OrangeJuicy

set all of his money as x.

3/5x is 4 highlighters, so 3/10x is 2 highlighters.

he only spent 1/10x of his money buying 10 rulers, which answers the first question given.

(b) he spends all his money buying rulers. which means ignoring the free rulers, he could buy 100 rulers. but then, since there are 8*12 = 96, we know he gets an extra 8 rulers and hence have 108 rulers if he spent all his money at first on rulers.

set whole pizza as x

day 1 she eats 1/2x

day 2 she eats 1/3(1/2x), which is 1/6x

day 3 she eats 1/4(1/3x), which is 1/12x

day 4 she eats 1/5(1/4x) which is 1/20x

Total eaten over 4 days: (1/2+1/6+1/12+1/20)x = 4/5x

Answer = left over = 1/5 of the whole pizza

I'd say it's pretty self-explanatory, cuz from unit conversion we get 1g/cm^3 =  1000kg/m^3

60:45 gets us 3:4 in circumference.

3:4 in circumference gets us 3:4 in radius, and that gets us 9:16 in the two circles' areas, which is the answer.

if we were to find the shortest distance, use the pythagorean thereom!

if you don't know what that is, it's a^2(short leg)+b^2(long leg) = c^2(hypotenuse) in a right triangle

Put into this question it's Sqrt(5^2+12^2) = sqrt(169) =_____(You know how to do this!)

Moving x and y terms to one side gets this: x^2-6x+y^2+18y = 127

completing the square: (x-3)^2+(y+9)^2 -9-81 = 127

Finally: (x-3)^2 + (y+9)^2 = 217

Now you can finish it up yourself.

Note: You can also view this graph visually as both forms overlap fully

According to the Vieta's Formula, we know that -b/a in the question is equal to the sum of the roots.

Plug in-> -7/2 is a+b which is the answer

The chance of the 1st selection greater than 3 is 6/10 or 3/5

The chance of the 2nd selection greater than 3 is 5/9

The chance of the 3rd selection greater than 3 is 4/8 or 1/2

The chance of the 4th selection greater than 3 is 3/7

The chance of 5th selection greater than 3 is 2/6 or 1/3

Multiply all chances together we get: 1/42

So, the answer is 1/42 chance the 5 numbers selected are greater than 3

Completing the square: (x+6)^2 - 27

BMC + A = 201

BMC + CMA = 180

BMC + C also = 201

3BMC + CMA + C +A = 582, and we know CMA + C + A = 180, so 3BMC = 582-180 = 402, and thus BMC = 134

B = MCB, and finish the last step to get B