Take Home Quiz 2, Math 166 Print Name__________________________
1. 
a) Find 
using your calculator
and write it.
b) Solve the matrix equation 
. Your answer will contain the unknown a.
2. An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar’s worth of agriculture requires $0.20 from each sector.
Production of a dollar’s worth of manufacturing requires $0.40 from agriculture, $0.10 from manufacturing, and $0.10 from energy.
Production of a dollar’s worth of energy requires $0.30 from agriculture, $0.15 from manufacturing, and $0.10 from energy.
Find the output from each sector required to meet a demand for $10 billion from agriculture, $12 billion from manufacturing, and $20 billion from energy.
3. He did not drink the water or eat the food but he became ill.
p is “he drank the water” q is “he ate the food” and r is “he became ill”.
Write the statement above in terms of p, q, r and connectives. Make a truth table for the statement.
You might or might not need all the boxes provided.
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4. Make a Venn diagram for each set. DeMorgan’s law might make it easier.
a) 
b) 
5. For this problem you will have to set up equations and solve them by substitution.
250 people were asked if they drink coffee, tea, or milk.
90 drink at least two of the three.
130 drink exactly one.
50 drink only coffee.
100 drink milk, possibly the others also.
120 drink tea, possibly the others also.
35 drink coffee and milk, possibly tea also.
45 drink only tea.
a) Make a Venn diagram for the sets C, T, and M and fill in each region with the number of elements in that region.
b) How many drink exactly two of the three?