All practice questions

Question 3221Question →

A team of paleontologists discovers identical fossil specimens in thin sedimentary rock strata across three widely separated continents. Geological records show that this specific organism existed for only a brief interval of geologic time. Which of the following best describes the primary scientific value of this index fossil?

Proving that upper undisturbed rock layers are consistently older than deeper underlying strata

Demonstrating that the enclosing sedimentary strata formed from the rapid cooling and crystallization of volcanic magma

Correlating and establishing the relative ages of distant rock layers across different geographic regions

Indicating that the rock underwent severe recrystallization under extreme metamorphic heat and pressure

Show answer & explanation

Answer: Correlating and establishing the relative ages of distant rock layers across different geographic regions

Answer

Correlating and establishing the relative ages of distant rock layers across different geographic regions

An index fossil must be easily recognizable, abundant, geographically widespread, and restricted to a short geologic time range. When geologists find the same index fossil in different locations, they can conclude that the corresponding rock layers formed during the same geologic period, enabling precise stratigraphic correlation.

Step-by-Step Solution

1

Identify the key defining characteristics of the fossil described in the scenario

The organism was geographically widespread (found on three continents) and existed for a short span of geologic time (confined to a thin stratum).

These are the diagnostic criteria that define an index fossil.

2

Determine how geologists utilize index fossils in stratigraphy

Because the organism only lived during one specific timeframe everywhere it existed, any rock layer containing it must have formed during that same time period.

This allows geologists to establish relative time equivalence across distant sedimentary formations.

Key Concept

Index fossils in stratigraphic correlation and relative dating

Estimated Time:1m 0s

Question 3222Question →

An electronics store purchases a computer monitor at wholesale cost. To determine the regular retail price, the store applies a $50\%$ markup to the wholesale cost. During a holiday sale, the monitor is discounted by $30\%$ off the regular retail price. A customer purchases the monitor during the sale and pays a final total of $\$453.60$ , which includes an $8\%$ sales tax applied to the discounted price. What was the store's original wholesale cost for the monitor?

\$240.00

\$300.00

\$400.00

\$350.00

Show answer & explanation

Answer: $\$400.00$

Answer

The original wholesale cost was

\$400.00

.

The correct wholesale cost is found by working backward from the final paid amount. First, dividing

\$453.60

by

1.08

removes the

8\%

tax, revealing the discounted sale price of

\$420.00

. Since this sale price reflects a

30\%

discount, it is

70\%

of the retail price; dividing

\$420.00

by

0.70

gives the retail price of

\$600.00

. Finally, the retail price includes a

50\%

markup, making it

150\%

of the wholesale cost. Dividing

\$600.00

by

1.50

yields the correct original wholesale cost of

\$400.00

.

Step-by-Step Solution

1

Remove the

8\%

sales tax from the final total to find the discounted sale price.

\$453.60 \div 1.08 = \$420.00

The final total includes an

8\%

tax applied to the sale price, which is mathematically equivalent to multiplying the sale price by

1.08

.

2

Reverse the

30\%

discount to determine the regular retail price.

\$420.00 \div 0.70 = \$600.00

The sale price represents

70\%

(

100\% - 30\%

) of the regular retail price.

3

Reverse the

50\%

markup to find the original wholesale cost.

\$600.00 \div 1.50 = \$400.00

The retail price represents a

50\%

increase over the wholesale cost, equivalent to

150\%

of the original cost (or multiplying by

1.50

).

Key Concept

Successive percentage changes and reversing percentages by division.

Question 3223Question →

A naval technician inspects a solid aluminum component intended for an aircraft assembly. The component has a mass of $162\text{ g}$ and the density of aluminum is $2.7\text{ g/cm}^3$ . What is the volume of the component in cubic centimeters ( $\text{cm}^3$ )?

Show answer & explanation

Answer: 60

Answer

The volume of the aluminum component is

60\text{ cm}^3

.

Density is defined by the formula

\rho = \frac{m}{V}

. Rearranging algebraically to solve for volume yields

V = \frac{m}{\rho}

. Substituting the given values:

V = \frac{162\text{ g}}{2.7\text{ g/cm}^3} = 60\text{ cm}^3

.

