Use logarithm table to evaluate 53.76 × 0.536 / (0.124)3 x 0.325. (b) Solve the equation 3/(x+2)…

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Use logarithm table to evaluate 53.76 × 0.536 / (0.124)3 x 0.325. (b) Solve the equation 3/(x+2) = 5/(2(x−3)). 12. Table 2.3: Frequency distribution (a) Draw the ogive for Table 2.3. (b) Use the ogive to estimate the: (i) Median (ii) Lower and upper quartiles (iii) Semi-interquartile range

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a) Use logarithm table to evaluate (53.76 × 0.536)/((0.124)³ × 0.325). Step 1: Let P = (53.76 × 0.536)/((0.124)³ × 0.325). Take the logarithm of both sides. log P = log(53.76 × 0.536) − log((0.124)³ × 0.325); log P = (log 53.76 + log 0.536) − (3 log 0.124 + log 0.325) Step 2: Find the logarithms of each number using a logarithm table. log 53.76 = 1.7305; log 0.536 = 1.7292; log 0.124 = 1.0934; log 0.325 = 1.5119 Step 3: Calculate the logarithm of the numerator. log(53.76 × 0.536) = 1.7305 + 1.7292; = 1.7305 + (−1 + 0.7292); = 0.7305 + 0.7292 = 1.4597 Step 4: Calculate the logarithm of the denominator. 3 log 0.124 = 3 × (1.0934) = 3 × (−1 + 0.0934) = −3 + 0.2802 = 3.2802; log((0.124)³ × 0.325) = 3.2802 + 1.5119; = (−3 + 0.2802) + (−1 + 0.5119); = −4 + 0.7921 = 4.7921 Step 5: Calculate log P. log P = 1.4597 − 4.7921; log P = 1.4597 − (−4 + 0.7921); log P = 1.4597 + 4 − 0.7921; log P = 5.4597 − 0.7921; log P = 4.6676 Step 6: Find the antilog of 4.6676. The mantissa is 0.6676. From the antilog table, the antilog of 0.6676 is approximately 4.652. The characteristic is 4, so the number has 4+1=5 digits before the decimal point. P = 46520 The value is 46520. b) Solve the equation (3)/((x+2)) − (1)/(2(x−3)) = (5)/(x−3). Step 1: Identify restrictions on x. The denominators cannot be zero, so x ≠ −2 and x ≠ 3. Step 2: Rearrange the equation to group terms with common denominators. Move the term (1)/(2(x−3)) to the right side of the equation. (3)/((x+2)) = (5)/(x−3) + (1)/(2(x−3)) Step 3: Combine the terms on the right side by finding a common denominator, which is 2(x−3). (3)/((x+2)) = (5 × 2)/(2(x−3)) + (1)/(2(x−3)); (3)/((x+2)) = (10 + 1)/(2(x−3)); (3)/((x+2)) = (11)/(2(x−3)) Step 4: Cross-multiply to eliminate the denominators. 3 × 2(x−3) = 11 × (x+2); 6(x−3) = 11(x+2) Step 5: Distribute and solve for x. 6x − 18 = 11x + 22 Subtract 6x from both sides and subtract 22 from both sides. −18 − 22 = 11x − 6x; −40 = 5x Divide by 5. x = (−40)/(5); x = −8 Step 6: Check the solution against the restrictions. Since x=−8 is not equal to −2 or 3, the solution is valid. The solution is x = −8.

Use logarithm table to evaluate 53.76 x 0.536 / (0.124)3 x 0.325. (b) Solve the equation 3/(x+2) = 5/(2(x-3)). 12. Table 2.3: Frequency distribution (a) Draw the ogive for Table 2.3. (b) Use the ogive to estimate the: (i) Median (ii) Lower and upper quartiles (iii) Semi-interquartile range

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Step-by-step solution

Part a· 6 steps

Let $P = \frac{53.76 \times 0.536}{(0.124)^3 \times 0.325}$ .

Find the logarithms of each number using a logarithm table.

Calculate the logarithm of the numerator.

Calculate the logarithm of the denominator.

Calculate $\log P$ .

Find the antilog of 4.6676.

Part b· 6 steps
$x = -8$

Identify restrictions on $x$ .

Rearrange the equation to group terms with common denominators.

Combine the terms on the right side by finding a common denominator, which is $2(x-3)$ .

Cross-multiply to eliminate the denominators.

Distribute and solve for $x$ .

Check the solution against the restrictions.

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