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.)
Answer: Choice C) Infinitely many solutions
If you solve the first equation for y, you get
2y = 14 - 2x
2y = 14 + (-2x)
2y = -2x + 14
2y/2 = (-2x)/2 + 14/2 ... divide every term by 2
y = -x + 7
This result of y = -x+7 is identical to the second equation in the system. So the two graphs are going to be the same. We only produce one line. One graph is right on top of the other. The two lines will intersect infinitely many times. Any point on the blue line is a solution to the system.
Answer:
x=-(9+1y)/2
y=-2x-9
Step-by-step explanation:
2x=-9-1y
x=-(9+1y)/2
-1y=2x+9
y=-2x-9
Answer:
~48$
Step-by-step explanation:
0.47/25=0.0188
0.0188×211=3.9
12 cause of 9am to pm
12×3.9=47$
