Tüm alıştırma soruları

Soru 5121Soru →

An industrial robotic manipulator in an assembly plant applies a steady vertical force of $400\text{ N}$ to lift a structural bracket through a height of $3\text{ meters}$ . If the manipulator delivers a constant power output of $150\text{ W}$ throughout the movement, how much time does the manipulator take to complete the lift?

3\text{ seconds}

8\text{ seconds}

0.125\text{ seconds}

50\text{ seconds}

Cevabı ve açıklamayı göster

Cevap: $8\text{ seconds}$

Cevap

The robotic manipulator takes

8\text{ seconds}

to complete the lift.

The correct answer is found by first determining the mechanical work performed and then dividing by the power output. The work done lifting the bracket is

W = F \times d = 400\text{ N} \times 3\text{ m} = 1{}200\text{ J}

. Since power is the rate of work done (

P = \frac{W}{t}

), the time required is

t = \frac{W}{P} = \frac{1{}200\text{ J}}{150\text{ W}} = 8\text{ seconds}

.

Adım Adım Çözüm

1

Calculate the total mechanical work done to lift the bracket.

W = \text{Force} \times \text{Distance} = 400\text{ N} \times 3\text{ m} = 1{}200\text{ J}

Work is defined as force multiplied by the distance over which that force is applied in the direction of motion.

2

Calculate the time elapsed using the power relationship.

t = \frac{W}{P} = \frac{1{}200\text{ J}}{150\text{ W}} = 8\text{ seconds}

Power represents the rate of doing work (

P = \frac{W}{t}

), which rearranges to

t = \frac{W}{P}

.

Anahtar Kavram

Relationship between mechanical work, force, distance, and power

Tahmini Süre:1m 0s

Soru 5122Soru →

Solar radiation warms the uppermost layer of the ocean, but sunlight cannot penetrate deeply into the water column. Which term identifies the oceanic layer where water temperature drops steeply with increasing depth?

Halocline

Thermocline

Pycnocline

Abyssopelagic zone

Cevabı ve açıklamayı göster

Cevap: Thermocline

Cevap

Thermocline

The thermocline is the intermediate ocean layer located directly beneath the warm surface mixed layer, characterized by a rapid decrease in water temperature with increasing depth.

Adım Adım Çözüm

1

Identify the physical property and gradient described in the question.

The stem describes an oceanic layer defined by a steep decrease in temperature over depth.

Recognizing that the gradient is thermal distinguishes it from salinity and density gradients.

2

Differentiate among oceanic gradient zones by their defining variables.

The thermocline ('thermo' relating to heat and 'cline' meaning gradient) specifically designates the rapid thermal transition zone.

Matching the thermal property directly identifies the thermocline as the correct oceanographic feature.

Anahtar Kavram

Oceanic thermal stratification and the thermocline layer

Tahmini Süre:45s

Soru 5123Soru →

A sound wave generated in air enters a pool of water, where its propagation speed increases by a factor of four. How are the frequency and wavelength of the sound wave affected upon entering the water?

The frequency quadruples, while the wavelength remains unchanged.

The frequency remains unchanged, while the wavelength quadruples.

The frequency remains unchanged, while the wavelength is reduced to one-fourth.

Both the frequency and the wavelength double.

Cevabı ve açıklamayı göster

Cevap: The frequency remains unchanged, while the wavelength quadruples.

Cevap

The frequency remains unchanged, while the wavelength quadruples.

When any wave crosses the boundary between two media, its frequency is conserved because frequency is determined solely by the source vibration. According to the wave equation

v = f\lambda

, if wave speed increases by a factor of 4 while frequency remains constant, the wavelength must also increase by a factor of 4 to maintain the equality.

Adım Adım Çözüm

1

Identify the behavior of wave frequency across a boundary.

The frequency (

f

) remains constant because it depends exclusively on the oscillating source.

When a wave transitions from one medium into another, particles at the boundary oscillate in synchronization with the incident wave, preserving frequency.

2

Apply the universal wave equation relating speed, frequency, and wavelength.

v = f\lambda

, which rearranges to

\lambda = \frac{v}{f}

.

This formula defines the relationship between the physical parameters of any wave.

3

Calculate the proportional change in wavelength when speed increases by a factor of 4.

Since

v_{\text{water}} = 4v_{\text{air}}

and

f

is constant,

\lambda_{\text{water}} = \frac{4v_{\text{air}}}{f} = 4\lambda_{\text{air}}

.

Wavelength is directly proportional to wave speed when frequency is constant.

Anahtar Kavram

Wave boundary behavior and the wave equation (

v = f\lambda

)

Tahmini Süre:1m 0s

Soru 5124Soru →

A camper uses a small portable propane stove to prepare a meal. Which of the following occurrences during this process is an example of a chemical change?

