Answers26.27 TCEC ALGEBRA 2.1Expected Value

Expected Value — Cumulative exam Answers

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102
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What is the following product?

Question illustration
A
–2
B
2
C
22 –
Option C
D
98 –
Option D
103
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Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction (y + 1) (y minus 1) Over y squared EndFraction
Option A
B
StartFraction y + 1 Over y minus 1 EndFraction
Option B
C
StartFraction y minus 1 Over y + 1 EndFraction
Option C
D
StartFraction y squared Over (y + 1) (y minus 1) EndFraction
Option D
104

64, –48, 36, –27, ...

A
f(x + 1) = f(x)
Option A
B
f(x + 1) = f(x)
Option B
C
f(x) = f(x + 1)
Option C
D
f(x) = f(x + 1)
Option D
105

What is the domain of the square root function graphed below?

Question illustration
A
x greater-than-or-equal-to negative 4
Option A
B
x greater-than negative 4
Option B
C
x greater-than-or-equal-to 0
Option C
D
x greater-than 0
Option D
106

The graph below shows the function .Which statement is true?

Question illustration
A
There is a hole at x = 3 and an asymptote at x = –1.
B
There is an asymptote at x = –1 and no hole.
C
There is a hole at x = 3 and no asymptote.
D
There is an asymptote at x = 3 and a hole at x = –1.
107

What is written as a single logarithm?

Question illustration
A
log Subscript 2 Baseline left-bracket StartFraction x cubed Over (StartFraction 3 Over x + 4 EndFraction) EndFraction Right-bracket
Option A
B
log Subscript 2 Baseline (StartFraction 3 x cubed Over x + 4 EndFraction)
Option B
C
log Subscript 2 Baseline left-bracket (StartStartFraction x cubed Over 3 EndFraction) Over x + 4 EndEndFraction Right-bracket
Option C
D
log Subscript 2 Baseline (StartFraction x cubed Over 3 + (x + 4) EndFraction)
Option D
108

The function that represents the average cost per person, including transportation, to a museum is . Which statement is true about the graph of the function?

Question illustration
A
The horizontal asymptote y = 0 means the cost approaches zero as the number of people increases.
B
The horizontal asymptote y = 8 means the average cost approaches $8 as the number of people increases.
C
The vertical asymptote x = 0 means the cost approaches zero as the number of people increases.
D
The vertical asymptote x = 8 means the cost approaches zero as the number of people increases.
109

The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the Sierpinski triangle has three shaded triangles. The third figure of the Sierpinski triangle has nine shaded triangles. Which summation represents the total number of shaded triangles in the first 15 figures?

A
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 1 (3) Superscript n minus 1
Option A
B
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 3 (1) Superscript n minus 1
Option B
C
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 1 (one-third) Superscript n minus 1
Option C
D
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts one-third (1) Superscript n minus 1
Option D
110

What is the value of ?

Question illustration
A
–4.00
B
–0.25
C
1.51
D
2.41
111

By what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3?M = the magnitude of an earthquakeI = the intensity of an earthquakeI0 = the smallest seismic activity that can be measured, which is 1

Question illustration
A
1.01
B
1.21
C
1.26
D
10.44
112

Which equation is the inverse of y = x2 + 16?

A
y = x2 – 16
B
y = plus-or-minus StartRoot x EndRoot minus 16
Option B
C
y = plus-or-minus StartRoot x minus 16 EndRoot
Option C
D
y = x2 – 4
113

What is the solution of ?

Question illustration
A
–8
B
–6
C
8
D
9
114

Which of the following is the inverse of ?

Question illustration
A
y = log Subscript one-twelfth Baseline x
Option A
B
y = log Subscript 12 Baseline StartFraction 1 Over x EndFraction
Option B
C
y = log Subscript x Baseline 12
Option C
D
y = log Subscript 12 Baseline x
Option D
115

What is the product? Assume

Question illustration
A
3 x StartRoot 5 EndRoot + 3 StartRoot 165 x EndRoot + 10 StartRoot 6 EndRoot
Option A
B
3 x StartRoot 5 EndRoot + 6 StartRoot 10 x EndRoot + 5 StartRoot 3 x EndRoot + 10 StartRoot 6 EndRoot
Option B
C
3 x StartRoot 5 EndRoot + 10 StartRoot 6 EndRoot
Option C
D
StartRoot 3 x EndRoot + 5 StartRoot 3 x EndRoot + 10 StartRoot 6 EndRoot
Option D
116

The table below shows the number of days, y, needed to complete a project as a function of the number of full-time staff, x, working on the project. Which rational function best models the data in the table?People Working, xDays, y36218489612

A
mc019-1.jpg
Option A
B
mc019-2.jpg
Option B
C
mc019-3.jpg
Option C
D
mc019-4.jpg
Option D
117

Two students created a game of dice. They determined that each roll would add the value of the die if it was an odd number. If the roll was even, it would subtract the value of the die. (For example, a roll of 2 would subtract two points, but a roll of 3 would add three points.) What is the expected value for this game?

A
–3
B
–0.5
C
0
D
0.5
118

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

Question illustration
A
1.5 days
B
2.5 days
C
9.4 days
D
21.1 days
119

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 3 and 4.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 3, 4, and 1.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 4 and 1.
Option D
120

What is the solution of ?

Question illustration
A
c = 0 and c = 3
B
all real numbers
C
all real numbers, except c ¹ 0 and c ¹ 3
D
no solution
121

Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research. Ant Colony Growth: Bee Hive Growth: Which insect population is growing at a faster rate?

Question illustration
A
The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week.
B
The bee hive is growing at a faster rate. It will multiply by 3.8 each week while the ant colony will add 3.8 each week.
C
The ant colony is growing at a faster rate. It will add 3.8 each week while the bee hive will subtract 3.8 each week.
D
The bee hive is growing at a faster rate. It will add 3.8 each week while the ant colony will divide by 3.8 each week.

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