The number of distinct non-empty subsets of b objects is 2^b -1. Since the subsets are distinct, each could represent a list of the buildings, from the set of b buildings, in which a student is taking courses.

(a) For 8 buildings, 2^8 -1 = 255 students could enroll. for 9 buildings, 2^9-1 = 511 students could enroll.

For 500 students, 9 buildings are required.

(b) The maximum number of students for n buildings is ...

2^n -1

3 0

3 years ago

The density of a certain material is such that it weighs 71 pounds for every 2.5 gallons of volume. Express this density in tons

kvasek [131]

Answer:

$d=3.75\ \text{tons per cubic meter}$

Step-by-step explanation:

Given that,

Mass of a certain material, m = 71 pounds

Since, 1 ton = 2000 pounds

71 pounds = 0.0355 ton

Volume of the material, V = 2.5 gallons

Since, 1 m³ = 264.172 gallon

2.5 gallon = (2.5/264.172 ) m³

Density,

$d=\dfrac{m}{V}\\\\d=\dfrac{0.0355\ \text{tons}}{\dfrac{2.5}{264.172}\ m^3}\\\\d=3.75\ \text{tons per cubic meter}$

5 0

2 years ago

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