All practice questions

Question 4521Question →

A laboratory mixture is prepared by combining three liquid solutions: Solution X, Solution Y, and Solution Z. Initially, Solution X makes up $20\%$ of the total volume of the mixture. Solution Y's volume is $\frac{1}{3}$ of the combined volume of Solution X and Solution Z, and Solution Z makes up the remaining portion of the mixture. If $3.0$ liters of Solution Z are added to the mixture, Solution Z then constitutes exactly $58\%$ of the new total volume. What was the original total volume, in liters, of the mixture before Solution Z was added?

15

24

35

42

100

Show answer & explanation

Answer: 42

Answer

The original total volume of the mixture was 42 liters.

The correct option represents the original volume of

42

liters. Setting the original total volume to

V

, we find that Solution X is

0.20V

. Since Solution Y is one-third of the combined volume of X and Z, we write

Y = \frac{1}{3}(V - Y)

, which simplifies to

Y = 0.25V

. The remaining portion, Solution Z, must be

V - 0.20V - 0.25V = 0.55V

. Adding

3.0

liters of Solution Z increases both the volume of Solution Z and the total volume of the mixture, yielding the proportion

(0.55V + 3) / (V + 3) = 0.58

. Solving this linear equation results in

0.03V = 1.26

, which gives

V = 42

.

Step-by-Step Solution

1

Express the initial fraction of Solution X as a decimal.

Solution X makes up

0.20

of the total volume.

Converting

20\%

to a decimal simplifies subsequent algebraic modeling.

2

Set up an equation for the fraction of Solution Y in terms of the total volume

V

.

Solution Y makes up

0.25

of the total volume.

If Solution Y's volume is

\frac{1}{3}

of the combined volume of Solution X and Solution Z, then

Y = \frac{1}{3}(V - Y)

. Multiplying by

3

gives

3Y = V - Y

, which simplifies to

4Y = V

, or

Y = 0.25V

.

3

Determine the initial fraction of Solution Z in the mixture.

Solution Z initially makes up

0.55

of the total volume.

Subtracting the fractions of Solution X and Solution Y from the whole yields

1 - 0.20 - 0.25 = 0.55

.

4

Set up and solve the equation representing the addition of Solution Z.

V = 42

liters

Adding

3.0

liters of Solution Z increases the volume of Solution Z to

0.55V + 3

and the total volume to

V + 3

. The equation is

\frac{0.55V + 3}{V + 3} = 0.58

. Multiplying both sides by

V + 3

yields

0.55V + 3 = 0.58(V + 3) \implies 0.55V + 3 = 0.58V + 1.74

. Rearranging terms gives

3 - 1.74 = 0.58V - 0.55V \implies 1.26 = 0.03V \implies V = 42

.

Key Concept

Solving multi-step mixture word problems using equations involving fractions, decimals, and percentages.

Alternative Method

Instead of variables for the total volume, solve the problem by tracking parts. Initially, the mixture consists of

20\%

Solution X,

25\%

Solution Y, and

55\%

Solution Z. The ratio of the volume of Solution Z to the combined volume of Solution X and Solution Y is

55 : 45

, which simplifies to

11 : 9

. Let the volume of X and Y combined be

9x

liters, and the initial volume of Z be

11x

liters, making the initial total volume

20x

liters. Adding

3.0

liters of Solution Z does not change the combined volume of X and Y (

9x

liters). In the new mixture, Solution Z constitutes

58\%

, meaning the combined volume of X and Y must constitute

100\% - 58\% = 42\%

of the new mixture. Thus, the new total volume is

9x / 0.42 = 150x / 7

liters. The difference between the new and original total volumes is the

3.0

liters added:

(150x / 7) - 20x = 3 \implies 10x / 7 = 3 \implies x = 2.1

. The original total volume was

20x = 20(2.1) = 42

liters.

Estimated Time:3m 0s

Question 4522Question →

### Models of Yellowstone Volcanism

Yellowstone National Park is characterized by intense geothermal activity and a history of supervolcanic eruptions. The Yellowstone volcanic system has produced a southwest-to-northeast track of progressively younger volcanic calderas over the past $16.5$ million years. Geologists debate the primary mechanism driving this volcanism.

Model 1 (Plume Hypothesis)
Yellowstone volcanism is driven by a deep mantle plume—a narrow column of hot, buoyant rock rising from the core-mantle boundary (approximately $2{}900\text{ km}$ deep). This plume remains relatively stationary relative to the deep mantle. As the North American plate moves southwestward over this stationary plume at a rate of $2.3\text{ cm/year}$ , decompression melting at the plume head generates magma that periodically erupts, leaving a path of calderas. The primary source of heat is primordial thermal energy from the Earth's core.

Model 2 (Lithospheric Extension Hypothesis)
Yellowstone volcanism is driven by shallow, upper-mantle processes and plate tectonics, not a deep plume. As the North American plate stretches and undergoes lithospheric extension due to tectonic forces, pre-existing crustal fault zones and shear lines fracture. This fracturing allows pre-existing, ambient magma in the upper mantle (at depths less than $200\text{ km}$ ) to escape to the surface. The age progression of the calderas is due to the sequential reactivations of these fault systems as stress propagates through the plate, rather than a stationary heat source. The primary source of heat is local radioactive decay and shear heating within the upper mantle.

