1) Joey is playing a game where winning means getting the biggest product. He rolls a 6 sided die 5 times getting the numbers 1, 3, 4, 5, 6. He creates a 3 digit number and a 2
digit number using each digit once. He wins if the product of his two numbers is bigger than the products of his competitors. What should his 3 digit number be?
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- The product of a 3 digit number and a 2 digit number are to be maximized, so it is clear that the units digits of both numbers should be the smallest 2 numbers, namely ___ and ___.
- So, we need the placement of 3 numbers in the 2 remaining digits of the 3-digit number and the 1 remaining digit of the 2-digit number.
- That leaves only 6 possible combinations of the remaining 3 numbers (___ , ___ and ___), so they can all be investigated.
List them here:
- So once you have the best 3-digit combination all we have to do is figure out where the 2 small digits go.
- Therefore, the largest product is _______ x ______
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2) Initially on Michael's hands there are 3.9 x 106
bacteria. He sprays his hands with a hand sanitizer, killing 99.5% of them. He then washes his hands twice, removing 10% of
the remaining bacteria each time. How many bacteria are left? Express your answer in scientific notation.
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Multiply the original number of bacteria by the decimal that remain after the hand sanitizer and then by the decimal that remain after the 2 hand washings.
= ________________
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