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During her research in the 1940s, geneticist Barbara McClintock made a revolutionary discovery while studying maize chromosomes. McClintock identified transposons ______ which challenged the prevailing scientific belief that genomes are static. Her pioneering work eventually earned her the Nobel Prize in Physiology or Medicine in 1983.

Which choice completes the text so that it conforms to the conventions of Standard English?

, genetic elements that can change positions within a genome—

—genetic elements that can change positions within a genome—

—genetic elements that can change positions within a genome,

genetic elements that can change positions within a genome,

Show answer & explanation

Answer: —genetic elements that can change positions within a genome—

Answer

—genetic elements that can change positions within a genome—

The sentence includes a nonessential appositive phrase that provides additional information about transposons. In Standard English, nonessential elements must be set off from the rest of the sentence using matching punctuation marks on both sides. The option that begins and ends the phrase with em dashes correctly isolates the nonessential clause.

Step-by-Step Solution

Identify the nonessential element in the sentence.

The phrase 'genetic elements that can change positions within a genome' functions as an appositive that describes 'transposons' and is not essential to the main clause structure.

Nonessential elements must be separated from the rest of the sentence by matching punctuation marks.

Check the punctuation choices for symmetry.

Standard English conventions require that if a nonessential element is set off by an em dash on one side, it must be closed by an em dash on the other side.

Mismatching punctuation marks (like a comma paired with an em dash) creates grammatically incorrect asymmetry.

Select the option with matching punctuation.

The option containing '—genetic elements that can change positions within a genome—' successfully closes the parenthetical information using a pair of em dashes.

This maintains punctuation symmetry and correctly conforms to standard English conventions.

Key Concept

Punctuation of Nonessential Elements

Estimated Time:45s

Question 922Question →

The passage below contains a blank. Which form of the verb 'examine' correctly completes the sentence to conform to the conventions of Standard English?

Fill in the blanks below

In her pioneering 1928 study on chromosomal dynamics in maize, geneticist Barbara McClintock faced skepticism from colleagues who doubted her early observations of genetic transposition. To resolve these doubts, McClintock insisted that any researcher who questioned her findings the cellular samples under a microscope for themselves before publishing a formal critique.

Show answer & explanation

Answer

examine (or should examine)

The verb 'insisted' is a verb of demand and command. In Standard English, subordinate 'that'-clauses following verbs of command, demand, or insistence require the subjunctive mood. The subjunctive mood is formed using the bare base form of the verb—in this case, 'examine' (or the modal option 'should examine'). The base form is used regardless of whether the subject ('any researcher') is singular or plural, and regardless of the past tense of the main verb ('insisted').

Step-by-Step Solution

Analyze the main verb of the matrix clause and its grammatical influence.

The matrix verb is 'insisted', which is a verb of demand, insistence, or command introducing a 'that'-clause.

Identifying the matrix verb helps determine the mood of the subordinate clause.

Determine the required grammatical mood for the subordinate clause.

Verbs expressing insistence or demand trigger the subjunctive mood in the subordinate clause.

Standard English conventions require the subjunctive mood to express mandates or demands.

Identify the correct verb form for the subjunctive mood.

The subjunctive mood uses the base form of the verb ('examine') for all subjects, regardless of the tense of the matrix verb or the singular subject 'any researcher'.

Applying the base form satisfies the requirement for a subjunctive construction.

Key Concept

Subjunctive Mood in Subordinate Clauses of Demand or Command

Estimated Time:1m 30s

Question 923Question →

Having been long dismissed by contemporaries as mere collectors of botanical specimens rather than active contributors to scientific theory, _______

Which choice completes the passage so that it conforms to the conventions of Standard English?

the development of evolutionary biology was actually shaped by early nineteenth-century women botanists through their meticulous documentation of plant hybridization.

early nineteenth-century women botanists actually shaped the development of evolutionary biology through their meticulous documentation of plant hybridization.

meticulous documentation of plant hybridization by early nineteenth-century women botanists actually shaped the development of evolutionary biology.

scientific journals in the early nineteenth century routinely ignored the work of women botanists, despite their crucial contributions to evolutionary biology.

Show answer & explanation

Answer: early nineteenth-century women botanists actually shaped the development of evolutionary biology through their meticulous documentation of plant hybridization.

Answer

The correct answer is the option starting with 'early nineteenth-century women botanists', which correctly identifies them as the subject of the introductory modifying phrase.

The correct choice is the option that begins with 'early nineteenth-century women botanists'. The introductory modifying phrase 'Having been long dismissed by contemporaries as mere collectors of botanical specimens rather than active contributors to scientific theory' describes people. Therefore, the main clause must begin with the noun phrase representing these people ('early nineteenth-century women botanists') to maintain proper subject-modifier agreement.