Match each scientific claim or description below to the model(s) that support or include it.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Proposes that the volcanic heat source originates from the core-mantle boundary matches Model 1 only; Proposes that caldera age progression is driven by tectonic stress propagating through crustal faults matches Model 2 only; Attempts to explain the linear progression of progressively younger calderas matches Both Model 1 and Model 2; Proposes that the magma is generated by an asteroid impact matches Neither Model 1 nor Model 2.

The claims are correctly matched based on the mechanisms and sources described in the passage: Model 1 features a core-mantle boundary heat source; Model 2 features fault reactivation from tectonic stress; both models attempt to explain the caldera age progression; and neither model suggests an asteroid impact.

Step-by-Step Solution

1

Analyze Model 1's claims regarding heat source and caldera progression.

Model 1 posits a deep core-mantle boundary plume source (~2900 km deep) and plate motion over a stationary heat source to explain caldera progression.

To identify which features are unique to Model 1.

2

Analyze Model 2's claims regarding heat source and caldera progression.

Model 2 posits a shallow upper-mantle heat source (<200 km deep) from local decay/shear, and fault reactivation propagation to explain caldera progression.

To identify which features are unique to Model 2.

3

Identify the common goals and external features mentioned in both models, and any claims absent from both.

Both models address the Yellowstone age progression track. Neither model mentions asteroid impacts, which is an external hypothesis not supported by either text.

To determine the matches for 'Both' and 'Neither' categories.

Key Concept

Comparing and Contrasting Scientific Models

Estimated Time:1m 30s

Question 4523Question →

### The Younger Dryas Cooling

The Younger Dryas was a period of abrupt cooling that occurred approximately $12,900$ years ago, temporarily reversing the warming trend after the last glacial maximum. Scientists debate the primary trigger of this event.

Hypothesis 1
Around $12,900$ years ago, a large cometary body fragmented and collided with Earth's atmosphere. This extraterrestrial impact caused widespread wildfires, rapid thermal shocks, and the sudden melting of large portions of the Laurentide Ice Sheet. The massive influx of freshwater into the North Atlantic Ocean reduced the salinity of the surface water. This dilution prevented the sinking of cold, dense water, shutting down the Atlantic Meridional Overturning Circulation (AMOC) and triggering global cooling.

Hypothesis 2
The cooling was initiated solely by terrestrial hydrological shifts, without any extraterrestrial influence. As the Laurentide Ice Sheet naturally retreated due to gradual solar warming, a massive ice dam holding back Lake Agassiz collapsed. This burst released an immense volume of freshwater directly into the Arctic Ocean and North Atlantic Ocean. The sudden decrease in ocean salinity disrupted the thermohaline circulation (AMOC), causing the rapid onset of the Younger Dryas cooling.

Hypothesis 3
The primary trigger was a period of intense volcanic activity. Multiple large-scale volcanic eruptions injected high volumes of sulfur dioxide ( $\text{SO}_2$ ) gas into the stratosphere. These gases reacted with water vapor to form highly reflective sulfate aerosols, which blocked incoming solar radiation and cooled the Northern Hemisphere. This atmospheric cooling led to increased sea ice extent, which secondarily altered ocean circulation currents like the AMOC, sustaining the cold period.

According to Hypothesis 2, the freshwater influx that disrupted the AMOC was directly caused by which of the following events?

The sudden melting of the Laurentide Ice Sheet caused by the thermal shock of a cometary impact

The collapse of an ice dam holding back a large freshwater lake during natural glacial retreat

A sequence of massive volcanic eruptions injecting sulfur dioxide gas into the stratosphere

A gradual, natural decrease in solar radiation that directly cooled the Atlantic Ocean

Show answer & explanation

Answer: The collapse of an ice dam holding back a large freshwater lake during natural glacial retreat

Answer

The collapse of an ice dam holding back a large freshwater lake during natural glacial retreat

According to Hypothesis 2, the Younger Dryas cooling was triggered by natural glacial retreat causing the collapse of an ice dam holding back Lake Agassiz, which released massive volumes of freshwater into the oceans and disrupted the AMOC. This is a purely terrestrial hydrological explanation.

Step-by-Step Solution

1

Locate the portion of the passage describing Hypothesis 2.

Hypothesis 2 attributes Younger Dryas cooling to terrestrial hydrological shifts, specifically the retreat of the Laurentide Ice Sheet and the collapse of an ice dam holding back Lake Agassiz.

To identify the core mechanism proposed by the target hypothesis.

2

Compare the mechanisms described in the options with the core claims of Hypothesis 2.

The collapse of the ice dam matches the description in Hypothesis 2. The other options describe mechanisms from Hypothesis 1 (cometary impact) and Hypothesis 3 (volcanic sulfur dioxide).

To determine which option accurately represents the trigger identified in Hypothesis 2 and rule out distractors.

Key Concept

Identifying the central claim and causal mechanism of a specific scientific hypothesis.

Question 4524Question →

Read the passage below about marine conservation. Choose the word that most precisely and clearly fits the blank to maintain the formal, academic register of the passage.

Fill in the blanks below

To protect vulnerable coral reefs from the damaging effects of tourism, marine biologists have established several artificial sanctuaries. By sinking decommissioned ships and concrete structures, conservationists hope to new marine life to the area, providing alternative diving sites that relieve ecological pressure on natural reefs.

Show answer & explanation

Answer

attract (or draw)

The word 'attract' is the most precise and contextually appropriate choice because it scientifically and neutrally describes the process of drawing marine life to a new habitat. It maintains the formal, academic register of the passage.

