Tüm alıştırma soruları

Soru 4701Soru →

A logistics convoy is transporting supplies to a remote base. On the first day of the trip, they complete $30\%$ of the total distance. On the second day, they complete $40\%$ of the remaining distance. If they still have $210$ miles left to travel, what is the total distance of the trip in miles?

350

500

700

750

Cevabı ve açıklamayı göster

Cevap: 500

Cevap

The total distance of the trip is 500 miles.

The correct answer accurately accounts for the successive percentages by applying the second day's percentage to the remaining distance. After traveling 30% of the trip, 70% remains. Leaving 40% of this remaining 70% completed means 60% of the 70% is left uncompleted, which equals 42% of the total distance. Setting 42% equal to the 210 remaining miles gives a total distance of 500 miles.

Adım Adım Çözüm

1

Determine the percentage of the trip remaining after the first day.

100\% - 30\% = 70\%

The second day's travel is based on the remaining distance, not the total distance.

2

Calculate the percentage of the remaining distance that is left after the second day.

100\% - 40\% = 60\%

Since they completed 40% of the remaining distance, 60% of that remaining distance is still uncompleted.

3

Calculate the percentage of the total distance that the final remaining 210 miles represents.

0.70 \times 0.60 = 0.42

, which is

42\%

of the total distance.

Successive percentages are applied by multiplying the decimal forms of the remaining portions.

4

Set up an equation to solve for the total distance, D.

0.42D = 210 \implies D = 210 \div 0.42 = 500

Dividing the remaining miles by the remaining percentage of the total trip yields the original total distance.

Anahtar Kavram

Calculating successive percentage changes by adjusting the base for each subsequent calculation.

Soru 4702Soru →

Which of the following is equivalent to the expression below?

2x(3x - 4) - 3[x(x - 2) - 4(2x + 1)] + x^2

4x^2 + 22x + 12

4x^2 - 38x - 12

4x^2 + 34x

4x^2 - 18x - 4

Cevabı ve açıklamayı göster

Cevap: $4x^2 + 22x + 12$

Cevap

The correct expression is

4x^2 + 22x + 12

.

The correct expression is found by following the order of operations: first expanding the terms inside the innermost parentheses, then combining like terms within the brackets, next distributing the negative multiplier to all terms in the brackets, and finally combining all remaining like terms.

Adım Adım Çözüm

1

Expand the first part of the expression by distributing

2x

.

2x(3x - 4) = 6x^2 - 8x

Distribution is required to remove the initial parentheses.

2

Simplify the expression inside the square brackets by distributing and combining like terms.

x(x - 2) - 4(2x + 1) = x^2 - 2x - 8x - 4 = x^2 - 10x - 4

According to the order of operations, simplify the innermost grouping symbols first.

3

Distribute the

-3

across the simplified expression from the brackets.

-3(x^2 - 10x - 4) = -3x^2 + 30x + 12

The negative sign and the constant must be multiplied by every term inside the brackets.

4

Substitute all parts back into the main expression and combine like terms.

(6x^2 - 8x) + (-3x^2 + 30x + 12) + x^2 = (6x^2 - 3x^2 + x^2) + (-8x + 30x) + 12 = 4x^2 + 22x + 12

Combining coefficients of terms with the same variables and exponents yields the final simplified polynomial.

Anahtar Kavram

Simplifying complex algebraic expressions by applying the distributive property, handling negative multipliers, and combining like terms.

Soru 4703Soru →

Read the following passage:

Modern aircraft rely on pitot-static systems to measure airspeed, altitude, and vertical speed by sampling external ambient and dynamic air pressures. During flight through freezing moisture or sub-zero cloud layers, ice accumulation can rapidly obstruct the narrow pitot tube opening, causing the airspeed indicator to give dangerously erroneous readings or drop to zero. To prevent this hazard, pilots engage electrical heating elements embedded directly inside the probe before entering icing conditions. Rather than serving as a de-icing mechanism to clear heavy existing ice, the primary operational doctrine of pitot heat is anti-icing—maintaining a surface temperature above freezing so that ice crystals never form in the first place.

Statement: The author's primary purpose in writing this passage is to explain that pitot heat is designed as a proactive preventive measure rather than a reactive clearing tool.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True (The author's primary purpose is to explain that pitot heat functions proactively to prevent ice from forming rather than reactively clearing existing ice).

