CubeyThePenguin

\(\frac{\text{students}}{\text{teachers}} = \frac{39}{360} \approx \boxed{0.1}\)

         Volume of prism: (2)(4)(8) = 64 ft^3

 -       Volume of cylinder: (pi)(1^2)(1) = pi

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   Volume of water left in prism: 64 - pi ft^3

The radius of the cone is 1/2 the triangle's side length, so 6 centimeters. The height is 6sqrt(3) centimeters.

\(V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \cdot (6^2)(6\sqrt{3}) = \boxed{72 \sqrt{3} \pi}\)

Area = (square)  + 2(semicircle)

\(4 \cdot 4 + 2(\frac{\pi \cdot 2^2}{2})\)

\(\boxed{16 + 4 \pi}\)

This is \(\frac{100}{1.3} = 76.923\).

1.3 can go into 100 76 times without going over.

surface area of cylinder = \(2 \pi rh + 2\pi r^2 = 2\pi r(2.5r) + 2\pi r^2\)

\(2\pi r (2.5r) + 2\pi r^2 = 112\pi\)

\(2r(2.5r) + 2r^2 = 112\)

\(7r^2 = 112\)

\(r = \sqrt{\frac{112}{7}} = 4 \quad \rightarrow \quad \boxed{h = 10}\)

triangle = T, square = S, diamond = D, club = C

5T = D                . (1)

T + 2S = D         . (2)

S + D = C            . (3)

Equations (1) and (2) are equal:

5T = T + 2S

4T = 2S

2T = S

Then we can look at equation (3):

S + T + 2S = C

7S/2 = C

Every symbol is an integer from 1 to 9, so S = 7.

From 1 to 9, each number takes up 1 digit.

From 10 to 99, each number takes up 2 digits. There are 90 two-digit numbers, so this makes 180 digits overall.

From 100 to 999, each number takes up 3 digits. There are 900 three-digit numbers, so this makes 2700 digits overall.

So far, we are on our 2889th digit. We now have to proceed more carefully.

From 1000 onwards, each number has 4 digits.

3007 - 4n = 2889, where n is the number of numbers we use after 1000.

n = 29.5, so we are on 1029. The second digit of 1029 is 0.

|x - 5| <= 7

x - 5 <= 7            OR             x - 5 >= -7

x <= 12                OR           x >= -2                  

\(\boxed{-2 \le x \le 12}\)