Answer:
Step-by-step explanation:
The LCD here is 10.
Multiplying numerator and denominator of (4*10^2) by 10 results in:
40*10^3
-------------
10
and rewriting (2x10^-1) with positive exponent in the denominator results in:
2
---------
10
So, before simplification, this difference comes out to be:
40000 - 2 39998 19999
----------------- = ---------------- or ------------
10 10 5
Answer:
To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;
3·4ⁿ is divisible by 3 and 51 is divisible by 3
Where we have;
= 3·4ⁿ + 51
= 3·4ⁿ⁺¹ + 51
- = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ
- = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ
∴ - is divisible by 9
Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7
∴ S₀ is divisible by 9
Since - is divisible by 9, we have;
- 
= 
- is divisible by 9
Therefore is divisible by 9 and is divisible by 9 for all positive integers n
Step-by-step explanation:
The entire shipment contains 9 2/7 tons of sugar
Step-by-step explanation:
- Step 1: Find the total amount of sugar in the entire shipment.
Number of containers in the shipment = 4 1/3 = 13/3
Number of tons of sugar = 2 1/7 = 15/7
⇒ Total amount of sugar = 13/3 × 15/7 = 65/7 = 9 2/7 tons