The author focuses on explaining the operational philosophy of pitot heat, explicitly emphasizing in the final sentence that its primary function is anti-icing (proactive prevention) rather than de-icing (reactive remediation).

Adım Adım Çözüm

1

Analyze the passage structure and concluding focus

The text introduces the critical role of pitot probes, describes the hazard of ice blockage, and concludes with a definitive statement about the system's operational doctrine.

Determining where the author places emphasis reveals the main intent behind the passage.

2

Evaluate the author's central distinction between anti-icing and de-icing

The author contrasts proactive prevention ('anti-icing') against reactive clearing ('de-icing') to clarify why pilots engage the system prior to entering icing conditions.

The contrast directly supports the overarching purpose of explaining how and why the equipment is intended to be used.

3

Compare the evaluation statement to the author's main communicative goal

The statement accurately reflects the passage's primary intent.

Verifying alignment ensures the True evaluation is completely supported by textual evidence.

Anahtar Kavram

Inferring Author Purpose and Intent

Tahmini Süre:1m 0s

Soru 4704Soru →

Match each complex algebraic expression with its completely simplified polynomial form.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The first expression maps to

-2x^2 - 2xy

, the second expression maps to

y^2

, the third expression maps to

-2xy + 9y^2

, and the fourth expression maps to

2x^2 - 4y^2

.

Each expression represents a distinct structural archetype for polynomial simplification. By systematically applying the order of operations—expanding binomials, distributing negative coefficients, and resolving nested grouping symbols from the inside out—all like terms can be properly combined to reach the correct canonical form.

Adım Adım Çözüm

1

Simplify the first expression by resolving innermost parentheses, then brackets, then combining terms.

3x^2 - 6xy - [2x^2 - 4xy + 3x^2]

simplifies to

3x^2 - 6xy - 5x^2 + 4xy

, which yields

-2x^2 - 2xy

.

Following the order of operations from the innermost grouping symbols prevents sign errors when distributing negative coefficients.

2

Simplify the second expression by expanding the binomial square and distributing.

(4x^2 - 4xy + y^2) - (4x^2 - 4xy)

simplifies directly to

y^2

.

Proper binomial expansion

(a-b)^2 = a^2 - 2ab + b^2

avoids the common error of dropping the middle term, allowing opposite terms to cancel.

3

Simplify the third expression using the difference of squares formula, then distribute the negative.

-(x^2 - 9y^2) + x^2 - 2xy

simplifies to

-x^2 + 9y^2 + x^2 - 2xy

, which reduces to

-2xy + 9y^2

.

Recognizing the difference of squares simplifies multiplication, and properly distributing the outer negative sign ensures the squared variable term has the correct positive sign.

4

Simplify the fourth expression by distributing within the brackets before multiplying by the outer coefficient.

4xy - 2[-x^2 + 2xy + 2y^2]

simplifies to

4xy + 2x^2 - 4xy - 4y^2 = 2x^2 - 4y^2

.

Combining like terms inside the bracket before multiplying by the outer constant significantly reduces the chance of sign and variable combination errors.

Anahtar Kavram

Simplifying Complex Multivariable Algebraic Expressions

Tahmini Süre:3m 0s

Soru 4705Soru →

A student needs to simplify the expression $7k - 2(k + 4) + 1$ . What is the fully simplified form of this expression?

5k - 7

5k + 9

5k + 5

-2k

Cevabı ve açıklamayı göster

Cevap: $5k - 7$

Cevap

The correct simplified expression is

5k - 7

.

The expression is simplified by first distributing the

-2

into

(k + 4)

to get

-2k - 8

. Next, the like terms are combined:

7k - 2k

becomes

5k

, and the constants

-8

and

1

combine to

-7

. This results in the final simplified expression of

5k - 7

.

Adım Adım Çözüm

1

Apply the distributive property to the term

-2(k + 4)

.

7k - 2k - 8 + 1

The multiplier

-2

must be distributed to both

k

and

4

inside the parentheses.

2

Group the like terms together.

(7k - 2k) + (-8 + 1)

Like terms (variables with the same exponent, and constants) are grouped so they can be combined.

3

Combine the grouped like terms to simplify the expression.

