Tüm alıştırma soruları

Fill in the blank with the correct numerical value.

Aşağıdaki boşlukları doldurun

A logistics detachment inspects

30

cargo containers in

45

minutes. Operating at this constant rate, it will take the detachment hours to inspect

160

cargo containers.

Cevabı ve açıklamayı göster

Cevap

4

Since the detachment operates at a constant rate, this is a direct proportion problem. They inspect

30

containers in

45

minutes. Using the proportion

\frac{30}{45} = \frac{160}{x}

, we find it takes

240

minutes to inspect

160

containers. Dividing

240

minutes by

60

minutes per hour gives the final answer of

4

hours.

Adım Adım Çözüm

1

Set up a direct proportion relating the number of containers to the time in minutes.

\frac{30}{45} = \frac{160}{x}

Because the inspection rate is constant, the ratio of containers to time remains the same.

2

Solve the proportion for

x

to find the total time required in minutes.

30x = 160 \times 45 \Rightarrow 30x = 7200 \Rightarrow x = 240 \text{ minutes}

Cross-multiplying and isolating

x

determines the unknown time in the same units (minutes) used in the initial ratio.

3

Convert the total time from minutes to hours.

\frac{240 \text{ minutes}}{60 \text{ minutes/hour}} = 4 \text{ hours}

The question specifically asks for the final answer in hours, requiring a unit conversion.

Anahtar Kavram

Direct proportions with unit conversion

Soru 3362Soru →

A social club reserves a private lounge for a holiday party. They receive a $25\%$ promotional discount on the standard food and beverage package price. A local hospitality tax of $6\%$ is applied to the discounted price, but the contract requires a mandatory $15\%$ gratuity calculated on the standard, pre-discount package price.

If the final bill paid by the club—consisting of the discounted package, the tax, and the gratuity—amounts to $\$378.00$ , what was the standard package price before any discounts or fees?

Aşağıdaki boşlukları doldurun

The standard package price was $\.

Cevabı ve açıklamayı göster

Cevap

The standard package price was $400.

The total bill is the sum of the discounted price, the tax on the discounted price, and the tip on the original price. By setting the original price as

P

, we can express the total cost algebraically:

0.75P

(discounted price)

+ 0.06(0.75P)

(tax)

+ 0.15P

(gratuity)

= 0.945P

. Setting

0.945P = 378

and solving for

P

yields exactly

400

.

Adım Adım Çözüm

1

Let

P

represent the standard package price. Express the discounted price in terms of

P

.

Discounted Price =

P - 0.25P = 0.75P

The club receives a

25\%

discount off the standard price.

2

Express the tax amount in terms of

P

.

Tax =

0.06 \times 0.75P = 0.045P

The problem states that the

6\%

hospitality tax is applied to the discounted price.

3

Express the gratuity amount in terms of

P

.

Gratuity =

0.15 \times P = 0.15P

The contract explicitly requires the

15\%

tip to be calculated on the original, pre-discount package price.

4

Set up an equation for the final bill and solve for

P

.

0.75P + 0.045P + 0.15P = 378 \implies 0.945P = 378 \implies P = 378 \div 0.945 = 400

The sum of the discounted package, the tax, and the gratuity equals the total final bill of

\$378.00

.

Anahtar Kavram

Solving for an original price when tax and tip are calculated using different base amounts (discounted vs. pre-discount).

Soru 3363Soru →

An atom of potassium has a mass number of $39$ and contains $20$ neutrons in its nucleus. When this atom forms a stable potassium ion ( $K^+$ ) by losing one electron, what is the total number of subatomic particles (protons, neutrons, and electrons) present in the ion?

39

57

58

77

Cevabı ve açıklamayı göster

Cevap: $57$

Cevap

The potassium ion contains a total of

57

subatomic particles.

The correct answer is

57

. The number of protons is found by subtracting the neutron count from the mass number (

39 - 20 = 19

). Because the potassium ion carries a

+1

charge (

K^+

), it has lost one electron, leaving

18

electrons. Adding all subatomic constituents gives

19\text{ protons} + 20\text{ neutrons} + 18\text{ electrons} = 57\text{ total particles}

.

