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

Here are the solutions to the problems: 6. A rubrics cube measures 4.5 cm on each side. Find its volume. Step 1: Identify the formula for the volume of a cube. The volume V of a cube with side length s is given by V = s^3. Step 2: Substitute the given side length into the formula. s = 4.5 cm V = (4.5 cm)^3 Step 3: Calculate the volume. V = 4.5 × 4.5 × 4.5 cm^3 V = 20.25 × 4.5 cm^3 V = 91.125 cm^3 The volume of the cube is 91.125 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 x = (sqrt(0.009441)) = (1)/(2) (0.009441). Step 1: Find the logarithm of 0.009441. (0.009441) = 3.9750 (using a calculator for precision, as tables are not available). The characteristic is -3. The mantissa for 9441 is approximately 0.9750. Step 2: Divide the logarithm by 2. x = (1)/(2) (3.9750) To divide 3.9750 by 2, we rewrite the characteristic: 3.9750 = -3 + 0.9750 = -4 + 1.9750 x = (1)/(2) (-4 + 1.9750) = -2 + 0.9875 = 2.9875 Step 3: Find the antilog of 2.9875. Antilog(2.9875) is the number whose logarithm is 2.9875. Using a calculator for precision (as a four-figure table would give an approximation): 10^2.9875 = 10^-2 + 0.9875 = 10^-2 × 10^0.9875 ≈ 0.01 × 9.716 x ≈ 0.09716 Rounding to four significant figures, as would be typical for a four-figure table: x ≈ 0.09716 The value is 0.09716. 8. Using a scientific calculator to find sqrt(49.9) correct to 3 significant figures. Step 1: Calculate the square root using a calculator. sqrt(49.9) ≈ 7.06400722 Step 2: Round the result 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. 7.06 The value of sqrt(49.9) correct to 3 significant figures is 7.06. 9. Express 0.09364 in standard form. Step 1: Move the decimal point to get a number between 1 and 10. Move the decimal point 2 places to the right to get 9.364. Step 2: Determine the power of 10. Since the decimal point was moved 2 places to the right, the power of 10 is -2. 0.09364 = 9.364 × 10^-2 The number in standard form is 9.364 × 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 x = (sqrt(94.36)) = (1)/(2) (94.36). Step 1: Find the logarithm of 94.36. (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. Step 2: Divide the logarithm by 2. x = (1)/(2) (1.9748) = 0.9874 Step 3: Find the antilog of 0.9874. 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 ≈ 9.713 Rounding to four significant figures, as would be typical for a four-figure table: x ≈ 9.713 The value is 9.713. 11. Given Express the square of 89 in standard form. Step 1: Calculate the square of 89. 89^2 = 89 × 89 = 7921 Step 2: Express the result 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. 7921 = 7.921 × 10^3 The square of 89 in standard form is 7.921 × 10^3. 12. Express 1 in logarithmic notation base 7. Step 1: Recall the property of logarithms that states _b b = 1. This means that the logarithm of a number to the same base is always 1. Step 2: Apply this property with base 7. Therefore, 1 = _7 7. The number 1 in logarithmic notation base 7 is _7 7. 13. Evaluate (125)^-(2)/(3). Step 1: Apply the negative exponent rule: a^-n = (1)/(a^n). (125)^-(2)/(3) = (1)/((125)^2)3 Step 2: Apply the fractional exponent rule: a^(m)/(n) = ([n]a)^m. (125)^(2)/(3) = ([3]125)^2 Step 3: Calculate the cube root of 125. [3]125 = 5 (since 5 × 5 × 5 = 125) Step 4: Square the result. 5^2 = 25 Step 5: Substitute back into the expression. (1)/(25) The evaluated expression is (1)/(25). 3 done, 2 left today. You're making progress.