Matt has a large family when looking at the dates of their birthdays, he noticed that every prime day had at least one birthday. this was also true for perfect squares cubes and multiples of 3,5,7, and 11. what days (1 to 31) are not represented
primes from 1 to 31
-- 2 3 5 7 11 13 17 19 23 29 31
perfect squares:
-- 1 4 9 16 25
perfect cubes:
-- 1 8 27
multiples of 3:
-- 3 6 9 12 15 18 21 24 27 30
multiples of 5:
-- 5 10 15 20 25 30
multiples of 7:
-- 7 14 21 28
multiples of 11:
-- 11 22
the only number I don't see in the above lists is 26
at 5pm a person 5 feet tall casts a 10 foot shadow. at the same time a flagpole casts a 40 foot shadow.what is the height of the flagpole?
To determine the days that are not represented in Matt's family's birthdays, we need to consider the prime numbers, perfect squares, cubes, and multiples of 3, 5, 7, and 11.
Let's start by identifying the prime days between 1 and 31. Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves. The prime numbers between 1 and 31 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
Next, let's consider the perfect squares. Perfect squares are numbers that can be expressed as the product of an integer with itself. The perfect squares between 1 and 31 are:
1, 4, 9, 16, 25.
Now, let's consider the cubes. Cubes are numbers that can be expressed as the product of an integer with itself twice. The cubes between 1 and 31 are:
1, 8, 27.
Finally, let's consider the multiples of 3, 5, 7, and 11. The multiples between 1 and 31 are:
3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.
Now, let's combine all the numbers that are represented in Matt's family's birthdays:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31.
To find the days that are not represented, we simply need to subtract these numbers from the set of all days between 1 and 31:
1 - Not represented