Liquid propane vaporizing into gas inside the fuel line

Propane gas burning at the burner to produce heat, carbon dioxide, and water vapor

Solid ice melting into liquid water in a pot on the stove

Liquid water boiling and evaporating into steam

Cevabı ve açıklamayı göster

Cevap: Propane gas burning at the burner to produce heat, carbon dioxide, and water vapor

Cevap

Propane gas burning at the burner to produce heat, carbon dioxide, and water vapor

Combustion of propane is a chemical change because propane molecules react chemically with atmospheric oxygen to break and reform chemical bonds, creating entirely new substances: carbon dioxide and water vapor.

Adım Adım Çözüm

1

Distinguish between physical and chemical changes.

A physical change alters only the form or state of a substance without forming new chemical bonds or substances. A chemical change rearranges atoms to create one or more new substances with different properties.

Classification requires identifying whether the molecular composition is preserved or altered.

2

Evaluate each occurrence in the scenario.

Vaporizing propane, melting ice, and boiling water are all phase transitions (physical changes). Burning propane (combustion) reacts propane with oxygen to produce new substances (carbon dioxide and water).

Only combustion results in the formation of new chemical substances.

Anahtar Kavram

Distinction between physical changes (phase changes) and chemical changes (reactions)

Tahmini Süre:45s

Soru 5125Soru →

A maintenance cart with a mass of $250\text{ kg}$ travels along a straight horizontal track. If the cart uniformly slows down from an initial velocity of $15\text{ m/s}$ due east to $5\text{ m/s}$ due east over a time interval of $5\text{ seconds}$ , what is the magnitude and direction of the net force acting on the cart?

500\text{ N}

directed due east

500\text{ N}

directed due west

4{}900\text{ N}

directed due west

0.5\text{ N}

directed due west

Cevabı ve açıklamayı göster

Cevap: $500\text{ N}$ directed due west

Cevap

The magnitude of the net force is

500\text{ N}

, directed due west.

Acceleration is the change in velocity divided by time:

a = (5\text{ m/s} - 15\text{ m/s}) / 5\text{ s} = -2\text{ m/s}^2

. The negative sign indicates an acceleration directed due west (opposite to the eastward motion). Applying Newton's Second Law (

F = ma

), the net force is

250\text{ kg} \times 2\text{ m/s}^2 = 500\text{ N}

directed due west.

Adım Adım Çözüm

1

Calculate the acceleration using the kinematics formula

a = \frac{v_f - v_i}{\Delta t}

.

a = \frac{5\text{ m/s} - 15\text{ m/s}}{5\text{ s}} = \frac{-10\text{ m/s}}{5\text{ s}} = -2\text{ m/s}^2

(or

2\text{ m/s}^2

directed west).

Acceleration is the rate of change of velocity over time.

2

Calculate the magnitude and direction of the net force using Newton's Second Law,

F_{\text{net}} = m \cdot a

.

F_{\text{net}} = 250\text{ kg} \times 2\text{ m/s}^2 = 500\text{ N}

directed west.

Net force is equal to mass multiplied by acceleration and always points in the same direction as the acceleration vector.

Anahtar Kavram

Newton's Second Law of Motion (

F_{\text{net}} = ma

) and Kinematics of Linear Deceleration

Alternatif Yöntem

Use the impulse-momentum theorem (

F_{\text{net}} \cdot \Delta t = m \cdot \Delta v

). Here,

\Delta p = 250\text{ kg} \times (5\text{ m/s} - 15\text{ m/s}) = -2{}500\text{ kg}\cdot\text{m/s}

. Dividing momentum change by

\Delta t = 5\text{ s}

yields

F_{\text{net}} = -500\text{ N}

, meaning

500\text{ N}

directed west.

Tahmini Süre:1m 0s

Soru 5126Soru →

An electric toaster toasts bread using glowing heating coils placed a short distance away from the slices without touching them. Which method of heat transfer is primarily responsible for warming and toasting the bread?

Conduction

Convection

Radiation

Condensation

Cevabı ve açıklamayı göster

Cevap: Radiation

Cevap

Radiation transfers thermal energy across the space between the coils and the bread via electromagnetic infrared waves.

Thermal radiation transfers energy via electromagnetic waves, such as infrared light. Because the bread does not touch the glowing wires, radiation is the primary mechanism heating the surface of the bread directly across the gap.

Adım Adım Çözüm

1

Analyze the physical arrangement in the toaster.

The bread is placed near the glowing elements across an air gap without making direct physical contact.

Determining whether physical contact occurs narrows down the possible heat transfer mechanisms.

