a.
By Fermat's little theorem, we have
5 and 7 are both prime, so 
and 
. By Euler's theorem, we get
Now we can use the Chinese remainder theorem to solve for 
. Start with
- Taken mod 5, the second term vanishes and
. Multiply by the inverse of 4 mod 5 (4), then by 2.
- Taken mod 7, the first term vanishes and
. Multiply by the inverse of 2 mod 7 (4), then by 6.
b.
We have 
, so by Euler's theorem,
Now, raising both sides of the original congruence to the power of 6 gives
Then multiplying both sides by 
gives
so that is the inverse of 25 mod 64. To find this inverse, solve for 
in 
. Using the Euclidean algorithm, we have
64 = 2*25 + 14
25 = 1*14 + 11
14 = 1*11 + 3
11 = 3*3 + 2
3 = 1*2 + 1
=> 1 = 9*64 - 23*25
so that 
.
So we know
Squaring both sides of this gives
and multiplying both sides by tells us
Use the Euclidean algorithm to solve for .
64 = 3*17 + 13
17 = 1*13 + 4
13 = 3*4 + 1
=> 1 = 4*64 - 15*17
so that 
, and so 
For an equal number of servings, the bananas will have three times as much sugar.
To put it in perspective:
When we have one serving of each fruit, the carrot will give you 5 grams of sugar whereas banana will give you 15 grams.
Hope this helps!
Answer:
The answer is B
Step-by-step explanation:
I made an approximation by looking and using paint 3D to even zoom up the image
pls mark me as brainliest
Answer:
the third one
Step-by-step explanation:
9 to the power of 4 is 9 multiplied by it's self 4 times