Adım Adım Çözüm

1

Calculate the number of protons in the potassium atom.

Protons =

39 - 20 = 19

The mass number (

A

) is the sum of protons (

Z

) and neutrons (

N

), so

Z = A - N

.

2

Determine the number of electrons in the

K^+

ion.

Electrons =

19 - 1 = 18

A neutral potassium atom has

19

electrons; forming a

+1

cation requires losing

1

electron.

3

Sum the total number of protons, neutrons, and electrons.

Total particles =

19 + 20 + 18 = 57

The question requests the combined count of all subatomic particles in the ion.

Anahtar Kavram

Subatomic particle calculations in atomic structure and ions

Tahmini Süre:1m 0s

Soru 3364Soru →

A maintenance crew uses $4$ identical pumps to empty a large aviation fuel tank in $12$ hours. If the crew decides to use $6$ of these identical pumps instead, how many hours will it take to completely empty the tank?

Cevabı ve açıklamayı göster

Cevap: 8

Cevap

8 hours

Because the number of pumps and time are inversely proportional, their product must remain constant. The initial scenario gives a product of 4 pumps × 12 hours = 48 pump-hours. To find the new time, divide the constant product of 48 by the new number of pumps (6). 48 ÷ 6 = 8 hours.

Adım Adım Çözüm

1

Identify the mathematical relationship between the variables.

The number of pumps and the time required are inversely proportional.

When working at a constant rate, increasing the number of machines decreases the time needed to complete the same job.

2

Set up the inverse proportion equation.

4 \times 12 = 6 \times x

For inverse proportions, the product of the two variables remains constant (

x_1 y_1 = x_2 y_2

).

3

Calculate the total pump-hours and solve for the new time.

x = 48 \div 6 = 8

Dividing the constant product (48) by the new number of pumps (6) isolates the unknown time variable.

Anahtar Kavram

Inverse Proportions

Tahmini Süre:45s

Soru 3365Soru →

During a facility expansion, a landscaping crew uses $2.5$ pounds of specialized grass seed to cover a $400$ -square-foot section of terrain. Operating at this exact constant rate, how many ounces of grass seed will be required to cover a $3,200$ -square-foot sector?

320

20

3,200

1.25

Cevabı ve açıklamayı göster

Cevap: $320$

Cevap

The correct answer is

320

.

The correct answer is found by setting up a direct proportion. Since

3,200

square feet is exactly

8

times larger than

400

square feet, the amount of seed required must also be

8

times the original amount. Multiplying

2.5

pounds by

8

gives

20

pounds of seed. Finally, converting

20

pounds into ounces by multiplying by

16

(since

1

pound =

16

ounces) yields exactly

320

ounces.

Adım Adım Çözüm

1

Determine the scale factor by dividing the target area by the initial area.

3,200 \div 400 = 8

This establishes how many times larger the new sector is compared to the original section.

2

Multiply the initial amount of grass seed by the scale factor to find the total pounds needed.

2.5 \times 8 = 20

pounds

Because this is a direct proportion, the amount of seed scales by the exact same factor as the area.

3

Convert the total weight from pounds to ounces.

20 \times 16 = 320

ounces

The question specifically asks for the final answer in ounces, and there are 16 ounces in 1 pound.

Anahtar Kavram

Direct Proportions and Unit Conversion

Alternatif Yöntem

Convert the initial seed amount to ounces first:

2.5

pounds =

40

ounces. Then, set up the proportion:

\frac{40}{400} = \frac{x}{3,200}

. Solving for

x

gives

x = 40 \times 8 = 320

.

Tahmini Süre:1m 15s

Soru 3366Soru →

A detail of $18$ recruits can sweep and mop a large warehouse in $20$ minutes. If the schedule allows $1.5$ hours for the task, how many recruits, working at the same constant rate, are required?

240

24

4

81

Cevabı ve açıklamayı göster

Cevap: $4$

Cevap

The correct answer is

4

.