2

Identify the primary mechanism of heat transfer through empty space and transparent air.

The glowing heating elements emit electromagnetic energy in the form of infrared radiation directly onto the bread's surface.

Thermal radiation does not require direct contact or fluid circulation currents to transfer energy.

Anahtar Kavram

Thermal radiation transfers heat through electromagnetic waves without requiring direct contact or a circulating medium.

Tahmini Süre:45s

Soru 5127Soru →

A painter is mixing a custom green paint. The formula requires mixing blue and yellow paint in a ratio of $1$ part blue to $3$ parts yellow. He needs exactly $22\frac{1}{2}$ gallons of the green paint mixture for a large commercial job. So far, he has poured $1\frac{3}{4}$ gallons of blue paint from one can, and $2$ quarts of blue paint from another can into the mixing bucket. How many more gallons of blue paint does he need to add to reach the correct amount of blue paint for the entire job?

3\frac{3}{8}

5\frac{1}{4}

3\frac{23}{24}

1\frac{7}{8}

Cevabı ve açıklamayı göster

Cevap: $3\frac{3}{8}$

Cevap

The painter needs

3\frac{3}{8}

more gallons of blue paint.

First, the correct fraction of blue paint is identified from the

1:3

ratio, which is

1

part out of

4

total parts (

\frac{1}{4}

). The total blue paint needed is

\frac{1}{4}

of

22\frac{1}{2}

gallons, which is

5\frac{5}{8}

gallons. The painter has already poured

1\frac{3}{4}

gallons and

2

quarts (which is

\frac{1}{2}

gallon). Adding these gives

2\frac{1}{4}

gallons poured. Finally, subtracting the poured amount from the total needed (

5\frac{5}{8} - 2\frac{1}{4}

) leaves

3\frac{3}{8}

gallons.

Adım Adım Çözüm

1

Determine the fraction of the mixture that is blue paint.

The ratio of blue to yellow is

1:3

, meaning there is

1

part blue for every

4

total parts (

1 + 3

). The fraction is

\frac{1}{4}

.

This is necessary to find out how much blue paint is required for the entire

22\frac{1}{2}

gallon mixture.

2

Calculate the total amount of blue paint needed for the job.

\frac{1}{4} \times 22\frac{1}{2} = \frac{1}{4} \times \frac{45}{2} = \frac{45}{8} = 5\frac{5}{8}

gallons.

Multiplying the total mixture volume by the fraction of blue paint gives the target amount of blue paint.

3

Convert the quarts of blue paint already poured into gallons.

Since

4

quarts equal

1

gallon,

2

quarts is equal to

\frac{2}{4}

or

\frac{1}{2}

gallon.

All measurements must be in the same unit (gallons) before adding them together.

4

Calculate the total amount of blue paint already poured.

1\frac{3}{4} + \frac{1}{2} = 1\frac{3}{4} + \frac{2}{4} = 1\frac{5}{4} = 2\frac{1}{4}

gallons.

This finds the combined volume of the two separate pours of blue paint.

5

Subtract the poured amount from the total needed amount.

5\frac{5}{8} - 2\frac{1}{4} = 5\frac{5}{8} - 2\frac{2}{8} = 3\frac{3}{8}

gallons.

Subtracting what has been poured from the target amount gives the remaining amount needed.

Anahtar Kavram

Fraction addition and subtraction in practical measurement scenarios, including basic unit conversion and proportional reasoning.

Soru 5128Soru →

A military cargo plane consumes $400$ gallons of fuel to fly $150$ miles. At this rate, how many gallons of fuel will the plane consume to fly a distance of $600$ miles?

100

320

1,600

16,000

Cevabı ve açıklamayı göster

Cevap: 1,600

Cevap

1,600

The relationship between distance and fuel consumption is a direct proportion. Because the new distance (

600

miles) is exactly

4

times the original distance (

150

miles), the fuel needed is also

4

times the original amount. Multiplying

400

gallons by

4

yields

1,600

gallons.

Adım Adım Çözüm

1

Determine the scale factor between the two distances.

600 \div 150 = 4

Since the rate of fuel consumption is constant, finding how many times greater the new distance is allows us to scale the fuel proportionally.

2

Multiply the original fuel amount by the scale factor.

400 \times 4 = 1,600

Direct proportion dictates that if the distance is multiplied by 4, the fuel required must also be multiplied by 4.

Anahtar Kavram

Direct Proportions

Soru 5129Soru →

A machinist has a steel rod of an unknown initial length. She cuts off a piece measuring $5 \frac{5}{8}$ inches for a fitting and another piece measuring $3 \frac{5}{6}$ inches for a bracket. She then welds on a spare segment that is $2 \frac{3}{4}$ inches long. After these modifications, she trims exactly $\frac{7}{12}$ of an inch off the end to square it up. If the final length of the rod is $14 \frac{1}{2}$ inches, what was its original length?

