NotThatSmart

First, let's convert every single measurement into feet from meters so we don't have to worry about it later.

We have $\frac{12m}{ 0.3048 m/ft }=39.3701 ft$ for the height

And we have $\frac{120m}{ 0.3048 m/ft }=393.7007 ft$ for the length. 

Now, we can find the total area of the wall. We do length times height, so we have

$(39.3701 ft)(393.7007 ft) = 15,500.0359 ft^2$

Now, we do some ugly math. We must divide by the gallons. 

Since each gallon of paint covers 150, we must do

$\frac{ 15,500.0359 sq ft}{ 150 sq ft/gallon }= 103.3335 gallons$

Since you can't actually by a fraction of a gallon, we must round up. 

So, we simply have

104 gallons as our answer. 

So 104 is our answer. 

Thanks! :)

We can write a system of equations to solve the problem. 

Let b be bageld. 

Let t be toast.

Let m be muffins. 

We have the system

$2T + 1B = 3.15 \\ 1M + 1B = 3.50 \\ 1T + 2B + 3M = 8.15$

We want to find what a bagel is. So, from the first two equations, we can isolate the other variables in terms of B. 

We get

$[3.15 - B ] / 2 = T \\ M = 3.50 - B$

Plugging this into the third and final solution, we find that

$[ 3.15 - B ] / 2 + 2B + 3 [ 3.50 - B ] = 8.15 \\ [3.15 - B ] + 4B + 6 [ 3.50 -B ] = 16.30 \\ -3B + 3.15 + 21 = 16.30 \\ -3B = 16.30 - 3.15 - 21 \\ -3B = -7.85 \\ B = 7.85 / 3 ≈ $2.62$

This is about 262 cents or 262.67

Thanks! :)

First, we must find the slope of the two points. 

Since we have

$\frac{150-17}{82-3} = \frac{133}{79}$

This means for every 133 latice points to the right of 3, you move up 79. 

However, note that when we add 133 to 17, we get $133+17=150$

This means there are no lattice points between $(3, 17), (82, 150)$

So 2 is our answer. 

Thanks! :)

The answer is 335. 

We have

$33 \cdot 781 = 27335$

So 335 is our answer. 

Thanks! :)

First, let's cross multiply. We have

$\sqrt{x}\left(2x\sqrt{6}+4\right)=\left(x\sqrt{3}+\sqrt{2}\right)\cdot \:1$

Now, we do some simplifying. Factoring and expanding out everything, we have

$2\sqrt{x}\left(\sqrt{6}x+2\right)=\sqrt{3}x+\sqrt{2}$

Squaring both sides of the equation, we find that

$24x^3+16\sqrt{6}x^2+16x=3x^2+2\sqrt{6}x+2$

Solving for this, we get

$x=\frac{1}{8}$

So x is 1/8.

So our answer is 1/8. 

Thanks! :)

There are 487 ways to choose the 3 circles. 

We can write an equation to solve this problem. 

First, let's note that every number in the form 5 modulo 171 can be written in the expression

$171x+5$ where x is an integer. 

We set this to equal 1000 to get the largest number possible. we have

$171x+5 = 1000$

We are trying to find x. We have

$171x=995$

Dividing, we get

$x=5.81871345029$

We actually have to round down, so we get x is 5. 

So our final answeer is 5. 

Thanks! :)

Let's make some observations. 

2 modulo 7 means that it leaves a remainder of 2 when divided by 7. 

Well, let's look at the numbers

$1, 2, 3, 4, 5, 6, 7$

Note that other than 2, other numbers leave a remainder of NOT 2. 

So our answer is just $2$

Thanks! :)