The scenario describes an inverse proportion because giving the detail more time to complete the task means fewer recruits are needed. By converting

1.5

hours to

90

minutes and applying the inverse proportion relationship (

18 \times 20 = x \times 90

), we find that exactly

4

recruits are required.

Adım Adım Çözüm

1

Calculate the total workload required to complete the task.

W_1 \times T_1 = 18 \times 20 = 360

recruit-minutes.

In inverse proportion problems involving work, the product of the number of workers and their time represents a constant total amount of work.

2

Convert the new target time into the same unit (minutes).

1.5 \text{ hours} = 1.5 \times 60 = 90 \text{ minutes}

.

Units must be consistent across the equation to yield a valid result.

3

Divide the total workload by the new target time to find the required number of recruits.

360 \div 90 = 4

recruits.

Applying the inverse proportion formula

W_2 = \text{Total Work} \div T_2

reveals how many workers are needed for the longer duration.

Anahtar Kavram

Inverse Proportions

Alternatif Yöntem

You can also solve this by finding the total work in 'recruit-hours'. First, convert

20

minutes to

1/3

of an hour. The total work is

18 \text{ recruits} \times (1/3) \text{ hour} = 6 \text{ recruit-hours}

. Since the new time is

1.5

hours, the required number of recruits is

6 \div 1.5 = 4

recruits.

Tahmini Süre:1m 0s

Soru 3367Soru →

An isotope of an alkaline earth metal located in Period 4 (Group 2) of the periodic table contains $24$ neutrons in its nucleus. What is the mass number of this neutral isotope?

Cevabı ve açıklamayı göster

Cevap: 44

Cevap

44

An element in Group 2 and Period 4 of the periodic table is calcium (

\text{Ca}

), which has an atomic number of

20

. This means every calcium atom contains

20

protons in its nucleus. The mass number of an isotope is the total number of protons and neutrons combined:

20\text{ protons} + 24\text{ neutrons} = 44

.

Adım Adım Çözüm

1

Determine the atomic number of the element using its periodic table position.

Atomic number is

20

(contains

20

protons).

The alkaline earth metal (Group 2) in Period 4 is calcium (

\text{Ca}

), which has an atomic number of

20

.

2

Calculate the mass number by summing the number of protons and neutrons.

\text{Mass number} = 20 + 24 = 44

.

The mass number (

A

) is defined as the total count of nucleons (protons plus neutrons) in the nucleus.

Anahtar Kavram

Determining mass number from periodic table position and subatomic particle counts

Tahmini Süre:1m 0s

Soru 3368Soru →

An electronics restorer buys a bulk lot of $40$ tablets for $\$120$ each. The restorer spends an additional $\$1,200$ total for replacement parts to repair them. Unfortunately, $10$ of the tablets are too severely damaged to repair and must be discarded. If the restorer wants to make exactly a $25\%$ profit on the total investment, what must be the selling price for each of the remaining functional tablets?

\$250

\$200

\$187.50

\$150

Cevabı ve açıklamayı göster

Cevap: $\$250$

Cevap

The restorer must sell each of the remaining tablets for

\$250

.

The total investment includes the bulk purchase price (

40 \times \$120 = \$4,800

) plus the cost of replacement parts (

\$1,200

), which totals

\$6,000

. A

25\%

profit on a

\$6,000

investment requires

\$1,500

in profit, meaning the total revenue must reach

\$7,500

. Because

10

tablets were discarded, the restorer only has

30

tablets left to sell. Dividing the target total revenue by the

30

remaining tablets (

\$7,500 \div 30

) gives a required selling price of

\$250

for each functional tablet.

Adım Adım Çözüm

1

Calculate the total cost of purchasing the tablets.

40 \text{ tablets} \times \$120 = \$4,800

To determine the initial part of the investment.

2

Add the overhead costs to find the total investment.

\$4,800 + \$1,200 \text{ (parts)} = \$6,000

Profit must be calculated based on the entire total investment, not just the purchase price.

3

Calculate the target total revenue required to achieve a

25\%

profit.