Step-by-Step Solution

1

Analyze the context of the sentence containing the blank to determine the required meaning and tone.

The sentence discusses conservationists using artificial structures to bring marine organisms to a new habitat.

Understanding the context helps narrow down the semantic field of the missing word.

2

Evaluate candidate words for precision, clarity, and register.

Words like 'invite' are too informal and personify marine life, while 'lure' carries a connotation of deception that does not fit a scientific conservation context. The word 'attract' precisely describes the natural process of organisms migrating to a new habitat due to favorable conditions.

Ensuring the chosen word matches the academic and formal tone of the passage is key to word precision.

Key Concept

Word Precision and Clarity

Question 4525Question →

While restoring the ancient Roman fresco, the delicate colors of the mural were carefully preserved by the conservator using organic solvents.

Which choice most clearly and logically corrects the underlined portion of the sentence?

the delicate colors of the mural were carefully preserved by the conservator using organic solvents.

organic solvents were used by the conservator to carefully preserve the delicate colors of the mural.

the conservator carefully preserved the mural's delicate colors using organic solvents.

the conservator, who carefully preserved the mural's delicate colors using organic solvents.

Show answer & explanation

Answer: the conservator carefully preserved the mural's delicate colors using organic solvents.

Answer

the conservator carefully preserved the mural's delicate colors using organic solvents.

The correct option resolves the dangling modifier by placing the logical subject, 'the conservator', directly after the introductory clause. This makes it clear who was restoring the fresco, and the rest of the sentence is a complete independent clause in the active voice.

Step-by-Step Solution

1

Identify the subject of the introductory phrase.

The introductory phrase 'While restoring the ancient Roman fresco' describes an action that requires a person to perform it.

To avoid a dangling modifier, the noun immediately following the comma must be the logical subject of that introductory action.

2

Evaluate the options to find one that places the logical subject immediately after the introductory phrase while forming a complete sentence.

The option beginning with 'the conservator' and ending with a complete predicate corrects the modifier error and avoids creating a fragment.

Placing 'the conservator' as the subject of the main clause makes the sentence grammatically logical, and avoiding relative clauses like 'who...' prevents a sentence fragment.

Key Concept

Misplaced and Dangling Modifiers

Estimated Time:1m 0s

Question 4526Question →

A landscaping company uses a grass seed mixture containing perennial ryegrass and Kentucky bluegrass in a ratio of $5:3$ by weight. If a bag of this mixture contains $15$ pounds of Kentucky bluegrass, how many pounds of perennial ryegrass does it contain?

9

24

25

40

75

Show answer & explanation

Answer: 25

Answer

25

The ratio of perennial ryegrass to Kentucky bluegrass is

5:3

, which means for every

5

pounds of ryegrass, there are

3

pounds of bluegrass. Setting up the proportion

\frac{5}{3} = \frac{x}{15}

and solving for

x

gives

3x = 75

, which simplifies to

x = 25

pounds of perennial ryegrass.

Step-by-Step Solution

1

Set up a proportion using the ratio of perennial ryegrass to Kentucky bluegrass.

\frac{5}{3} = \frac{x}{15}

, where

x

represents the weight of perennial ryegrass.

The ratio of perennial ryegrass to Kentucky bluegrass by weight is

5:3

, and the actual weight of Kentucky bluegrass is

15

pounds.

2

Solve the proportion for

x

by cross-multiplying.

3x = 5 \times 15 \implies 3x = 75

Cross-multiplication allows us to clear the denominators to solve for the unknown value.

3

Divide both sides of the equation by

3

.

x = 25

Isolating

x

gives the weight of perennial ryegrass in pounds.

Key Concept

Solving proportions based on a given part-to-part ratio

Alternative Method

Identify the scaling factor: since the ratio of Kentucky bluegrass is

3

parts and the actual weight is

15

pounds, each part of the ratio represents

15 \div 3 = 5

pounds. Multiplying the

5

parts of perennial ryegrass by this factor of

5

gives

5 \times 5 = 25

pounds.

Estimated Time:45s

Question 4527Question →

The museum curator wanted to display the rare, delicate artifacts that were recovered from the shipwreck, she carefully arranged them in a temperature-controlled case.

Which choice best punctuates the underlined portion of the sentence?

NO CHANGE

rare, delicate artifacts that were recovered from the shipwreck; she

rare, delicate artifacts, that were recovered from the shipwreck; she

rare, delicate artifacts that were recovered from the shipwreck; she, who

Show answer & explanation

Answer: rare, delicate artifacts that were recovered from the shipwreck; she

Answer

The correct option correctly punctuates the coordinate adjectives, avoids inserting a comma before the restrictive clause, and uses a semicolon to separate the two independent clauses.

The correct option correctly punctuates 'rare, delicate' as coordinate adjectives, does not place a comma before the restrictive 'that' clause, and uses a semicolon to separate the two independent clauses, avoiding a comma splice.

Step-by-Step Solution

1

Determine if the adjectives 'rare' and 'delicate' are coordinate.

The adjectives can be reversed ('delicate, rare') and joined with 'and' ('rare and delicate') naturally, meaning they are coordinate and require a comma between them.

Coordinate adjectives modify a noun in parallel and must be separated by a comma.

2

Analyze the relative clause 'that were recovered from the shipwreck' for punctuation.

The clause is restrictive because it defines the specific artifacts being referenced.

Restrictive clauses are essential to sentence meaning and should not be set off by commas.