5k - 7

Subtracting

2k

from

7k

gives

5k

, and adding

1

to

-8

gives

-7

.

Anahtar Kavram

Simplifying algebraic expressions by using the distributive property with negative multipliers and combining like terms.

Tahmini Süre:45s

Soru 4706Soru →

Evaluate each of the following arithmetic expressions. Then, arrange the expressions in order from the smallest resulting value to the largest resulting value.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence from smallest to largest is:

10 - 2 \times (4 - 1)^2

,

10 - (2 \times 4) - 1^2

,

10 - 2 \times 4 - (-1)^3

, and

(10 - 2) \times 4 - 1^2

.

Evaluating each expression using the correct order of operations yields -8, 31, 1, and 3 respectively. Arranging these integer values from smallest to largest dictates the correct order.

Adım Adım Çözüm

1

Evaluate the first expression:

10 - 2 \times (4 - 1)^2

-8

Applying PEMDAS: solve inside parentheses

(3)

, apply the exponent

(3^2 = 9)

, multiply

(2 \times 9 = 18)

, and subtract

(10 - 18 = -8)

.

2

Evaluate the second expression:

(10 - 2) \times 4 - 1^2

31

Applying PEMDAS: solve inside parentheses

(8)

, apply the exponent

(1^2 = 1)

, multiply

(8 \times 4 = 32)

, and subtract

(32 - 1 = 31)

.

3

Evaluate the third expression:

10 - (2 \times 4) - 1^2

1

Applying PEMDAS: multiply inside parentheses

(8)

, apply the exponent

(1^2 = 1)

, and subtract from left to right

(10 - 8 = 2; 2 - 1 = 1)

.

4

Evaluate the fourth expression:

10 - 2 \times 4 - (-1)^3

3

Applying PEMDAS: apply the exponent

((-1)^3 = -1)

, multiply

(2 \times 4 = 8)

, and subtract from left to right

(10 - 8 = 2; 2 - (-1) = 3)

.

5

Arrange the evaluated numbers from smallest to largest

-8 < 1 < 3 < 31

Comparing the integer values yields the final logical order of the respective expressions.

Anahtar Kavram

Evaluating arithmetic expressions sequentially by applying the correct order of operations (PEMDAS) and then sorting the numerical values.

Soru 4707Soru →

Consider the following one-variable inequality:

12 - 3x \leq 27

Which of the following represents the correct solution set for $x$ ?

x \geq -5

x \leq -5

x \geq 5

x \geq -13

Cevabı ve açıklamayı göster

Cevap: $x \geq -5$

Cevap

x \geq -5

To solve the inequality, first subtract 12 from both sides to get

-3x \leq 15

. Next, divide both sides by -3. Because the division involves a negative number, the direction of the inequality symbol must be reversed, resulting in the correct solution of

x \geq -5

.

Adım Adım Çözüm

1

Subtract

12

from both sides of the inequality.

-3x \leq 15

This step isolates the term containing the variable on one side of the inequality.

2

Divide both sides by

-3

and reverse the inequality symbol.

x \geq -5

According to the rules of algebra, whenever you multiply or divide an inequality by a negative number, the direction of the inequality sign must be flipped.

Anahtar Kavram

Solving One-Variable Inequalities

Tahmini Süre:45s

Soru 4708Soru →

A naval fleet has a certain number of vessels. Currently, $20\%$ of the fleet is undergoing long-term maintenance. Of the operational vessels remaining, $25\%$ are currently deployed on active missions. If there are exactly $33$ operational vessels remaining at the home port, what is the total number of vessels in the entire fleet?

44

60

55

165

Cevabı ve açıklamayı göster

Cevap: $55$

Cevap

The total number of vessels in the entire fleet is

55

.

The correct answer is found by tracking the remaining percentages step-by-step. Since 20% of the fleet is in maintenance, 80% remains operational. The 25% deployment rate applies to this 80%, meaning 20% of the total fleet is deployed (0.25 * 0.80 = 0.20). Subtracting the deployed vessels leaves 60% of the original fleet at the port. Finally, dividing the 33 vessels by 0.60 yields the original total fleet size of 55.

Adım Adım Çözüm

1

Determine the percentage of the fleet that is not in maintenance.

