9514 1404 393
Answer:
r = 2
Step-by-step explanation:
The first differences between successive terms are ...
10 -5 = 5
20 -10 = 10
The differences are not constant, so the sequence is NOT arithmetic.
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The ratios of successive terms are ...
10/5 = 2
20/10 = 2
The ratios are constant, so the sequence is ...
geometric with a common ratio of 2.
Answer:
10
Step-by-step explanation:
QT=ST/2=√(12^2+16^2)/2=10
Answer:
Beatrice will accumulate $1230.72 at the end of the year.
Step-by-step explanation:
We can write:
for deposits
The first month would have only the deposit reflected in her balance, then, expanding some steps of the calculation would yield:
A geometric series is given by:
Translating our series to the short form:
plugin in the values for the 12 month gives:
The answer choices are sufficiently far apart that you can work this backward. The sum will be ...
236,196*(1 + 1/3 + 1/9 + 1/27 + ...)
so a reasonable estimate can be given by an infinite series with a common ratio of 1/3. That sum is
236,196*(1/(1 - 1/3)) = 236,196*(3/2)
Without doing any detailed calculation, you know the best answer choice is ...
354,292
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There are log(236196/4)/log(3) + 1 = 11 terms* in the series, so the sum will be found to be 4(3^11 -1)/(3-1) = 2*(3^11-1) = 354,292.
Using the above approach (working backward from the last term), the sum will be 236,196*(1-(1/3)^11)/(1-(1/3)) = 236,196*1.49999153246 = 354,292
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* If you just compute log(236196/4)/log(3) = 10 terms, then your sum comes out 118,096--a tempting choice. However, you must realize that the last term is larger than this, so this will not be the sum. (In fact, the sum is this value added to the last term.)
well, we know the piece-wise function is 
hmmm so what's f(-1), namely what is f(x) when x = -1?
well, when x = -1, hmm -1 is less than 0, so the subfunction that applies to that will be when "x" is less than 0, namely the part of 7x + 10, so we can say
f(-1) = 7(-1) + 10
f(-1) = 3
so hmm what's f(0) or namely, what's f(x) when x = 0?
well, what subfunction applies when x = 0? well, it has to be the subfunction with "x greater or <u>equals</u> to 0", x ⩾ 0, so then is 7x + 20
f(0) = 7(0) + 20
f(0) = 20.
