BuilderBoi

There are \(6 \times 6 \times 6 = 216\) possibilities. 

The only way to get a sum of 17 is to have a 6, 6, and 5, which can be done in \(3! \div 2 = 3\) ways (divide by 2 because there are 2 6's)

So, the probability is \({3 \over 216} = \color{brown}\boxed{{1 \over 72}}\)

Don't be rude...

wait.. is the side length of b 4x inches?

substitute the slope for m: \(y = {3 \over 7}x + b\).

Now, plug in the point \((14,8)\) and solve for b: \(8 = {3 \over 7} \times 14 + b\).

Solving for b, we find \(b = 2 \), so our answer is \(\color{brown}\boxed{y = {3 \over 7}x + 2}\)

The correct answer is all of them by the way...

She has \(40 \times 3x = 120x\)cents. 

Now, if the price was \(5x\) cents, how many oranges would she be able to buy?

\(3^{2c + 1} = 28 \times 3^c - 3^c\)

\(3^{2c + 1} = 27 \times 3^c\)

\(3^{2c + 1} = 3^3 \times 3^c\)

\(3^{2c+1} = 3^ {3 + c}\)

\(2c + 1 = 3 + c\)

\(c + 1 = 3\)

\(c = \color{brown}\boxed{2}\)

Draw altitude \(JM \). Because the triangle is isosceles, \(KM = ML = 15\). 

Then, by the Pythagorean Theorem, \(JM = \sqrt{25^2 - 15^2} = 20\).

This means that the area of the triangle is \(2 \times( 20 \times 15 \div 2) = 300\).

Now, recall the formula for inradius, which is \({\text{Area} \over \text{semiperimeter} } = {300 \over 40} = \color{brown}\boxed{7.5}\)

Now, recall the formula for circumradius, which is \({\text{product of the side lengths} \over 4\times \text{Area}} = {18,750 \over 1,200} = \color{brown}\boxed{15.625}\)

Let \(s\) be the side length of the square. 

We have \(s^2 = 4 \times 4s\), which simplifies to \(s^2 = 16s\).

The answer will be the solution to this equation. 

The probability is the area of the blue region over the total square.