1. If 3ᵃ = 27 and 3ᵇ = 9, what is 3ᵃ⁺ᵇ?
Since 27 = 3³, a = 3. Since 9 = 3², b = 2. Therefore 3ᵃ⁺ᵇ = 3⁵ = 243.
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Since 27 = 3³, a = 3. Since 9 = 3², b = 2. Therefore 3ᵃ⁺ᵇ = 3⁵ = 243.
Subtract the fixed charge: 31.20 - 4.20 = 27.00. Then divide by 1.80, giving d = 15 km.
Use tan(36°) = height / 42. The height is 42 × tan(36°) = 30.516..., which rounds to 30.5 m.
Areas scale by the square of the length scale factor. The area factor is (3/2)² = 9/4, so the larger area is 48 × 9/4 = 108 cm².
The six known values sum to 85. Seven values with mean 15 must sum to 105, so x = 105 - 85 = 20.
The probability is 5/8 for the first blue and 4/7 for the second blue after one blue is removed. So P(two blue) = 5/8 × 4/7 = 20/56 = 5/14.
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