Let a be the number of positive multiples of 6 that are less than 30. let b be the number of positive integers that are less than $30$, and a multiple of $3$ and a multiple of $2$. compute $(a - b)^3$.

0 or -3375

Explanation:

The question is somewhat ambiguous because we can't be sure whether B will be positive integers which are multiples of both 3 and 2 or 3 and 2 separately.

For the former:

There a 4 multiples of 6 less than 30: 6, 12, 18, 24.

Positive integers (whole numbers) less than 30: 1-29 ; multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27 and of those, only 6, 12, 18 and 24 are multiples of both 2 and 3.            

Therefore we have (4-4)^3 = 0

For the latter:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27 ; Multiples of 2:  2 4 6 8 10 12 14 16 18 20 22 24 26 28 (remove common multiples)

Therefore (4-19)^3 = -3375

1. read the following excerpt from franklin d. roosevelt's "fireside chat 19":

on the other side of the picture, we must learn also to know that guerilla warfare against the germans in, let us say serbia or norway, us; that a successful russian offensive against the germans us; and that british successes on land or sea in any part of the world strengthen our hands.

remember always that germany and italy, regardless of any formal declaration of war, consider themselves at war with the united states at this moment just as much as they consider themselves at war with britain or russia. and germany puts all the other republics of the americas into the same category of enemies. the people of our sister republics of this hemisphere can be honored by that fact.  

the true goal we seek is far above and beyond the ugly field of battle. when we resort to force, as now we must, we are determined that this force shall be directed toward ultimate good as well as against immediate evil. we americans are not destroyers — we are builders.

analyze the effectiveness of this excerpt. how does it function within the speech as a whole? how does the structure of the excerpt to convey the speech's purpose and key points? support your argument with evidence from the speech. (10 points)