Answer:
$3360 combined. $1560 from acct b and $2100 from acct a
Answer:
13 14/15
Step-by-step explanation:
The numerator and denominator of 28/30 have a greatest common factor of 2. Dividing that from each of those numbers gives 14/15. This is the reduced fraction of the mixed number. The integer portion stays the same.
13 28/30 = 13 14/15
<span>The area of the square is d^2. The area of the circle sandbox is πr^2=πd^2/4. So the area of play area only is equal to square area minus circle area which is d^2-πd^2/4.</span>
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 