3

Evaluate the boundary between the two independent clauses 'The museum curator wanted to display...' and 'she carefully arranged...'.

Both clauses can stand alone, meaning they must be separated by appropriate punctuation such as a semicolon rather than just a comma.

Using only a comma to connect two independent clauses results in a comma splice.

Key Concept

Punctuation rules for coordinate adjectives, restrictive clauses, and independent clause boundaries.

Question 4528Question →

Because geodesic domes are constructed from a network of triangles, they distribute stress evenly throughout the structure, which is why they can support heavy loads and weights.

Which choice is the most effective and concise revision of the underlined portion of the sentence?

which is why they can support heavy loads and weights

allowing them to support heavy loads

they can support heavy loads, this makes them strong

supporting heavy loads. Which makes them durable.

Show answer & explanation

Answer: allowing them to support heavy loads

Answer

The choice that reads 'allowing them to support heavy loads' is correct because it eliminates the redundant synonym 'and weights' and is grammatically correct.

The correct choice is the option that reads 'allowing them to support heavy loads', which removes the redundant synonym 'and weights' to make the sentence concise and grammatically correct.

Step-by-Step Solution

1

Identify the redundant information in the underlined portion of the sentence.

The words 'loads' and 'weights' are synonyms that repeat the same concept of carrying capacity.

Redundant phrasing should be eliminated to make the writing concise and clear.

2

Evaluate the options for conciseness, grammatical correctness, and sentence structure.

The option using the participle 'allowing' provides a concise, grammatically correct structure without repeating synonyms, while other options introduce grammatical errors like comma splices or fragments.

The correct choice on the ACT English section must be both grammatically correct and free of unnecessary redundancy.

Key Concept

Eliminating Redundancy

Estimated Time:1m 0s

Question 4529Question →

The following passage is about the nineteenth-century paleontologist Mary Anning. Read the passage and write the correct form of the verb 'unearth' in the blank to maintain a consistent verb tense throughout the text.

Fill in the blanks below

During the early nineteenth century, Mary Anning combed the cliffs of Lyme Regis in England, searching for prehistoric remains to sell to collectors. In 1811, her brother Joseph discovered a four-foot-long skull embedded in the shale, and a few months later, Anning herself the rest of the fossilized skeleton.

Show answer & explanation

Answer

unearthed

The verb must be in the simple past tense ('unearthed') to match the surrounding verbs in the passage, such as 'combed' and 'discovered'. This maintains the consistent past-tense narrative of the historical event.

Step-by-Step Solution

1

Analyze the temporal context of the passage by identifying the tenses of the surrounding verbs.

The verbs 'combed' and 'discovered' are in the simple past tense, indicating that the events described occurred in the past.

Establishing the dominant tense of the passage is necessary to maintain consistency.

2

Determine the correct tense for the verb in the blank based on this context.

Since Anning's action of finding the skeleton happened at the same time in the past as her brother's discovery, the verb must also be in the simple past tense.

A shift to a different tense (like present or future) would create an illogical timeline.

3

Conjugate the base verb 'unearth' into the simple past tense.

The simple past tense of 'unearth' is 'unearthed'.

This is the standard regular past-tense conjugation for this verb.

Key Concept

Verb Tense and Consistency

Question 4530Question →

Before the spacecraft launched into orbit, engineers conducted several safety tests on the primary booster rockets.

Which choice is the best version of the underlined portion of the sentence?

NO CHANGE

orbit; engineers

orbit. Engineers

orbit, and engineers

Show answer & explanation

Answer: NO CHANGE

Answer

The correct choice is the original phrasing, which uses a comma to properly separate the introductory dependent clause from the main independent clause.

The sentence begins with the dependent clause 'Before the spacecraft launched into orbit,' which functions as an introductory adverbial clause. According to standard punctuation rules, an introductory dependent clause must be followed by a comma when it precedes the independent main clause. The original sentence correctly applies this rule.

Step-by-Step Solution

1

Identify the boundary of the introductory clause in the sentence.

The clause 'Before the spacecraft launched into orbit' is an introductory dependent clause because it begins with the subordinating conjunction 'Before'.

Determining clause types is necessary to apply correct punctuation rules.

2

Evaluate the punctuation needed to connect the introductory dependent clause to the main independent clause.

A comma is required immediately after the introductory clause to transition to the main subject and verb ('engineers conducted').

Introductory dependent clauses must be followed by a comma when they precede the main clause.

3

Assess the options to find the correct punctuation mark.

The original punctuation (comma) is correct, while semicolons, periods, or coordinating conjunctions create fragment errors.

Choosing the option that preserves grammatical correctness.

Key Concept

Introductory dependent clauses must be followed by a comma when they precede the main independent clause.

Question 4531Question →

A positive integer $n$ is a multiple of $7$ , and the greatest common factor of $n$ and $120$ is $15$ . Which of the following is a possible value for $n$ ?

75

105

120

210

420

Show answer & explanation

Answer: 105

Answer

105

The correct answer is 105. Since the greatest common factor of

n

and 120 is 15,

n

must be a multiple of 15. We are also given that

n

is a multiple of 7. Since 7 and 15 share no common factors other than 1,

n

must be a multiple of

7 \times 15 = 105

. Let

n = 105k

for some positive integer

k

. We must ensure that the greatest common factor of

105k

and 120 is exactly 15. Since

\text{GCF}(105k, 120) = 15 \times \text{GCF}(7k, 8)

, we require

\text{GCF}(7k, 8) = 1

, which means

k

must be an odd integer. Choosing the smallest positive odd integer

k = 1

yields

n = 105

, which is a possible value.

