# Being a tutor, I’m an academic by nature.  I found the definition of lipogram in my literary terms guide….

Well, New Years Eve is here.  Some people’s holiday displays are off, saying even Yule season is over.

Of course, one will likely look back on a year with some sorrow over failure or missed chances.

Here, we are ending in a cold snap:  our morning reading is -8 Celsius, sunny all day.

Oil is low, America’s economy, seemingly, is bouncing back, and our (Canadian) dollar is weaker (86¢), which is probably good for our sellers. Economically, we may be looking up.

To our topic: a lipogram is a written work in which a selected letter is purposely absent. You’ve already read one: if you look back at the previous four paragraphs (my New Years reflection), you’ll find no “t” was used.

Have fun tonight:)

Sources:

Literary Terms. Coles Notes Study Guide. Toronto: Coles Publishing, 2009.

marketwatch.com

www.xe.com/currencycharts

# Tutoring math, I continue to discover new functions on calculators.  The tutor gives a brief introduction to the Sharp EL-520W equation solver.

Let’s imagine you need to solve the equation

5x2 – x – 6 = 0

The roots (aka answers) happen to be -1 and 1.2. Let’s see what the solver says:

Step 1: Press Mode 0

Step 2: Enter the equation, using alpha rcl to key the x. Press = at the end, but not 0. A value (-6, for example) might appear at the bottom of the screen; just ignore it.

Step 3: Press math, after which you’ll see the SOLV option with a blinking 0 underneath. Press 0.

Step 4: The calculator will ask for a start value. If you have no idea, you might choose 0, then press =. Now it asks dx?, which (I think) means the step value it should use as it searches for the answer. Just press = again to go with the step size it suggests.

Step 5: The screen should say calculating!. Within a few seconds, it will offer an answer.

The equation in this example has two answers. If you chose a start value of 0, the answer you see is likely -1. If you return to Step 3 now, pressing math and so on, but selecting 1 as the start value, you’ll receive the other answer: 1.2.

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring biology 12, you cover the circulatory system.  The tutor mentions a specific issue about it.

The number one reason for the circulatory system is transport of oxygen to the cells and carbon dioxide away from them.  This is done via the blood, which is water-based.  The immediate problem might be that gases don’t necessarily dissolve very well in water.

Red blood cells contain hemoglobin (which is why they are red).  Hemoglobin attracts and holds oxygen very effectively, enabling the red blood cells to carry the oxygen through the circulatory system to the capillaries.  There, the oxygen is dropped off to the cells.

Carbon dioxide can be carried by red blood cells (as carbaminohemoglobin), but not very effectively.  In the blood, most carbon dioxide combines with water to form carbonic acid (H2CO3), next breaking into hydrogen ion H+ and bicarbonate ion HCO3. Ions travel easily in water. At the lungs, the hydrogen ion and bicarbonate ion recombine into carbonic acid, which then separates into carbon dioxide and water. The carbon dioxide is exhaled.

HTH:)

Source:

Mader, Sylvia S. Inquiry into Life, 11th edition. New York: McGraw-Hill, 2006.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# A tutor, or anyone else, might be interested in power plant efficiency.  Here’s a handy starting place for anyone facing the question.

In my continuing quest of information about energy, I’ve found numbers about power plant efficiency. Once again, the folks at the US Energy Information Administration come through.

As they explain it, they give numbers called “heat rates” for fuel-consuming modes (coal, petroleum, natural gas, nuclear) of electricity generation. The heat rate is the number of Btu spent to produce 1 kWh. (The higher the heat rate, the lower the efficiency.) You take the number of Btu in a kWh (3412 Btu), then divide it by the heat rate to get the efficiency (afterwards multiplying by 100 to get the percent).

The numbers on nuclear generation are very interesting (the table is here). Apparently, petroleum is the least efficient, with coal and nuclear in the middle, while natural gas is the most efficient of the fuel-consuming generation modes.