100\% - 20\% = 80\%

The

25\%

deployment rate applies only to the remaining operational vessels.

2

Calculate the percentage of the total fleet that is deployed.

25\%

of

80\% = 0.25 \times 80\% = 20\%

To find the deployed amount relative to the whole fleet, multiply the successive percentages.

3

Determine the percentage of the total fleet that remains at the home port.

80\% - 20\% = 60\%

Subtracting the deployed vessels from the operational vessels gives the portion remaining at port.

4

Set up an equation and solve for the total number of vessels in the fleet (

x

).

0.60x = 33 \Rightarrow x = \frac{33}{0.60} = 55

The

60\%

of the total fleet is equal to the

33

vessels explicitly counted at the port.

Anahtar Kavram

Successive Percentage Calculations and Reversing Percentages

Soru 4709Soru →

Although the newly introduced pneumatic dispatch tubes promised instantaneous delivery of orders throughout the factory complex, the system frequently jammed when handling heavier parchment manifests. Plant supervisors praised the technology's theoretical velocity, yet their haste in dismantling the reliable messenger corps proved premature. Without manual couriers as a fail-safe, minor vacuum pressure fluctuations routinely brought administrative operations to a complete standstill, exposing the folly of abandoning proven protocols for unproven mechanical speed.

Which of the following best describes the author's attitude toward replacing the manual couriers with pneumatic dispatch tubes?

Appreciative of the system's theoretical velocity and modern design

Confident that vacuum pressure adjustments will soon stabilize operations

Critical of the hasty abandonment of a dependable method for an untested system

Neutral and objective regarding the daily management of factory communications

Cevabı ve açıklamayı göster

Cevap: Critical of the hasty abandonment of a dependable method for an untested system

Cevap

The author is critical of the hasty abandonment of a dependable method for an untested system.

The correct response accurately reflects the author's disapproval. Words such as 'premature,' 'complete standstill,' and 'folly' demonstrate that the author views the elimination of manual couriers as an ill-conceived and reckless decision.

Adım Adım Çözüm

1

Identify the specific subject the question asks about.

The target subject is the decision to replace manual messengers with pneumatic tubes.

Determining the subject ensures that tone analysis focuses on the author's evaluation of the policy rather than incidental facts.

2

Scan the passage for evaluative diction and connotative phrasing used by the author.

Key descriptors include 'frequently jammed,' 'proved premature,' 'complete standstill,' and 'folly of abandoning proven protocols.'

Word choice and connotation directly reveal the author's underlying attitude and stance.

3

Synthesize the diction to infer the overall attitude.

The author clearly disapproves of the rushed transition, viewing it as an ill-advised mistake.

Matching the synthesized attitude to the options confirms that a critical perspective is conveyed.

Anahtar Kavram

Inferring author tone and attitude through evaluative diction and contextual clues

Tahmini Süre:1m 0s

Soru 4710Soru →

In a military motor pool, the ratio of trucks to jeeps is $2:3$ , and the ratio of jeeps to motorcycles is $4:5$ . If there are exactly $140$ vehicles among these three types, how many more motorcycles are there than trucks?

28

30

42

60

Cevabı ve açıklamayı göster

Cevap: 28

Cevap

There are 28 more motorcycles than trucks.

To solve this, the two separate ratios must be unified. By finding the least common multiple for the overlapping term (jeeps, which are represented by 3 in the first ratio and 4 in the second), we scale the ratios to 8:12 and 12:15. This creates a combined ratio of 8:12:15 for trucks to jeeps to motorcycles. Adding these parts gives 35 total proportional units. Dividing the actual total (140 vehicles) by 35 units reveals that each unit equals 4 vehicles. The difference between motorcycles (15 units) and trucks (8 units) is 7 units. Multiplying 7 units by 4 vehicles per unit yields 28.

Adım Adım Çözüm

1

Identify the common entity between the two given ratios to create a single, unified ratio.

Jeeps are the common entity. Trucks : Jeeps =

2:3

, and Jeeps : Motorcycles =

4:5

.

You cannot compare trucks and motorcycles directly or find the total parts until all three vehicles share the same proportional scale.

2

Find the least common multiple (LCM) for the 'Jeeps' portion of both ratios and scale them.