Step-by-Step Solution

1

Analyze the prime factorization of 120 and the greatest common factor requirement.

Since the greatest common factor (

\text{GCF}

) of

n

and 120 is 15,

n

must be divisible by 15. The prime factorization of 120 is

2^3 \times 3 \times 5

, and

15 = 3 \times 5

. Therefore,

n

must contain the prime factors 3 and 5, but cannot contain any powers of 2.

To establish which prime factors

n

must and must not have to satisfy the GCF condition.

2

Combine the GCF divisibility condition with the multiple of 7 constraint.

Since

n

is a multiple of 7 and also a multiple of 15, and because 7 and 15 are coprime (they share no common prime factors),

n

must be a multiple of

7 \times 15 = 105

. Let

n = 105k

for some positive integer

k

.

To find the general form of

n

by finding the least common multiple of the required factor components.

3

Test the constraints on

k

to identify valid values for

n

.

We need

\text{GCF}(105k, 120) = 15

. This can be written as

\text{GCF}(15 \times 7k, 15 \times 8) = 15 \times \text{GCF}(7k, 8) = 15

, which requires

\text{GCF}(7k, 8) = 1

. Since 7 and 8 are coprime,

k

must not share any common factors with 8 (i.e.,

k

must be odd). The smallest positive odd integer is

k = 1

, which gives

n = 105

.

To determine the valid values of

n

and check them against the options.

Key Concept

Using prime factorizations to determine greatest common factors under multiple divisibility constraints.

Estimated Time:1m 0s

Question 4532Question →

A positive integer $K$ is a multiple of $10$ and has exactly $8$ positive factors (including $1$ and $K$ ). What is the least possible value of $K$ ?

Show answer & explanation

Answer: 30

Answer

The least possible value of

K

is

30

.

The correct answer is

30

because it is the smallest multiple of

10

that has exactly

8

positive factors (

1, 2, 3, 5, 6, 10, 15,

and

30

).

Step-by-Step Solution

1

Determine the prime factors required for a multiple of

10

.

K

must have at least one factor of

2

and at least one factor of

5

.

Since

10 = 2 \times 5

, any multiple of

10

must be divisible by both

2

and

5

.

2

Set up the factor counting formula.

The number of factors is

(a+1)(b+1)(c+1)\cdots = 8

, where

a, b, c, \dots

are the exponents of the prime factorization.

The number of positive divisors of

p_1^a p_2^b \cdots

is found by adding

1

to each exponent and multiplying the results.

3

Evaluate the smallest multiples of

10

to find the first one with exactly

8

factors.

10

has

4

factors (

1, 2, 5, 10

);

20

has

6

factors (

1, 2, 4, 5, 10, 20

);

30

has

8

factors (

1, 2, 3, 5, 6, 10, 15, 30

).

Testing the positive multiples of

10

in ascending order ensures that the first number with exactly

8

factors is the smallest possible value.

Key Concept

Factors, Multiples, and Prime Factorization

Question 4533Question →

Arrange the following numbers in order from least to greatest: $\frac{2}{5}$ , $0.38$ , $45\%$ , and $0.42$ .

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order of the values from least to greatest is

0.38

,

\frac{2}{5}

,

0.42

, and

45\%

.

Converting all numbers to decimals allows for direct comparison:

0.38

remains

0.38

; the fraction

\frac{2}{5}

equals

0.40

;

0.42

remains

0.42

; and

45\%

equals

0.45

. Comparing these decimal values, we get

0.38 < 0.40 < 0.42 < 0.45

. Therefore, the correct order from least to greatest is

0.38

,

\frac{2}{5}

,

0.42

, and

45\%

.

Step-by-Step Solution

1

Convert the fraction to a decimal.

\frac{2}{5} = 0.40

Converting all values to decimals makes them easier to compare.

2

Convert the percentage to a decimal.

45\% = 0.45

Percentages represent values out of 100, so

45\% = \frac{45}{100} = 0.45

.

3

Compare the four decimal numbers.

0.38 < 0.40 < 0.42 < 0.45

By comparing the tenths and hundredths place, we find the correct order from smallest to largest.

Key Concept

Comparing and ordering fractions, decimals, and percents by converting them to a common decimal format.

Question 4534Question →

When oceanographers first discovered hydrothermal vents in 1977, they were astounded by the thriving ecosystems surrounding these volcanic fissures. Located miles below the ocean surface, where sunlight cannot penetrate, these vents host unique organisms that rely on chemosynthesis rather than photosynthesis. To study these deep-sea communities, researchers must deploy sophisticated submersibles capable of withstanding the immense pressure of the abyss. This advanced equipment allows scientists to gather heaps of data about how life persists in such extreme environments.

Which choice best maintains the established style and tone of the passage?

gather heaps of data

amass a grandiose plenitude of empirical details

glean data in association to

collect essential data

Show answer & explanation

Answer: collect essential data

Answer

collect essential data

The correct choice, which uses the phrase 'collect essential data,' maintains a clear, professional, and objective scientific tone that aligns with the academic vocabulary and style of the surrounding text.

Step-by-Step Solution

1

Analyze the established tone of the passage.

The passage uses formal, scientific, and objective vocabulary such as 'hydrothermal vents,' 'chemosynthesis,' and 'submersibles,' establishing an academic tone.

