All practice questions

Question 3421Question →

The supervisor noticed that the worker became inattentive toward the end of a long shift. In this sentence, what does the word inattentive most nearly mean?

Observant

Distracted

Inactive

Disrespectful

Show answer & explanation

Answer: Distracted

Answer

Distracted

The word 'inattentive' is formed by attaching the negative prefix 'in-' (meaning 'not') to 'attentive' (meaning 'mindful' or 'observant'). Therefore, 'inattentive' means 'not paying attention', which is the exact definition of 'distracted'.

Step-by-Step Solution

1

Break down the target word into its morphological components.

The word inattentive consists of the negative prefix in- (meaning not), the base attent (from attend, meaning to direct one's mind or care), and the adjective suffix -ive (meaning having the quality of).

Deconstructing affixes reveals the core literal definition of the word.

2

Synthesize the affix meanings to identify the corresponding synonym.

Combining not with attentive yields not paying attention, which directly matches the meaning of distracted.

Sentence context indicates that fatigue near the end of a work shift causes a worker to lose concentration.

Key Concept

Prefix and Suffix Analysis

Estimated Time:35s

Question 3422Question →

The instructor provided a lucid explanation of the engine repair procedure, making every complex step easy for the students to follow. In this sentence, what does the word lucid most nearly mean?

bright

confusing

clear

lengthy

Show answer & explanation

Answer: clear

Answer

The word lucid most nearly means clear.

In the sentence, the phrase 'making every complex step easy for the students to follow' indicates that the explanation was readily comprehensible. Therefore, the word 'clear' is the precise synonym for lucid in this context.

Step-by-Step Solution

1

Identify the target word and analyze the surrounding sentence for contextual clues.

The target word is 'lucid', and the clue is 'making every complex step easy for the students to follow'.

Context clues provide the definition or functional meaning of the word as used in the specific sentence.

2

Evaluate the answer choices to find the word that best replaces the target word based on the clue.

The word 'clear' means easily understood, which matches the clue.

An explanation that makes complex concepts easy to understand is clear.

Key Concept

Identifying Context Clues for Synonyms

Estimated Time:35s

Question 3423Question →

Based on the analysis of word affixes, which word formed from the prefix meaning 'all' and the root meaning 'to know' correctly completes the sentence below?

Fill in the blanks below

The novel is narrated from an perspective that reveals the private thoughts and feelings of every character.

Show answer & explanation

Answer

omniscient

The correct term 'omniscient' is derived from the Latin prefix 'omni-' (meaning 'all') and the root 'sci-' (meaning 'to know'), combined with the adjective suffix '-ent'. In the context of the sentence, an all-knowing narrator who has insight into every character's private thoughts is accurately described as omniscient.

Step-by-Step Solution

1

Analyze the constituent affixes and root specified in the prompt instructions.

The Latin prefix meaning 'all' is 'omni-', and the root meaning 'to know' is 'sci-'.

Breaking down the required word parts identifies the base morphology needed.

2

Synthesize the prefix, root, and adjective suffix to form the target word.

Combining 'omni-' + 'sci-' + '-ent' produces 'omniscient'.

The suffix '-ent' creates an adjective that grammatically modifies 'perspective'.

3

Verify the synthesized word within the context of the sentence.

An 'omniscient' perspective possesses all-encompassing knowledge of every character's inner thoughts.

Ensures the semantic meaning and grammatical role match the sentence frame precisely.

Key Concept

Prefix and Suffix Analysis (omni- + sci- + -ent)

Estimated Time:45s

Question 3424Question →

Which term is most similar in definition to the word DISPARATE?

desperate

dissimilar

identical

divided

Show answer & explanation

Answer: dissimilar

Answer

dissimilar

The word 'disparate' describes things that are distinct in character and essentially different from one another. Therefore, 'dissimilar' is the most accurate synonym.

Step-by-Step Solution

1

Identify the part of speech and primary definition of the capitalized target word

The target word DISPARATE is an adjective meaning fundamentally different in quality or character, lacking a common basis for comparison.