21 \frac{19}{24}

inches

20 \frac{5}{8}

inches

7 \frac{5}{24}

inches

27 \frac{7}{24}

inches

Cevabı ve açıklamayı göster

Cevap: $21 \frac{19}{24}$ inches

Cevap

The original length of the steel rod was

21 \frac{19}{24}

inches.

The correct answer is found by working backward from the final length. This requires reversing all operations: adding back the pieces that were cut and trimmed, and subtracting the piece that was welded. Using the least common denominator of 24, the calculation becomes

14 \frac{12}{24} + 5 \frac{15}{24} + 3 \frac{20}{24} - 2 \frac{18}{24} + \frac{14}{24}

, which accurately sums to

21 \frac{19}{24}

inches.

Adım Adım Çözüm

1

Set up an equation representing the physical changes to the rod from its initial length.

\text{Initial} - 5 \frac{5}{8} - 3 \frac{5}{6} + 2 \frac{3}{4} - \frac{7}{12} = 14 \frac{1}{2}

Cutting and trimming decrease the overall length (subtraction), while welding increases the length (addition).

2

Rearrange the equation to solve for the initial length by applying inverse operations.

\text{Initial} = 14 \frac{1}{2} + 5 \frac{5}{8} + 3 \frac{5}{6} - 2 \frac{3}{4} + \frac{7}{12}

To work backward from the final length to the initial length, we must reverse all operations (add what was removed, subtract what was added).

3

Determine the least common denominator (LCD) for the fractions

\frac{1}{2}

,

\frac{5}{8}

,

\frac{5}{6}

,

\frac{3}{4}

, and

\frac{7}{12}

.

The LCD of 2, 8, 6, 4, and 12 is 24.

Fractions must share a common denominator before they can be added or subtracted.

4

Convert each mixed number to an equivalent fraction with a denominator of 24.

14 \frac{12}{24} + 5 \frac{15}{24} + 3 \frac{20}{24} - 2 \frac{18}{24} + \frac{14}{24}

Equivalent fractions allow for direct arithmetic on the numerators.

5

Perform the addition and subtraction for the whole numbers and the fractions.

Whole numbers:

14 + 5 + 3 - 2 = 20

. Fractions:

\frac{12 + 15 + 20 - 18 + 14}{24} = \frac{43}{24} = 1 \frac{19}{24}

. Total length =

20 + 1 \frac{19}{24} = 21 \frac{19}{24}

inches.

Combining the whole number and fractional sums yields the fully simplified initial length of the rod.

Anahtar Kavram

Fraction Addition and Subtraction in Context

Tahmini Süre:4m 0s

Soru 5130Soru →

A grocery store purchases bags of coffee beans from a supplier at a wholesale cost of $\$40$ per bag. The store applies a $25\%$ markup to the wholesale cost to determine the retail price. What is the retail price of one bag of coffee beans?

\$50

\$65

\$10

\$41

Cevabı ve açıklamayı göster

Cevap: $\$50$

Cevap

The retail price of one bag of coffee beans is

\$50

.

To find the retail price, first determine the markup amount by calculating

25\%

of

\$40

. Since

25\%

is equivalent to the fraction

\frac{1}{4}

or the decimal

0.25

, multiplying

40 \times 0.25

equals

\$10

. Add this

\$10

markup to the original

\$40

wholesale cost to get the final retail price of

\$50

.

Adım Adım Çözüm

1

Calculate the dollar amount of the markup by finding

25\%

of

\$40

.

0.25 \times 40 = 10

The markup percentage must be converted to a dollar amount before it can be added to the cost.

2

Add the markup amount to the original wholesale cost.

40 + 10 = 50

The retail price is the sum of the wholesale cost and the markup.

Anahtar Kavram

Calculating a markup by finding a percentage of a base value and adding it to the original amount.

Tahmini Süre:45s

Soru 5131Soru →

A carpenter is working with a wooden board that is exactly $80$ inches long. He needs to cut three separate pieces from this board with the following lengths: $14 \frac{7}{8}$ inches, $21 \frac{5}{16}$ inches, and $19 \frac{1}{2}$ inches. To extract these three pieces, he makes exactly $3$ cuts. Each cut removes exactly $\frac{1}{8}$ of an inch of wood as sawdust (kerf).

What is the exact length of the remaining portion of the board?
(Enter your answer as a simplified mixed number with a space between the whole number and the fraction, like 5 1/2)

Aşağıdaki boşlukları doldurun

The remaining portion of the board measures inches.

