Problem 4
Answer: 136 feet
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Work Shown:
1/2 = 0.5
3 and 1/2 ft = 3 + 1/2 = 3.5 ft
Each window is 3.5 ft by 5 ft. The perimeter is 2*(L+W) = 2*(3.5+5) = 17 ft
Or you could say 3.5+3.5+5+5 = 7+10 = 17
One window's perimeter is 17 feet, so 8 of these identical windows leads to 8*17 = 136 feet
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Problem 5
Answer in exponential form = 10^4 keys
Answer in standard form = 10,000 keys
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Work Shown:
For now, let's just consider 1 day. Also, let's consider one elf.
One elf makes 10 xylophones, and each xylophone has 10 keys. This means we have 10*10 = 100 keys so far. We can write this as 10^2.
If we then move onto 10 elves, then we have 10*10^2 = 10^3 = 1000 keys.
You could also write it as 100+100+100+... and add up ten copies of 100. This is because each elf is doing the same thing (making 100 keys)
So far we've shown that in the course of one day, we have 1000 keys.
We'll multiply this by 10 to get the final answer 10*1000 = 10,000 = 10^4
You could also do 1000+1000+1000+... and add up ten copies of 1000 to represent adding up the amounts made per days over the ten days.
In short, we basically do: 10*10*10*10 = 10^4
As you can probably see by now, the exponent tells us how many copies of the base to multiply together.