MATH 1030-005
Homework #1
Instructions: Answer the following questions on a separate sheet of paper.
1. Simplify the following expression: (x3y
−1)2
x5y
2. Solve for xin the following: 3x
4
−
8
3= 1
3. Suppose there are 240 people (men, women, and children) trapped in a burning building. If 40%
of them are men and 1/3 of them are women, how many children are caught in the fire?
4. Among Benjamin Franklin’s inventions are the lightning rod, the Franklin Stove, and the carriage
odometer, none of which he patented. In an old survey of 105 people, it was found that:
56 people had a Franklin Stove
70 people had a lightning rod
40 people had a carriage odometer
30 people had a lightning rod and a carriage odometer
25 people had a lightning rod and a Franklin Stove
15 people had a carriage odometer and a Franklin Stove
8 people had all three
Draw a Venn diagram to describe this survey and answer the following questions:
(a) How many people have none of these three of Benjamin Franklin’s inventions?
(b) How many people own a lightning rod or a Franklin Stove?
(c) How many people only have a carriage odometer?
5. Curiously, most human brains tend to favor optical input from one eye over the other, a
phenomenon known as ocular dominance, and it is estimated that two-thirds of humans are right-eye
dominant. Similarly, most humans are right handed, but there are the obvious exceptions. Consider
the following data collected from Lucinda Surber’s 4th grade class in the 2006-2007 acaemic year,
in which 21 students were surveyed:
15 students are left-eyed
18 students are right-handed
1 student is right-eyed and left-handed
Create a Venn diagram to describe the above situation, and determine how many students are both
left-eyed and right-handed.
1
