BuilderBoi

\((1+i)^2 = i^2+2i+1 = -1 + 2i +1 = 2i\)

\((2i)^2 = 4i^2 = 4 \times -1 = -4\)

\(-4^3 = -64\)

\(-64^3 = \color{brown}\boxed{-262,144}\)

I will assume the question is supposed to be a 9. 

We can write as equation:

\(3 \times 8 + 9 \times 2 + 9x = 6(10+x)\)

\(42 + 9x = 60 + 6x\)

\(18 = 3x\)

\(x = \color{brown}\boxed{6}\)

The medium hose can fill 2.5% of the pool in an hour. 

The large hose can fill 5% of the pool in an hour. 

Both together can fill 7.5% of the pool in an hour. 

This means it will take \(100/7.5 \approx \color{brown}\boxed{13}\) hours. 

 I will try this one. 

There are 3 cases to consider: 

1) He rolls a sum of 3 on the first turn

2) He rolls a sum greater than 3 on the first turn, and then he rolls a sum of 3

3) He rolls a sum of 2 that get him to 99 and then he rolls a sum of 4 

P(1)

He rolls: (2,1) or (1,2), meaning the probability is 2/36. 

P(2)

The first roll of getting a number greater than 3: 11/12. Second roll of rolling a 3: 1/18 This means the total probability is 11/12 x 1/18 = 11/216

P(3)

The probabilty of getting a 2 to get to 99: 1/36. The probability of getting a 4: 1/12. This means that teh total propbabilty is 1/36 x 1/12 = 1/432

Add em all up, and you find the total probability is \(\color{brown}\boxed{47\over 432}\)

There are 4 factors of 5

25 = 5 x 5

20 = 5 x 4

15 = 5 x 3

There is also 27 factors of 2, meaning that there are 4 zeros at the end

Corrected... Thanks Guest!!!

The easiest way to solve this is to use Vietas. The sum and products of the roots are -8 and 7, respectively. 

We know the sum is \(-b\over a\). We also know a = 1, so b must be 8. 

We also know the product is \(c \over a\). Because we know a = 1, c must be 7. 

This means that the quadratic is \(\color{brown}\boxed{ x^2 + 8x+ 7}\)

Only \(\color{brown}\boxed{4}\) do, I, A, E, and D. 

Write as system:

a = apples

b = bananas

1.5a + 0.3b = 6

a+b = 8

1.5a + 1.5b = 12

1.5a + 1.5b = 12

1.5a + 0.3b =  6

           1.2b =  6

                b = 5

Now plug 5 into the second equation and solve for a 

Write it as an equation: \(20m= {m(m+1) \over 2}\)

The first term is the height of the first plant, and the second term is the sum of an arithmatic series that represents the height of the second plant. 

Solving, we find it took \(\color{brown}\boxed{39}\) months

I will solve A, and let you solve B. 

A is c = 0.75p, 

To solve B, you subsitute p for 2.