Step-by-Step Solution

Analyze the introductory modifying phrase at the beginning of the sentence.

The phrase 'Having been long dismissed by contemporaries as mere collectors of botanical specimens rather than active contributors to scientific theory' describes people who could be dismissed as collectors (i.e., women botanists).

Identifying the logical subject of the modifier is the first step in resolving modifier agreement.

Evaluate the beginning of each answer choice to find the noun or pronoun that the modifier logically describes.

The noun phrase 'early nineteenth-century women botanists' is the only logical match.

The conventions of Standard English require that an introductory modifier be placed immediately before the noun or pronoun it modifies to avoid dangling or misplaced modifiers.

Select the choice that starts with the correct subject and maintains grammatical flow.

The choice beginning with 'early nineteenth-century women botanists' is the only one that places the logical subject immediately after the comma.

Other choices place 'the development of evolutionary biology', 'meticulous documentation', or 'scientific journals' as the subject, which creates dangling or misplaced modifiers.

Key Concept

Subject-Modifier Agreement

Question 924Question →

The graph of a linear function is shown in the $xy$ -plane. The line passes through the points $(-2, -3)$ and $(2, 5)$ . If the point $(k, 11)$ lies on the line, what is the value of $k$ ?

Show answer & explanation

Answer: 5

Answer

The slope of the line is calculated as

m = \frac{5 - (-3)}{2 - (-2)} = 2

. Using the point-slope form with the point

(2, 5)

, the equation of the line is

y - 5 = 2(x - 2)

, which simplifies to

y = 2x + 1

. Substituting the point

(k, 11)

into this equation gives

11 = 2k + 1

, which solves to

k = 5

Step-by-Step Solution

Calculate the slope of the line using the points

(-2, -3)

and

(2, 5)

m = 2

The slope formula is

m = \frac{y_2 - y_1}{x_2 - x_1}

. Substituting the given coordinates:

m = \frac{5 - (-3)}{2 - (-2)} = \frac{8}{4} = 2

Determine the equation of the line using point-slope form

y = 2x + 1

Using

y - y_1 = m(x - x_1)

with the point

(2, 5)

and

m = 2

, we get

y - 5 = 2(x - 2)

, which simplifies to

y = 2x + 1

Substitute

(k, 11)

into the line equation and solve for

k

k = 5

Substituting

x = k

and

y = 11

yields

11 = 2k + 1

. Subtracting 1 from both sides gives

10 = 2k

, and dividing by 2 gives

k = 5

Key Concept

Finding the linear equation from coordinates and solving for variables

Question 925Question →

In 1972, French analysts at the Pierrelatte uranium enrichment plant discovered a bizarre anomaly in uranium samples from Gabon. The proportion of the fissile isotope uranium-235 was significantly lower than the standard value found everywhere else on Earth. Further investigation revealed that the Oklo deposits ______ had actually undergone self-sustaining nuclear fission reactions approximately two billion years ago.

Which choice completes the text so that it conforms to the conventions of Standard English?

—which contained a unique combination of physical conditions—

, which contained a unique combination of physical conditions—

—which contained a unique combination of physical conditions,

, which contained a unique combination of physical conditions

Show answer & explanation

Answer: —which contained a unique combination of physical conditions—

Answer

—which contained a unique combination of physical conditions—

The correct answer correctly uses a pair of em dashes to set off the nonessential relative clause modifying the subject. In English, nonessential elements must be bracketed by matching punctuation marks: either two commas or two em dashes. Since the clause is followed by the main verb of the sentence, wrapping the clause in em dashes successfully maintains grammatical symmetry.

Step-by-Step Solution

Identify the grammatical role of the clause inside the blank.

The clause 'which contained a unique combination of physical conditions' is a nonessential relative clause that modifies the noun phrase 'the Oklo deposits'.

Because the sentence remains grammatically complete and retains its core meaning without this clause, the clause is nonessential and must be set off with punctuation.

Determine the correct punctuation rules for nonessential elements.

Nonessential elements must be set off by matching punctuation marks: either two commas, two em dashes, or two parentheses.

Using mismatched punctuation (like a comma and an em dash) creates an asymmetrical construction, which violates standard grammatical conventions.

Evaluate the choices to find the matching pair of punctuation marks.

The option containing '—which contained a unique combination of physical conditions—' uses two em dashes, which is a correct matching pair.

This establishes a consistent and grammatically correct boundary for the parenthetical clause.

Key Concept

Punctuation of Nonessential Elements

Question 926Question →

Before the Rosetta Stone was deciphered in the early nineteenth century, scholars ______ the meaning of Egyptian hieroglyphs for over a millennium, mistakenly assuming that the script was purely ideographic rather than phonetic. This breakthrough eventually allowed historians to read ancient records, showing that the system of writing actually represented a sophisticated combination of logographic, syllabic, and alphabetic elements.