Understanding the context's tone helps filter out options that are either too informal or excessively flowery.

2

Evaluate the underlined phrase and the options against this established tone.

The original phrase is too informal. One option is overly dramatic and wordy, and another contains a prepositional idiom error. The option containing 'collect essential data' fits perfectly without being too casual or unnecessarily ornate.

This identifies the single choice that maintains consistency in tone and follows standard English grammar conventions.

Key Concept

Tone Consistency

Estimated Time:1m 0s

Question 4535Question →

Many urban planners are championing vertical farming as a sustainable method to produce fresh vegetables in crowded cities. Because these farms stack crops in vertical layers inside controlled environments, they save vast amounts of water and land. Furthermore, they eliminate the need for long-distance shipping, they can operate year-round regardless of weather conditions. This localized production significantly reduces carbon emissions associated with transporting food.

Which of the following options is the most grammatically correct replacement for the underlined portion?

NO CHANGE

shipping; they can

shipping; because they can

shipping. Since they can

Show answer & explanation

Answer: shipping; they can

Answer

shipping; they can

The correct option correctly uses a semicolon to separate two independent clauses ('Furthermore, they eliminate the need for long-distance shipping' and 'they can operate year-round regardless of weather conditions'). Since both clauses can stand alone as complete sentences, a semicolon is a grammatically correct punctuation mark to join them.

Step-by-Step Solution

1

Analyze the clauses on both sides of the underlined portion to determine their grammatical structure.

The clause before the underlined portion ('Furthermore, they eliminate the need for long-distance shipping') and the clause after it ('they can operate year-round regardless of weather conditions') are both independent clauses.

Identifying clause independence helps determine whether punctuation or a conjunction is needed to join them.

2

Evaluate the choices to find a punctuation mark or conjunction that joins the two independent clauses without creating a comma splice or fragment.

A semicolon is the correct punctuation mark to join two independent clauses without a coordinating conjunction.

This resolves the comma splice error of the original sentence without creating any new errors.

Key Concept

Identifying and correcting comma splices and run-on sentences using appropriate punctuation such as semicolons, periods, or coordinating conjunctions.

Question 4536Question →

A scientist monitors the temperature in three different chambers, $A$ , $B$ , and $C$ . The temperature in Chamber $B$ is $T^\circ\text{C}$ . The temperature in Chamber $A$ is always $5^\circ\text{C}$ colder than the temperature in Chamber $B$ , and the temperature in Chamber $C$ is always $9^\circ\text{C}$ warmer than the temperature in Chamber $B$ . If $T$ must be an integer, and the sum of the absolute values of the temperatures in all three chambers is minimized, what is the value of $T$ ?

-9

-1

0

2

5

Show answer & explanation

Answer: 0

Answer

The correct answer is

0

.

The correct answer is the value

0

. The sum of the absolute values of the temperatures in all three chambers is represented by the function

S(T) = |T - 5| + |T| + |T + 9|

. Geometrically, this sum represents the total distance from a point

T

to the coordinates

5

,

0

, and

-9

on a number line. For any set of points, the sum of absolute differences is minimized at their median. The median of the set

\{-9, 0, 5\}

is

0

. Evaluating the sum at

T = 0

yields

|0 - 5| + |0| + |0 + 9| = 5 + 0 + 9 = 14

. Any other integer choice yields a larger sum (for example, a value of

1

or

-1

yields a sum of

15

).

Step-by-Step Solution

1

Write expressions for the temperatures of the three chambers in terms of

T

.

The temperature in Chamber

A

is

T - 5

, in Chamber

B

is

T

, and in Chamber

C

is

T + 9

.

To represent the temperature of each chamber relative to Chamber

B

.

2

Write the sum of the absolute values of the three temperatures.

The sum is represented by the expression

S(T) = |T - 5| + |T| + |T + 9|

.

To formulate the function that needs to be minimized.

3

Find the key values that make each absolute value term zero.

The points are

5

,

0

, and

-9

. Ordered on a number line, these points are

-9

,

0

, and

5

.

The sum of absolute differences is geometrically equivalent to the sum of distances on a number line, which is minimized at the median of the points.

4

Evaluate the sum of absolute values at the median value,

T = 0

, and compare it to other values.

For

T = 0

,

S(0) = |-5| + |0| + |9| = 14

. For

T = 1

,

S(1) = |-4| + |1| + |10| = 15

. For

T = -1

,

S(-1) = |-6| + |-1| + |8| = 15

. Thus, the minimum sum occurs at

T = 0

.

To verify that the median yields the minimum sum of absolute values.

Key Concept

Minimizing the sum of absolute values of linear terms by finding the median of their zero-points on a number line.

Question 4537Question →

A water purification plant processes raw water through three successive filtration stages: Stage A, Stage B, and Stage C. Stage A removes $\frac{3}{8}$ of the impurities present in the raw water. Stage B removes $40\%$ of the remaining impurities. Stage C removes $0.75$ of the impurities that remain after Stage B. If $4.5$ kilograms of impurities are successfully removed in Stage C, how many kilograms of impurities were originally in the raw water?

Show answer & explanation

Answer: 16

Answer

The original amount of impurities in the raw water was

16

kilograms.