The LCM of

3

and

4

is

12

. Multiply the first ratio by

4

to get

8:12

. Multiply the second ratio by

3

to get

12:15

. The combined ratio of Trucks : Jeeps : Motorcycles is

8:12:15

.

Scaling ensures the common term is equal in both ratios, allowing them to be combined safely.

3

Calculate the value of a single ratio part based on the total number of vehicles.

Total parts =

8 + 12 + 15 = 35

. Divide the total vehicles by total parts:

140 \div 35 = 4

vehicles per part.

This establishes the multiplier needed to convert ratio units into actual vehicle counts.

4

Find the difference in parts between motorcycles and trucks, then multiply by the part value.

Motorcycles (

15

parts) minus trucks (

8

parts) equals

7

parts.

7 \times 4 = 28

vehicles.

Subtracting the parts before multiplying by the scale factor is more efficient than finding the total of each vehicle first, though both methods yield 28.

Anahtar Kavram

Combining multiple distinct ratios using a least common multiple to form a unified proportional relationship.

Soru 4711Soru →

Simplify the given mathematical expression. Which of the following represents its final value?

-5 - 3 \times (-2) + 4

-11

-7

5

20

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

5

According to the order of operations, multiplication must be evaluated before addition and subtraction. First, multiply 3 by -2 to get -6. Subtracting this negative product from -5 gives -5 - (-6), which correctly simplifies to -5 + 6 = 1. Finally, add 4 to reach the correct final answer of 5.

Adım Adım Çözüm

1

Identify the operations in the expression and determine their correct order of execution.

The expression contains subtraction, multiplication, and addition. Multiplication must be performed first.

According to the standard order of operations (PEMDAS), multiplication has a higher priority than addition and subtraction.

2

Perform the multiplication step.

3 \times (-2) = -6

. The expression becomes

-5 - (-6) + 4

.

Calculate the product before processing the outer subtraction.

3

Simplify the subtraction of a negative number.

-5 - (-6) + 4

becomes

-5 + 6 + 4

.

Subtracting a negative integer is mathematically equivalent to adding its positive counterpart.

4

Evaluate the remaining addition and subtraction from left to right.

-5 + 6 = 1

, and

1 + 4 = 5

.

Addition and subtraction hold the same operational priority and are resolved sequentially from left to right.

Anahtar Kavram

Order of Operations with Signed Integers

Alternatif Yöntem

Instead of subtracting the product of 3 and -2, you can treat the subtraction symbol as a negative sign attached to the 3. This changes the multiplication step to (-3) * (-2) = 6. The entire expression then immediately becomes -5 + 6 + 4, which easily sums to 5.

Tahmini Süre:45s

Soru 4712Soru →

A naval shipyard increases its dry dock maintenance workforce by $12.5\%$ to meet new project demands. If the current workforce size after the increase is $810$ personnel, what was the original size of the workforce before the increase?

Cevabı ve açıklamayı göster

Cevap: 720

Cevap

720

The scenario requires a reverse percentage calculation. The final count of

810

personnel represents the original workforce plus a

12.5\%

increase, meaning

810

is exactly

112.5\%

(or

\frac{9}{8}

) of the original amount. To find the original amount, you set up the equation

\frac{9}{8}x = 810

and solve for

x

by multiplying

810

by the reciprocal

\frac{8}{9}

, which equals

720

.

Adım Adım Çözüm

1

Identify the relationship between the final amount and the initial amount.

A

12.5\%

increase means the final amount is

100\% + 12.5\% = 112.5\%

of the original amount.

To correctly set up an algebraic representation of the percentage growth based on the unknown starting value.

2

Convert the new percentage multiplier into a fraction.

Knowing that

12.5\% = \frac{1}{8}

, the multiplier for a

12.5\%

increase is

1 + \frac{1}{8} = \frac{9}{8}

.

Using fractions makes mental arithmetic much simpler and faster without a calculator.

3

Set up the equation to solve for the original amount.

Letting

x

represent the original workforce size, the equation is

\frac{9}{8}x = 810

.

This translates the word problem into a solvable mathematical equation.

4

Solve the equation for

x

.

x = 810 \times \frac{8}{9} = 90 \times 8 = 720

.

Isolating

x

provides the initial workforce size before the increase.

Anahtar Kavram

Reverse percentage calculations and percentage-to-fraction conversions.

