Tüm alıştırma soruları

Soru 4841Soru →

A flashing red light blinks every $12$ seconds, and a flashing blue light blinks every $15$ seconds. If both lights blink together at exactly 8:00 PM, how many seconds will pass before they blink together again?

3

27

60

180

Cevabı ve açıklamayı göster

Cevap: 60

Cevap

60

To find when two periodic events will occur together again, the least common multiple (LCM) of their individual intervals must be determined. The LCM of

12

and

15

is

60

, meaning the lights will blink together every

60

seconds.

Adım Adım Çözüm

1

Identify the goal of the problem.

Find the Least Common Multiple (LCM) of the two blinking intervals to determine when the lights will sync up again.

Because the lights blink periodically, their next simultaneous blink occurs at a common multiple of both intervals.

2

Find the prime factorization of 12 and 15.

12 = 2^2 \times 3

, and

15 = 3 \times 5

.

Prime factorization is a reliable method for finding the LCM.

3

Calculate the LCM using the prime factors.

LCM = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60

.

The LCM is calculated by multiplying the highest power of each prime factor present in either number.

Anahtar Kavram

Least Common Multiple (LCM) applied to periodic events

Soru 4842Soru →

Three automated beacons are programmed to flash at specific intervals. Beacon A flashes every $24$ seconds, Beacon B flashes every $36$ seconds, and Beacon C flashes every $45$ seconds. If all three beacons flash simultaneously at exactly 8:00:00 PM, how many more times will they flash together within exactly one hour?

6

10

330

1,200

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10

To determine when multiple periodic events occur at the exact same time, we must find their Least Common Multiple (LCM). Using prime factorization, we find the LCM of

24

,

36

, and

45

by taking the highest power of each distinct prime factor present:

2^3 \times 3^2 \times 5 = 360

seconds. This means the beacons align and flash together once every

360

seconds. Because the total timeframe is exactly one hour, we convert this duration to seconds (

60 \text{ minutes} \times 60 \text{ seconds/minute} = 3,600 \text{ seconds}

). Finally, dividing the total time by the simultaneous interval (

3,600 \div 360

) results in exactly

10

additional synchronized flashes.

Adım Adım Çözüm

1

Determine the prime factorization of each beacon's flashing interval.

24 = 2^3 \times 3

,

36 = 2^2 \times 3^2

, and

45 = 3^2 \times 5

Finding the prime factors is necessary to calculate the Least Common Multiple (LCM), which dictates when the independent events align.

2

Calculate the Least Common Multiple (LCM) of the three intervals.

\text{LCM} = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360

seconds

The LCM represents the exact time interval in seconds at which all three beacons will flash together again.

3

Convert the total given time window (one hour) into the same units (seconds).

1 \text{ hour} = 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3,600 \text{ seconds}

Both the flashing interval and the total time frame must be in identical units before dividing.

4

Divide the total time window by the LCM interval.

3,600 \div 360 = 10

This division yields the total number of times the beacons will synchronize during the designated one-hour period.

Anahtar Kavram

Applying the Least Common Multiple (LCM) and unit conversions to solve periodic real-world alignment problems.

Soru 4843Soru →

When establishing forward supply caches in arid regions, logistical personnel must verify that stored rations remain desiccated—that is to say, completely dried—before sealing storage lockers. Excess moisture inside shipping containers promotes fungal growth and rapid food spoilage. Inspecting packing seals and humidity indicators guarantees that emergency supplies remain wholesome and ready for field distribution.

As used in the passage, the word "desiccated" most nearly means:

subject to fungal growth

completely dried

rapidly distributed

heavily fortified

Cevabı ve açıklamayı göster

Cevap: completely dried

Cevap

completely dried

The correct answer is directly stated in the text through a synonymous context clue. The author uses em-dashes and the explanatory transition 'that is to say' to explicitly clarify that 'desiccated' means 'completely dried'.

Adım Adım Çözüm

1

Locate the target word in the passage.