The table gives yearly averages for heat rates from 2002 to 2012. The numbers seem to suggest that efficiency rates have trended slightly downward for coal, petroleum, and nuclear generation, while natural gas generation has grown significantly more efficient:

 type of generation approx. efficiency change 2002-2012 coal -1.8% petroleum -3.3% nuclear -0.35% natural gas +16%

One wonders why natural gas, in particular, has improved so much. The question sounds like the basis for another post:)

Source:

www.eia.gov

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring science, one might expect questions like these more often. The tutor seeks the answer to another childhood curiosity….

I remember seeing Mohs’ hardness scale when I was a kid. On it, quartz is 7, corundum 9, and diamond 10.  I think in grade five, we spent a week on minerals.  Additionally, we watched educational films on Thursday afternoons; eventually, one happened to be about minerals.

I was never interested in minerals as a kid, but I knew there was a big world about them for those who were.  In the film we saw about them, the voice said, “The hardest mineral you’ll probably find is quartz.”  Having lived on rocky coastal areas much of my life, I knew I’d seen quartz already.  Corundum, however, was among the minerals of which I’d never heard.  Why, I wondered, would I not find it?

The week ended, life continued, and I soon forgot about finding corundum.  I was eleven years old, living in Nova Scotia.  While I never found corundum, someone else did.

Corundum is the mineral that makes sapphires and rubies. In an article dated 2005, Hans Durstling tells of the discovery of rubies in Cape Breton, Nova Scotia. The discovery was, ironically, in a quarry that had produced dolomitic limestone for twenty years. He points out that rubies would likely have been shipped out in the limestone, overlooked.

Nova Scotia is a geological curiosity for more than one reason. I don’t know much about it, but I hear bits and pieces.

I’ll be discussing geology, Nova Scotia, corundum, and other minerals in future posts. Like the discovery of rubies in Cape Breton, this topic is a rich find that comes from re-examining the past:)

Sources:

virtualfundy.com

Wolley, Alan. Spotter’s Guide to Rocks and Minerals. New York: Mayflower Books,   1979.

maplandia.com

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring math, a likely destination of some of your students is computer science. The tutor continues coverage of the Perl language, which seems flush with simple solutions to programming problems….

In yesterday’s post, which was about Perl subroutines, I introduced an example program that calculates the final price of an item from its sticker price, the discount, and the tax rate.

In my context, anyway, the program works great – but any zealots who typed and ran it on Boxing Day noticed that it does not format the answers as a cash register would. For example, if you give it the inputs

price: 78
discount: 33
tax rate: 12

it will give back

final price: 58.5312

Prices are given to two decimal places, not four. How can the program be fixed to give answers formatted as from a cash register?

Perl has two answers to this problem: printf(format, number) and sprintf(format, number). Today, we’ll look at a few lines of code that show the use of these built-in functions:

#!/usr/bin/perl

print “This program will round your number to two decimal places.”;
\$num=<STDIN>;
\$rounded=sprintf(“%.2f”,\$num);
print “Using printf, your number, rounded to two decimal places, is “;
printf(“%.2f”,\$num);
print “\n\nRecall: the number you entered is \$num”;
print “\n\nFrom sprintf, rounded to two decimal places, “;

Let’s compare sprintf and printf. Both leave the input number unchanged. The function sprintf reformats it, and saves the reformatted number in a new variable. The function printf simply prints the number in the specified format.

I wish all of you the best of nights:)

Source:

McGrath, Mike. Perl in easy steps. Southam: Computer Step, 2004.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# The tutor continues about programming with Perl.  Tutoring computer science, subroutines have both theoretical and practical importance.

Back in my November 14 post I opened up the discussion on subroutines. In computer science, a subroutine is a self-contained body of code that performs a specific task.

Today, we’ll look at a simple example: a subroutine that calculates the final price of merchandise with a price, discount, and tax rate given by the user. The subroutine itself resides at the bottom of the program, but is called earlier.

#!/usr/bin/perl
print “Hello. Welcome to the final price calculator.\n”;
print “Enter the sticker price of the merchandise, please.”;
\$price=<STDIN>;
print “Enter the discount percentage, if there is one.\n”;
print “For example, 25 means 25 percent off.”;
\$discount=<STDIN>;
if(!\$discount){
\$discount=0;
}
print “Now, enter the tax percentage; eg., 12 means 12 percent.”;
\$taxrate=<STDIN>;
&finalprice(\$price,\$discount,\$taxrate);

sub finalprice{
\$finprice=\$_[0]*(1-\$_[1]/100)*(1+\$_[2]/100);
print “Sticker price is \$_[0]”;
print “Discount is \$_[1]”;
print “Tax rate is \$_[2]\n”;
print “The final price at the till should be \$finprice\n\n”;
}

Note the subroutine definition starts with sub. A subroutine defined as sub bob1 would be invoked with the call &bob1(parameter list).

