Question 1 Rewrite the following as an equivalent logarithmic equation. 𝑒 3 = 20.0855 e 3 =20.0855. An equivalent logarithmic form for 𝑒 3 = 20.0855 e 3 =20.0855 is? Answer 1 𝑒 3 = 20.0855 e 3 =20.0855 Taking the log on both sides: ln ⁡ 𝑒 3 = ln ⁡ 20.0855 lne 3 =ln20.0855 Using the property ln ⁡ 𝑒 𝑚 = 𝑚 lne m =m: 3 = ln ⁡ 20.0855 3=ln20.0855 Thus, the equivalent logarithmic form is: 3 = ln ⁡ 20.0855 3=ln20.0855 Question 2 To subtract: 0.064 − 10.2 0.064−10.2 Answer 1 Align the decimals vertically to subtract: 0.064 − 10.2 = − 10.136 0.064−10.2=−10.136 Question 3 The number multiplied on both sides of the equation 0.9 𝑧 − 4.3 = 0.47 0.9z−4.3=0.47 in order to clear decimals. Answer 1 Multiply both sides by 100 to remove the decimals: 100 × ( 0.9 𝑧 − 4.3 ) = 100 × 0.47 100×(0.9z−4.3)=100×0.47 This gives: 90 𝑧 − 430 = 47 90z−430=47 Question 4 Compute the following binomial probabilities directly from the formula for 𝑏 ( 𝑥 , 𝑛 , 𝑝 ) b(x,n,p): a) 𝑏 ( 3 , 8 , 0.6 ) b(3,8,0.6) b) 𝑏 ( 5 , 8 , 0.6 ) b(5,8,0.6) c) 𝑃 ( 3 ≤ 𝑋 ≤ 5 ) P(3≤X≤5) when 𝑛 = 8 n=8 and 𝑝 = 0.6 p=0.6 d) 𝑃 ( 1 ≤ 𝑋 ) P(1≤X) when 𝑛 = 12 n=12 and 𝑝 = 0.1 p=0.1 Answer 1 a) For 𝑏 ( 3 , 8 , 0.6 ) b(3,8,0.6): 𝑏 ( 3 , 8 , 0.6 ) = ( 8 3 ) ( 0.6 ) 3 ( 1 − 0.6 ) 8 − 3 b(3,8,0.6)=( 3 8 )(0.6) 3 (1−0.6) 8−3 Calculating each part yields approximately 0.124. b) For 𝑏 ( 5 , 8 , 0.6 ) b(5,8,0.6): 𝑏 ( 5 , 8 , 0.6 ) = ( 8 5 ) ( 0.6 ) 5 ( 1 − 0.6 ) 8 − 5 b(5,8,0.6)=( 5 8 )(0.6) 5 (1−0.6) 8−5 This evaluates to approximately 0.279. c) For 𝑃 ( 3 ≤ 𝑋 ≤ 5 ) P(3≤X≤5): Sum 𝑏 ( 3 , 8 , 0.6 ) + 𝑏 ( 4 , 8 , 0.6 ) + 𝑏 ( 5 , 8 , 0.6 ) b(3,8,0.6)+b(4,8,0.6)+b(5,8,0.6): This results in approximately 0.635. d) For 𝑃 ( 1 ≤ 𝑋 ) P(1≤X): Use the complement rule: 𝑃 ( 1 ≤ 𝑋 ) = 1 − 𝑃 ( 𝑋 = 0 ) P(1≤X)=1−P(X=0) Calculating 𝑃 ( 𝑋 = 0 ) ≈ 0.7176 P(X=0)≈0.7176, so: 𝑃 ( 1 ≤ 𝑋 ) ≈ 0.2824 P(1≤X)≈0.2824 Question 5 Round 1451.5254 to the indicated place: (a) hundred (b) ten (c) unit (one) (d) tenth (e) hundredth (f) thousandth. Answer 1 (a) Hundred place: 1500 (b) Ten place: 1450 (c) Unit (one) place: 1452 (d) Tenth place: 1451.5 (e) Hundredth place: 1451.53 (f) Thousandth place: 1451.525