A rubrics cube measures 4.5 cm on each side. Find its volume. Using a four-figure mathematical table, evaluate sqrt(0.009441).

The volume $V$ of a cube with side length $s$ is given by $V = s^3$.

$s = 4.5\text{ cm}$

The volume of the cube is $\boxed{91.125\text{ cm}^3}$.

7. Using a four-figure mathematical table, evaluate $\sqrt{0.009441}$.

To evaluate $\sqrt{0.009441}$ using a four-figure mathematical table, one would typically use logarithms.
Let $x = \sqrt{0.009441}$.
Then $\log x = \log(\sqrt{0.009441}) = \frac{1}{2} \log(0.009441)$.

$\log(0.009441) = \overline{3}.9750$ (using a calculator for precision, as tables are not available).
The characteristic is $-3$. The mantissa for 9441 is approximately 0.9750.

To divide $\overline{3}.9750$ by 2, we rewrite the characteristic:

Antilog($\overline{2}.9875$) is the number whose logarithm is $\overline{2}.9875$.
Using a calculator for precision (as a four-figure table would give an approximation):
$10^{\overline{2}.9875} = 10^{-2 + 0.9875} = 10^{-2} \times 10^{0.9875} \approx 0.01 \times 9.716$

Rounding to four significant figures, as would be typical for a four-figure table:

The value is $\boxed{0.09716}$.

8. Using a scientific calculator to find $\sqrt{49.9}$ correct to 3 significant figures.

The first three significant figures are 7, 0, 6. The fourth digit is 4, which is less than 5, so we round down.

The value of $\sqrt{49.9}$ correct to 3 significant figures is $\boxed{7.06}$.

9. Express 0.09364 in standard form.

Move the decimal point 2 places to the right to get 9.364.

Since the decimal point was moved 2 places to the right, the power of 10 is $-2$.

The number in standard form is $\boxed{9.364 \times 10^{-2}}$.

10. Using a four-figure mathematical table evaluate $\sqrt{94.36}$.

To evaluate $\sqrt{94.36}$ using a four-figure mathematical table, one would typically use logarithms.
Let $x = \sqrt{94.36}$.
Then $\log x = \log(\sqrt{94.36}) = \frac{1}{2} \log(94.36)$.

$\log(94.36) = 1.9748$ (using a calculator for precision, as tables are not available).
The characteristic is 1. The mantissa for 9436 is approximately 0.9748.

Antilog(0.9874) is the number whose logarithm is 0.9874.
Using a calculator for precision (as a four-figure table would give an approximation):
$10^{0.9874} \approx 9.713$
Rounding to four significant figures, as would be typical for a four-figure table:

The value is $\boxed{9.713}$.

11. Given Express the square of 89 in standard form.

Move the decimal point 3 places to the left to get 7.921.
Since the decimal point was moved 3 places to the left, the power of 10 is 3.

The square of 89 in standard form is $\boxed{7.921 \times 10^3}$.

12. Express 1 in logarithmic notation base 7.

This means that the logarithm of a number to the same base is always 1.

Therefore, $1 = \log_7 7$.

The number 1 in logarithmic notation base 7 is $\boxed{\log_7 7}$.

13. Evaluate $(125)^{-\frac{2}{3}}$.

$a^{-n} = \frac{1}{a^n}$.

$a^{\frac{m}{n}} = (\sqrt[n]{a})^m$.

The evaluated expression is $\boxed{\frac{1}{25}}$.