Which choice completes the text so that it conforms to the conventions of Standard English?

debate

have debated

had debated

will debate

Show answer & explanation

Answer: had debated

Answer

had debated

The correct answer is 'had debated' because the sentence describes an action (scholars debating) that took place and was ongoing over a period of time ('for over a millennium') prior to another completed past action ('was deciphered'). The past perfect tense is the appropriate verb form to convey this sequence of events in the past.

Step-by-Step Solution

Analyze the timeline established by the context clues in the passage.

The passage establishes a past temporal framework with the verbs 'was deciphered' and 'allowed'.

Identifying the correct temporal anchors helps determine the chronological relationship of the missing verb.

Determine the relationship between the blank and the past time anchor.

The scholars' debating occurred and was ongoing 'for over a millennium' prior to the decipherment in the early nineteenth century.

An action that occurred and was ongoing before a specific point in the past requires the past perfect tense.

Select the verb form that corresponds to the past perfect tense.

The form 'had debated' is the past perfect of the verb 'debate'.

Choosing 'had debated' maintains grammatical consistency and logical temporal ordering.

Key Concept

Verb Tense, Aspect, and Mood

Question 927Question →

Hoping to document the migration patterns of monarch butterflies, _______

Which choice completes the text so that it conforms to the conventions of Standard English?

tiny tracking tags were placed by biologist Elena Vance on the insects' wings.

Elena Vance, a biologist, placed tiny tracking tags on the insects' wings.

the tagging of the insects was conducted by biologist Elena Vance.

tracking tags were used by biologist Elena Vance to mark their wings.

Show answer & explanation

Answer: Elena Vance, a biologist, placed tiny tracking tags on the insects' wings.

Answer

Elena Vance, a biologist, placed tiny tracking tags on the insects' wings.

The introductory phrase 'Hoping to document the migration patterns of monarch butterflies' is a modifying phrase that must logically describe the subject of the main clause. The subject who is hoping to document the migration is the biologist Elena Vance. Therefore, the main clause must begin with the noun phrase 'Elena Vance' to ensure proper subject-modifier agreement.

Step-by-Step Solution

Identify the introductory modifying phrase and determine what or who it logically describes.

The modifying phrase 'Hoping to document the migration patterns of monarch butterflies' describes a person who has this hope, which is the biologist Elena Vance.

A modifying phrase must be placed next to the noun or pronoun it logically modifies to avoid a dangling modifier.

Select the option that begins with the logical subject described by the modifying phrase.

The option starting with the proper noun 'Elena Vance' correctly aligns the subject with the modifier.

This alignment ensures that the sentence follows the conventions of Standard English regarding subject-modifier agreement.

Key Concept

Subject-modifier agreement requires that an introductory modifying phrase be followed immediately by the noun or pronoun it logically modifies.

Question 928Question →

In the mid-twentieth century, ecologists generally assumed that kelp forests were stable ecosystems that could withstand significant environmental fluctuations. However, recent studies on marine trophic cascades have challenged this view. Observing the rapid collapse of kelp canopies following the local extinction of sea otters, __________

Which choice completes the text so that it conforms to the conventions of Standard English?

marine biologists realized that top-down predatory control is crucial for maintaining coastal biodiversity.

remote sensing technology allowed marine biologists to realize that top-down predatory control is crucial for maintaining coastal biodiversity.

the crucial role of top-down predatory control in maintaining coastal biodiversity was realized by marine biologists.

marine biology's understanding of coastal biodiversity was transformed, revealing that top-down predatory control is crucial.

Show answer & explanation

Answer: marine biologists realized that top-down predatory control is crucial for maintaining coastal biodiversity.

Answer

marine biologists realized that top-down predatory control is crucial for maintaining coastal biodiversity.

The introductory modifying phrase 'Observing the rapid collapse of kelp canopies following the local extinction of sea otters' describes an action that must be logically performed by the subject of the main clause. The group performing the action of observing is the marine biologists. Therefore, the main clause must begin with the noun phrase 'marine biologists' as its subject. The option beginning with 'marine biologists' correctly establishes this relationship, making the sentence grammatically sound.

Step-by-Step Solution

Identify the introductory modifying phrase and determine the entity that logically performs the action described.

The action of 'observing' must be performed by a conscious observer, which in this context is 'marine biologists'.

An introductory participial phrase must modify the subject of the clause that immediately follows it.

Evaluate the subject of each option to find the one that begins with the logical subject.

Only the option starting with 'marine biologists' provides the correct logical subject immediately following the modifier.