Establishing the precise semantic boundary of the word in isolation prevents confusion with lookalike or soundalike terms.

2

Evaluate the answer choices to identify the equivalent adjective

'Dissimilar' describes entities that are not alike or distinct, accurately matching the definition of 'disparate'.

Direct semantic comparison isolates the correct synonym while filtering out antonyms and phonetic traps.

Key Concept

Isolated Word Synonyms

Question 3425Question →

A hotel manager is ordering custom acoustic paneling for a large rectangular conference room wall. The wall measures $36 \text{ feet}$ in length and $15 \text{ feet}$ in height. The wall contains $3$ identical rectangular windows, each measuring $6 \text{ feet}$ wide and $4 \text{ feet}$ high, which will not be covered by the paneling. If the acoustic paneling costs $\$45$ per square yard, what is the total cost of the paneling needed for this wall?

\$1,530

\$2,340

\$7,020

\$21,060

Show answer & explanation

Answer: $\$2,340$

Answer

The total cost of the acoustic paneling needed is

\$2,340

.

The correct answer is found by first determining the gross area of the wall (

36 \times 15 = 540 \text{ sq ft}

) and subtracting the area of the three windows (

3 \times 24 = 72 \text{ sq ft}

) to get a net coverage area of

468 \text{ sq ft}

. Because the paneling is sold by the square yard, the square footage must be converted by dividing by

9

(since

1 \text{ sq yd} = 9 \text{ sq ft}

). This gives

52 \text{ sq yd}

. Multiplying this by the price of

\$45

per square yard yields a total cost of

\$2,340

.

Step-by-Step Solution

1

Calculate the total area of the rectangular wall in square feet.

36 \times 15 = 540 \text{ sq ft}

The gross area is needed before accounting for the cutouts.

2

Calculate the combined area of the three identical windows.

3 \times (6 \times 4) = 72 \text{ sq ft}

The windows will not be covered by paneling, so their total area must be subtracted.

3

Subtract the window area from the total wall area to find the net area to be covered.

540 - 72 = 468 \text{ sq ft}

This provides the exact amount of paneling needed in square feet.

4

Convert the net area from square feet to square yards.

468 \div 9 = 52 \text{ sq yd}

Since the cost is given per square yard, the area must match this unit. There are

3 \times 3 = 9 \text{ sq ft}

in a square yard.

5

Multiply the required area in square yards by the cost per square yard.

52 \times 45 = \$2,340

This yields the total cost for the materials.

Key Concept

Calculating subtractive rectangular area and converting square units before applying a cost rate.

Question 3426Question →

Select the option that shares the closest semantic value with the capitalized term.

PUNCTILIOUS equates to which of the following?

Meticulous

Remiss

Prompt

Punitive

Show answer & explanation

Answer: Meticulous

Answer

Meticulous

The term 'punctilious' describes someone who is extremely careful about details, rules, or correct behavior. 'Meticulous' shares this exact definition, indicating extreme care, precision, and thoroughness.

Step-by-Step Solution

1

Analyze the isolated vocabulary word 'PUNCTILIOUS'.

Identify that it refers to strict attention to detail, rules, or correct behavior.

Establishing the precise definition of the target word is the required first step before evaluating options.

2

Evaluate the given options to find a matching definition.

Identify 'Meticulous' as the word meaning showing great attention to detail.

Direct semantic comparison isolates the correct synonym.

3

Eliminate deceptive distractors.

Discard 'Prompt', 'Punitive', and 'Remiss' as they represent unrelated concepts or direct antonyms.

Verifying that the distractors do not match the target meaning confirms the chosen answer is definitively correct.

Key Concept

Isolated Word Synonyms

Question 3427Question →

An armored convoy travels from Camp Alpha to Camp Bravo. For the first segment of the trip, the convoy travels at an average speed of 45 mph for 1 hour and 20 minutes. They then stop for a 45-minute rest. After the rest, the convoy resumes travel at an average speed of 30 mph for 2 hours and 15 minutes to reach Camp Bravo. Upon arrival, the convoy immediately takes a different, more direct route back to Camp Alpha. The return route is 20% shorter than the total distance they traveled to reach Camp Bravo. What is the total distance the convoy traveled during the entire round trip?