The word 'desiccated' appears in the first sentence: '...verify that stored rations remain desiccated—that is to say, completely dried—before sealing storage lockers.'

Finding the specific sentence allows for analysis of immediate contextual markers.

2

Identify the punctuation and transitional phrase signaling a definition or synonym.

The dashes set off the restatement phrase 'that is to say, completely dried'.

The phrase 'that is to say' functions as an explicit synonymous context clue defining the preceding term.

3

Select the option that matches the synonym provided in the text.

The meaning 'completely dried' matches the restated definition precisely.

The correct choice must strictly mirror the textually provided definition without adding outside assumptions.

Anahtar Kavram

Identifying Synonymous Context Clues

Tahmini Süre:1m 0s

Soru 4844Soru →

Shipboard Halon 1301 total flooding systems are designed to extinguish engine room fires rapidly while allowing personnel time to evacuate. When the manual pull station is activated, pneumatic actuators release nitrogen pilot gas, which triggers a pneumatic 30-second time-delay mechanism before opening the main Halon storage cylinder valves. This delay allows ventilation dampers to close automatically and audible evacuation alarms to sound. An emergency bypass valve is installed parallel to the time delay; opening this bypass valve overrides the countdown and discharges the Halon agent immediately into the protected space.

According to the passage, what specific action immediately discharges the Halon agent without waiting for the time delay?

Activating the manual pull station

Opening the emergency bypass valve

Waiting for the thirty-second countdown to expire

Closing the engine room ventilation dampers

Cevabı ve açıklamayı göster

Cevap: Opening the emergency bypass valve

Cevap

Opening the emergency bypass valve overrides the countdown and immediately discharges the Halon extinguishing agent.

The passage explicitly states that opening the emergency bypass valve overrides the countdown and discharges the Halon agent immediately into the protected space.

Adım Adım Çözüm

1

Identify the key requirement in the question stem

The question asks for the specific action that causes an immediate discharge of Halon without waiting for the delay.

Clarifying the specific factual condition prevents confusion with standard activation procedures.

2

Scan the passage for explicit statements regarding immediate discharge or overriding the delay

The final sentence states: 'An emergency bypass valve is installed parallel to the time delay; opening this bypass valve overrides the countdown and discharges the Halon agent immediately into the protected space.'

Direct fact retrieval requires matching the stated condition directly with the author's explicit words.

3

Match the identified fact with the corresponding answer choice

Opening the emergency bypass valve directly matches the passage text.

Eliminating options that describe standard activation or automated side effects confirms the unambiguous correct answer.

Anahtar Kavram

Direct factual extraction from technical text based strictly on explicit stated statements

Tahmini Süre:45s

Soru 4845Soru →

Read the following passage:

Early attempts to harness tidal currents for municipal power generation in coastal estuaries often encountered severe mechanical fouling from marine organisms and saltwater corrosion. Although modern composite turbine blades and cathodic protection systems have significantly reduced wear, deploying submerged generation arrays remains an economically precarious venture due to unpredictable maintenance cycles. As a result, while engineers acknowledge the vast kinetic potential of oceanic tides, energy planners remain guarded regarding the immediate commercial viability of large-scale estuary arrays.

Statement: Based on the passage, the author's tone toward the near-term commercial implementation of tidal energy arrays is best described as cautiously reserved.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True

The correct answer is True because the author balances recognition of engineering improvements and energy potential with explicit warnings about high maintenance costs and financial uncertainty, creating a tone of cautious reserve.

Adım Adım Çözüm

1

Analyze the passage for keywords and descriptive language indicating the author's stance.

Phrases like 'economically precarious venture,' 'unpredictable maintenance cycles,' and 'remain guarded' reflect hesitation and realism despite acknowledging 'vast kinetic potential.'

Identifying the author's specific word choices reveals the emotional coloring and perspective of the text.

2

Evaluate whether the tone leans toward unbridled optimism, total skepticism, or balanced caution.

The author recognizes technological progress while highlighting lingering financial and logistical risks.

Balancing positive acknowledgment with highlighted risks defines a tone of cautious reserve.