Placing any other noun or phrase immediately after the modifier creates a dangling or misplaced modifier error.

Key Concept

Subject-Modifier Agreement

Question 929Question →

In 1967, astrophysicist Jocelyn Bell Burnell detected a series of regularly spaced radio pulses while analyzing data from a newly constructed radio telescope. Initially, some researchers hypothesized that the signals were artificial transmissions from an extraterrestrial civilization. However, this anomaly ______ ultimately proved to be the first discovered pulsar, a highly magnetized rotating neutron star.

Which choice completes the text so that it conforms to the conventions of Standard English?

, which she and her advisor Antony Hewish initially referred to as "Little Green Men 1" (LGM-1),

—which she and her advisor Antony Hewish initially referred to as "Little Green Men 1" (LGM-1),

which she and her advisor Antony Hewish initially referred to as "Little Green Men 1" (LGM-1),

, which she and her advisor Antony Hewish initially referred to as "Little Green Men 1" (LGM-1)

Show answer & explanation

Answer: , which she and her advisor Antony Hewish initially referred to as "Little Green Men 1" (LGM-1),

Answer

The correct option is the one that begins and ends the nonessential clause with a comma: ", which she and her advisor Antony Hewish initially referred to as "Little Green Men 1" (LGM-1),"

The sentence contains the nonessential relative clause 'which she and her advisor Antony Hewish initially referred to as "Little Green Men 1" (LGM-1)'. To conform to standard English conventions, this nonessential clause must be set off from the rest of the sentence with a matching pair of punctuation marks. The correct choice uses a comma at both the beginning and the end of the clause, properly isolating it.

Step-by-Step Solution

Identify the nonessential element in the sentence.

The clause starting with 'which she and her advisor...' is nonessential because the main sentence ('this anomaly ultimately proved to be the first discovered pulsar...') remains grammatically complete and retains its core meaning without it.

Recognizing that the clause is nonessential helps determine that it must be set off by matching punctuation marks.

Examine the punctuation options to identify matching pairs.

The correct option must use the same punctuation mark at both the beginning and the end of the nonessential clause.

Standard English conventions require that nonessential elements be set off with a matching pair of commas, em dashes, or parentheses.

Select the choice that correctly implements matching punctuation.

The choice starting with a comma and ending with a comma is the only grammatically correct and symmetrical option.

All other choices create asymmetry by mixing different punctuation marks or omitting one of the paired marks entirely.

Key Concept

Nonessential elements must be set off from the rest of the sentence using a matching pair of punctuation marks (commas, em dashes, or parentheses).

Question 930Question →

In 1915, chemist Alice Ball pioneered a groundbreaking technique to make chaulmoogra oil injectable, offering hope to thousands of leprosy patients. Her innovative process ______ involved chemically modifying the oil's fatty acids so they could be easily dissolved in water and absorbed by the human body.

Which choice completes the text so that it conforms to the conventions of Standard English?

, which became known as the Ball Method

—which became known as the Ball Method,

, which became known as the Ball Method,

which became known as the Ball Method,

Show answer & explanation

Answer: , which became known as the Ball Method,

Answer

The correct option is the one that sets off the nonessential relative clause with matching commas: ', which became known as the Ball Method,'

The sentence contains a nonessential relative clause, 'which became known as the Ball Method,' that describes the 'innovative process.' Nonessential elements must be set off from the rest of the sentence with matching punctuation marks at both the beginning and the end of the phrase. The correct choice uses a comma at the beginning of the clause and a matching comma at the end of the clause, properly isolating the nonessential information.

Step-by-Step Solution

Identify the core subject and verb of the main clause to determine sentence structure.

The subject is 'process' and the main verb is 'involved.'

Understanding the core structure helps identify whether the intervening clause is essential or nonessential.

Evaluate the clause 'which became known as the Ball Method' to see if it is essential to the sentence.

The clause provides extra parenthetical details about the process but is not required for the sentence to be grammatically complete.

Nonessential elements must be set off with matching punctuation marks, such as two commas or two em dashes.

Check the answer choices for a matching pair of punctuation marks that correctly isolates the nonessential clause.

The choice using a comma before 'which' and a comma after 'Method' successfully isolates the clause.

Using mismatched punctuation (such as an em dash and a comma) or omitting one of the marks creates grammatical asymmetry.

Key Concept

Punctuation of Nonessential Elements

Estimated Time:1m 0s

Question 931Question →

Complete the text by filling in the blank with the correct phrase from the options in parentheses: (Claude Monet painted / Claude Monet's paintings depicted). Which phrase conforms to the conventions of Standard English?

Fill in the blanks below

In the late nineteenth century, Impressionist artists sought to move away from traditional studio painting in order to study the natural world directly. Hoping to capture the fleeting effects of light and atmospheric conditions, the Rouen Cathedral at dozens of different times of day.

