AnswersTX-Precalculus AUnit Test

Unit Test — Unit test Answers

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The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

Question illustration
A
–1.5
B
–0.5
C
1.5
D
3.6
2
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What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–6, 6
B
–4, 1, 3
C
–3, –1, 4
D
1, 3
3

What is the solution of ?

Question illustration
A
or x > 4
Option A
B
or x > 4
Option B
C
mc008-4.jpg
Option C
D
mc008-5.jpg
Option D
4

What is the solution set of ?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-4.jpg
Option C
D
mc023-5.jpg
Option D
5

The square root of a number is greater than the square of the number. For what set of numbers is this true?

A
(0, 1)
B
[0, 1]
C
[1, ꝏ)
D
(1, ꝏ)
6

The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?

Question illustration
A
8
B
9
C
19
D
80
7

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. Jessica is listening to soft music at a sound intensity level of 10-9 on her computer while she does her homework. Braylee is completing her homework while listening to very loud music at a sound intensity level of 10-3 on her headphones. How many times louder is Braylee’s music than Jessica’s?

Question illustration
A
times louder
Option A
B
3 times louder
C
30 times louder
D
90 times louder
8

What is the solution to (x – 3)3(x + 1)(x – 2) ≤ 0?

A
(–ꝏ, –1) U (2, 3)
B
(–ꝏ, –1] U [2, 3]
C
(–1, 2) U (3, ꝏ)
D
[–1, 2] U [3, ꝏ)
9

A colony of bacteria has 10,000 bacteria and is growing exponentially. The inequality 10,000(4x) ≥ 320,000 represents the hours, x, for which the colony will have at least 320,000 bacteria.Which interval represents the hours when the colony will have at least 320,000 bacteria?

A
[2.5, ∞)
B
[3, ∞)
C
[32, ∞)
D
[0, 2.5]
10

Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

Question illustration
A
–3, –2, 3
B
–3, 2
C
18, 32
D
18, 32, 66
11

An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?

A
3.3 years
B
5.0 years
C
5.6 years
D
6.6 years
12

What is the correct form of the partial fraction decomposition for ?

Question illustration
A
StartFraction A Over x + 2 EndFraction + StartFraction B Over (x + 2) squared EndFraction
B
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over (x + 2) squared EndFraction
C
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C Over (x + 2) squared EndFraction
D
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C x + D Over (x + 2) squared EndFraction
13

What is the least integer value in the solution set to log3(8x – 37) > 5?

A
34
B
35
C
36
D
37
14

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A
Makayla invests her money 1 year longer.
B
Makayla invests her money 2 years longer.
C
Calvin invests his money 1 year longer.
D
Calvin invests his money 2 years longer.
15

What is the partial fraction decomposition of ?

Question illustration
A
StartFraction 1 Over 3 x EndFraction + StartFraction x minus 2 Over 4 x squared + 9 EndFraction
B
StartFraction 1 Over 3 x EndFraction + StartFraction x + 2 Over 4 x squared + 9 EndFraction
C
StartFraction negative 2 Over 3 x EndFraction + StartFraction x minus 1 Over 4 x squared + 9 EndFraction
D
StartFraction negative 2 Over 3 x EndFraction + StartFraction x + 1 Over 4 x squared + 9 EndFraction
16

Which expression is equivalent to ?

Question illustration
A
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)
Option A
B
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline StartFraction x cubed Over 2 EndFraction minus 5 log Subscript 12 Baseline 1
Option B
C
log Subscript 12 Baseline 4 x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x) + 1
Option C
D
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)
Option D
17

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. What is the approximate loudness of a rock concert with a sound intensity of 10–1?

Question illustration
A
2 Db
B
22 Db
C
60 Db
D
110 Db
18

What is the solution of ?

Question illustration
A
mc012-2.jpg
Option A
B
mc012-3.jpg
Option B
C
mc012-4.jpg
Option C
D
mc012-5.jpg
Option D
19

What is the solution of log2 (3x - 7) = 3?

A
One-third
Option A
B
4
C
5
D
Sixteen-thirds
Option D
20

A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

A
2.5 days
B
5.0 days
C
46.6 days
D
66.7 days

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