1. What is the units digit of the integer value of \(2007^{2008} + 2008^{2007}?\) ?
2. A restaurant mixes 2 gallons of milk containing 1% fat and 3 gallons of milk containing 2% fat. What is the percent of fat in the mixture? Express your answer to the nearest tenth of a percent.
+128407 1. Look at the eding digits for powers of 7
7^1 = 7
7^2 = 9
7^3 = 3
7^4 = 1
And this pattern repeats for every 4 powers of 7
So 2008 mod 4 = 0
So....the units digit for 2007 ^2008 = 1
Likewise.....look at the ending digits for powers of 8
8^1 = 8
8^2 = 4
8^3 = 2
8^4 = 6
This also repeats for every 4 powers of 8
So....2007 mod 4 = 3
The units digit for 2008^2007 = 2
So.....the ending units digit for 2007^2008 + 2007^2008 = 1 + 2 = 3
+128407 2. A restaurant mixes 2 gallons of milk containing 1% fat and 3 gallons of milk containing 2% fat. What is the percent of fat in the mixture? Express your answer to the nearest tenth of a percent.
1% of 2 = .02 gallons of fat
2% of 3 = ,06 gallons of fat
% fat in the mixture = [ .02 + .06 \ / [ 2 + 3 ] = .08 / 5 = .016 = 1.6%
