I have 2 questions that I am struggling with. I know the answer for them but I have no idea how to find the answer. So please tell me how to solve them.
1. Suppose you have the following six coins in your pocket : 5 cents, 10 cents, 20 cents, 50 cents, $1, $2. How many different sums of money can you make?
-Answer: 63 Sums
2. Find the smaller of 2^175 and 5^75 without a calculator.
- Answer: 5^75
Thank you!
2007-09-08 15:32:29 · 3 answers · asked by SiwooHasAnswers 2 in Science & Mathematics ➔ Mathematics
Number 1 has to do with counting theory and combinations.
The answer is going to be a sum of the combinations from picking 1 coin, 2 coins, ..., up to all 6 coins.
The formula is (n!)/[k!(n-k)!] where n is the number of coins, and k is the number of coins you choose. So you find it for k=1, 2, 3, 4, 5, and 6 and sum those values.
For number two, notice that the exponents both are multiples of 25. Take the 25th root of both numbers to give you 2^7 and 5^3. then just calculate. 2^7=128 and 5^3=125. Therefore 5^75 is smaller.
2007-09-08 15:43:48 · answer #1 · answered by jonimp9 1 · 1⤊ 0⤋
5^75=(5^3)^25
2^175 = (2^7)^25 so
compare 5^3 = 125 with 2^7 = 128
so 2^175>5^75
1) = 1C6+2C6 +3C6 +4C6 +5C6 +6C6=6+15+20+15+6+1=63
2007-09-08 23:01:24 · answer #2 · answered by santmann2002 7 · 1⤊ 0⤋
the first answer is IMPOSSIBLE.... There is no such thing as a 20 cent coin.... Put a big X thru the question..
I hate to admit it but I have no idea what the upside down carat means.. I see it all the time.. It must be something new.. Im old and stupid but I do know there is no 20cent coin...
2007-09-08 22:43:24 · answer #3 · answered by Anonymous · 0⤊ 1⤋