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Stock Value. Compute value from number of shares × purchase price for a
stock.
Once upon a time, stock prices were quoted in fractions of a
dollar, instead of dollars and cents. Create a simple print
statement for 125 shares purchased at 3 and 3/8. Create a second
simple print statement for 150 shares purchased at 2 1/4 plus an
additional 75 shares purchased at 1 7/8.
Don't manually convert 1/4 to 0.25. Use a complete expression
of the form 2+1/4.0, just to get more practice writing
expressions.
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Convert Between °C and °F. Convert temperatures from one system to another.
Conversion Constants: 32°F = 0°C, 212°F = 100°C.
The following two formulae converts between °C (Celsius) and
°F (Fahrenheit).
Equation 4.2. Convert °C (Celsius) to °F (Fahrenheit)
Equation 4.3. Convert °F (Fahrenheit) to °C (Celsius)
Create a print statement to convert 18° C to °F.
Create a print statement to convert -4° F to °C.
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Periodic Payment on a Loan. How much does a loan really cost?
Here are three versions of the standard mortgage payment
calculation, with
m
=payment,
p
=principal due,
r
=interest rate,
n
=number
of payments.
Equation 4.4. Mortage Payment, version 1
Equation 4.5. Mortgage, payments due at the end of each period
Equation 4.6. Mortgage, payments due at the beginning of each
period
Use any of these forms to compute the mortgage payment,
m
, due with a principal,
p
, of $110,000, an interest rate,
r
, of 7.25% annually, and payments,
n
, of 30 years. Note that banks actually
process things monthly. So you'll have to divide the interest rate
by 12 and multiply the number of payments by 12.
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Surface Air Consumption Rate. SACR is used by SCUBA divers to predict air used at a
particular depth.
For each dive, we convert our air consumption at that dive's
depth to a normalized air consumption at the surface. Given depth
(in feet),
d
, starting tank pressure (psi),
s
, final tank pressure (psi),
f
, and time (in minutes) of
t
, the SACR,
c
, is given
by the following formula.
Equation 4.7. Surface Air Consumption Rate
Typical values for pressure are a starting pressure of 3000,
final pressure of 500.
A medium dive might have a depth of 60 feet, time of 60
minutes.
A deeper dive might be to 100 feet for 15 minutes.
A shallower dive might be 30 feet for 60 minutes, but the
ending pressure might be 1500. A typical
c
(consumption) value might be 12 to 18 for most people.
Write print statements for each of the three dive profiles
given above: medium, deep and shallow.
Given the SACR,
c
, and a tank starting
pressure,
s
, and final pressure,
f
, we can plan a dive to depth (in feet),
d
, for time (in minutes),
t
, using the following formula. Usually the
33(
s
-
f
)/
c
is a constant, based on your SACR and tanks.
Equation 4.8. Time and Depth from SACR
For example, tanks you own might have a starting pressure of
2500 and and ending pressure of 500, you might have a
c
(SACR) of 15.2. You can then find possible
combinations of time and depth which you can comfortably
dive.
Write two print statements that shows how long one can dive at
60 feet and 70 feet.
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Force on a Sail. How much force is on a sail?
A sail moves a boat by transferring force to its mountings.
The sail in the front (the jib) of a typical fore-and-aft rigged
sailboat hangs from a stay. The sail in the back (the main) hangs
from the mast. The forces on the stay (or mast) and sheets move the
boat. The sheets are attached to the clew of the sail.
The force on a sail,
f
, is based on sail
area,
a
(in square feet) and wind speed,
w
(in miles per hour).
Equation 4.9. Sail Clew Load
For a small racing dinghy, the smaller sail in the front might
have 61 square feet of surface. The larger, mail sail, might have
114 square feet.
Write a print statement to figure the force generated by a 61
square foot sail in 15 miles an hour of wind.
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Craps Odds. What are the odds of winning on the first throw of the
dice?
There are 36 possible rolls on 2 dice that add up to values
from 2 to 12. There is just 1 way to roll a 2, 6 ways to roll a 7,
and 1 way to roll a 12. We'll take this as given until a later
exercise where we have enough Python to generate this
information.
Without spending a lot of time on probability theory, there
are two basic rules we'll use time and again. If any one of multiple
alternate conditions needs to be true, usually expressed as
“or”, we add the probabilities. When there are several
conditions that must all be true, usually expressed as
“and”, we multiply the probabilities.
Rolling a 3, for instance, is rolling a 1-2
or
rolling a 2-1. We add the probabilities:
1/36+1/36 = 2/36 = 1/18.
On a come out roll, we win immediately if 7 or 11 is rolled.
There are two ways to roll 11 (2/36) or 6 ways to roll 7
(6/36).
Write a print statement to print the odds of winning on the
come out roll. This means rolling 7 or rolling 11. Express this as a
fraction, not as a decimal number; that means adding up the
numerator of each number and leaving the denominator as 36.
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Roulette Odds. How close are payouts and the odds?
An American (double zero) roulette wheel has numbers 1-36, 0
and 00. 18 of the 36 numbers are red, 18 are black and the zeroes
are green. The odds of spinning red, then are 18/38. The odds of
zero or double zero are 2/36.
Red pays 2 to 1, the real odds are 38/18.
Write a print statement that shows the difference between the
pay out and the real odds.
You can place a bet on 0, 00, 1, 2 and 3. This bet pays 6 to
1. The real odds are 5/36.
Write a print statement that shows the difference between the
pay out and the real odds.