3

Compare the synthesized tone to the statement provided in the prompt.

The statement accurately reflects the author's cautiously reserved attitude toward immediate large-scale commercialization.

Confirming alignment between the passage evidence and the statement validates the truth value.

Anahtar Kavram

Inferring Author Tone and Attitude

Tahmini Süre:1m 0s

Soru 4846Soru →

A military engineering unit is laying communication cable between two outposts. The total required distance for the connection is $4.5 \text{ miles}$ . The supply depot issues this specific cable in standard spools containing $500 \text{ meters}$ of cable each. If $1 \text{ mile}$ is approximately equal to $1.6 \text{ kilometers}$ , what is the minimum number of spools the unit must request to ensure they have enough cable to cover the entire distance?

6

9

15

144

Cevabı ve açıklamayı göster

Cevap: 15

Cevap

15

To find the total number of spools needed, first unify the units of measurement. Convert 4.5 miles into kilometers by multiplying by 1.6, yielding 7.2 kilometers. Since the spools are measured in meters, convert 7.2 kilometers into meters by multiplying by 1,000, which equals 7,200 meters. Next, divide the 7,200-meter total distance by the 500 meters contained on each spool, resulting in 14.4 spools. Because a fraction of a spool cannot be requested and the full distance must be covered, the number must be rounded up to the nearest whole spool, making 15 the correct amount to request.

Adım Adım Çözüm

1

Convert the total distance from miles to kilometers using the given conversion factor.

4.5 \text{ miles} \times 1.6 \text{ km/mile} = 7.2 \text{ kilometers}

To standardize the units, the distance must first be brought into the metric system where the spool length is measured.

2

Convert the distance from kilometers to meters.

7.2 \text{ km} \times 1,000 \text{ m/km} = 7,200 \text{ meters}

The spools are measured in meters, so the total distance required must match this unit.

3

Determine the exact number of spools required by dividing the total meters by the meters per spool.

7,200 \text{ meters} \div 500 \text{ meters/spool} = 14.4 \text{ spools}

This finds how many 500-meter increments are needed to cover the 7,200-meter distance.

4

Round up to the nearest whole number.

15 \text{ spools}

Since the unit cannot be issued a fraction of a spool and 14 spools would leave them short of the required distance, they must request the next whole number.

Anahtar Kavram

Converting across measurement systems (US Customary to Metric) and solving practical constraints using the ceiling function.

Soru 4847Soru →

Determine the total number of positive factors for each of the following integers. Then, place the integers in order from the one with the fewest factors to the one with the most factors.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence is: The integer

7

(2 factors), The integer

9

(3 factors), The integer

8

(4 factors), and The integer

12

(6 factors).

By counting the positive divisors of each number, we find that

7

has two factors,

9

has three factors,

8

has four factors, and

12

has six factors. Placing them in ascending order of their factor counts yields

7, 9, 8

, and

12

.

Adım Adım Çözüm

1

List all positive factors for the integer

12

.

The factors of

12

are

1, 2, 3, 4, 6

, and

12

. There are

6

factors in total.

Finding the total count of factors is required to compare and order the integers.

2

List all positive factors for the integer

7

.

The factors of

7

are

1

and

7

. There are

2

factors in total.

Determining the factor count for each number allows for proper sorting.

3

List all positive factors for the integer

8

.

The factors of

8

are

1, 2, 4

, and

8

. There are

4

factors in total.

We must evaluate every integer provided in the list.

4

List all positive factors for the integer

9

.

The factors of

9

are

1, 3

, and

9

. There are

3

factors in total.

This completes the factor counting for all items.

5

Sort the integers based on their factor counts from fewest to most.

The sequence is

2

factors (The integer

7

), then

3

factors (The integer

9

), then

4

factors (The integer

8

), and finally

6

factors (The integer

12

).

The question asks to place the integers in order from fewest factors to most factors.

Anahtar Kavram

Factors and Prime Numbers

Tahmini Süre:45s

Soru 4848Soru →

Which of the following equations correctly represents the statement: 'Twelve subtracted from five times the sum of a number $y$ and six is equal to three less than twice the number'?

