maximum possible points:  50

1.      Plate Tectonics (8 pts)

A new chain of islands is discovered, with a high frequency of volcanic activity.  Four hypotheses are proposed to explain the cause of the volcanic activity.

H1: The islands are found on a convergent boundary.

H2: The islands are found on a divergent boundary.

H3: The islands are found on a transform boundary.

H4: The islands are found on a hotspot.

a.      (2 pts) Which of the four hypotheses could be ruled out immediately as the cause of the volcanic activity?  Why?

b.      (6 pts) For each of the other three hypotheses, find one other piece of physical evidence (earthquake, elevation, volcanic, age of ocean floor, or other) that could be used as evidence to support the hypothesis above the remaining hypotheses.  Explain your answers.

2.      Logic, Plate Tectonics and Radioactivity (22 pts)

Are the following statements true or false?  If it is true, explain.  If it is false, provide a counterexample (i.e. a specific example which shows the statement to be false).  This question may involve research beyond the course notes.

a.      If a boundary has deep earthquakes, then it is a convergent boundary.

b.      If a boundary is convergent, then it has deep earthquakes.

c.       If a boundary is in the ocean, then it is divergent.

d.      If a boundary is divergent, then it is in the ocean.

e.      If a boundary is transform, then it has shallow earthquakes.

f.        If a boundary has shallow earthquakes, then it is a transform boundary.

h.      If an isotope is an alpha emitter, then its atomic number is the same as lead’s (Pb) or greater.

i.        If an isotope has a greater atomic number than lead, then it is an alpha emitter.

j.        If an area has a high level of background radiation, then it has a high elevation.

k.       If an area has a high elevation, it has a high level of background radiation.

3.       Logic (8 pts)

Consider the following statements:

A: x is not even and x is a not a perfect square.

B: x is not even or x is not a perfect square.

C: it is not true that x is even or a perfect square.

D: It is not true that x is even and a perfect square.

a.       (4 pts) For each of A, B, C, and D, which values of x (from 1 to 10) make the statement true?

b.      (4 pts) Which pairs of statements are logically equivalent?  Complete the following truth table to demonstrate your answers.  In the truth table below, p is the proposition x is even and q is the proposition x is a perfect square.

 p q ~p ~q p ^ q p v q D: ~(p ^ q) C: ~(p v q) A: ~p ^ ~q B: ~p v ~q

4.       Probability (12 pts)   Look at the contingency table at http://www.weatheroffice.gc.ca/saisons/tables_e.html?season=fma&year=2012&type=t

to answer the following questions.  The table describes observations of the temperature for February, March and April of 2012 in Alberta.  Forecasts during this time period, and they were compared with the observed temperature.  In each case, the temperature was described as below average, average, or above average.

a.       (1 pt)    How many forecasts are described by the table in total?

b.       (2 pts)  For a randomly selected day during this time period, what is the probability that an above average temperature was observed?

c.       (2 pts)   For a random day during this time period, what is the probability that an above average temperature was forecast?

d.      (2 pts)   Given that the forecast was for an above average temperature, what was the probability that an above average temperature was actually observed?

e.      (2 pt)    Were the following mutually exclusive events:  a forecast of an above average temperature and an observation of a below average temperature?  Why or why not?

f.        (3 pts)   Were the following independent events:  forecast of above average temperature and observation of above average temperature?    Give a mathematical explanation of why your answer is true.

 Subject Mathematics Due By (Pacific Time) 03/22/2013 01:00 am
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