Least common multiple question
Ronald: count by 6's
6, 12, 18, 24, 30, 36, 42, 48, 54 ....
Tim: count by 9's
9, 18, 27, 36, 45, 54,
every 18 days they do their laundry together
Answer:
3x^2 (y^5)^1/4 which is the first choice
Explanation:
The fourth root means that the bracket under has the root has a power of 1/4.
So, the given expression is:
(81 * x^8 * y^5)^1/4
Now, we will distribute the power as follows:
(81 * x^8 * y^5)^1/4 = (81)^1/4 * (x^8)^1/4 * (y^5)^1/4
= 3 * x^2 * y^5/4
This expression is equivalent to:
3x^2 (y^5)^1/4 which is the first choice
Hope this helps :)
36....we need to break this down...12 * 3 = 36
12 * 3....we can break this down because 12 is not prime...4 * 3 = 12
4 * 3 * 3...we can break the 4 down because it is not prime
2 * 2 * 3 * 3 <==== prime factorization
Assuming simple interest (i.e. no compounding within first year), then
At 6%, interest = 10000*0.06=$600
At 9% interest = 10000*0.09 = $900
Two ways to find the ratio
method A. let x=proportion at 6%
then
600x+900(1-x)=684
Expand and solve
300x=900-684=216
x=216/300=0.72 or 72%
So 10000*0.72=7200 were invested at 6%
10000-7200=2800 were invested at 9%
method B: by proportions
Ratio of investments at 6% and 9%
= 900-684 : 684-600
=216 : 84
= 18 : 7
Amount invested at 6% = 18/(18+7) * 10000 = 0.72*10000 = 7200
Amount invested at 8% = 7/(18+7)*10000=0.28*10000=2800