The correct answer is

16

kg. To find this, we express the remaining impurities at each stage as a fraction of the initial amount

x

. After Stage A,

\frac{5}{8}x

remains. In Stage B,

40\%

is removed, meaning

60\%

of

\frac{5}{8}x

, or

\frac{3}{8}x

, remains. In Stage C,

0.75

(or

\frac{3}{4}

) of this remainder is removed, which is

\frac{3}{4} \times \frac{3}{8}x = \frac{9}{32}x

. Setting

\frac{9}{32}x = 4.5

gives

x = 16

.

Step-by-Step Solution

1

Represent the initial mass of impurities in the raw water with a variable.

Let

x

be the initial kilograms of impurities.

Establishing a variable allows setting up an equation to track the changes through each stage.

2

Calculate the remaining impurities after Stage A.

Impurities remaining =

x - \frac{3}{8}x = \frac{5}{8}x

kg.

Stage A removes

\frac{3}{8}

of the initial impurities, so

1 - \frac{3}{8} = \frac{5}{8}

of the impurities remain.

3

Calculate the impurities removed and remaining after Stage B.

Impurities removed in Stage B =

0.40 \times \frac{5}{8}x = \frac{1}{4}x

kg. Impurities remaining after Stage B = \frac{5}{8}x - \frac{1}{4}x = \frac{3}{8}x$ kg.

Stage B removes

40\%

of the impurities that remained after Stage A. Subtracting the removed portion from the starting amount for this stage yields the remaining fraction.

4

Express the impurities removed in Stage C.

Impurities removed in Stage C =

0.75 \times \frac{3}{8}x = \frac{9}{32}x

kg.

Stage C removes

0.75

(or

\frac{3}{4}

) of the impurities remaining after Stage B.

5

Equate the Stage C expression to the given value and solve for

x

.

\frac{9}{32}x = 4.5 \implies x = 4.5 \times \frac{32}{9} = 16

kg.

The problem states that

4.5

kg of impurities are removed in Stage C, so solving this equation yields the initial value.

Key Concept

Solving multi-step word problems involving successive applications of fractions, decimals, and percentages.

Alternative Method

Working backwards from the final stage can simplify the calculations. Since Stage C removes

0.75

of the impurities remaining after Stage B, and this amount equals

4.5

kg, the amount remaining after Stage B is

\frac{4.5}{0.75} = 6

kg. Since Stage B removes

40\%

of the impurities remaining after Stage A, the

6

kg represents

100\% - 40\% = 60\%

of the impurities remaining after Stage A. Thus, the amount remaining after Stage A is

\frac{6}{0.60} = 10

kg. Finally, since Stage A removes

\frac{3}{8}

of the original impurities, the

10

kg represents

1 - \frac{3}{8} = \frac{5}{8}

of the original impurities. The original amount is therefore

10 \times \frac{8}{5} = 16

kg.

Estimated Time:3m 0s

Question 4538Question →

The passage below describes a famous historical site. The second sentence of the passage has been split into four segments.

'Overlooking the Urubamba River Valley, the ruins of a fifteenth-century Inca citadel continue to fascinate historians. [Segment 1] [Segment 2] [Segment 3] [Segment 4]'

Arrange the four segments below in the correct order to form a grammatically correct second sentence that avoids misplaced or dangling modifiers.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence of segments to form a grammatically correct sentence is: 'the ancient city of Machu Picchu', followed by 'which is located in the Andes mountains', followed by 'attracts thousands of tourists', and ending with 'who hope to see the sunrise over the ruins'.

The correct order constructs the sentence: 'The ancient city of Machu Picchu, which is located in the Andes mountains, attracts thousands of tourists who hope to see the sunrise over the ruins.' This placement keeps the non-restrictive relative clause next to 'the ancient city of Machu Picchu' and the restrictive relative clause next to 'tourists', ensuring proper modifier alignment and subject-verb agreement throughout the sentence.

Step-by-Step Solution

1

Identify the main subject of the sentence.

'the ancient city of Machu Picchu' is identified as the subject because it is the only noun phrase that can logically start the sentence and serve as the subject for the main verb.

Establishing the main subject provides the grammatical foundation for the rest of the sentence.

2

Determine the placement of the relative clause starting with 'which'.

'which is located in the Andes mountains' must be placed immediately after 'the ancient city of Machu Picchu'.

To avoid a misplaced modifier, the relative clause must be adjacent to the noun it modifies. Placing it elsewhere creates a subject-verb agreement error with the singular verb 'is' and makes the meaning illogical.

3

Locate the main verb phrase.

'attracts thousands of tourists' follows the modified subject.

The main verb must follow the complete subject noun phrase to complete the independent clause.

4

Place the final relative clause modifying the object.

'who hope to see the sunrise over the ruins' must follow 'tourists'.

The relative pronoun 'who' refers to people ('tourists') and must be placed immediately after its antecedent to prevent ambiguity or misplacement.

Key Concept

Modifier Placement

Question 4539Question →

### Models of Martian Atmospheric Loss

Scientists agree that Mars once possessed a much thicker, warmer carbon dioxide ( $CO_2$ ) atmosphere than it does today. However, they disagree on the primary mechanism responsible for the loss of this atmosphere.

Model 1
Mars lost its atmosphere primarily through *solar wind stripping*. Early in its history, Mars had a liquid core that generated a strong global magnetic field, protecting the atmosphere. Approximately 4 billion years ago, the core cooled, and the magnetic field decayed. Without magnetic protection, high-energy particles from the solar wind directly struck the upper atmosphere. These particles transferred energy to gaseous molecules (primarily $CO_2$ and $H_2O$ ), accelerating them past Mars's escape velocity. This continuous stripping depleted the atmosphere over hundreds of millions of years.