\$6,000 \times 1.25 = \$7,500

A

25\%

profit means the revenue must be

125\%

of the total investment.

4

Determine the number of functional tablets available to sell.

40 - 10 = 30 \text{ tablets}

The discarded tablets generate no revenue, so the entire target revenue must be generated by the remaining inventory.

5

Calculate the required selling price per functional tablet.

\$7,500 \div 30 = \$250

Dividing the target total revenue by the number of sellable items gives the unit selling price.

Anahtar Kavram

Profit and Loss with Overhead and Inventory Shrinkage

Tahmini Süre:1m 30s

Soru 3369Soru →

Match each military personnel or equipment scenario to its correctly simplified part-to-part ratio.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct matches simplify each starting ratio by finding the greatest common divisor for both terms in the specified order.

Each scenario describes a straightforward part-to-part relationship. By arranging the quantities in the requested order and dividing both numbers by their greatest common divisor, we arrive at the simplest equivalent ratio for each match.

Adım Adım Çözüm

1

Identify the initial quantities in the specific order requested by each scenario.

20:5 for trucks to command vehicles; 6:18 for medics to infantry; 10:15 for water to food; 12:8 for officers to enlisted.

Establishing the correct order is strictly required to prevent inverted ratios.

2

Determine the greatest common divisor (GCD) for each pair of numbers.

The GCD for 20 and 5 is 5. The GCD for 6 and 18 is 6. The GCD for 10 and 15 is 5. The GCD for 12 and 8 is 4.

Dividing by the GCD reduces the ratio to its lowest, simplest form.

3

Divide both terms of each raw ratio by their respective GCD.

20:5 becomes 4:1. 6:18 becomes 1:3. 10:15 becomes 2:3. 12:8 becomes 3:2.

This calculation yields the final simplified part-to-part ratio for each scenario, which directly pairs with the right-hand items.

Anahtar Kavram

Simplifying part-to-part ratios

Soru 3370Soru →

Although the battalion commander initially proposed an aggressive dawn assault, he tempered his strategy after reconnaissance reports revealed fortified defensive positions along the ridge. In this context, the word "tempered" most nearly means which of the following?

hardened

moderated

intensified

abandoned

Cevabı ve açıklamayı göster

Cevap: moderated

Cevap

moderated

In the sentence, the word 'tempered' is used in its secondary sense meaning to dilute, moderate, or soften the intensity of something. The contrast clue 'Although' shows that the commander moved away from an 'aggressive' stance after learning about enemy fortifications, making 'moderated' the precise synonym.

Adım Adım Çözüm

1

Analyze the sentence structure and identify transition signals

The subordinating conjunction 'Although' introduces a contrast between the initial plan ('aggressive dawn assault') and the subsequent revision.

Contrast context clues establish an opposing relationship between two clauses in a sentence.

2

Evaluate the cause-and-effect relationship in the main clause

The discovery of 'fortified defensive positions' logically compels a prudent commander to make the attack less risky and less aggressive.

Context clues from surrounding details dictate the direction of the semantic shift.

3

Match the contextual deduction to the synonym choices

To 'temper' an aggressive plan means to soften, moderate, or tone it down, which matches 'moderated'.

The correct synonym must preserve both the grammatical function and the specific contextual nuance.

Anahtar Kavram

Using contrast and situational context clues to determine the secondary meaning of a polysemous word

Tahmini Süre:45s

Soru 3371Soru →

A couple hires a professional photographer for their wedding. The photographer's base package costs $\$1,200.00$ . The contract includes a $9\%$ state service tax and a $15\%$ mandatory gratuity for the photography assistants. Both the tax and the gratuity are calculated based on the base package cost. What is the final total amount the couple will pay?

\$288.00

\$1,228.80

\$1,488.00

\$1,504.20

Cevabı ve açıklamayı göster

Cevap: $\$1,488.00$

Cevap

The final total amount is

\$1,488.00

.