5(y + 6) - 12 = 2y - 3

12 - 5(y + 6) = 3 - 2y

5y + 6 - 12 = 2y - 3

5(y + 6) - 12 = 3 - 2y

Cevabı ve açıklamayı göster

Cevap: $5(y + 6) - 12 = 2y - 3$

Cevap

The equation

5(y + 6) - 12 = 2y - 3

correctly translates all verbal phrases in the appropriate order with necessary grouping symbols.

The translation process requires breaking the sentence into smaller chunks. The left side starts with 'five times the sum of a number

y

and six', written as

5(y + 6)

. Then, 'twelve subtracted from' means we subtract

12

from that product, yielding

5(y + 6) - 12

. The right side is 'three less than twice the number'. Twice the number is

2y

, and three less than that is

2y - 3

. Setting them equal gives

5(y + 6) - 12 = 2y - 3

.

Adım Adım Çözüm

1

Translate 'the sum of a number

y

and six'.

(y + 6)

The word 'sum' indicates addition, and because this entire expression will be multiplied in the next step, it must be enclosed in parentheses.

2

Translate 'five times the sum'.

5(y + 6)

The multiplier

5

must apply to the entire grouped quantity of the sum.

3

Translate 'Twelve subtracted from' the previous result.

5(y + 6) - 12

The phrase 'subtracted from' means

12

is taken away from the established quantity, so it is placed after the minus sign.

4

Translate 'three less than twice the number'.

2y - 3

First, 'twice the number' is

2y

. 'Three less than' means

3

is subtracted from

2y

. This forms the right side of the equation.

Anahtar Kavram

Translating complex algebraic phrases requires careful attention to grouping words like 'sum' or 'difference' and order-reversing phrases like 'less than' or 'subtracted from'.

Soru 4849Soru →

Match each unsimplified algebraic expression on the left with its completely simplified equivalent on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The unsimplified expressions must be correctly expanded using the distributive property, observing proper handling of negative multipliers and nested grouping symbols, and then reduced by combining like terms.

Each expression correctly matches its fully reduced polynomial form. The reductions require systematic application of the distributive property, careful tracking of positive and negative coefficients, and the grouping and addition of like variables.

Adım Adım Çözüm

1

Simplify the first expression:

3(2a - b) - 4(a + 2b)

6a - 3b - 4a - 8b = 2a - 11b

Multiply each term inside the parentheses by the outside factor, then group like terms (

6a - 4a

and

-3b - 8b

).

2

Simplify the second expression:

-2(a - 3b) + 5(2a - b)

-2a + 6b + 10a - 5b = 8a + b

Properly distribute the negative sign in the first term (

-2 \times -3b = 6b

), then combine like terms.

3

Simplify the third expression:

a(3 - 2b) - 2(a - ab)

3a - 2ab - 2a + 2ab = a

Distribute the variables and constants, recognizing that

-2ab

and

+2ab

are additive inverses and cancel to zero.

4

Simplify the fourth expression:

4a - [2b - 3(a - b)]

4a - [2b - 3a + 3b] = 4a - [5b - 3a] = 4a - 5b + 3a = 7a - 5b

Work from the innermost parentheses outward. Distribute

-3

, combine like terms inside the bracket, and distribute the outer negative sign.

Anahtar Kavram

Simplifying Algebraic Expressions

Tahmini Süre:2m 0s

Soru 4850Soru →

Read the following technical evaluations regarding specialized industrial equipment. Match each excerpt to the author's primary tone or attitude based on the word choice and phrasing used.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Match the excerpt praising the geothermal design as a 'brilliant leap forward' with 'Appreciative and enthusiastic'; match the excerpt criticizing the valve failure and 'reckless disregard' with 'Critical and disapproving'; match the excerpt providing numerical flow rates and pressures with 'Objective and matter-of-fact'.

