So, the prime factors of 96 are written as 2 x 2 x 2 x 2 x 2 x 3 or 3 x 25, where 2 and 3 are the prime numbers.
Answer:
a) Yes
b) No
c) Yes
d) No
e) No
Step-by-step explanation:
Right triangle:
The square of the larger side is equals to the sum of the squares of the smaller sides.
a. 6, 8, 10
The answer is yes.
b. 8, 15, 16
So no.
c. 10, 24, 26
So yes
d. 20, 21, 28
So no.
e. 9, 35, 41
About 492 feet per minute
9 • 54.68066 = 492.126
Rounding to the nearest whole number gets you 492
Let's call the stamps A, B, and C. They can each be used only once. I assume all 3 must be used in each possible arrangement.
There are two ways to solve this. We can list each possible arrangement of stamps, or we can plug in the numbers to a formula.
Let's find all possible arrangements first. We can easily start spouting out possible arrangements of the 3 stamps, but to make sure we find them all, let's go in alphabetical order. First, let's look at the arrangements that start with A:
ABC
ACB
There are no other ways to arrange 3 stamps with the first stamp being A. Let's look at the ways to arrange them starting with B:
BAC
BCA
Try finding the arrangements that start with C:
C_ _
C_ _
Or we can try a little formula; y×(y-1)×(y-2)×(y-3)...until the (y-x) = 1 where y=the number of items.
In this case there are 3 stamps, so y=3, and the formula looks like this: 3×(3-1)×(3-2).
Confused? Let me explain why it works.
There are 3 possibilities for the first stamp: A, B, or C.
There are 2 possibilities for the second space: The two stamps that are not in the first space.
There is 1 possibility for the third space: the stamp not used in the first or second space.
So the number of possibilities, in this case, is 3×2×1.
We can see that the number of ways that 3 stamps can be attached is the same regardless of method used.
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