Show answer & explanation

Answer

Claude Monet painted

The introductory phrase 'Hoping to capture the fleeting effects of light and atmospheric conditions' is a participial modifier. Under Standard English conventions, an introductory modifying phrase must logically describe the subject that immediately follows it. Because an artist (Claude Monet) is the one who can logically hope to capture light, the main clause must begin with 'Claude Monet'. The phrase 'Claude Monet painted' correctly places the logical subject immediately after the modifier.

Step-by-Step Solution

Identify the introductory modifying phrase at the start of the sentence.

The phrase is 'Hoping to capture the fleeting effects of light and atmospheric conditions,' which is a present participial phrase.

Recognizing the modifier is necessary to determine what noun it must logically describe.

Determine the logical subject of the modifying phrase.

The entity doing the 'hoping to capture' must be a person, specifically the artist Claude Monet, rather than his paintings.

Standard English requires that an introductory modifier logically describe the subject that immediately follows it.

Evaluate the parenthetical choices to see which one correctly begins with the logical subject.

The phrase 'Claude Monet painted' starts with the correct subject 'Claude Monet'. The phrase 'Claude Monet's paintings depicted' starts with 'paintings', causing a dangling modifier.

Matching the modifier to the correct noun ensures the sentence conforms to Standard English conventions.

Key Concept

Subject-Modifier Agreement

Question 932Question →

In the equation below, $m$ is a constant.

\frac{3}{5}(5x - 10) - 2(x - m) = 18

If the solution to the equation is $x = 12$ , what is the value of $m$ ?

Show answer & explanation

Answer: 6

Answer

The correct value of

m

is 6.

Substituting

x = 12

into the equation yields

\frac{3}{5}(5(12) - 10) - 2(12 - m) = 18

, which simplifies to

30 - 24 + 2m = 18

. Combining constant terms gives

6 + 2m = 18

. Subtracting 6 from both sides gives

2m = 12

, and dividing by 2 yields

m = 6

Step-by-Step Solution

Substitute

x = 12

into the given equation.

\frac{3}{5}(5(12) - 10) - 2(12 - m) = 18

Since

x = 12

is the solution, it must satisfy the equation.

Simplify the expression inside the first set of parentheses.

5(12) - 10 = 60 - 10 = 50

Evaluate the terms inside the parentheses first.

Multiply the simplified term by the fraction

\frac{3}{5}

\frac{3}{5}(50) = 30

Multiply 50 by 3 and divide by 5.

Substitute 30 back into the equation and distribute

-2

to the terms inside the second set of parentheses.

30 - 24 + 2m = 18

Distributing

-2

12 - m

yields

-24 + 2m

due to sign rules.

Combine the constant terms on the left side of the equation.

6 + 2m = 18

30 - 24 = 6

Subtract 6 from both sides to isolate the term with

m

2m = 12

Isolate the variable term on one side of the equation.

Divide both sides by 2 to solve for

m

m = 6

Divide 12 by 2 to find the final value.

Key Concept

Solving a linear equation in one variable by substitution and isolation.

Question 933Question →

The passage below contains a nonessential clause set off by punctuation. What punctuation mark should be typed in the blank to correctly complete the sentence?

Fill in the blanks below

1908

, German chemist Fritz Haber developed a method to synthesize ammonia directly from atmospheric nitrogen. This chemical process—which later won Haber the Nobel Prize in Chemistryenabled the mass production of synthetic fertilizers, ultimately sustaining global food supplies.

Show answer & explanation

Answer

An em dash (— or --) is required in the blank to match the em dash that introduces the nonessential clause.

The nonessential relative clause 'which later won Haber the Nobel Prize in Chemistry' is introduced by an em dash. To maintain grammatical symmetry, the clause must also end with an em dash. Therefore, an em dash (—) is the correct punctuation mark.

Step-by-Step Solution

Identify the nonessential element in the sentence.

The phrase 'which later won Haber the Nobel Prize in Chemistry' is a nonessential relative clause because removing it does not change the core meaning of the sentence.

Nonessential elements must be set off from the rest of the sentence with matching punctuation marks.

Identify the punctuation mark that begins the nonessential clause.

The clause is introduced by an em dash ('—').

To maintain punctuation symmetry, the nonessential clause must end with the same type of punctuation mark that started it.

Determine the correct punctuation mark for the blank.

The blank must be filled with an em dash ('—') to match the opening em dash.

Mixing different punctuation marks (such as starting with an em dash and ending with a comma or parenthesis) is grammatically incorrect.

Key Concept

Punctuation of Nonessential Elements

Question 934Question →

Complete the text by filling in the blank with the word or phrase that conforms to the conventions of Standard English.