Tone is determined by examining an author's diction and perspective. The first statement utilizes laudatory language ('brilliant,' 'remarkable') showing appreciation; the second uses condemnatory phrasing ('routinely jammed,' 'reckless disregard') establishing a critical attitude; the third relies strictly on unbiased numerical parameters, creating an objective tone.

Adım Adım Çözüm

1

Analyze the descriptive adjectives and emotive language in the first excerpt.

Identified positive descriptors ('brilliant leap forward', 'remarkable quietness') indicating praise.

Word choice reveals the author's supportive and admiring stance toward the design.

2

Examine the diction in the second excerpt for signs of evaluation or judgment.

Identified negative evaluative terms ('routinely jammed', 'reckless disregard') indicating strong disapproval.

The author explicitly condemns the safety oversight and challenges marketing claims.

3

Evaluate the third excerpt for the presence or absence of subjective commentary.

Found only measurable quantities ('twelve liters per minute', 'forty to forty-five pounds per square inch') with zero emotional coloring.

The absence of value judgments indicates a purely factual, neutral presentation.

Anahtar Kavram

Inferring Author Tone and Attitude

Tahmini Süre:1m 15s

Soru 4851Soru →

Simplify the following algebraic expression:

8x - 2[x - 3(2x - y)]

Which of the following represents the completely simplified form?

18x + 2y

18x + 6y

18x - 6y

-30x^2 + 18xy

Cevabı ve açıklamayı göster

Cevap: $18x - 6y$

Cevap

The completely simplified form is

18x - 6y

.

The expression is fully simplified by applying the distributive property iteratively, starting from the innermost parentheses, carefully tracking all negative signs, and finally combining like terms to arrive at

18x - 6y

.

Adım Adım Çözüm

1

Distribute the -3 into the innermost parentheses.

-3(2x - y) = -6x + 3y

According to the order of operations, innermost grouping symbols must be evaluated first. Distributing a negative number flips the signs of the terms inside.

2

Substitute this back and combine like terms inside the brackets.

x - 6x + 3y = -5x + 3y

Combining the like variable terms simplifies the expression inside the brackets before moving to the next operation.

3

Distribute the -2 across the newly simplified terms inside the bracket.

-2(-5x + 3y) = 10x - 6y

The distributive property applies the outside multiplier to every term within the brackets.

4

Combine this result with the remaining term outside the brackets.

8x + 10x - 6y = 18x - 6y

Adding the like x terms yields the final, completely simplified algebraic expression.

Anahtar Kavram

Simplifying Nested Algebraic Expressions

Soru 4852Soru →

Simplify the following algebraic expression:

(3y^4)(-5y^2)

Which of the following is the correctly simplified expression?

15y^6

-15y^6

-15y^8

-2y^6

Cevabı ve açıklamayı göster

Cevap: $-15y^6$

Cevap

-15y^6

The expression is simplified by first multiplying the numerical coefficients (

3 \times -5 = -15

). Then, the product rule for exponents is applied to the variables by adding their exponents (

y^4 \times y^2 = y^{4+2} = y^6

). Combining these two parts yields the correct simplified expression,

-15y^6

.

Adım Adım Çözüm

1

Group and multiply the numerical coefficients.

3 \times (-5) = -15

The commutative property allows us to group the constant numbers together for multiplication.

2

Multiply the variable terms using the product rule for exponents.

y^4 \times y^2 = y^{4+2} = y^6

When multiplying exponential terms with the same base, their exponents must be added.

3

Combine the resulting coefficient and variable term.

-15y^6

This represents the final simplified form of the expression.

Anahtar Kavram

Product Rule for Exponents and Integer Multiplication

Soru 4853Soru →

Determine the numerical value of the variable $x$ that satisfies the algebraic equation below.

Aşağıdaki boşlukları doldurun

\frac{3}{8}(16x - 24) + 5 = -2(2x - 1) + 4x + 6

x =

Cevabı ve açıklamayı göster

Cevap

The value of x that satisfies the equation is 2.