Model 2
Mars lost its atmosphere primarily through *impact erosion* during the Late Heavy Bombardment, a period of intense asteroid and comet impacts between 4.1 and 3.8 billion years ago. When large impactors struck Mars, they produced massive vapor plumes that expanded faster than Mars's escape velocity, driving large portions of the overlying atmosphere into space. Because Mars has a relatively low gravitational acceleration ( $3.71\text{ m/s}^2$ ), these explosive impacts were highly efficient at ejecting gases. In contrast, the solar wind has a negligible long-term effect because the planet's gravity is strong enough to retain molecules energized solely by solar particles.

According to Model 1 and Model 2, which of the following statements describes a point of disagreement between the two models regarding the mechanism of atmospheric loss on Mars?

Model 1 proposes that atmospheric loss occurred primarily during the Late Heavy Bombardment, whereas Model 2 proposes that atmospheric loss occurred continuously after the decay of Mars's magnetic field.

Model 1 suggests that vapor plumes from asteroid impacts directly drove gases into space, whereas Model 2 suggests that gaseous molecules were stripped directly by solar particles.

Model 1 asserts that high-energy solar wind particles drove atmospheric gases past escape velocity, whereas Model 2 asserts that solar wind particles had a negligible long-term effect on atmospheric depletion.

Model 1 claims that Mars's low gravity was the primary factor allowing solar wind particles to strip the atmosphere, whereas Model 2 claims that a liquid core protected the atmosphere during impacts.

Show answer & explanation

Answer: Model 1 asserts that high-energy solar wind particles drove atmospheric gases past escape velocity, whereas Model 2 asserts that solar wind particles had a negligible long-term effect on atmospheric depletion.

Answer

Model 1 asserts that high-energy solar wind particles drove atmospheric gases past escape velocity, whereas Model 2 asserts that solar wind particles had a negligible long-term effect on atmospheric depletion.

The correct answer states that Model 1 asserts high-energy solar wind particles drove atmospheric gases past escape velocity, whereas Model 2 asserts that solar wind particles had a negligible long-term effect on atmospheric depletion. This accurately reflects that Model 1 attributes atmospheric loss directly to the energy transferred from solar wind particles, while Model 2 discounts solar wind stripping, arguing that Mars's gravity is strong enough to retain molecules energized solely by solar particles.

Step-by-Step Solution

1

Analyze Model 1's stance on solar wind and atmospheric loss.

Model 1 states that solar wind particles directly struck the upper atmosphere and transferred energy to gaseous molecules, accelerating them past escape velocity and depleting the atmosphere.

To identify how Model 1 views the role of the solar wind.

2

Analyze Model 2's stance on solar wind and atmospheric loss.

Model 2 states that the solar wind has a negligible long-term effect on atmospheric depletion because Mars's gravity is strong enough to retain those molecules.

To identify how Model 2 views the role of the solar wind and compare it to Model 1.

3

Compare the analyzed stances against the given choices to find the statement that represents a point of disagreement.

The statement detailing Model 1's claim about solar wind stripping and Model 2's counter-claim that solar wind has a negligible effect matches the differences described in the passage.

To determine the correct choice demonstrating a clear point of disagreement.

Key Concept

Comparing and Contrasting Models

Estimated Time:1m 30s

Question 4540Question →

Two integers, $x$ and $y$ , are positioned on a number line. The distance between $x$ and $1$ is twice the distance between $y$ and $2$ . If the distance between $x$ and $y$ is exactly $5$ units, what is the sum of all possible values of $x + y$ ?

Show answer & explanation

Answer: 17

Answer

The sum of all possible values of

x + y

is

17

.

Representing the distances algebraically yields the system

|x - 1| = 2|y - 2|

and

|x - y| = 5

. Since

x

and

y

must be integers, splitting these equations into positive and negative cases yields exactly three valid integer coordinate pairs:

(13, 8)

,

(5, 0)

, and

(-7, -2)

. The sums (

x + y

) for these pairs are

21

,

5

, and

-9

, respectively. Adding these possible sums together gives a final total of

17

.

Step-by-Step Solution

1

Set up the absolute value expressions representing the distances.

|x - 1| = 2|y - 2|

and

|x - y| = 5

Distance on a number line between two points

a

and

b

is mathematically defined as

|a - b|

.

2

Split the distance condition

|x - y| = 5

into two coordinate cases.

x = y + 5

or

x = y - 5

An absolute value equation of the form

|A| = B

splits into

A = B

or

A = -B

.

3

Substitute

x = y + 5

into the first equation and solve for integer values of

y

.

y = 8

(which gives

x = 13

) and

y = 0

(which gives

x = 5

)

This generates the first set of valid integer coordinates satisfying all constraints.

4

Substitute

x = y - 5

into the first equation and solve for integer values of

y

.

y = -2

(which gives

x = -7

); the second algebraic option

y = 10/3

is discarded because it is not an integer

This generates the remaining valid integer coordinates satisfying all constraints.

5

Sum the value of

x + y

for all three valid coordinate pairs.

(13 + 8) + (5 + 0) + (-7 - 2) = 21 + 5 - 9 = 17

The question asks for the sum of all possible values of the expression

x + y

.

Key Concept

Using absolute value to represent distances on a number line and solving systems of absolute value equations under integer constraints.

Estimated Time:2m 30s

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