Cevabı ve açıklamayı göster

Cevap

23 15/16

The correct answer accurately accounts for both the sum of the three pieces and the material lost from the three saw cuts. By converting all fractions to a common denominator of 16, adding the pieces together, adding the total kerf waste, and then subtracting that combined sum from the initial 80 inches, we find the exact remaining length.

Adım Adım Çözüm

1

Find a common denominator for all fractions to make addition straightforward.

The common denominator is 16. The pieces convert to

14 \frac{14}{16}

,

21 \frac{5}{16}

, and

19 \frac{8}{16}

. The kerf waste per cut converts to

\frac{2}{16}

.

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

2

Calculate the total length of the three cut pieces.

14 \frac{14}{16} + 21 \frac{5}{16} + 19 \frac{8}{16} = 54 \frac{27}{16}

, which simplifies to

55 \frac{11}{16}

inches.

This represents the total usable material extracted from the board.

3

Calculate the total amount of wood lost to sawdust (kerf) and add it to the pieces' length.

3 cuts

\times \frac{2}{16}

inch/cut =

\frac{6}{16}

inch lost. Total wood consumed is

55 \frac{11}{16} + \frac{6}{16} = 55 \frac{17}{16}

, which simplifies to

56 \frac{1}{16}

inches.

Each cut removes material that is turned into sawdust, so this length must be accounted for as part of the board that is no longer available.

4

Subtract the total wood consumed from the original length of the board.

80 - 56 \frac{1}{16} = 79 \frac{16}{16} - 56 \frac{1}{16} = 23 \frac{15}{16}

inches.

Subtracting the total used (pieces plus waste) from the starting length gives the exact remaining length.

Anahtar Kavram

Adding and subtracting mixed numbers with unlike denominators while accounting for systemic deductions (like kerf waste) in real-world contexts.

Soru 5132Soru →

A $12\text{ V}$ direct-current car battery is connected to a circuit powering a single headlight with a resistance of $4\,\Omega$ . What is the electric current, in amperes, flowing through the headlight?

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The electric current flowing through the headlight is 3 amperes.

According to Ohm's law, electric current (

I

) equals voltage (

V

) divided by resistance (

R

). Dividing a voltage of

12\text{ V}

by a resistance of

4\,\Omega

yields an electric current of

3\text{ A}

.

Adım Adım Çözüm

1

Identify the relationship between voltage, current, and resistance using Ohm's law.

V = I \times R

, which rearranges to

I = \frac{V}{R}

.

Ohm's law governs the relationship between electric potential difference, current flow, and resistance in a DC circuit.

2

Substitute the given values into the formula and solve for current.

I = \frac{12\text{ V}}{4\,\Omega} = 3\text{ A}

Dividing the electromotive force (voltage) by the total circuit resistance yields the resulting electric current.

Anahtar Kavram

Ohm's Law (

V = IR

)

Soru 5133Soru →

In classical mechanics, fundamental laws and principles define how forces govern the motion and interaction of physical bodies. Match each mechanical principle with its correct scientific definition or governing rule.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Newton's First Law pairs with the statement describing an object maintaining constant velocity unless acted upon by a net force; Newton's Second Law pairs with the statement that acceleration is directly proportional to net force and inversely proportional to mass; Newton's Third Law pairs with the statement regarding equal and opposite force interactions between two bodies; and the Law of Conservation of Momentum pairs with the statement that total mass times velocity remains constant in a closed system.

Each mechanical principle aligns directly with its formal physical definition: Newton's First Law governs inertia and zero-acceleration states; Newton's Second Law defines how net force produces acceleration proportional to force and inversely proportional to mass; Newton's Third Law defines equal and opposite force pairs between interacting bodies; and the Law of Conservation of Momentum dictates the invariance of total system momentum in closed systems.

Adım Adım Çözüm

1

Identify the foundational definition of inertia and unaccelerated motion.

Newton's First Law matches the description of objects maintaining rest or uniform straight-line motion unless a net external force intervenes.

Inertia requires zero net force for constant velocity.

2

Identify the quantitative relationship governing net force, acceleration, and mass.

Newton's Second Law matches the relationship where acceleration is proportional to net force and inversely proportional to mass (

F_{\text{net}} = ma

).

This law provides the direct causal formula for changing an object's velocity.

3

Identify the law governing reciprocal force pairs between interacting objects.

Newton's Third Law matches the statement of equal and opposite forces acting simultaneously on two separate bodies.

Forces in nature always exist in matched action-reaction pairs across interacting bodies.

4

Identify the principle governing total quantity of motion across collisions in isolated systems.

The Law of Conservation of Momentum matches the constant total vector product of mass and velocity (

mv

) in closed systems.