127.5 miles

153.0 miles

213.3 miles

229.5 miles

Show answer & explanation

Answer: 229.5 miles

Answer

229.5 miles

The correct answer accurately synthesizes multiple principles: converting mixed time units into exact hourly fractions, calculating distance for separate legs using

D = RT

, applying a percent reduction to find a new distance, and summing all legs to find the aggregate total distance of a round trip.

Step-by-Step Solution

1

Calculate the distance covered during the first travel segment.

60

miles

Convert 1 hour 20 minutes into hours:

1 + \frac{20}{60} = 1 + \frac{1}{3} = \frac{4}{3}

hours. Multiply by speed:

45 \times \frac{4}{3} = 60

miles.

2

Calculate the distance covered during the second travel segment.

67.5

miles

Convert 2 hours 15 minutes into hours:

2 + \frac{15}{60} = 2 + \frac{1}{4} = 2.25

hours. Multiply by speed:

30 \times 2.25 = 67.5

miles. (The 45-minute rest adds 0 distance).

3

Find the total outbound distance to Camp Bravo.

127.5

miles

Add the distances from the first and second segments:

60 + 67.5 = 127.5

miles.

4

Calculate the distance of the return route.

102

miles

The return route is 20% shorter than the outbound trip. This means it is

100\% - 20\% = 80\%

of the outbound distance. Multiply:

127.5 \times 0.8 = 102

miles.

5

Calculate the total distance traveled for the entire round trip.

229.5

miles

Add the total outbound distance and the return distance:

127.5 + 102 = 229.5

miles.

Key Concept

Calculating total distance across multiple legs with varying speeds, mixed time units, and percent reductions.

Estimated Time:3m 0s

Question 3428Question →

Read the sentence below. Based on the context clues provided, what word best completes the blank as a synonym for the italicized word?

Fill in the blanks below

Because the mountain pass was covered in thick ice and visibility dropped to zero, driving conditions became *hazardous*, meaning traveling along the route was extremely for the transport vehicles.

Show answer & explanation

Answer

dangerous (or unsafe / perilous / risky / treacherous)

The context clues 'thick ice' and 'visibility dropped to zero' establish that the driving conditions presented serious threats to the vehicles. Therefore, 'hazardous' means full of risk or peril, making 'dangerous' (or acceptable synonyms like 'unsafe', 'perilous', or 'risky') the correct word to complete the blank.

Step-by-Step Solution

1

Analyze the descriptive context clues surrounding the italicized word.

The clues 'thick ice' and 'visibility dropped to zero' indicate severe hazards and a high potential for accidents.

Identifying the situational tone and environmental conditions reveals the intended meaning of the target word.

2

Identify the precise synonym for 'hazardous' that completes the definition.

The word 'hazardous' means full of risk or peril, so 'dangerous' accurately completes the restatement.

The clause 'meaning traveling along the route was extremely...' explicitly defines and restates the meaning of 'hazardous'.

Key Concept

Using cause-and-effect and restatement context clues to determine the synonym of a target word.

Question 3429Question →

Match each target vocabulary word on the left with its most precise isolated synonym on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

ABSTRUSE pairs with Obscure; BELLICOSE pairs with Combative; FASTIDIOUS pairs with Meticulous; SPURIOUS pairs with Inauthentic.

Each word pairs uniquely with its closest direct synonym: 'ABSTRUSE' corresponds to 'Obscure' (hard to comprehend), 'BELLICOSE' corresponds to 'Combative' (warlike/aggressive), 'FASTIDIOUS' corresponds to 'Meticulous' (careful and exacting), and 'SPURIOUS' corresponds to 'Inauthentic' (false or illegitimate).

Step-by-Step Solution

1

Analyze 'ABSTRUSE' by evaluating its exact definition and semantic field.

Identified that 'ABSTRUSE' refers to concepts that are difficult to understand, matching 'Obscure'.

