Problem 7)
The answer is choice B. Only graph 2 contains an Euler circuit.
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To have a Euler circuit, each vertex must have an even number of paths connecting to it. This does not happen with graph 1 since vertex A and vertex D have an odd number of vertices (3 each). The odd vertex count makes it impossible to travel back to the starting point, while making sure to only use each edge one time only.
With graph 2, each vertex has exactly two edges attached to it. So an Euler circuit is possible here.
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Problem 8)
The answer is choice B) 5
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Work Shown:
abc base 2 = (a*2^2 + b*2^1 + c*2^0) base 10
101 base 2 = (1*2^2 + 0*2^1 + 1*2^0) base 10
101 base 2 = (1*4 + 0*2 + 1*1) base 10
101 base 2 = (4 + 0 + 1) base 10
101 base 2 = 5 base 10
Question 8 is D
Question 9 is -6
And sorry I don't know the last question
Answer:
City's Area = 507.44 sq. mi.
Step-by-step explanation:
We will use population density formula to solve this problem easily.
We have:
Population Density = Total Population/ Land Area
Given,
Population Density = 24,403
Total Population = 12,383,007
We want land area, so we simply plug in the numbers into the formula and solve for City's Area. Shown below:
THe units is Square Miles, so we can say:
City's Area = 507.44 sq. mi.
Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
tan(x)/sec(x) = sin(x)
Hint: | Eliminate the denominator on the left hand side.
Multiply both sides by sec(x):
tan(x) = ^?sec(x) sin(x)
Hint: | Express both sides in terms of sine and cosine.
Write secant as 1/cosine and tangent as sine/cosine:
sin(x)/cos(x) = ^?1/cos(x) sin(x)
Hint: | Come to a conclusion.
The left hand side and right hand side are identical:
Answer: (identity has been verified)
<em>while the two were at the movies Katie spent $40.00</em>