Both the tax and the gratuity are calculated independently on the base package cost. The tax is

9\%

of

\$1,200.00

, yielding

\$108.00

. The gratuity is

15\%

of

\$1,200.00

, yielding

\$180.00

. Adding these charges to the base cost gives

\$1,200.00 + \$108.00 + \$180.00 = \$1,488.00

. Alternatively, combining the rates gives a total additional charge of

24\%

(

9\% + 15\%

).

24\%

of

\$1,200.00

is

\$288.00

, and

\$1,200.00 + \$288.00 = \$1,488.00

.

Adım Adım Çözüm

1

Calculate the cost of the state service tax.

\$1,200.00 \times 0.09 = \$108.00

The

9\%

tax is applied directly to the base package cost.

2

Calculate the cost of the mandatory gratuity.

\$1,200.00 \times 0.15 = \$180.00

The

15\%

gratuity is also applied directly to the base package cost, as stated in the problem.

3

Add the tax and gratuity to the base cost to find the final total.

\$1,200.00 + \$108.00 + \$180.00 = \$1,488.00

The final bill is the sum of the original price and all additional percentage-based fees.

Anahtar Kavram

Calculating and combining multiple percentages based on a single original amount.

Soru 3372Soru →

An interior communications electrician is wiring a new bulkhead and starts with a spool containing $50$ yards of specialized copper cabling. They use $14 \frac{2}{3}$ yards for the primary circuit and $21 \frac{3}{4}$ yards for a secondary circuit. What is the remaining length of cabling on the spool in yards?

Aşağıdaki boşlukları doldurun

The remaining length of cabling on the spool is yards.

Cevabı ve açıklamayı göster

Cevap

13 7/12

The total amount of cabling used is found by adding

14 \frac{2}{3}

and

21 \frac{3}{4}

, which equals

36 \frac{5}{12}

yards after finding a common denominator and regrouping. Subtracting this total from the initial

50

yards by borrowing (

49 \frac{12}{12} - 36 \frac{5}{12}

) yields the correct remaining length of

13 \frac{7}{12}

yards.

Adım Adım Çözüm

1

Find a common denominator to add the lengths of cabling used for the primary and secondary circuits.

The least common multiple of 3 and 4 is 12. Convert the fractions:

14 \frac{2}{3} = 14 \frac{8}{12}

and

21 \frac{3}{4} = 21 \frac{9}{12}

.

Fractions must have the same denominator before they can be added together.

2

Add the converted mixed numbers to find the total amount of cabling used.

14 \frac{8}{12} + 21 \frac{9}{12} = 35 \frac{17}{12}

. Since

\frac{17}{12}

is an improper fraction, regroup it as

1 \frac{5}{12}

. Adding this to 35 gives

36 \frac{5}{12}

yards used in total.

This step determines the combined amount of cabling taken from the spool.

3

Subtract the total amount used from the original amount on the spool.

Subtract

36 \frac{5}{12}

from

50

. To do this, borrow 1 from 50 to create a fraction:

50 = 49 \frac{12}{12}

. Then subtract:

49 \frac{12}{12} - 36 \frac{5}{12} = 13 \frac{7}{12}

yards.

Subtracting the part used from the whole determines the remaining length of cabling.

Anahtar Kavram

Adding mixed numbers with unlike denominators and subtracting a mixed number from a whole number.

Soru 3373Soru →

An observer at a construction site watches a worker strike a steel pipe with a hammer and hears the sound transmitted through the pipe before hearing it through the open air. Which of the following best explains why sound travels faster through solid steel than through air?

The frequency of the sound wave increases significantly when traveling through denser matter.

The closely packed particles and high elasticity of solids allow vibrational energy to transfer more rapidly between molecules.

Sound waves convert into electromagnetic transverse waves when moving through solid materials.

The amplitude of the wave increases automatically because solid matter absorbs less acoustic energy.

Cevabı ve açıklamayı göster

Cevap: The closely packed particles and high elasticity of solids allow vibrational energy to transfer more rapidly between molecules.

Cevap

Sound travels faster through solid steel than through air because the closely packed particles and high elasticity of solids allow mechanical vibrational energy to transfer more rapidly between molecules.