Internal interaction forces cancel out vectorially across the entire system, preserving total momentum.

Anahtar Kavram

Fundamental Principles and Governing Laws of Classical Mechanics

Tahmini Süre:1m 0s

Soru 5134Soru →

Paleontologists classify prehistoric biological remains according to the specific geological and chemical mechanisms that preserved them. Match each fossil preservation mode with its defining geological characteristic.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Trace fossil correctly pairs with sedimentary evidence of biological activity without body parts; Mold and cast correctly pairs with a hollow cavity filled with secondary minerals replicating external morphology; Carbonization correctly pairs with compression expelling volatiles to leave a thin carbon film; Amber entombment correctly pairs with complete organisms sealed in hardened tree resin.

Each fossilization process corresponds directly to distinct physical and geochemical mechanisms: trace fossils capture indirect activity (footprints and burrows); mold and cast formations represent hollow dissolution cavities filled by mineral crystallization; carbonization results from volatile loss under pressure leaving a thin carbonaceous film; and amber entombment seals whole specimens in fossilized resin.

Adım Adım Çözüm

1

Differentiate body fossils from behavioral artifacts

Trace fossils are matched to behavioral evidence like footprints, trackways, burrows, and coprolites rather than skeletal or soft-tissue remains.

Paleontological taxonomy defines trace fossils strictly as structural manifestations of activity.

2

Distinguish between hollow impressions and secondary mineral infills

Mold and cast is matched to the two-stage process of dissolution cavity creation followed by mineral precipitation.

Molds preserve external negative space, while casts produce positive physical replicas from mineral deposits.

3

Identify chemical distillation under compaction

Carbonization is matched to the expulsion of hydrogen, nitrogen, and oxygen, leaving behind an outline of residual carbon.

Carbonization specifically preserves detailed flat outlines of leaves, fish, and arthropod exoskeletons in fine-grained shale.

4

Identify unaltered resin preservation

Amber entombment is matched to organisms trapped and preserved inside fossilized tree sap.

Resin hardens into an airtight amber matrix that shields delicate insects from microbial decomposition.

Anahtar Kavram

Modes of fossil preservation in paleontology and sedimentary stratigraphy

Tahmini Süre:1m 0s

Soru 5135Soru →

A contractor purchases lumber for a deck project at a wholesale price of $\$600$ . To cover transportation and handling, the contractor applies a $15\%$ markup to the cost of the lumber. What is the total amount, in dollars, the contractor bills the client for the lumber?

Cevabı ve açıklamayı göster

Cevap: 690

Cevap

690

To find the total amount billed, first calculate the

15\%

markup on the

\$600

cost. Multiplying

\$600

by

0.15

gives a markup of

\$90

. Since it is a markup, this value is added to the original wholesale price.

\$600 + \$90 = \$690

.

Adım Adım Çözüm

1

Calculate the markup amount.

\$90

The contractor applies a

15\%

markup to the

\$600

wholesale cost.

0.15 \times 600 = 90

.

2

Add the markup to the wholesale cost.

\$690

The final amount billed to the client is the original cost plus the markup.

600 + 90 = 690

.

Anahtar Kavram

Calculating a percentage markup and adding it to the original cost to find the final price.

Soru 5136Soru →

A military aviation fuel facility has a bulk storage tank that is full. First, $\frac{2}{7}$ of the total capacity is pumped out to supply an active squadron. Then, $\frac{2}{3}$ of the remaining fuel is transferred to an underground reserve tank. The fuel that is left in the bulk tank is then divided equally to fill 15 identical fuel transport vehicles. If each transport vehicle holds $1 \frac{3}{4}$ tons of fuel when filled from this process, what was the original total capacity of the bulk storage tank in tons?

36

43 \frac{3}{4}

110 \frac{1}{4}

551 \frac{1}{4}

Cevabı ve açıklamayı göster

Cevap: $110 \frac{1}{4}$

Cevap

The original total capacity of the bulk storage tank was

110 \frac{1}{4}

tons.

By working step-by-step through the fractions, we determine that the final amount of fuel distributed to the trucks represents 5/21 of the original total capacity. Dividing this evenly among 15 trucks means each truck gets 1/63 of the original total. Since each truck holds 7/4 tons, the original capacity is exactly 63 times 7/4, which simplifies to 441/4, or 110 1/4 tons.

Adım Adım Çözüm

1

Calculate the fraction of total fuel remaining after supplying the squadron.

1 - \frac{2}{7} = \frac{5}{7}

The active squadron takes

\frac{2}{7}

of the total fuel, so the rest is left in the tank.

2

Calculate the fraction of total fuel left after transferring to the underground reserve.

