Mosspelt6

Assuming that each square is one unit, the first one is $2*1+5*2+1*1=13$ units

2. This is two equal triangles. So $(4*2)/2+(4*2)/2$=4

3.  There are two pentagons of equal area. So the area would be $7.5*2=15$

4. Make a 4x5 square around it. Subtract 4 from one of the outside triangles. Subract 2 from another. Finally subtract 5 from the last. So $20-4-5-2=9$.

A solution exists if and only if 8 is invertible modulo p. In other words, $\gcd(8,p)=1$. Since $8=2^3$ is a power of 2, 8 is invertible modulo q if and only if q is an odd integer. All primes except for 2 are odd, so the number we are looking for is 2.

Those aren't consecutive!

Numbers that digits sum to 8: 8, 17, 26, 35, 44, 53, 62, 71, 80.

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

The answer is 71 and 72.

Hope this helps, 

~Mosspelt6 

$527_{10}$ means 527 in base 10.

The answer would be $20033_4$

-Mosspelt6

8 players are taking biology, so 20-8=12 players are not taking biology, which means 12 players are taking chemistry alone. Since 4 are taking both, there are 12+4=16 players taking chemistry.

~Mosspelt6

it doesn't work for me either

yeah i've seen this problem before, but it was with mothers and daughters

Use the standard method for solving "working together" problems: make an equation showing the fractions of the job that each worker does in a fixed amount of time.

Let x be the number of hours required by the slower machine; then x-1 is the number of hours required by the faster machine.


Then the fractions of the job each does in 1 hour are 1/x and 1/x-1.

And the fraction of the job they do together in 1 hour is 1/2.

So

1/x + 1/(x-1) = 1/2

Multiply both sides of the equation by the least common denominator to clear fractions. You will end up with a quadratic equation that does not factor; so you will need to get your irrational answer using the quadratic formula or something like a graphing calculator.

Does this help?

For a positive number N which is not a perfect square, exactly half of the positive factors will be less than $\sqrt{n}$. Since 60 is not a perfect square, half of the positive factors of 60 will be less than $\sqrt{60}$, or about 7.746. 

Clearly, there are no positive factors of  between 7 and $\sqrt{60}$.

Therefore half of the positive factors will be less than 7.

So the answer is 1/2.

Using the formula (1/a)*b= b/a we get

$\frac{1}{3}*30 = \frac{30}{3} = 10.0$