Fill in the blanks below

To investigate the composition of Saturn's rings, the Cassini spacecraft was launched in 1997. Having traveled for nearly seven years to reach the gas giant, began transmitting unprecedented data back to Earth in 2004.

Show answer & explanation

Answer

the spacecraft (or 'Cassini' / 'it')

The introductory modifier 'Having traveled for nearly seven years to reach the gas giant' describes the entity that physically journeyed to Saturn. The Cassini spacecraft (referred to as 'the spacecraft', 'Cassini', or 'it') is the only noun that logically fits this description. Placing it immediately after the comma satisfies the rule of subject-modifier agreement.

Step-by-Step Solution

Identify the introductory modifying phrase.

The modifying phrase is 'Having traveled for nearly seven years to reach the gas giant'.

Understanding what the modifier describes is the first step to resolving subject-modifier agreement.

Determine the logical subject of this modifier.

The entity that traveled for nearly seven years to reach Saturn is the Cassini spacecraft.

The modifier must directly describe the subject that performs the action of traveling.

Fill the blank with a noun or pronoun representing this logical subject.

The sentence is completed with 'the spacecraft', 'Cassini', or 'it'.

This ensures that the subject matches the introductory modifier, preventing a dangling modifier.

Key Concept

Subject-Modifier Agreement

Question 935Question →

Observations from the New Horizons spacecraft have revolutionized our understanding of the Kuiper belt, a region of icy bodies beyond Neptune. Among the most surprising findings is the geological complexity of the dwarf planet Pluto, which [blank] boasts vast plains of nitrogen ice and towering mountains of water ice.

Which choice completes the text so that it conforms to the conventions of Standard English?

—contrary to the expectations of planetary scientists who had predicted a geologically dead world—

, contrary to the expectations of planetary scientists who had predicted a geologically dead world—

—contrary to the expectations of planetary scientists who had predicted a geologically dead world,

contrary to the expectations of planetary scientists who had predicted a geologically dead world,

Show answer & explanation

Answer: —contrary to the expectations of planetary scientists who had predicted a geologically dead world—

Answer

The choice that begins and ends the parenthetical phrase with matching em dashes, specifically '—contrary to the expectations of planetary scientists who had predicted a geologically dead world—', is the correct answer.

The correct option uses a matching pair of em dashes ('—contrary to... world—') to set off the nonessential parenthetical phrase that interrupts the relative clause 'which boasts...'. Setting off this parenthetical element symmetrically with either two commas or two em dashes conforms to the rules of Standard English.

Step-by-Step Solution

Identify the nonessential element in the sentence.

The phrase 'contrary to the expectations of planetary scientists who had predicted a geologically dead world' acts as an parenthetical insertion modifying the main assertion about Pluto's active features.

Recognizing nonessential elements is necessary to determine where punctuation marks (like commas, em dashes, or parentheses) must be placed.

Determine the required punctuation pattern to set off this nonessential element.

Standard English conventions require that nonessential elements be set off by matching pairs of punctuation: either two commas, two em dashes, or two parentheses.

Using mismatched punctuation (such as a comma at the beginning and an em dash at the end) violates the rule of punctuation symmetry.

Evaluate the options to find the one with matching punctuation marks.

The option using matching em dashes ('—contrary to... world—') is correct. All other options mix commas and em dashes or omit one of the boundaries.

Selecting the option with symmetrical punctuation ensures the sentence conforms to Standard English conventions.

Key Concept

Punctuation of Nonessential Elements

Question 936Question →

Had the board of the Royal Society of London accepted Mary Anning’s fossil discoveries and geological theories in the 1840s, her pioneering work in paleontology _______ recognition much earlier, potentially sparing her the financial difficulties that plagued her later years. Instead, because of her gender and working-class background, she was excluded from the scientific community, and her findings were frequently published by male collectors without attribution.

Which choice completes the text so that it conforms to the conventions of Standard English?

would have received

would receive

received

had received

Show answer & explanation

Answer: would have received

Answer

would have received

The sentence begins with the inverted past hypothetical condition 'Had the board... accepted,' which describes a past situation that did not actually occur. To complete this third conditional structure, the main clause requires a past conditional verb phrase ('would have' followed by the past participle). The phrase 'would have received' fits this structure perfectly.

Step-by-Step Solution

Identify the sentence structure

The sentence begins with the inverted conditional clause 'Had the board... accepted,' which indicates a hypothetical past condition (a past counterfactual or third conditional structure).

Recognizing the conditional type helps determine the matching tense and mood for the independent clause.

Determine the correct verb form for the main clause

The main clause of a past counterfactual condition requires the past conditional form ('would have' + past participle) to express the hypothetical past outcome.