By successfully applying the distributive property to both sides of the equation, the expression simplifies to 6x - 9 + 5 = -4x + 2 + 4x + 6. Combining like terms reduces this to 6x - 4 = 8. Adding 4 to both sides yields 6x = 12, which gives exactly 2.

Adım Adım Çözüm

1

Distribute the fraction on the left side and the negative integer on the right side.

6x - 9 + 5 = -4x + 2 + 4x + 6

Applying the distributive property removes the grouping parentheses, which is necessary before combining any terms.

2

Combine the constant terms on the left side and the like terms on the right side.

6x - 4 = 8

Simplifying both sides of the equation by grouping like terms makes it straightforward to isolate the variable. The -4x and +4x cancel each other out.

3

Isolate the term containing the variable by adding 4 to both sides of the equation.

6x = 12

Using the addition property of equality maintains the balance while moving constants to one side.

4

Divide both sides by 6 to solve for x.

x = 2

Dividing by the coefficient of x isolates the variable completely and provides the final solution.

Anahtar Kavram

Solving multi-step linear equations involving fractional distribution and combining like terms across both sides of the equals sign.

Soru 4854Soru →

Read the passage below:

In 1879, the steamship Strathleven successfully transported forty tons of frozen beef from Melbourne to London, proving that artificial refrigeration could conquer equatorial heat. While contemporary headlines hailed the voyage as an unmitigated triumph, shipping ledgers told a more sobering story. The ship’s compressed-air cooling apparatus consumed staggering amounts of coal, leaving scant cargo space for profitable freight, and erratic temperature spikes spoiled portions of the outer carcasses. The voyage demonstrated technical possibility, yet commercial viability remained a distant prospect.

Statement: The author's attitude toward the commercial readiness of early refrigerated steamships is best characterized as guarded skepticism.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True

The author acknowledges the historical achievement of transporting chilled cargo across the equator but relies on critical phrasing such as 'sobering story,' 'staggering amounts of coal,' and 'distant prospect' to convey clear doubt regarding immediate business viability. Therefore, characterizing the author's attitude as guarded skepticism is accurate.

Adım Adım Çözüm

1

Identify the author's diction and contrasting viewpoints in the passage.

The author contrasts public celebration ('unmitigated triumph') with practical realities ('sobering story', 'staggering amounts of coal', 'scant cargo space').

Tone is revealed through the author's evaluative language and the contrast between public reaction and factual analysis.

2

Analyze the concluding evaluation regarding the voyage's broader success.

The author separates technical feasibility from economic readiness, concluding that 'commercial viability remained a distant prospect.'

This distinction demonstrates that the author respects the engineering proof of concept while remaining doubtful about practical deployment.

3

Evaluate whether 'guarded skepticism' accurately describes this stance.

Guarded skepticism accurately characterizes an attitude that acknowledges a milestone while questioning its immediate practicality.

Matching the textual evidence to the term confirms the statement is true.

Anahtar Kavram

Inferring author tone and attitude by analyzing contrasting diction and evaluative conclusions in a passage.

Tahmini Süre:1m 0s

Soru 4855Soru →

Determine the solutions for $x$ in the given absolute value equation.

Aşağıdaki boşlukları doldurun

Given the equation

2|5 - x| - 4 = 10

, the smaller value of

x

is and the larger value of

x

is .

Cevabı ve açıklamayı göster

Cevap

The smaller value is -2 and the larger value is 12.

To solve

2|5 - x| - 4 = 10

, first isolate the absolute value term. Adding 4 to both sides yields

2|5 - x| = 14

. Dividing both sides by 2 gives

|5 - x| = 7

. The absolute value of an expression equals a positive number when the expression itself equals that positive number or its negative counterpart. Therefore, we set up two cases:

5 - x = 7

and

5 - x = -7

. Solving the first case gives

-x = 2

, so

x = -2

. Solving the second case gives

-x = -12

, so

x = 12

. Comparing the two solutions, the smaller value is

-2

and the larger value is

12

.

Adım Adım Çözüm

1

Isolate the absolute value expression.

Add 4 to both sides to get

2|5 - x| = 14

, then divide by 2 to get

|5 - x| = 7

.