Isolates the meaning of intellectual complexity and eliminates confusion with phonetic look-alikes like 'obtuse'.

2

Analyze 'BELLICOSE' using root word analysis ('bellum' meaning war).

Identified that 'BELLICOSE' describes a hostile, warlike disposition, matching 'Combative'.

Directly links the martial root to aggression rather than general agitation.

3

Analyze 'FASTIDIOUS' by determining its precise descriptive usage.

Identified that 'FASTIDIOUS' describes demanding exacting standards and thoroughness, matching 'Meticulous'.

Differentiates genuine meaning from the false association with speed suggested by the superficial letters 'fast'.

4

Analyze 'SPURIOUS' by assessing its truth-value connotation.

Identified that 'SPURIOUS' signifies something forged, illegitimate, or counterfeit, matching 'Inauthentic'.

Separates the concept of deception and illegitimacy from superficial phonetic resemblances to words like 'furious'.

Key Concept

Direct semantic pairing of advanced isolated vocabulary words without contextual clues.

Estimated Time:1m 30s

Question 3430Question →

A courier drives from a dispatch center to a client's location $60$ miles away and then returns to the dispatch center along the exact same route. The outbound drive to the client takes exactly $2$ hours. If the courier's average speed for the entire round trip is $24$ miles per hour, what is the courier's average speed on the return trip?

18

miles per hour

20

miles per hour

40

miles per hour

120

miles per hour

Show answer & explanation

Answer: $20$ miles per hour

Answer

The courier's average speed on the return trip is

20

miles per hour.

To find the return speed, we first determine the total time of the trip. The total round-trip distance is

120

miles (

60

miles each way). Using the overall average speed of

24

mph, the total time is

120 \div 24 = 5

hours. Since the outbound trip took

2

hours, the return trip must have taken

5 - 2 = 3

hours. Finally, the return speed is the return distance (

60

miles) divided by the return time (

3

hours), which equals

20

miles per hour.

Step-by-Step Solution

1

Calculate the total round-trip distance.

Total distance =

60 \times 2 = 120

miles.

The one-way distance is

60

miles, so the round trip is twice that amount.

2

Determine the total time taken for the entire round trip.

Total time =

120 \text{ miles} \div 24 \text{ mph} = 5

hours.

Average speed for the entire trip is total distance divided by total time.

3

Calculate the time taken for the return leg.

Return time =

5 \text{ hours} - 2 \text{ hours} = 3

hours.

The total trip time minus the outbound time gives the time remaining for the return trip.

4

Calculate the average speed for the return trip.

Return speed =

60 \text{ miles} \div 3 \text{ hours} = 20

miles per hour.

Speed is distance divided by time. The return distance is

60

miles and the return time is

3

hours.

Key Concept

Round Trip Average Speed

Question 3431Question →

Which of the following is the closest synonym for the word AFFLUENT?

fluent

impoverished

wealthy

arrogant

Show answer & explanation

Answer: wealthy

Answer

The word most similar in meaning to 'AFFLUENT' is 'wealthy'.

The adjective 'affluent' describes someone or something characterized by prosperity, abundance, and material riches. Therefore, 'wealthy' is the exact synonym.

Step-by-Step Solution

1

Identify the part of speech and primary definition of the target word.

'AFFLUENT' is an adjective meaning possessing an abundance of wealth, property, or financial resources.

Understanding the core definition is the primary requirement for isolated word synonym identification.

2

Examine the answer choices to identify the true synonym while eliminating distractors based on false cognates, antonyms, or connotation errors.

'wealthy' directly matches the definition of having large amounts of money or resources.

Direct semantic comparison confirms the correct equivalent term.

Key Concept

Identifying isolated direct synonyms for vocabulary words relating to economic status.

Estimated Time:30s

Question 3432Question →

MITIGATE most nearly means which of the following?

Aggravate

Alleviate

Migrate

Prosecute

Show answer & explanation

Answer: Alleviate

Answer

Alleviate

To mitigate means to make something less severe, serious, or painful. The term alleviate carries the exact same meaning of reducing the intensity of a negative condition or burden, making it the indisputable direct synonym.