\frac{1}{3} \times \frac{5}{7} = \frac{5}{21}

Since

\frac{2}{3}

of the remaining fuel is transferred out, exactly

\frac{1}{3}

of that remaining fuel is kept in the tank.

3

Calculate the fraction of the total capacity that each of the 15 transport vehicles receives.

\frac{5}{21} \div 15 = \frac{5}{21} \times \frac{1}{15} = \frac{1}{63}

The remaining

\frac{5}{21}

of the total fuel is distributed equally among 15 vehicles.

4

Set up an equation to find the total capacity (

C

) based on the known weight in one vehicle.

\frac{1}{63} \times C = 1 \frac{3}{4}

Each vehicle receives

\frac{1}{63}

of the total capacity, which we are given as

1 \frac{3}{4}

tons (or

\frac{7}{4}

tons).

5

Solve the equation for the original total capacity.

C = \frac{7}{4} \times 63 = \frac{441}{4} = 110 \frac{1}{4}

tons

Multiply the fraction

\frac{7}{4}

by the reciprocal of

\frac{1}{63}

to isolate and solve for

C

.

Anahtar Kavram

Solving multi-step fraction problems involving parts of remainders and distribution into equal batches.

Soru 5137Soru →

A solid rectangular block of an unknown metal has dimensions of $5\text{ cm}$ in length, $4\text{ cm}$ in width, and $2\text{ cm}$ in height. If the total mass of the block is $316\text{ g}$ , what is the density of the metal in $\text{g/cm}^3$ ?

Cevabı ve açıklamayı göster

Cevap: 7.9

Cevap

The density of the metal block is

7.9\text{ g/cm}^3

.

Density measures mass per unit volume (

D = \frac{m}{V}

). The volume of the rectangular prism is calculated by multiplying its dimensions (

5\text{ cm} \times 4\text{ cm} \times 2\text{ cm} = 40\text{ cm}^3

). Dividing the mass (

316\text{ g}

) by this volume (

40\text{ cm}^3

) yields

7.9\text{ g/cm}^3

.

Adım Adım Çözüm

1

Calculate the volume of the rectangular metal block from its dimensions.

V = 5\text{ cm} \times 4\text{ cm} \times 2\text{ cm} = 40\text{ cm}^3

To determine density, the total volume must first be calculated from the given geometric measurements.

2

Divide the mass of the block by its calculated volume.

\text{Density} = \frac{316\text{ g}}{40\text{ cm}^3} = 7.9\text{ g/cm}^3

Density is defined as mass per unit volume (

D = \frac{m}{V}

).

Anahtar Kavram

Density is a characteristic physical property of matter defined as mass divided by volume (

D = \frac{m}{V}

).

Tahmini Süre:1m 0s

Soru 5138Soru →

A logistics company is purchasing diesel fuel for its fleet. The base price of diesel is $\$4.50$ per gallon. The company uses a corporate discount card that provides a $\$0.30$ per gallon reduction on the first $120$ gallons, and a $20\%$ discount off the base price for any additional gallons purchased beyond the first $120$ .

The company purchases a total of $250$ gallons of diesel.

After calculating the cost of the fuel with the discounts applied, a federal excise tax of $\$0.40$ per gallon is added for the entire purchase volume. Finally, a $5\%$ state sales tax is applied to the subtotal (the subtotal includes both the discounted fuel cost and the excise tax).

If the company pays for the entire transaction using a prepaid account that currently has a balance of $\$1,500.00$ , what will be the remaining balance in dollars after the purchase?

Cevabı ve açıklamayı göster

Cevap: 374.4

Cevap

374.40

The correct answer is found by first calculating the tiered fuel costs:

\$504.00

for the first 120 gallons (at

\$4.20

/gal) and

\$468.00

for the remaining 130 gallons (at

\$3.60

/gal). Adding the

\$100.00

federal excise tax gives a subtotal of

\$1072.00

. The

5\%

state tax is calculated on this subtotal, adding

\$53.60

for a final cost of

\$1125.60

. Subtracting this from the

\$1500.00

account balance leaves

\$374.40

.

Adım Adım Çözüm

1

Calculate the fuel cost for the first tier (120 gallons).

$504.00

The first 120 gallons receive a

0.30 flat discount. The price per gallon is

4.50 -

0.30 =

4.20. Multiplying 120 by

4.20 gives

504.00.

2

Calculate the fuel cost for the second tier (remaining gallons).

$468.00

There are 250 - 120 = 130 remaining gallons. A 20% discount on

4.50 gives a price of

3.60 per gallon. Multiplying 130 by

3.60 gives

468.00.

3

Find the total discounted fuel cost before taxes.

$972.00

Add the costs of both tiers together:

504.00 +

468.00 = $972.00.

