Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:


Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:



Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Answer:
30.06
Step-by-step explanation:
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Answer:</h3>
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Step-by-step explanation:</h3>
We can let the variables A and B stand for the length in inches of fish A and fish B, respectively.
If we assume each person bought fish having a total length of 1 inch per gallon of aquarium, then we can write equations ...
... 3A +2B = 33 . . . . . total length of Marta's fish
... 3A +4B = 45 . . . . . total length of Hank's fish
Subtracting the first equation from the second, we get ...
... 2B = 12
... B = 6 . . . . . divide by 2
Using this value in the first equation, we have ...
... 3A + 2·6 = 33
... 3A = 21 . . . . . . . . subtract 12
... A = 7 . . . . . . . . . . divide by 3
Fish A is 7 inches long; fish B is 6 inches long.
Answer:
Sierra's profit was $41.
Step-by-step explanation:
Sierra realized she lost two-third of a dollar each hour when the shop was closed.
The expression that models this situation is, ............. (1)
Now, we have to calculate Sierra's profit if the shop was closed for 6 hours.
So, putting h = 6 hours in the equation (1) we get,
dollars.
So, Sierra's profit was $41. (Answer)
Step-by-step explanation:
62 is 50% of 124 (62*2=124)