Sound is a mechanical wave that propagates through the physical displacement and elastic restoration of medium particles. In solids like steel, atoms are tightly bonded in a crystal lattice with high elastic modulus, enabling compressions and rarefactions to transfer rapidly from particle to particle. In contrast, gas molecules in air are widely spaced and require longer travel times between collisions, resulting in a much lower propagation speed.

Adım Adım Çözüm

1

Identify the nature of sound waves and the medium requirement

Sound is a mechanical wave that propagates via sequential collisions and oscillations of particles in a physical medium.

Understanding that mechanical waves rely on intermolecular interactions is necessary to evaluate the effect of the medium on wave speed.

2

Compare particle arrangement and elasticity between solids and gases

Molecules in steel are closely bound with high elastic modulus, whereas air molecules are widely separated with low elasticity.

Greater medium elasticity and density of packing directly increase the speed of acoustic transmission (

v = \sqrt{E/\rho}

).

3

Relate medium properties to wave speed differences

Sound travels at roughly

5{}960\text{ m/s}

in steel compared to approximately

343\text{ m/s}

in air.

The rapid transfer of kinetic energy between adjacent atoms in the solid explains why the sound arrives first through the steel pipe.

Anahtar Kavram

Mechanical sound wave propagation speed depends on the elasticity and atomic density of the transmitting medium, traveling fastest in solids, slower in liquids, and slowest in gases.

Tahmini Süre:1m 0s

Soru 3374Soru →

A neutral atom has $2$ electrons in its first energy level, $8$ electrons in its second energy level, and $6$ valence electrons in its third energy level. If the mass number of this atom is $34$ , what is the total number of neutrons located in its nucleus?

16

28

18

50

Cevabı ve açıklamayı göster

Cevap: $18$

Cevap

18

neutrons

In a neutral atom, the total number of electrons equals the number of protons (atomic number,

Z

). Summing the electrons across all three energy levels (

2 + 8 + 6

) yields

16

electrons, which means the nucleus contains

16

protons. Because mass number (

A

) is the sum of protons and neutrons (

A = Z + N

), the number of neutrons is found by subtracting the protons from the mass number:

34 - 16 = 18

.

Adım Adım Çözüm

1

Calculate the total number of electrons in the neutral atom by summing all energy levels.

2 + 8 + 6 = 16

electrons

The total electron count is the sum of electrons distributed across the inner shells and the valence shell.

2

Determine the atomic number (number of protons) from the electron count.

Atomic number (

Z

) =

16

protons

In any neutral atom, the number of positively charged protons equals the number of negatively charged electrons.

3

Calculate the number of neutrons by subtracting the atomic number from the mass number.

Number of neutrons =

34 - 16 = 18

Mass number (

A

) equals protons (

Z

) plus neutrons (

N

), so

N = A - Z

.

Anahtar Kavram

Subatomic particle relationships and electron configuration in neutral atoms

Tahmini Süre:1m 0s

Soru 3375Soru →

The visible light spectrum consists of electromagnetic radiation spanning various wavelengths and frequencies. Arrange the following colors of visible light in order of increasing frequency, from lowest frequency to highest frequency.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct order from lowest frequency to highest frequency is Red light, Yellow light, Blue light, and Violet light.

Electromagnetic waves in the visible spectrum have frequencies that are inversely related to their wavelengths. Red light has the longest wavelength (around

700\text{ nm}

) and thus the lowest frequency. As wavelength decreases across the spectrum toward violet (around

400\text{ nm}

), wave frequency increases progressively from yellow to blue to violet.

Adım Adım Çözüm

1

Recall the fundamental wave relationship connecting wave speed, frequency, and wavelength.

Since all electromagnetic waves travel at the same speed in a vacuum (

c = f\lambda

), frequency is inversely proportional to wavelength (

f = c / \lambda

).

This relationship demonstrates that colors with the longest wavelengths have the lowest frequencies, while colors with the shortest wavelengths have the highest frequencies.

2

Determine the relative wavelengths and frequencies of the given visible light colors using the standard spectral sequence.

