Bearing in mind that, if you multiply, any integer whatsoever by 2, you end up with a even integer, 17*2, or 19*2, 88*2 you name it, you get an even number
now, you can get an odd integer by simply going from an even integer, back or forth, so if you have an even number of say 24, 24 - 1, 23, 24+1, 25, 23 and 25 are the odd ones next to 24
so.. let's pick some number, let's say hmm "a", we know 2*a is even, so 2a, thus, 2a +1 or 2a -1 is an odd one.... let's use hmm 2a + 1 as our first odd integer
to jump from an odd integer to another, you simply add 2, 3+2, 5, 5+2, 7 and so on
so... our first one is 2a + 1, so the next consecutive one, will then be (2a+1)+2
and next consecutive after that is (2a+1+2)+2
so our three consecutive odd integers are then
2a + 1
2a + 3
2a + 5
now, 4 times the middle is 4(2a+3)
the sum of the first and last is (2a+1) + (2a+5)
now, two more than that is just (2a+1) + (2a+5) + 2
thus
4(2a + 3) = (2a + 1) + (2a + 5) + 2
solve for "a"
Answer:
The required equation is (1) and the number of boys is 211.
Step-by-step explanation:
Let the number of boys be x.
It is given that there are 100 more girls than boys. It means the number of girls is x+100.
The total number of students is 522.
Number of boys + Number of girls = 522
... (1)
Combine like terms.
Subtract 100 from both the sides.
Divide both sides by 2.
Therefore the required equation is (1) and the number of boys is 211.
Simplify √20 to 2√5
2 * 2√5 - 3√7 - 2√5 + 4√63
Simplify √63 to 3√7
2 * 2√5 - 3√7 - 2√5 + 4 * 3√7
Simplify 2 * 2√5 to 4√5
4√5 - 3√7 - 2√5 + 4 * 3√7
Simplify 4 * 3 √7 to 12√7
Collect like terms
(4√5 - 2√5) + (-3√7 + 12√7)
Simplify
2√5 + 9√7
Answer: B
This will help if you don’t know how to use ask
A) Suppose
is the set of juniors and
is the set of social science majors. There are 35 students in all, but 12 of them don't belong to either set, so
. Then
So the probability that a random student is both a junior and social science major is
b) We're looking for the probability
. By definition, this would be
