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Probability with Combinations and Permutations — Cumulative exam Answers

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A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids.

Question illustration
A
3 units
B
4 units
C
6 units
D
8 units
2
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Which measurements are correct? Select two options.

A
m = 60°
Option A
B
m = 120°
Option B
C
m = 180°
Option C
D
m∠XWZ = 60°
E
m∠YWZ = 120°
3

Segment MP is a diameter of circle O.

Question illustration
A
m + 150 = 180
Option A
B
m + 150 = 360
Option B
C
m – 150 = 180
Option C
D
m – 150 = 360
Option D
4

Consider the sets below.U = {x | x is a real number}A = {x | x is an odd integer}R = {x | x = 3, 7, 11, 27}Is R ⊂ A?

A
yes, because all the elements of set A are in set R
B
yes, because all the elements of set R are in set A
C
no, because each element in set A is not represented in set R
D
no, because each element in set R is not represented in set A
5

A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent.What is the probability that a student chooses drama as an elective?

A
5 percent
B
7 percent
C
33 percent
D
37 percent
6

One exterior angle of a regular pentagon has a measure of (2x)°. What is the value of x?

A
x = 18
B
x = 20
C
x = 30
D
x = 36
7

Which three-dimensional figure has half the number of vertices as the rectangular prism?

A
hexagonal prism
B
rectangular pyramid
C
triangular prism
D
triangular pyramid
8

The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8.Why are the events not mutually exclusive?

A
The sum of P(A) and P(B) is less than P(A or B).
B
The product of P(A) and P(B) is less than P(A or B).
C
The product of P(A) and P(B) is not equal to P(A or B).
D
The sum of P(A) and P(B) is not equal to P(A or B).
9

Rectangle J K L M is shown. Diagonals are drawn from point J to point L and from point K to point M and intersect in the middle. All angles are right angles. The length of J M is 12 and the distance from M to the center point is 10.

Question illustration
A
32 units
B
44 units
C
56 units
D
64 units
10

The area of the regular octagon is 10.15 cm2.

Question illustration
A
1.27 cm
B
1.75 cm
C
2.33 cm
D
2.54 cm
11

Circle R is shown. Line segments Q R and S R are radii. The length of Q R is 18. Sector Q R S is shaded.

Question illustration
A
36
Option A
B
72
Option B
C
144
Option C
D
324
Option D
12

On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N has points (0, negative 1), (2, negative 4), and (negative 2, negative 3).

Question illustration
A
The area of △RST is 2 square units less than the area of △LMN.
B
The area of △RST is equal to the area of △LMN.
C
The area of △RST is 2 square units greater than the area of △LMN.
D
The area of △RST is 4 square units greater than the area of △LMN.
13

Which statements must be true about the two congruent, shaded figures? Select two options.

A
The figures are rectangles because they are formed inside a rectangle.
B
The figures are rhombi because they are formed by four congruent line segments.
C
The figures are trapezoids because each has exactly one pair of parallel sides.
D
The figures are parallelograms because their opposite sides are parallel.
E
The figures are quadrilaterals because each has four sides.
14

A parabola can be represented by the equation y2 = 12x.

A
y = –3
B
y = 3
C
x = –3
D
x = 3
15

Which of these shapes have rectangular cross sections when they are cut perpendicular to the base? Select three options.rectangular prismtriangular prismcylinderconesquare pyramidtriangular pyramid

A
rectangular prism
B
triangular prism
C
cylinder
D
cone
E
square pyramid
F
triangular pyramid
16

The base of a solid right pyramid is a square with an edge length of n units. The height of the pyramid is n − 1 units.

Question illustration
A
n(n − 1) units3
Option A
B
n(n − 1)2 units3
Option B
C
n2(n − 1) units3
Option C
D
n3(n − 1) units3
Option D
17

In circle N, KL ≅ ML.

Question illustration
A
66°
B
74°
C
77°
D
80°
18

Parallelogram L M N O is shown. Angle N is (5 x) degrees and angle L is (3 x + 40) degrees.

Question illustration
A
20°
B
60°
C
80°
D
100°
19

Circle Y is shown. Chords R T and S U intersect at a point. Arc S R is 55 degrees and the angle that intercepts that arc is 63 degrees.

Question illustration
A
59°
B
67°
C
71°
D
118°
20

Circle B is shown. Line segments C B, D B, and E B are radii. Angle C B E is 52 degrees and angle E B D is 160 degrees.

Question illustration
A
106°
B
108°
C
148°
D
212°

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