Tahmini Süre:1m 0s

Soru 4713Soru →

The solution to the one-variable inequality $-2x > 10$ is $x > -5$ .

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False

The correct answer is False because isolating

x

requires dividing by

-2

, which means the greater-than sign (

>

) must flip to a less-than sign (

<

). The actual mathematically correct solution is

x < -5

.

Adım Adım Çözüm

1

Divide both sides of the inequality by

-2

.

\frac{-2x}{-2}

and

\frac{10}{-2}

To isolate the variable

x

on one side of the inequality.

2

Reverse the inequality symbol.

x < -5

When dividing or multiplying an inequality by a negative number, the direction of the inequality symbol must be flipped to maintain a mathematically true statement.

Anahtar Kavram

Solving One-Variable Inequalities

Soru 4714Soru →

An engineer is calculating the total weight supported by two structural pillars. The weight on the first pillar is given by the algebraic expression $5y - 2$ , and the weight on the second pillar is given by $3y + 6$ . What is the fully simplified algebraic expression for the total weight supported by both pillars combined?

Cevabı ve açıklamayı göster

Cevap: 8y + 4; 8y+4; 4 + 8y; 4+8y; 8y +4; 8y+ 4; 8y+ 4

Cevap

8y + 4

The total weight is found by adding the two individual weight expressions. By identifying and grouping like terms, the variable terms are combined (

5y + 3y = 8y

) and the constant terms are combined (

-2 + 6 = 4

) to get the final simplified expression of

8y + 4

.

Adım Adım Çözüm

1

Set up the addition of the two individual expressions

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

To find the total weight, both individual weight expressions must be added together.

2

Group the like terms

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

Like terms (terms with the same variable, and constant terms) must be grouped to simplify the expression.

3

Combine the grouped terms

8y + 4

Adding the coefficients of

y

(

5 + 3 = 8

) and adding the constants (

-2 + 6 = 4

) yields the fully simplified form.

Anahtar Kavram

Combining Like Terms

Soru 4715Soru →

If $x = -3$ and $y = -5$ , what is the value of the following expression?

x^2 + 2x \times |y| - (x - y)

-41

-23

13

37

Cevabı ve açıklamayı göster

Cevap: -23

Cevap

The correct answer is -23.

By accurately applying the rules for negative integers, (-3)^2 evaluates to a positive 9. The absolute value |-5| evaluates to a positive 5. Following the order of operations, the multiplication 2(-3) * 5 is performed next, yielding -30. Finally, subtracting the evaluation of the parenthetical group (2) from the sum of 9 and -30 results in exactly -23.

Adım Adım Çözüm

1

Substitute the values of x and y into the expression.

(-3)^2 + 2(-3) \times |-5| - (-3 - (-5))

Direct substitution is the first step in evaluating algebraic expressions.

2

Evaluate the terms inside parentheses and absolute value brackets.

|-5| = 5

and

(-3 - (-5)) = (-3 + 5) = 2

. The expression becomes:

(-3)^2 + 2(-3) \times 5 - 2

According to the order of operations, grouping symbols like absolute value and parentheses must be resolved first.

3

Evaluate the exponent.

(-3)^2 = 9

. The expression becomes:

9 + 2(-3) \times 5 - 2

Exponents must be calculated before multiplication, addition, and subtraction. A negative number squared yields a positive result.

4

Perform the multiplication.

2(-3) \times 5 = -6 \times 5 = -30

. The expression becomes:

9 + (-30) - 2

Multiplication is performed before addition and subtraction.

5

Perform the remaining addition and subtraction from left to right.

9 - 30 - 2 = -21 - 2 = -23

Addition and subtraction are the final steps in the order of operations.

Anahtar Kavram

Evaluating expressions using properties of negative integers and absolute value

Tahmini Süre:1m 0s

Soru 4716Soru →

An industrial pump requires $2$ gallons, $3$ quarts, and $1$ pint of lubricating oil to completely fill its reservoir. If a maintenance technician needs to completely fill the empty reservoirs of $8$ identical pumps, what is the total volume of oil required, in gallons?

21

23

46

92

Cevabı ve açıklamayı göster

Cevap: 23

Cevap

The total volume of oil required is 23 gallons.