4

Calculate the federal excise tax.

$100.00

The excise tax applies to all 250 gallons at

0.40 per gallon. Multiplying 250 by

0.40 gives $100.00.

5

Calculate the subtotal and the state sales tax.

$53.60

The subtotal is

972.00 (fuel) +

100.00 (excise) =

1072.00. The 5% state tax on this subtotal is

1072.00 * 0.05 = $53.60.

6

Find the final transaction cost.

$1125.60

Add the state sales tax to the subtotal:

1072.00 +

53.60 = $1125.60.

7

Calculate the remaining balance in the prepaid account.

$374.40

Subtract the total transaction cost from the starting balance:

1500.00 -

1125.60 = $374.40.

Anahtar Kavram

Solving multi-step financial word problems involving tiered discounts, dual tax application sequences, and balance deductions.

Tahmini Süre:3m 0s

Soru 5139Soru →

The periodic table organizes chemical elements into vertical columns known as groups or families, where members share similar valence electron configurations and chemical behaviors. Match each periodic table group on the left with its defining chemical characteristic on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Alkali Metals match with having 1 valence electron and reacting vigorously with water; Alkaline Earth Metals match with having 2 valence electrons and forming

+2

cations; Halogens match with having 7 valence electrons and forming salts; Noble Gases match with possessing a complete valence shell and extreme chemical inertness.

The periodic table organizes elements by valence electron configurations. Group 1 elements (Alkali Metals) have 1 valence electron and react vigorously with water. Group 2 elements (Alkaline Earth Metals) have 2 valence electrons and form

+2

cations. Group 17 elements (Halogens) have 7 valence electrons and readily gain an electron to form salts. Group 18 elements (Noble Gases) have complete valence shells, making them chemically inert.

Adım Adım Çözüm

1

Determine valence electron count and characteristic reactivity for Group 1 elements.

Group 1 elements (Alkali Metals) have 1 valence electron and react violently with water.

The single outermost electron is readily lost, forming

+1

cations.

2

Determine valence electron count and ion formation for Group 2 elements.

Group 2 elements (Alkaline Earth Metals) have 2 valence electrons and form

+2

cations.

Losing two electrons achieves a stable preceding noble gas electron configuration.

3

Determine valence electron count and bonding behavior for Group 17 elements.

Group 17 elements (Halogens) have 7 valence electrons and readily gain 1 electron to form salts.

Gaining a single electron completes the outer valence octet.

4

Determine valence shell status and reactivity for Group 18 elements.

Group 18 elements (Noble Gases) possess full outer electron shells and are chemically inert.

A full complement of valence electrons provides maximum thermodynamic and chemical stability.

Anahtar Kavram

Periodic Table Groups and Valence Electron Trends

Soru 5140Soru →

A military logistics planner is calculating fuel requirements for a supply convoy consisting of $9$ identical heavy transport trucks. The planned route on a tactical map measures $10$ inches, and the map's scale is $1 \text{ inch} = 20 \text{ miles}$ . Field tests show that a group of $3$ of these trucks operating together consumes $5$ gallons of diesel fuel for every $2$ miles traveled. Assuming all trucks maintain this exact rate of consumption, what is the total amount of diesel fuel, in gallons, required for the entire convoy of $9$ trucks to complete the route?

15,000

240

75

1,500

Cevabı ve açıklamayı göster

Cevap: 1,500

Cevap

The total amount of diesel fuel required is 1,500 gallons.

The correct calculation involves three proportional steps: converting the map distance to actual distance (10 × 20 = 200 miles), finding the fuel rate per mile for the 3-truck group (5 / 2 = 2.5 gal/mi), and scaling this rate for the 9-truck convoy (which is 3 groups of 3). Multiplying the 3 groups by the 2.5 gal/mi rate and the 200-mile distance yields exactly 1,500 gallons.

Adım Adım Çözüm

1

Calculate the actual route distance using the map scale.

10 inches × 20 miles/inch = 200 miles.

The map distance must be converted to actual miles using the given scale to determine the true travel distance.

2

Determine the fuel consumption rate per mile for a group of 3 trucks.

5 gallons ÷ 2 miles = 2.5 gallons per mile.

Finding the unit rate (gallons per single mile) simplifies the calculation for the total distance.

3

Calculate the total fuel required for the entire convoy of 9 trucks.

(9 trucks ÷ 3 trucks/group) × 2.5 gallons/mile × 200 miles = 3 × 2.5 × 200 = 1,500 gallons.

The rate is given for 3 trucks, so we find how many groups of 3 are in the convoy (3 groups), multiply by the group rate, and then by the total distance.

Anahtar Kavram

Direct proportions in multi-step scenarios involving map scales and grouped rates.

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