Step-by-Step Solution

1

Define the target isolated word

The verb mitigate means to make something bad or harmful less severe, intense, or painful.

Establishing the precise definition of the isolated target word is required to identify its closest direct synonym.

2

Evaluate the choices to identify the equivalent term

Alleviate means to relieve or lessen severity, matching the core definition of mitigate.

Comparing option meanings identifies the correct synonym while eliminating antonyms and visually similar words.

Key Concept

Direct synonym identification for isolated vocabulary

Estimated Time:30s

Question 3433Question →

Analyze the prefixes and root structures of the following words. Which synonym on the right correctly matches each target word on the left?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Antecedent pairs with Precursor; Benefactor pairs with Supporter; Malcontent pairs with Dissident; Postscript pairs with Addendum.

Each pair aligns through direct morphological correspondence: 'Antecedent' and 'Precursor' both rely on prefixes meaning 'before' (ante-, pre-); 'Benefactor' uses 'bene-' (good) to designate a benevolent 'Supporter'; 'Malcontent' uses 'mal-' (bad) to describe a dissatisfied 'Dissident'; and 'Postscript' uses 'post-' (after) to signify an 'Addendum'.

Step-by-Step Solution

1

Examine the prefix and root in 'Antecedent'.

'Ante-' (before) + 'cedere' (to go) indicates an entity preceding another in time or logic.

Identify morphological indicators to establish alignment with 'Precursor'.

2

Examine the prefix and suffix in 'Benefactor'.

'Bene-' (good) + '-or' (agent) denotes an agent performing good deeds or giving aid.

Identify morphological indicators to establish alignment with 'Supporter'.

3

Examine the prefix and base in 'Malcontent'.

'Mal-' (bad/poor) + 'content' (satisfied) denotes someone who is dissatisfied or rebellious.

Identify morphological indicators to establish alignment with 'Dissident'.

4

Examine the prefix and root in 'Postscript'.

'Post-' (after) + 'script' (written) denotes supplementary text added after completion.

Identify morphological indicators to establish alignment with 'Addendum'.

Key Concept

Morphological analysis of Latin prefixes (ante-, bene-, mal-, post-) to deduce word meanings and determine precise synonyms.

Estimated Time:1m 0s

Question 3434Question →

A rescue helicopter flies at a rate of $3$ miles per minute for $40$ minutes to reach an extraction point. After the pickup, it flies to a hospital at a cruising speed of $120$ miles per hour for $90$ minutes. What is the total distance the helicopter traveled in miles?

182

300

1,920

10,920

Show answer & explanation

Answer: 300

Answer

The correct answer is 300 miles, which is the sum of the 120 miles traveled in the first stage and the 180 miles traveled in the second stage.

The correct answer accurately accounts for the units in both stages of the flight. For the first stage, the units match (miles per minute and minutes), yielding 120 miles. For the second stage, 90 minutes is converted to 1.5 hours to match the miles per hour speed, yielding 180 miles. Adding them together gives 300 miles.

Step-by-Step Solution

1

Calculate the distance for the first stage by multiplying the rate by the time.

3

miles/minute ×

40

minutes =

120

miles.

The rate is given in miles per minute and the time is given in minutes, so the units already match and no time conversion is necessary.

2

Convert the time for the second stage from minutes to hours.

90

minutes ÷

60

minutes/hour =

1.5

hours.

The cruising speed is given in miles per hour, so the travel time must be converted to hours before calculating distance.

3

Calculate the distance for the second stage using the converted time.

120

miles/hour ×

1.5

hours =

180

miles.

Multiplying the speed in mph by the time in hours yields the distance in miles.

4

Add the distances from both stages to find the total distance traveled.

120

miles +

180

miles =

300

miles.

The total distance of a multi-leg journey is the sum of the distances of each individual leg.

Key Concept

Calculating multi-leg distances requiring attention to varying speed units and necessary time conversions.