To find the total, you must first convert the requirement for one pump into a standard unit:

2

gallons is

8

quarts, plus

3

quarts, plus

1

pint (

0.5

quarts) equals

11.5

quarts per pump. Multiplying

11.5

quarts by

8

pumps yields

92

quarts. Since there are

4

quarts in a gallon, dividing

92

by

4

gives the correct total of

23

gallons.

Adım Adım Çözüm

1

Convert the capacity of one pump into a single unit, such as quarts.

2

gallons =

8

quarts, and

1

pint =

0.5

quarts. Adding these together gives

8 + 3 + 0.5 = 11.5

quarts per pump.

Standardizing all measurements into one unit prevents addition errors and simplifies the multiplication step.

2

Multiply the single-pump volume by the total number of pumps.

11.5

quarts

\times 8

pumps =

92

quarts.

This determines the total volume of oil needed for all the equipment combined.

3

Convert the total volume back into gallons.

92 \div 4 = 23

gallons.

The question specifically asks for the final answer in gallons, and there are

4

quarts in

1

gallon.

Anahtar Kavram

Multiplying mixed US Customary capacity measurements and converting between units.

Soru 4717Soru →

A fuel tank at a military base is initially filled to $80\%$ of its total capacity. After a training exercise, the fuel level decreases by $35\%$ of its current volume. If $260$ gallons of fuel remain in the tank after the exercise, what is the total capacity of the fuel tank in gallons?

Cevabı ve açıklamayı göster

Cevap: 500

Cevap

500

To find the total capacity, we must track the percentage of fuel at each stage relative to the total capacity. Initially, the tank holds

80\%

of its capacity, or

0.80

. A decrease of

35\%

means

65\%

of that fuel remains. Multiplying the initial proportion (

0.80

) by the remaining proportion (

0.65

) yields

0.52

. This indicates that the final

260

gallons represent exactly

52\%

of the tank's total capacity. Setting up the equation

0.52C = 260

and dividing

260

by

0.52

gives a total capacity of

500

gallons.

Adım Adım Çözüm

1

Define a variable for the total capacity and express the initial fuel volume.

Initial volume =

0.80C

The tank is starting at

80\%

of its total capacity (

C

).

2

Determine the percentage of fuel remaining after the exercise.

Remaining percentage =

100\% - 35\% = 65\%

A

35\%

decrease means that

65\%

of the fuel that was in the tank before the exercise is still there.

3

Express the final remaining volume in terms of the total capacity (

C

).

0.65 \times 0.80C = 0.52C

Applying the

65\%

remaining proportion to the initial

0.80C

volume gives the final percentage of the total capacity.

4

Set up an equation using the known final volume and solve for

C

.

0.52C = 260 \Rightarrow C = \frac{260}{0.52} = 500

Equating the algebraic expression to the

260

gallons given in the problem isolates the unknown base capacity.

Anahtar Kavram

Calculating successive percentages and identifying an unknown base value.

Soru 4718Soru →

Match each complex unsimplified algebraic expression with its correctly simplified equivalent.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct pairings match each multi-step expression to its exact simplified polynomial counterpart: L1 matches R1, L2 matches R2, L3 matches R3, and L4 matches R4.

Each correct match is formed by strictly following the order of operations: clearing innermost groupings first, distributing outer multipliers across all contained terms, and combining structurally identical variable terms into standard canonical form.

Adım Adım Çözüm

1

Simplify the first expression

-3x[2y - (x - 4y)] + 2x(x - y)

.

The expression simplifies to

5x^2 - 20xy

.

By following the order of operations, innermost parentheses are cleared first, followed by distribution and combining like terms.

2

Simplify the second expression

4xy - 2[x(3y - x) - y(x + 2y)]

.

The expression simplifies to

2x^2 + 4y^2

.

Expanding the terms inside the bracket yields

-x^2 + 2xy - 2y^2

. Distributing the

-2

flips the signs, and the

xy

terms successfully cancel.

3

Simplify the third expression

x^2(y - 2) - [xy(x - 3) - x(2x + y)] - xy

.

The expression simplifies to

3xy

.

Careful distribution of the negative sign across the simplified bracket

(x^2y - 2x^2 - 4xy)

allows multiple high-degree terms to cancel out perfectly.

4

Simplify the fourth expression

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

.