The absolute value must be isolated before separating the equation into cases.

2

Set up the positive case equation.

5 - x = 7

The first case assumes the expression inside the absolute value is positive or zero.

3

Solve the positive case.

Subtract 5 to get

-x = 2

, which means

x = -2

.

This finds the first potential value for

x

.

4

Set up the negative case equation.

5 - x = -7

The second case accounts for the expression inside the absolute value being negative.

5

Solve the negative case.

Subtract 5 to get

-x = -12

, which means

x = 12

.

This finds the second potential value for

x

.

Anahtar Kavram

Solving Linear Absolute Value Equations

Tahmini Süre:1m 30s

Soru 4856Soru →

Consider the process of evaluating the numerical expression below using the standard order of operations:

14 + 3 \times (7 - 2^2) - 8 \div 4

How should the following intermediate simplified forms be arranged to represent the exact chronological sequence of the step-by-step evaluation?

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The expressions should be ordered starting with the exponent evaluation, followed by the parentheses, then multiplication and division, and finally addition.

The proper application of the order of operations (PEMDAS/BODMAS) ensures that we first simplify inside the parentheses (handling the exponent first, then subtraction), next process multiplication and division from left to right, and finally address addition and subtraction from left to right. This produces the exact sequence of intermediate expressions shown in the correct arrangement.

Adım Adım Çözüm

1

Evaluate the exponent inside the grouping symbols.

2^2

simplifies to

4

, changing the expression to

14 + 3 \times (7 - 4) - 8 \div 4

.

Order of operations dictates that exponents inside parentheses take precedence over other operations.

2

Complete the operation inside the parentheses.

7 - 4

simplifies to

3

, yielding

14 + 3 \times 3 - 8 \div 4

.

All operations within grouping symbols must be fully resolved before proceeding to external operations.

3

Evaluate multiplication and division.

3 \times 3

becomes

9

and

8 \div 4

becomes

2

, resulting in

14 + 9 - 2

.

Multiplication and division share the same priority and are executed from left to right before addition or subtraction.

4

Perform the addition.

14 + 9

becomes

23

, leaving

23 - 2

.

Addition and subtraction share the lowest priority and are evaluated from left to right.

5

Perform the final subtraction.

23 - 2

simplifies to the final answer of

21

.

This is the final remaining mathematical operation.

Anahtar Kavram

Order of Operations (PEMDAS)

Soru 4857Soru →

A word problem describes a quantity as being 'ten less than three times a number, $x$ '. What is the correct algebraic expression for this quantity?

3x - 10

10 - 3x

3(x - 10)

3x + 10

Cevabı ve açıklamayı göster

Cevap: $3x - 10$

Cevap

The correct mathematical expression is

3x - 10

.

The phrase 'three times a number,

x

' translates directly to

3x

. The phrase 'ten less than' indicates a subtraction of

10

from that initial quantity. Therefore, the correct combined expression is

3x - 10

.

Adım Adım Çözüm

1

Translate the multiplication part of the phrase: 'three times a number,

x

'.

3x

The word 'times' indicates multiplication between

3

and the variable

x

.

2

Translate the subtraction part of the phrase: 'ten less than'.

Subtract

10

from the result of step 1.

The phrase 'less than' is a turnaround phrase, meaning the value that comes before 'less than' must be subtracted from the value that comes after it.

3

Combine the translated parts into a single expression.

3x - 10

This correctly places the subtraction after the multiplied term.

Anahtar Kavram

Translating Word Phrases into Algebraic Equations

Soru 4858Soru →

Determine the final inventory count and the net percentage change by filling in the blanks.

Aşağıdaki boşlukları doldurun

A military supply depot initially stored

5,000

tactical vests. During a regional exercise, the inventory was reduced by

30\%

. Afterward, a new shipment increased the remaining stock by

40\%

. The depot now holds tactical vests. Compared to the original inventory, this represents a net of \%.

Cevabı ve açıklamayı göster

Cevap

The depot now holds 4,900 vests, representing a net decrease of 2%.

