Let L be the language defined by the regular expression 0(0 | 1)?1(0 | 1)?.
(a) Write 3 strings that belong to L
(b) Use words to describe L.
a. 0010, 0000110010, 01 (Answers will vary. This is just a small sample.)
b. L is the set of all strings of 0’s and 1’s starting with a 0, followed by any finite number of
1’s and/or 0’s (including none at all), followed by one 1, and ending in any finite number of
1’s and/or 0’s (including none at all).
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Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.ln 7 - 5 ln x
A. ln
12
B. ln
C. ln
D. 
Use a calculator to find the following to four decimal places.ln 0.000876
A. -7.0401 B. 7.0401 C. -3.0575 D. 3.0575
Find the average value of 
over the given region.
over the cube in the first octant bounded by the coordinate planes and the planes 
, 
, 
A. 54
B. 
C. 45
D. 
Simplify.(6 + 5)[7 + (4 + 5)]
A. 74 B. 480 C. 176 D. 810