This maintains grammatical consistency within the conditional framework.

Select the option that matches this form

The verb phrase 'would have received' fits this requirement.

It uses the correct past conditional aspect.

Key Concept

Verb Tense, Aspect, and Mood in Conditional Clauses

Estimated Time:1m 30s

Question 937Question →

In the $xy$ -plane, line $k$ has the equation $y = -2x + 10$ . Line $m$ is parallel to line $k$ and passes through the point $(6, 8)$ . Line $l$ is perpendicular to line $k$ and intersects the $x$ -axis at the point $(a, 0)$ , where $a > 10$ . If the region bounded by lines $k$ , $m$ , $l$ , and the $y$ -axis has an area of $110$ , what is the value of $a$ ?

Show answer & explanation

Answer: 25

Answer

To find the value of

a

, we determine the equations of the lines

m

and

l

based on their geometric relationships to line

k

. Line

m

is parallel to line

k

(

y = -2x + 10

), so its slope is

-2

. Using the point

(6, 8)

, its equation is

y = -2x + 20

. Line

l

is perpendicular to line

k

, so its slope is

\frac{1}{2}

. It intersects the

x

-axis at

(a, 0)

, giving the equation

y = \frac{1}{2}x - \frac{1}{2}a

. The bounded region formed by the parallel lines

k

and

m

, the perpendicular line

l

, and the

y

-axis is a trapezoid. Calculating the area of this trapezoid by dividing it into a parallelogram and a triangle yields the area formula

60 + 2a

. Setting this equal to the given area of

110

yields

60 + 2a = 110

, which solves to

a = 25

Step-by-Step Solution

Determine the equation of line

m

using the parallel slope and the given point.

Line

m

has the equation

y = -2x + 20

Parallel lines have equal slopes. Since line

k

has a slope of

-2

, line

m

also has a slope of

-2

. Substituting the point

(6, 8)

into the point-slope form gives

y - 8 = -2(x - 6)

Determine the equation of line

l

using the perpendicular slope and its

x

-intercept.

Line

l

has the equation

y = \frac{1}{2}x - \frac{1}{2}a

Perpendicular lines have negative reciprocal slopes. The negative reciprocal of

-2

\frac{1}{2}

. Using the point

(a, 0)

in the point-slope form gives

y - 0 = \frac{1}{2}(x - a)

Calculate the vertices of the bounded region by finding the intersection points of the boundary lines.

The vertices of the bounded region are

(0, 20)

(0, 10)

(4 + 0.2a, 2 - 0.4a)

, and

(8 + 0.2a, 4 - 0.4a)

The region is bounded by the parallel lines

k

and

m

, the perpendicular line

l

, and the

y

-axis (

x = 0

Find the area of the region as an algebraic expression in terms of

a

The area is equal to

60 + 2a

The region can be divided into a parallelogram with a vertical base of

10

and width

4 + 0.2a

, and a right triangle with a vertical base of

10

and width

4

. The sum of their areas is

10(4 + 0.2a) + \frac{1}{2}(10)(4) = 40 + 2a + 20 = 60 + 2a

Set the area expression equal to the given area of

110

and solve for

a

a = 25

Setting the area equal to

110

yields

60 + 2a = 110

, which simplifies to

2a = 50

, or

a = 25

Key Concept

Linear functions, parallel and perpendicular lines, finding line equations, and coordinate geometry area.

Alternative Method

The area can also be calculated using the geometric properties of a trapezoid. The height of the trapezoid is the perpendicular distance between the parallel lines

k

and

m

, which is

\frac{|20 - 10|}{\sqrt{(-2)^2 + 1^2}} = 2\sqrt{5}

. The bases of the trapezoid are the segments of lines

k

and

m

from the

y

-axis to their intersection points with line

l

. The length of the base on line

k

9\sqrt{5}

and the length of the base on line

m

13\sqrt{5}

(when

a = 25

). Using the formula for the area of a trapezoid,

\text{Area} = \frac{9\sqrt{5} + 13\sqrt{5}}{2} \times 2\sqrt{5} = 11\sqrt{5} \times 2\sqrt{5} = 110

Estimated Time:3m 0s

Question 938Question →

The passage below contains a blank indicating a missing punctuation mark. Which punctuation mark should be placed in the blank to correctly set off the nonessential element?

Fill in the blanks below

Although many historians attribute the invention of the marine chronometer solely to John Harrison, the contribution of his son William—who made several arduous voyages across the Atlantic to test the device's accuracy under harsh maritime conditionswas equally vital to solving the long-standing longitude problem. William's meticulous record-keeping helped prove the reliability of the marine chronometer to the Board of Longitude.

