Answer:
Step-by-step explanation:
You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.
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<h3>a)</h3>
Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.
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<h3>c)</h3>
For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...
Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r
We want to find n such that ...
Sn ≥ 1,000,000
1 × (2^n -1)/(2 -1) ≥ 1,000,000
2^n ≥ 1,000,001 . . . . add 1
n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm
n ≥ 19.93
The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.
Answer: The fraction 301/900
Note: I'm assuming the 4's continue on forever
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Work Shown:
I'm going to assume that the 4s go on forever. I'll represent this with three dots after the last 4 like so
0.334444...
Now let x = 0.334444...
Multiply both sides by 100
x = 0.334444...
100x = 100*(0.334444...)
100x = 33.444444...
And repeat with 1000
x = 0.334444...
1000x = 1000*(0.334444...)
1000x = 334.444444...
Then subtract and solve for x. Notice how the decimal parts line up and cancel
1000x-100x = (334.444444...) - (33.444444...)
1000x-100x = (334+0.444444...) - (33+0.444444...)
1000x-100x = 334+0.444444... - 33 - 0.444444...
1000x-100x = (334-33)+(0.444444... - 0.444444...)
900x = 334 - 33
900x = 301
x = 301/900
If a system has at least one solution, it is said to be consistent .
If a consistent system has an infinite number of solutions, it is dependent
Answer:
26 snack packs
Step-by-step explanation:
2.83+5.18=8.01
8.01/.30=26.7
26 snack packs
The answer is 0.3
Do you want me to explain?