For Christmas Day, this is probably enough. I will be discussing the issue of parameters in a coming post.

To all my readers: Happy Holidays. As with every post, I hope this one finds you in good spirits:)

Source:

McGrath, Mark. Perl in easy steps. Southam: Computer Step, 2004.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Since 2008, the tutor has listened for economic news.  While it doesn’t often arise in tutoring, economic performance is important across to the board.

In 2008, the US gross public debt, which I’d just call “government debt”, was around 64.8% of GDP (ieconomics.com).  The Eurozone situation wasn’t too different, at 66.2% (tradingeconomics.com). Over here, we might suspect the US got hit worse in 2008 than Europe did; I’m not saying that’s true, or even knowable. What we can do is look over some of today’s numbers from both places to get a sense of the fallout.

Today, the US government debt is at 102% GDP, while the Eurozone’s is at 90.9%. From that point of view, Europe has fared better since 2008 – around 35% better.

Looking at “real” deficit, the US continues to lag the EU. The true US government financing of its economy, according to the oecd, is currently 5.1% of GDP, while its GDP growth is 2.2%. The figures, both being percent of GDP, sum to progress of -2.9%. The Eurozone’s financing of its economy is 2.6% GDP, with GDP growth of 0.8%, suggesting progress of -1.8%. In 2015, the US should match the Eurozone at -1.2% progress, but by 2016, the Eurozone takes the lead again with -0.2% to the US -1.0%.

Regarding unemployment, the US is expected to beat the EU by over 5% in all three of 2014, 2015, and 2016. In 2014, the US unemployment rate is estimated at 6.2% to Europe’s 11.4%. In both 2015 and 2016, the European unemployment rate is expected to exceed the US rate by 5.5%.

While deficit and debt hurt a country’s economy, unemployment may menace it even more because it can damage the human capital. The worker in the US, for now, seems to be in a more optimistic position. Of course, the US has always prided itself on such a premise.

I’ll be discussing the complex comparison of these different economies in future posts:)

Sources:

ieconomics.com

oecd

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Following up from the previous post, the tutor tries out the standard deviation estimator range/6.  Standard deviation is a common topic during high school math tutoring.

Imagine the following results from a fictional midterm:

56, 42, 71, 66, 45, 81, 75, 59, 62, 49, 68, 79, 58, 91, 63

First, we’ll arrange the marks in order:

42, 45, 49, 56, 58, 59, 62, 63, 66, 68, 71, 75, 79, 81, 91

Now, we’ll calculate the standard deviation using the formula (actually, using the Sharp EL-520W:)

σ=13.7 (sx), σ=13.2 (σx)

Now, using range/6:

range=91-42=49

σ=range/6=49/6=8.2

We see that, for a small sample anyway, the estimate range/6 is not necessarily close to σ.

Source:

Zimmer, Cooke, et. al. Mathematics of Data Management. Toronto: Nelson, 2003.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring statistics, I’m happy to add this method to my repertoire.  The tutor brings forth a shortcut for finding the standard deviation.

According to my source listed below, the standard deviation (σ) can be estimated as follows:

σ=range/6

The range is defined as the greatest-least values of the data set.

The reasoning behind the estimate is that, with a normal distribution, 99.7% of the data lies between µ-3σ and µ+3σ, µ being the mean, or center point, of the data.  (µ+3σ) – (µ-3σ)=µ+3σ-µ+3σ=6σ, but also equals the range. Since the range equals 6σ, σ=range/6.

In my next article, I’ll compare the standard deviation computed from the proper formula to what you get from the estimate above.  I’m as curious as you are:)

Source:

Zimmer, Cooke, et.al.  Mathematics of Data Management.  Toronto:   Nelson, 2003.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.