The final inventory is

4,900

vests, which is

100

vests fewer than the original

5,000

. This equates to a net decrease of

2\%

. In successive percentage problems, it is crucial to recalculate the base amount for each step.

Adım Adım Çözüm

1

Calculate the inventory after the initial

30\%

reduction.

5,000 - (0.30 \times 5,000) = 5,000 - 1,500 = 3,500

vests.

The first event reduces the starting stock by

30\%

, establishing a new base amount for the subsequent calculation.

2

Calculate the inventory after the

40\%

increase.

3,500 + (0.40 \times 3,500) = 3,500 + 1,400 = 4,900

vests.

The

40\%

increase applies only to the remaining stock (

3,500

), not the original

5,000

.

3

Determine the net change from the original inventory.

5,000 - 4,900 = 100

vests fewer than the original.

Comparing the final inventory (

4,900

) to the original inventory (

5,000

) reveals a net decrease.

4

Calculate the net percentage change.

(\frac{100}{5,000}) \times 100\% = 0.02 \times 100\% = 2\%

.

The percentage change is found by dividing the absolute change by the original base amount, then multiplying by

100\%

.

Anahtar Kavram

Successive Percentages and Changing Base Values

Soru 4859Soru →

Read the following technical report on naval submarine trials:

During deep-submergence pressure trials, the experimental hull alloy remained remarkably impervious to corrosive seawater, whereas standard steel plating was vulnerable to oxidation. Furthermore, while the interior seals remained pliable despite freezing depths, older rubber gaskets grew brittle and cracked. Finally, instead of producing a sluggish response, the newly fitted hydraulic steering system was agile under heavy hydrodynamic loads.

Based on the contrast clues in the passage, match each highlighted term to its correct contextual meaning.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

impervious matches 'Resistant to penetration and unaffected by corrosive forces'; pliable matches 'Flexible and supple under pressure without cracking'; agile matches 'Nimble and capable of quick, efficient movement'.

Each match is established through explicit contrast indicators in the passage: 'impervious' contrasts with 'vulnerable' across 'whereas'; 'pliable' contrasts with 'brittle' across 'while'; and 'agile' contrasts with 'sluggish' across 'instead of'.

Adım Adım Çözüm

1

Locate contrast signal words for each target term in the passage.

Identified 'whereas' for impervious, 'while'/'despite' for pliable, and 'instead of' for agile.

Contrast signal words establish opposing relationships between the target vocabulary and known benchmark descriptions.

2

Determine the opposing phrase for each target word to deduce its true definition.

'Impervious' opposes 'vulnerable to oxidation'; 'pliable' opposes 'brittle and cracked'; 'agile' opposes 'sluggish response'.

The contextual definition of each target word is the opposite of the condition described in the contrasting clause.

3

Pair each word with its corresponding contextual definition.

All three terms are successfully matched to their precise contextual definitions.

Matching each term to its positive equivalent verifies complete reading comprehension.

Anahtar Kavram

Identifying Antonym and Contrast Context Clues

Tahmini Süre:1m 0s

Soru 4860Soru →

What is the smallest positive integer that is a multiple of both $8$ and $12$ ?

Cevabı ve açıklamayı göster

Cevap: 24

Cevap

24

The smallest positive integer that is a multiple of both

8

and

12

is their least common multiple (LCM). The multiples of

8

are

8, 16, 24, 32, \dots

and the multiples of

12

are

12, 24, 36, \dots

. The smallest number that appears in both lists is

24

.

Adım Adım Çözüm

1

Find the positive multiples of

8

.

8, 16, 24, 32, 40, \dots

We need to determine a number that is a multiple of

8

.

2

Find the positive multiples of

12

.

12, 24, 36, 48, \dots

We need the number to also be a multiple of

12

.

3

Identify the smallest common multiple from both lists.

24

The question asks for the smallest positive integer that is a multiple of both numbers.

Anahtar Kavram

Least Common Multiple (LCM)

Tahmini Süre:45s

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