Reflec

The question sort-of gets cut off at "There are 15"

So there are 3 ways to make a number divisable by 6 with these numbers.

6

2 and 4

2, 4, and 6

So there is 1 one-digit mutiple. (1!)

There are 2 two-digit mutiples. (2!)

And there are 6 three-digit mutiples. (3!)

So you get 9.

So the first thing to notice is that it is a 45 - 45 - 90 right triangle.

This means that the ratio of the sides are 1 - 1 - \(\sqrt2\)

This means that one leg has the length of\(4\over\sqrt2\) which simplifies to \(2\sqrt2\)

Now because it is a right triangle, you get \(\frac{1}{2} \times 2\sqrt2 \times 2\sqrt2\)

So the answer is 4.

The answer is 60.

So first draw a diagram and label everything.

Then because of the angle bisector theorem, so AB/AD = CB/CD

You can write it as 2x/x = CB/x

From this you get CB = 2x.

Now you can tell the triangle is equilateral so the answer is 60.

So there are 226 numbers because 250-25+1=226.

The squares 5-15 fit between 25 and 250.

Also the cubes 3-6 fit.

So we get 11+4=15.

But 64 is a square and a cube.

So we get 15-1=14.

We can subtract 226 by 14 to get an answer of 212.

So the formula to calculate the remainder is

 \(a^{p-1}\equiv1(mod \space p)\)

When a and p are relatively prime.

So we get

\(5^{23}\equiv1(mod\space 8)\)

From this we can get

\(1^{23}\times5^7\equiv78125\equiv125\equiv5(mod\space8)\)

So the remainder is 5

The question gets cut off at "bus B takes 35 minutes to complete its ro"

First there is 36 choices because 6*6=36

So now you can count the ways to get 8.

2 and 6

6 and 2

3 and 5

5 and 3

4 and 4

So you get 5/36.

First set r to the speed Ryan paints the room.

So the equation is

40r+20(2r)=1

80r=1

This would work if the speed of paint the room was consent.

So

20r/80r=1/4

This is the amount of the room before Leonardo started helping.

Then 80r-20r=60r

60r/2=30r

30r/80r+1/4=3/8+1/4=3/8+2/8=5/8

So 5/8 of the room was painted by 9:30.