Estimated Time:2m 0s

Question 3435Question →

To ensure safety aboard the vessel, the captain enforced *stringent* regulations, demanding strict compliance with all emergency protocols. In this sentence, *stringent* most nearly means which of the following?

rigorous

lenient

complicated

routine

Show answer & explanation

Answer: rigorous

Answer

rigorous

The sentence clearly states that the captain was 'demanding strict compliance,' providing a direct context clue that 'stringent' means strict or demanding. Among the choices, 'rigorous' is the accurate synonym.

Step-by-Step Solution

1

Locate the context clue following the target word in the sentence.

The phrase 'demanding strict compliance with all emergency protocols' acts as an explanatory clue for the word 'stringent.'

Sentences often provide direct restatements or clarifying phrases that explain the meaning of an unfamiliar term.

2

Identify the option that matches the meaning of strict and demanding.

'Rigorous' means extremely thorough, strict, and demanding, providing an exact synonym for 'stringent' in this context.

Substituting 'rigorous' into the sentence preserves its original meaning and grammatical structure.

Key Concept

Identifying restatement and definition context clues to determine word meaning

Estimated Time:45s

Question 3436Question →

Until the permanent communications tower could be repaired after the storm, the logistics team set up a provisional relay station to maintain emergency broadcasts. In the sentence above, the word provisional most nearly means which of the following?

permanent

temporary

professional

defective

Show answer & explanation

Answer: temporary

Answer

The word provisional most nearly means temporary.

In the provided sentence, the opening phrase 'Until the permanent communications tower could be repaired' sets up a clear temporal contrast. The relay station was established as a short-term solution while awaiting repairs, indicating that 'provisional' signifies an interim or temporary measure.

Step-by-Step Solution

1

Analyze the sentence structure and identify the contextual contrast clue.

The clause 'Until the permanent communications tower could be repaired' establishes that the relay station is an interim measure used before a lasting fix.

Understanding the timeline and contrasting condition reveals how the relay station is intended to function.

2

Select the synonym that matches the interim, short-term nature of the station.

The word 'temporary' directly corresponds to an arrangement serving for a limited time until the permanent facility returns to service.

Substituting 'temporary' preserves the logical flow and intended meaning of the sentence.

Key Concept

Using contrast and temporal transition context clues to deduce word meaning

Estimated Time:45s

Question 3437Question →

Read each scenario below carefully. Based on the semantic and structural context clues within each sentence, which contextual synonym correctly matches each bolded word?

Click a left item, then click its matching right item

Show answer & explanation

Answer

taciturn matches 'Reserved and habitually silent in speech'; salutary matches 'Producing beneficial or wholesome results'; superfluous matches 'Exceeding what is necessary; redundant'; and lucid matches 'Intelligible, transparent, and easy to comprehend'.

Each match is established through direct contextual relationships in the stems: 'taciturn' is defined by speaking sparingly amidst debate; 'salutary' is shown through the restorative outcome of a policy; 'superfluous' is demonstrated by unnecessary duplicate gear; and 'lucid' is illustrated by explaining intricate concepts with clarity.

Step-by-Step Solution

1

Analyze the sentence context for 'taciturn'.

Identify the contrast between 'heated debate' and the behavior of 'uttering only a few measured words'.

Contextual contrast clues establish that the analyst is quiet and speaks minimally, matching 'Reserved and habitually silent in speech'.

2

Analyze the sentence context for 'salutary'.

Identify the concession 'Although... resistance' resolving into the positive outcome 'restoring financial integrity'.

The shift from initial pushback to positive organizational recovery demonstrates that 'salutary' signifies 'Producing beneficial or wholesome results'.

3

Analyze the sentence context for 'superfluous'.

Identify the logical premise that the kit already has 'all essential survival gear' and extra items would just add unnecessary weight.

Because essential needs are already met, duplicate gear is extra and unneeded, which corresponds directly to 'Exceeding what is necessary; redundant'.

4

Analyze the sentence context for 'lucid'.

Identify the contrast between the complex topic ('convoluted cryptographic systems') and the outcome ('clear and straightforward to follow').

The ability to make complicated technical material straightforward means the delivery was 'Intelligible, transparent, and easy to comprehend'.