The expression simplifies to

xy + 6y^2

.

FOILing the first binomial and keeping the negative sign outside ensures signs are correctly flipped before combining with the other distributed terms.

Anahtar Kavram

Simplifying complex algebraic expressions through precise application of the distributive property, order of operations (PEMDAS), and combination of like terms.

Tahmini Süre:4m 0s

Soru 4719Soru →

Naval high-pressure breathing air compressors use multi-stage filtration assemblies to produce breathable air for diving and firefighting. Atmospheric air first enters a mechanical separator to remove gross moisture droplets before passing into the desiccant tower. The desiccant tower utilizes activated alumina to absorb remaining water vapor, lowering the dew point to minus sixty-five degrees Fahrenheit. Downstream, an active hopcalite catalyst converts lethal carbon monoxide into carbon dioxide at ambient operating temperatures. Finally, an activated carbon canister captures residual hydrocarbon vapors before the purified air reaches the high-pressure storage flasks.

According to the passage, which component is used to convert carbon monoxide into carbon dioxide?

Activated alumina inside the desiccant tower

A mechanical moisture separator

An active hopcalite catalyst

An activated carbon canister

Cevabı ve açıklamayı göster

Cevap: An active hopcalite catalyst

Cevap

An active hopcalite catalyst

The passage explicitly states that an active hopcalite catalyst is responsible for converting carbon monoxide into carbon dioxide at ambient operating temperatures.

Adım Adım Çözüm

1

Scan the text for the key term 'carbon monoxide' and locate the specific mechanism associated with its transformation.

Located the sentence: 'Downstream, an active hopcalite catalyst converts lethal carbon monoxide into carbon dioxide at ambient operating temperatures.'

Direct fact retrieval requires pinpointing the exact sentence where the target condition is described.

2

Match the explicit fact from the sentence to the answer choices without extrapolating.

Identified 'An active hopcalite catalyst' as the exact material performing the conversion.

The correct choice must strictly reflect what is stated in the passage.

Anahtar Kavram

Direct Fact Retrieval

Tahmini Süre:1m 0s

Soru 4720Soru →

Submarine commanders navigating deep ocean waters must constantly monitor thermoclines—distinct horizontal layers where water temperature drops sharply with depth. Because the speed of sound is directly governed by water temperature and pressure, acoustic sonar pulses bend away from warmer layers and refract across these thermal boundaries. This physical phenomenon creates acoustic shadow zones where vessels can conceal their acoustic signatures from surface detection. By understanding how thermal gradients manipulate sonar propagation, naval operators can strategically position their vessels beneath thermocline layers to evade active surface pinging while maintaining surveillance of nearby maritime traffic.

Which of the following best describes the author's primary purpose in the passage?

Define thermoclines as distinct horizontal layers where water temperature drops sharply with depth

Explain how underwater thermal layers influence sonar propagation and vessel concealment

Argue that active surface sonar has become obsolete in modern naval warfare

Provide step-by-step technical instructions for calibrating sonar frequencies at sea

Cevabı ve açıklamayı göster

Cevap: Explain how underwater thermal layers influence sonar propagation and vessel concealment

Cevap

Explain how underwater thermal layers influence sonar propagation and vessel concealment

The author explains the scientific principle of how temperature layers refract sound waves and connects this mechanism directly to how naval operators exploit these layers to conceal submarines. This synthesis reflects the complete scope and primary communicative purpose of the passage.

Adım Adım Çözüm

1

Analyze the passage structure and central topic

The text discusses thermoclines, how they alter sound wave paths (sonar propagation), and how submarines use this phenomenon to hide from surface sonar.

Determining what the passage covers as a whole is necessary to infer why the author wrote it.

2

Differentiate between supporting details and the author's overarching purpose

The definition of thermoclines in the opening sentence is background context supporting the larger explanation of acoustic shadow zones and tactical concealment.

A passage's primary intent encompasses the full scope of ideas rather than isolated introductory facts.

3

Evaluate the rhetorical tone and goal of the author

The tone is explanatory and informative, describing a physical principle and its practical tactical outcome.

Identifying the rhetorical mode ensures the selected answer reflects an explanatory goal rather than an argumentative or procedural one.

Anahtar Kavram

Inferring Author Purpose and Intent

Tahmini Süre:1m 0s

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