Make up brainliest for LavenderLauren
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The first digit is one of {1, 3, 5, 7, 9}, and the last digit is one of {1, 2, 3, 4, 5}.
If the first digit is one of {1, 3, 5} (3 choices), then the last digit is one of {1, 2, 3, 4, 5} minus whatever is picked for the first digit (4 choices, and the remaining eight digits can be arranged in 8! ways, so there are 12*8! possible permutations.
If the first digit is one of {7, 9} (2 choices, then the last digit is one of {1, 2, 3, 4, 5} (5 choices), and again there are 8! ways of arranging the remaining digits, so there are 10*8! possible permutations.
Then the total number of permutations that fit the criteria is 12*8! + 10*8! = 22*8!. There are 10! total permutations that can be made overall, so the probability of randomly picking one we want is
Answer: 8 and 9 or -9 and -8
Step-by-step explanation:
Let be the first of the two integers. Then, since the numbers are consecutive,
is the other integer. We then know that the sum of the squares of
and
is equal to 145. So, now we have the equation
which can be expanded and simplified to
which then gives us the quadratic equation
This can then be factored into
Which can be simplified further into
So either or
. This gives us two solutions: 8 and 9 or -9 and -8.
Hope this helps! CHEERS!
Answer:
Step-by-step explanation:
We are supposed to write an inequality to determine the number of hot dogs per minute Joey must eat for the last 9 minutes to break his record.
Let d represent the number of hot dogs Joey eats per minute for the next 9 minutes.
We have been given that after 1 minute, Joey has eaten hot dogs.
Hot dogs eaten in next 9 minutes would be 9 times d that is .
Total hot dogs eaten by Joey would be hot dogs eaten in 1 minute plus next 9 minutes: .
Since to break the record Joey needs to eat more than 72 hot dogs. We can represent this information in an inequality as:
Therefore, our required inequality would be .