From longest to shortest wavelength, the visible spectrum follows the sequence: Red

\rightarrow

Orange

\rightarrow

Yellow

\rightarrow

Green

\rightarrow

Blue

\rightarrow

Indigo

\rightarrow

Violet.

Mapping the colors to this sequence directly determines their relative positions regarding frequency.

3

Arrange the specified colors in order of increasing frequency.

The sequence from lowest frequency (longest wavelength) to highest frequency (shortest wavelength) is Red light

\rightarrow

Yellow light

\rightarrow

Blue light

\rightarrow

Violet light.

This orders the items accurately according to the specified physical criteria.

Anahtar Kavram

Visible Light Spectrum and Wave Frequency

Tahmini Süre:1m 0s

Soru 3376Soru →

A base carpenter is purchasing premium oak trim priced at $\$3.20$ per linear foot. He needs to buy $4.5$ feet of trim for one room and $30$ inches of trim for a hallway. If the supplier charges a flat delivery fee of $\$8.75$ , what is the total cost of the purchase?

\$31.15

\$119.15

\$32.75

\$10.99

Cevabı ve açıklamayı göster

Cevap: $\$31.15$

Cevap

The total cost of the purchase is

\$31.15

.

First, the measurements must be harmonized. Since the price is per foot, convert

30

inches to feet by dividing by

12

, which gives

2.5

feet. Add this to the

4.5

feet required for the other room to get a total of

7.0

feet. Multiply the total length by the unit price (

7.0 \times \$3.20

) to determine the material cost of

\$22.40

. Finally, add the flat delivery fee of

\$8.75

to reach the correct total cost of

\$31.15

.

Adım Adım Çözüm

1

Convert the hallway trim measurement from inches to feet.

30 \div 12 = 2.5

feet

Measurements must be in the same unit (feet) because the price is given per linear foot.

2

Calculate the total linear feet of trim needed.

4.5 + 2.5 = 7.0

feet

To find the total material cost, you must combine the lengths needed for both rooms.

3

Calculate the cost of the wood.

7.0 \times \$3.20 = \$22.40

Multiply the total length by the price per linear foot.

4

Add the delivery fee to the material cost to find the final total.

\$22.40 + \$8.75 = \$31.15

The flat delivery fee must be included in the total cost of the purchase.

Anahtar Kavram

Decimal Operations and Unit Conversions in Cost Calculations

Soru 3377Soru →

A merchant buys a radio for $40$ dollars and sells it for $50$ dollars. What is the merchant's profit percentage on this item?

20\%

25\%

10\%

125\%

Cevabı ve açıklamayı göster

Cevap: $25\%$

Cevap

The correct answer is

25\%

.

To find the profit percentage, first determine the total profit by subtracting the cost price (

40

dollars) from the selling price (

50

dollars), which gives a profit of

10

dollars. Then, divide the profit by the original cost price (

\frac{10}{40} = 0.25

) and multiply by

100

to get

25\%

.

Adım Adım Çözüm

1

Calculate the profit amount.

50 - 40 = 10

Profit is defined as the difference between the selling price and the cost price.

2

Calculate the profit percentage.

\frac{10}{40} \times 100 = 25\%

Profit percentage is the profit amount divided by the original cost price, expressed as a percentage.

Anahtar Kavram

Profit Percentage

Soru 3378Soru →

An investor divides her $24,000 savings into two different accounts. She places a portion into a high-yield certificate earning 9% annual simple interest, and the remainder into a short-term bond earning 6% annual simple interest. After 18 months, the combined simple interest earned from both accounts is exactly$ 2,430. How much money was originally invested at the 9% rate?

$6,000

$18,000

$14,400

$600

Cevabı ve açıklamayı göster

Cevap: $6,000

Cevap

The amount invested at the 9% rate is $6,000.

The correct answer is derived by modeling the split investment algebraically. By assigning

x

to the 9% investment, the 6% investment becomes

24,000 - x

. Applying the formula

I = Prt

with

t = 1.5

years to both parts yields

0.09(1.5)x + 0.06(1.5)(24,000 - x) = 2,430

. Simplifying this to

0.135x + 2,160 - 0.09x = 2,430

leaves

0.045x = 270

. Dividing 270 by 0.045 confirms that $6,000 was invested at 9%.