Key Concept

Using semantic contrast, concession, and cause-effect context clues to deduce precise synonyms of advanced vocabulary.

Estimated Time:1m 30s

Question 3438Question →

A city planner is designing a rectangular public square that measures $60 \text{ yards}$ by $40 \text{ yards}$ . The entire square will be paved with brick, except for a central rectangular fountain that measures $10 \text{ yards}$ by $8 \text{ yards}$ . If the paving bricks cost $\$2.50$ per square foot, what is the total cost of the bricks needed for the square in dollars?

Show answer & explanation

Answer: 52200

Answer

52200

The correct answer is

52200 because the net area of the square to be paved is

2,320

square yards (

2400 \text{ sq yd total} - 80 \text{ sq yd fountain}

). Since

1

square yard equals

9

square feet, this converts to

20,880

square feet. Multiplying the total square footage by the brick cost of

\

2.50

per square foot yields a total cost of

\$52,200

.

Step-by-Step Solution

1

Calculate the total area of the public square in square yards.

2400 \text{ sq yd}

The total area is the product of its length and width (

60 \text{ yards} \times 40 \text{ yards}

).

2

Calculate the area of the central fountain in square yards.

80 \text{ sq yd}

The area of the fountain is the product of its length and width (

10 \text{ yards} \times 8 \text{ yards}

).

3

Subtract the fountain's area from the total area to find the net paved area in square yards.

2320 \text{ sq yd}

The fountain will not be paved, so its area must be removed from the total square yardage (

2400 - 80

).

4

Convert the net area from square yards to square feet.

20880 \text{ sq ft}

The cost of the bricks is given per square foot. Since

1 \text{ yard} = 3 \text{ feet}

,

1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}

. Therefore, we multiply the area in square yards by

9

(

2320 \times 9 = 20880

).

5

Calculate the total cost by multiplying the net area in square feet by the price per square foot.

52200

Multiplying the total square footage (

20880

) by the cost per square foot (

\$2.50

) yields the final cost in dollars.

Key Concept

Subtractive area calculations and square unit conversions

Question 3439Question →

A ferry transports vehicles from the mainland to an island $18$ miles away. The ferry travels to the island at a speed of $9$ miles per hour and returns to the mainland along the same route at a speed of $6$ miles per hour.

How many hours does the complete round trip take?

Show answer & explanation

Answer: 5

Answer

The complete round trip takes 5 hours.

The round trip consists of two legs with different speeds. The outbound leg takes

18 \div 9 = 2

hours. The return leg takes

18 \div 6 = 3

hours. Adding these together yields a total time of

5

hours for the entire trip.

Step-by-Step Solution

1

Calculate the time taken for the outbound trip.

18 \div 9 = 2

hours

Time is equal to distance divided by rate. This gives the time spent traveling to the island.

2

Calculate the time taken for the return trip.

18 \div 6 = 3

hours

The return trip covers the same distance but at a slower speed.

3

Calculate the total round-trip time.

2 + 3 = 5

hours

The total time for a round trip is the sum of the time spent on each individual leg.

Key Concept

Calculating total round-trip time by finding the time for each leg separately.

Question 3440Question →

A contractor is preparing to apply sealant to a new rectangular patio that measures $14$ yards in length and $5$ yards in width. If the sealant costs $3$ dollars per square yard, what is the total cost, in dollars, to seal the entire patio?

Show answer & explanation

Answer: 210

Answer

210

To find the total cost, you must first determine the area of the patio by multiplying the length (

14

yards) by the width (

5

yards), which equals

70

square yards. Then, multiply this area by the cost per square yard (

3

dollars) to get the total cost of

210

dollars.

Step-by-Step Solution

1

Calculate the area of the rectangular patio.

Area =

14 \times 5 = 70

square yards

The cost of the sealant is based on the surface area of the patio.

2

Calculate the total cost to seal the patio.

Total cost =

70 \times 3 = 210

dollars

Multiplying the total square yards by the price per square yard gives the final cost.

Key Concept

Calculating rectangular area and applying a unit rate.

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept