AnswersNC-Math 4Cumulative Exam

Cumulative Exam — Cumulative exam Answers

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Aeronautical researchers have developed three different processes to pack a parachute. They want to compare the different processes in terms of time to deploy and reliability. There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison.

A
3
B
400
C
800
D
1,200
22
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Which of the following accurately lists all of the discontinuities for the function graphed below?

Question illustration
A
jump discontinuity at x = 0; point discontinuity at x = 8
B
jump discontinuity at x = 0; point discontinuities at x = –2 and x = 8
C
jump discontinuities at x = 0 and x = 8; point discontinuity at x = –2
D
jump discontinuity at x = 0; point discontinuities at x = –2, x = 3 and x = 8
23

In triangle MNP, and units. What is the approximate length of PN?

Question illustration
A
3.8 units
B
6.5 units
C
15.3 units
D
26.1 units
24

A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study, and 100 subjects replied. They are informed that one group of 50 will receive a new cream and the remaining group of 50 will receive a cream with no active ingredient. The subjects are numbered 1–100 and these numbers are put into a random number generator. The first 50 unique numbers will represent the subjects that will receive the new cream and the remaining 50 subjects will receive the inactive cream. All subjects are exposed to poison ivy and given their cream. They are asked to return in three days and report their level of irritation. The average scores for each cream are compared.

A
Yes, the subjects will be exposed to the poison ivy.
B
Yes, the subjects are randomly assigned to each treatment.
C
No, the subjects are asked to return in three days. It is possible that some of them may not return, which will introduce bias into the results.
D
No, the subjects are randomly assigned to the two treatment groups, but the groups are not guaranteed to have 50 subjects in each.
25

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
26

What is the value of ?

Question illustration
A
3
B
5
C
15
D
25
27

A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers put an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then assigned to the group with the new cream, and 50 were assigned to the group with the cream with no active ingredient. After three days, technicians recorded the subjects’ level of irritation.

A
This experiment should be single blind. The subjects will not know which treatment they are receiving to control for the placebo effect, but the technicians need to know which group received the new cream.
B
This experiment should be double blind. Neither the subject nor the technician knows which group is receiving the new cream to control for the placebo effect, and the response measured is not affected.
C
This experiment should be single blind. The subjects know which treatment they are receiving but the technicians do not know which group received the new cream, so the response being measured is not affected.
D
This experiment should not use blinding. It is unethical for the subjects not to know which treatment they are receiving, placebo or new cream, and for the technicians not to know which group received which treatment.
28

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
29

The acceleration y, in meters per second squared, of an object after x seconds is given by y = .During the first 10 seconds, over which intervals is the acceleration increasing?

Question illustration
A
(2, 6)
B
(4, 8)
C
(0, 2) and (6, 10)
D
(0, 4) and (8, 10)
30

The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. She gets an alphabetical list of the students, and numbers them from 0001 to 1020. Then, using a random number table, and starting at a random line, she selects 100 unique numbers between 0001 and 1020. Is this a simple random sample?

A
No, because the sample could contain repeating numbers.
B
No, because the sample could contain numbers other than numbers between 0001 and 1020.
C
Yes, because each student and sample of 100 has the same chance of being selected.
D
Yes, because each student is represented by a 4-digit number from 0001 to 1020.
31

A city official would like to know if there is public support for increasing funding for arts programs. To collect data, the city official stands outside a concert hall after a show and surveys the first 20 people to exit about their opinion of raising funds for the arts. Which of the following best describes any bias that may arise from the results?

A
Because only the first 20 people were surveyed, the city official may underestimate support for raising funds.
B
Because a convenience sample was taken, the city official should have an unbiased estimate of public support.
C
Because those in the sample generally support the arts, the city official may overestimate support for raising funds.
D
Because those in the sample generally support the arts, the city official should have an unbiased estimate of public support for raising funds.
32

What is the additive inverse of the complex number –12 + 4i?

A
–12 – 4i
B
–12 + 4i
C
12 – 4i
D
12 + 4i
33

A tree is leaning at a 5° angle from vertical, making an 85° angle with the ground. When the sun is at a 65° angle of elevation, the tree casts a 25-foot shadow. What is the approximate length of the tree?

A
23 ft.
B
27 ft.
C
45 ft.
D
50 ft.
34

Ingrid claims that . Review Ingrid’s steps in verifying her claim.Which statement describes Ingrid’s claim that and her steps in verifying her claim?

Question illustration
A
Ingrid’s claim is correct, and her steps are correct.
B
Ingrid’s claim is correct, but her steps are incorrect.
C
Ingrid’s claim is incorrect, but her steps are correct.
D
Ingrid’s claim is incorrect, and her steps are incorrect.
35

Consider the function f(x) = . What transformation results in g(x)?

Question illustration
A
Translate units left and 7 units up.
Option A
B
Translate units right and 7 units up.
Option B
C
Translate units left and 7 units down.
Option C
D
Translate units right and 7 units down.
Option D
36

A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company has access to 24 different vehicles. Each vehicle will receive four tires with the new tread and four with the original tread. The position, front or back, will be randomly determined for a pair of each type of tread. For example, a vehicle will have the new type of tread on the front tires and the original tread on the back tires. After six months, the pairs of unused tires will be used with the position switched on the car. The vehicles will be driven for six more months. At the end of one year, the depths of the remaining tread will be measured for each tire and the average differences between the new and original tread types will be determined. The average differences will then be used to determine if the new tread does last longer.

A
Yes, the company used 24 different vehicles.
B
Yes, both types of tread were randomly assigned to each vehicle.
C
No, the vehicles were not put into groups of two.
D
No, the tires with the different types of tread were not randomly assigned to each vehicle.
37

A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of 10 corn plants. He labels the 100 plants 00–99. Refer to the given line from a random number table. Which numbers represent the sample of 10 corn plants?58160 09695 38399 40400 32662 46254

A
58, 16, 00, 96, 95, 38, 39, 94, 04, 00
B
58, 16, 00, 96, 95, 38, 39, 94, 04, 32
C
58, 16, 96, 95, 38, 39, 94, 04, 32, 66
D
58, 16, 09, 69, 38, 39, 40, 32, 66, 46
38

Given: < A < and , < B < What is the value of cos(A – B)?

Question illustration
A
Negative StartFraction 2 StartRoot 5 EndRoot Over 25 EndFraction
Option A
B
Negative StartFraction StartRoot 5 EndRoot Over 5 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
StartFraction 11 StartRoot 5 EndRoot Over 25 EndFraction
Option D
39

Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, 2 curves intersect at (1, 1). One curve curves up and to the right from quadrant 3 into quadrant 1. The other curve curves down from quadrant 1 into quadrant 4.
Option A
B
On a coordinate plane, 2 identical curves are shown. One curve starts at y = negative 3, and the other curve starts at y = 1.
Option B
C
On a coordinate plane, a curve and a line are shown.
Option C
D
On a coordinate plane, a curve and a cubic function are shown.
Option D
40

The relationship between voltage E, current I, and resistance Z is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 – i, what is the voltage of the circuit?

A
4 – i
B
4 + i
C
8 + i
D
8 + 7i

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