Adım Adım Çözüm

1

Convert the investment duration from months to years.

18 months = 1.5 years.

The simple interest formula

I = Prt

requires time

t

to be expressed in years when dealing with annual interest rates.

2

Define variables for the two investment amounts.

Let

x

be the amount invested at 9%. The remaining amount invested at 6% is

(24,000 - x)

.

This allows us to represent both unknown principals in terms of a single variable, making the equation solvable.

3

Set up the total interest equation using

I = Prt

.

x(0.09)(1.5) + (24,000 - x)(0.06)(1.5) = 2,430

The sum of the simple interest earned from the 9% account and the 6% account must equal the total interest of $2,430.

4

Distribute and simplify the terms in the equation.

0.135x + (24,000 - x)(0.09) = 2,430 \Rightarrow 0.135x + 2,160 - 0.09x = 2,430

Multiplying the rate and time constants makes it easier to isolate

x

.

5

Combine like terms and solve for

x

.

0.045x = 270 \Rightarrow x = \frac{270}{0.045} = 6,000

Isolating

x

provides the original amount invested at the 9% rate.

Anahtar Kavram

Systems of Simple Interest

Tahmini Süre:3m 0s

Soru 3379Soru →

A flight line crew has $18$ gallons of specialized hydraulic fluid. They need to fill aircraft reservoirs that each require $\frac{3}{4}$ of a gallon of the fluid. How many reservoirs can the crew fill?

13 \frac{1}{2}

24

72

18 \frac{3}{4}

Cevabı ve açıklamayı göster

Cevap: $24$

Cevap

24

The correct answer is 24 because finding how many times a portion fits into a total requires division. Setting up

18 \div \frac{3}{4}

and multiplying by the reciprocal yields

18 \times \frac{4}{3} = 24

.

Adım Adım Çözüm

1

Identify the total amount of fluid and the amount needed per reservoir.

Total fluid is 18 gallons; each reservoir requires 3/4 gallon.

Understanding the given quantities is required to set up the correct mathematical operation.

2

Set up the division expression to find the number of reservoirs.

18 \div \frac{3}{4}

Finding how many times a fractional amount fits into a total requires division.

3

Convert the division of a fraction into multiplication by its reciprocal.

18 \times \frac{4}{3}

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal (flipping the numerator and denominator).

4

Perform the multiplication.

\frac{18 \times 4}{3} = \frac{72}{3} = 24

Multiplying the whole number by the numerator and dividing by the denominator yields the final whole number of reservoirs.

Anahtar Kavram

Dividing a whole number by a fraction to determine quantities in a real-world scenario.

Soru 3380Soru →

The technician found that the replacement parts were substandard. In this sentence, what does the word substandard most nearly mean?

Superior

Standardized

Inferior

Elevated

Cevabı ve açıklamayı göster

Cevap: Inferior

Cevap

Inferior

The word 'substandard' combines the Latin prefix 'sub-', which means 'under' or 'below', with the base word 'standard', meaning an accepted level of quality. Therefore, something that is substandard is below regular standards, making 'Inferior' the correct synonym.

Adım Adım Çözüm

1

Analyze the prefix and root of the target word.

The prefix 'sub-' means 'under' or 'below', and the base word 'standard' refers to an established level of quality or requirement.

Breaking down the word into its morphological components reveals its core meaning.

2

Combine the morphological meanings to determine the overall definition.

'Substandard' literally translates to 'below standard' or failing to meet quality requirements.

Synthesizing the prefix and root produces the definition needed to identify the correct synonym.

3

Evaluate the choices to find the matching synonym.

'Inferior' matches the definition of falling below standard or being lower in quality.

Aligning the derived definition with the options identifies the correct synonym.

Anahtar Kavram

Prefix analysis using 'sub-' (meaning under or below)

Tahmini Süre:30s

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap