A rectangular prism with a volume of 44 cubic units is filled with cubes with side lengths of 1/3 unit How many 1/3 unit cubes d
oes it take to fill the prism?
2 answers:
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Bearing in mind that the major axis runs over the y-axis, therefore the "a" component will be under the fraction with the "y", check the picture below.
20: Let be the amount of money. If this amount is shared between 8 people, each person will get x/8 dollars. But there actually are 6 people, so everyone is getting x/6 dollars. We know that this difference results in 30 dollars more, so we have
Rearrange the left hand side as
And multiply both sides by 24 to get
21: Let and
be the number of marbles owned by Mike and Judy, respectively. At the beginning, we have
If they both get 9 more marbles, Mike will have marbles, and Judy will have
marbles. So, we have
Plug this value in the first equation and we have
And we deduce
So, the difference is
22: Let be the number of $10, $20 and $50 coupon, respectively. We're given:
Rearrange as follows:
And now we can deduce the number of the other coupons:
So, the total value is
23: a) In order to find the first three terms of the sequence, you just need to plug n=1,2,3:
b) We have
c) 105 is a term of the sequence if and only if there exists an integer k such that
So, 105 is not a term of the sequence.