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Problem Solving #4
Question #1: While competing in a marathon event, John is behind Mike by 100 yards. John runs (x - 2) yards while Mike runs (x + 10) yards. What is the new distance between them?
112 yards
108 yards
102 yards
110 yards
The answer is a function of x
Question #2: What is the sum of 10% of x and 20% of 2x?
10% of x
20% of x
30% of x
50% of x
100% of x
Question #3: What are the solutions of the equation 5
^{x(x + 1)}
·5
^{x}
= 1?
x
_{1}
= 0 and x
_{2}
= 2
x
_{1}
= 0 and x
_{2}
= 1
x
_{1}
= 2 and x
_{2}
= -2
x
_{1}
= 0 and x
_{2}
= -2
x
_{1}
= 1 and x
_{2}
= -2
Question #4: Out of all of the houses characterized in the table below, what is the percentage of new ranches?
Houses
Old
New
Total
Ranch
23
?
30
Colonial
?
40
?
Total
23
?
?
10%
12%
15%
25%
8%
Question #5: If one of the houses from the previous question is randomly selected, what is the probability that the selected house is a ranch?
Houses
Old
New
Total
Ranch
23
7
30
Colonial
0
40
40
Total
23
47
70
1/10
4/7
3/7
2/7
23/70
Question #6: The AB side of the ABCD trapezoid is 4 and the BC side is 3. What is the area of the triangle ABD?
4
7/2
9/2
6
7
Question #7: The side AB of the ABCD square is 10, AE = ED and BF = FC. What is the area of parallelogram BFDE?
20
25
50
60
75
Question #8: The graphs of two lines, y = f(x) and y = g(x) are given below, and four regions,
M
,
N
,
O
, and
P
are also shown with different colors on the same graph.
Which region is the solution set of the system of inequalities y < f(x) and y > g(x)?
M
N
O
P
Question #9: Find the value of x if:
x + y + z = 5
x + y - z = 3
x - y = 2
-3
-1
1
3
5
Question #10:What is 2% of 8%?
.0016%
.016%
.16%
1.6%
16%