Show answer & explanation

Answer

An em dash (—)

The sentence sets off the nonessential relative clause describing William's voyages with an em dash after his name ('William—'). To maintain grammatical symmetry, the clause must also end with a matching em dash. Therefore, an em dash (—) is required in the blank.

Step-by-Step Solution

Identify the nonessential element in the sentence.

The phrase 'who made several arduous voyages across the Atlantic to test the device's accuracy under harsh maritime conditions' is a nonessential relative clause modifying the noun 'William.'

This clause provides descriptive information about William but is not grammatically necessary for the main clause to function.

Analyze the punctuation starting the nonessential element.

An em dash (—) is used immediately before the relative clause starts, right after the name 'William.'

Nonessential elements must be set off by matching punctuation on both sides to maintain parallel structure.

Select the matching punctuation to close the nonessential element.

An em dash (—) must be placed in the blank.

Ending the clause with a comma or any other punctuation mark would create asymmetry with the opening em dash.

Key Concept

Punctuation of Nonessential Elements

Question 939Question →

In a science experiment, the temperature

y

, in degrees Celsius, and the time

x

, in minutes, are related by a system of equations. The relationships are given by:

y = 2x - 3

3x - y = 8

What is the value of

x

in the solution to this system?

Show answer & explanation

Answer: 5

Answer

The correct answer is 5. Substituting the expression for

y

from the first equation into the second equation yields

3x - (2x - 3) = 8

. Distributing the negative sign results in

3x - 2x + 3 = 8

. Combining the variable terms gives

x + 3 = 8

. Subtracting 3 from both sides isolates

x

, giving

x = 5

Step-by-Step Solution

Substitute the expression for

y

from the first equation,

y = 2x - 3

, into the second equation.

3x - (2x - 3) = 8

This eliminates the variable

y

so the equation can be solved directly for

x

Distribute the negative sign to both terms inside the parentheses.

3x - 2x + 3 = 8

Distributing the negative sign to both

2x

and

-3

simplifies the expression correctly.

Combine like terms on the left side of the equation.

x + 3 = 8

Subtracting

2x

from

3x

leaves a single

x

term.

Subtract 3 from both sides of the equation to isolate

x

x = 5

This isolates the variable

x

to find the final solution.

Key Concept

Solving systems of linear equations using substitution

Estimated Time:1m 0s

Question 940Question →

In the equation below,

a

and

b

are constants.

\frac{a(x - 1) - 2(3x + b)}{3} = \frac{4(x - 5) - a(b - x)}{6}

If the equation has infinitely many solutions for

x

, what is the value of

a - b

Show answer & explanation

Answer: 15

Answer

The value of

a - b

is 15.

The correct answer is 15. Multiplying the entire equation by 6 to clear the denominators, distributing the terms, and grouping them yields

(2a - 12)x - (2a + 4b) = (a + 4)x - (ab + 20)

. For the equation to have infinitely many solutions, the coefficients of

x

on both sides must be equal (

2a - 12 = a + 4

), and the constant terms must also be equal (

2a + 4b = ab + 20

). Solving this system of equations yields

a = 16

and

b = 1

. The difference

a - b

16 - 1 = 15

Step-by-Step Solution

Eliminate the denominators by multiplying both sides of the equation by 6.

2[a(x - 1) - 2(3x + b)] = 4(x - 5) - a(b - x)

Multiplying both sides by the least common multiple of 3 and 6 simplifies the equation by removing the fractions.

Expand both sides of the equation using the distributive property.

2[ax - a - 6x - 2b] = 4x - 20 - ab + ax

which simplifies to

2ax - 2a - 12x - 4b = ax + 4x - ab - 20

Distributing the constants outside the parentheses allows us to group like terms.

Group the

x

-terms and constant terms on each side of the equation.

(2a - 12)x - (2a + 4b) = (a + 4)x - (ab + 20)

Structuring the equation in the form

Ax + B = Cx + D

makes it easier to compare the coefficients.

Set up a system of equations by equating the coefficients of

x

and the constant terms from both sides.

2a - 12 = a + 4

and

2a + 4b = ab + 20

For a linear equation to have infinitely many solutions, the coefficient of

x

on both sides must be equal, and the constant terms on both sides must also be equal.

Solve the first equation for

a

a = 16

Subtracting

a

and adding 12 to both sides isolates the variable

a

Substitute

a = 16

into the second equation and solve for

b

2(16) + 4b = 16b + 20 \implies 32 + 4b = 16b + 20 \implies 12 = 12b \implies b = 1

Substituting the known value of

a

leaves a single linear equation in terms of

b

Calculate the value of

a - b

16 - 1 = 15

This is the final value requested by the question.

Key Concept

Solving linear equations in one variable with infinitely many solutions by equating coefficients on both sides of the equation.

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