Download CLASS SMART-NOTES for CLASS #026 FRI. 10.26.12.

26_ac_Ch6Apps_fri20121026_f12.notebook
October 27, 2012
MGF 1107 - 109843 | Fall 2012 |
Class #026 | Fri. 10.26.12 |
Selected Topics in Ch.6 -- Mainly 6.2 and 6.4.
Chapter 6 Applications
Sampling in Nature
Capture-recapture method - Helps to
estimate the total size of a wildlife
population
Ngorongoro Crater ­ Tanzania (Eastern Africa)
Sep 15­8:29 PM
[ 1 ].
BACKGROUND
A fraction can also be
known as a ratio.
For instance, the fraction
can be pronounced
"A is to B" or
"the ratio of A to B."
Kenya ­ Eastern Africa
[ 2 ]. The mathematical statement that two ratios are equal is
called a proportion.
The proportion
is sometimes pronounced
"A is to B as C is to D."
Sep 15­9:17 PM
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26_ac_Ch6Apps_fri20121026_f12.notebook
October 27, 2012
To estimate the number of bass in a lake, wildlife biologists
tagged 50 bass and released them in the lake. Later they
netted 108 bass and found that 27 of them were tagged.
Approximately how many bass are in the lake?
(Ref: Sect. 6.2: p. 330: #114.)
Solution:
If you are lucky, you may be
able to reduce the proportion.
But don't expect for this to
always be available.
Set up the proportion.
Tagged is to Pop. as Sample
Tagged is to Sample Number.
[ 1 ].
The reduced
proportion.
[ 2 ].
[ 3 ].
Isolate x.
"Cross Multiply"
Simplify.
[ 4 ].
[ 6 ].
[ 5 ].
Optional: Re-write the solution
[ 7 ]. so that it looks pretty.
[ 8 ]. Write final answer in sentence form.
Thus, there are approximately 200
bass in the lake.
Sep 15­9:17 PM
Proportions
can also be used to help work other types
of applications.
You have three numbers & you want to find the fourth.... Looks like
you should write a proportion!
Now it's just a matter of
filling in the "boxes."
The maintenance bill for a shopping center containing
180,000 square feet is $45,000. What is the bill for a
store in the center that is 4800 square feet?
Solution:
[ 1 ]. Idea for this PROPORTION: Translating words into a proportion.
The "trick" here is that you have to be consistent with your fractions (ratios).
Solve the proportion.
[ 2 ].
[ 3 ].
Sentence answer.
The maintenance bill for the 4800 s.f. store
is $1,200.
Sep 15­9:19 PM
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26_ac_Ch6Apps_fri20121026_f12.notebook
October 27, 2012
The volume of blood in a person's body is proportional
to body weight. A person who weighs 160 pounds has
approximately 5 quarts of blood. Estimate the number
of quarts of blood in a person who weighs 200 pounds.
Notice: You can set up your
proportion either way, AS
LONG AS YOU ARE
CONSISTENT WITH BOTH
SIDES OF THE EQUALS.
Sep 15­9:53 PM
To estimate the number of people in Springfield,
population 10,000, who have a swimming pool in their
backyard, 250 people were interviewed. Of those polled,
62 had a swimming pool. How many people in the city
might one expect to have a swimming pool? Round to the
nearest whole number, if necessary.
Your steps: (1). See the PATTERN... Decide it's a PROPORTION.
(2). Set up a CONSISTENT PROPORTION.
(3). Solve the proportion:
(a). Cross multiply to eliminate the fractions.
(b). Isolate the x (Divide both sides by the number in front of x.
Sep 15­9:26 PM
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26_ac_Ch6Apps_fri20121026_f12.notebook
October 27, 2012
II. Here is the second type problem that we study in Ch.6: The "what grade do I
need to get in order to get an A (or maybe B or C or 'pass') in this class."
As the end of the semester gets closer, the next type of
problem is on students' minds.
On three examinations, you have grades of 86, 75, and 84.
There is still another test grade which counts the same as
each of the other grades. To earn a B in a course, you
must have a final average of at least 80. What must you
core.
get on test four to earn a B in the course? n't yet know this s
I want my average . . . . . . . .
And I
do
To equal 80.
Sep 15­9:31 PM
Cost, Revenue, Profit
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sell small radios. Use the information to solve the following:
Where the graphs cross gives you the
BE (Break Even) point.
Using algebra, you don't even need
the graphs to find the BE point.
You just set C(x) = R(x) and
solve for x.
How many radios must be produced and sold for the company to break even?
More than how many radios must be produced and sold for the company to have a profit?
Oct 3­4:19 PM
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26_ac_Ch6Apps_fri20121026_f12.notebook
October 27, 2012
A company is selling canoes. The cost to produce x
canoes is C = 2500 + 25x. The revenue earned by
selling x canoes is given by R = 45x. How many canoes
must be sold to make a profit?
If it's multiple choice and you say
125 to answer the question as stated
above, you are WRONG. You must say
126.
You must sell more than 125 canoes to make a profit.
OR
You must sell 126 or more canoes to make a profit.
Sep 15­9:41 PM
A basic cellular phone plan costs $12 per month for 40
calling minutes. Additional time costs $.10 per minute.
the formula C = 12 + 0.10(x - 40) gives the monthly cost
for this plan, C, for x calling minutes, where x > 40.
How many calling minutes are possible for a monthly cost
of at least $16 and at most $32?
We'll have to start off with this problem on Monday.
Sep 15­9:45 PM
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