Step-by-Step Solution

1

Identify the relevant physical formula and isolate the unknown variable

\text{Volume} = \frac{\text{Mass}}{\text{Density}}

Density (

\rho

) is a characteristic physical property defined as mass per unit volume (

\rho = \frac{m}{V}

).

2

Substitute the measured mass and known density to calculate volume

\text{Volume} = \frac{162\text{ g}}{2.7\text{ g/cm}^3} = 60\text{ cm}^3

Dividing

162

by

2.7

gives

60

, with units simplifying to

\text{cm}^3

.

Key Concept

Density as a fundamental physical property relating mass and volume

Estimated Time:1m 0s

Question 3224Question →

A motorized winch pulls a $250\text{ kg}$ equipment sled across a level, frictionless sheet of ice. If the winch exerts a constant horizontal force of $750\text{ N}$ starting from rest, what is the speed of the sled, in meters per second ( $\text{m/s}$ ), after $4\text{ seconds}$ ?

Show answer & explanation

Answer: 12

Answer

The sled reaches a speed of

12\text{ m/s}

after

4\text{ seconds}

.

Applying Newton's second law gives an acceleration of

a = \frac{F}{m} = \frac{750\text{ N}}{250\text{ kg}} = 3\text{ m/s}^2

. Since the sled begins at rest (

v_0 = 0

), its speed after

4\text{ s}

is

v = at = 3\text{ m/s}^2 \times 4\text{ s} = 12\text{ m/s}

.

Step-by-Step Solution

1

Determine the acceleration produced by the net horizontal force

a = \frac{F_{\text{net}}}{m} = \frac{750\text{ N}}{250\text{ kg}} = 3\text{ m/s}^2

According to Newton's second law of motion (

F = ma

), acceleration equals the net force divided by mass.

2

Calculate final speed from initial rest and constant acceleration over time

v = v_0 + at = 0\text{ m/s} + (3\text{ m/s}^2)(4\text{ s}) = 12\text{ m/s}

Uniform acceleration kinematic equation relates velocity change to acceleration multiplied by elapsed time.

Key Concept

Combining Newton's second law (

F = ma

) with linear kinematics (

v = v_0 + at

) to determine final velocity under constant net force.

Alternative Method

Use the impulse-momentum theorem:

\text{Impulse} = F \cdot \Delta t = \Delta p = m \cdot v

. Substituting known values gives

(750\text{ N})(4\text{ s}) = (250\text{ kg})(v) \implies 3,000\text{ N}\cdot\text{s} = 250\text{ kg} \cdot v \implies v = \frac{3,000}{250} = 12\text{ m/s}

.

Estimated Time:1m 0s

Question 3225Question →

Fill in the blank with the correct numeric value to complete the statement.

Fill in the blanks below

A printing press can print

50

identical banners in

2

minutes. At this constant rate, the press will print banners in

10

minutes.

Show answer & explanation

Answer

250

Because the printing press operates at a constant rate, the number of banners produced is directly proportional to the time spent printing. Since

10

minutes is exactly

5

times longer than the initial

2

minutes, the press will produce

5

times as many banners. Multiplying the original

50

banners by

5

results in

250

banners.

Step-by-Step Solution

1

Identify the given ratio of banners to time.

The press produces

50

banners per

2

minutes.

Establishing the baseline rate is the first step in setting up a direct proportion.

2

Determine the scaling factor for the time.

The time increases from

2

minutes to

10

minutes. The scaling factor is

\frac{10}{2} = 5

.

Finding how many times greater the new time is compared to the original time tells us how to scale the output.

3

Multiply the baseline production by the scaling factor.

50 \times 5 = 250

banners.

In a direct proportion, as time increases by a certain multiple, the quantity produced increases by that exact same multiple.

Key Concept

Direct Proportions

Question 3226Question →

A storage warehouse is currently filled to $\frac{1}{4}$ of its total capacity. A new shipment arrives and is stored, bringing the warehouse to $\frac{5}{6}$ of its total capacity. What fraction of the warehouse's capacity was filled by the new shipment?

\frac{7}{12}

\frac{3}{5}

\frac{2}{3}

\frac{1}{6}

Show answer & explanation

Answer: $\frac{7}{12}$

Answer

The new shipment filled

\frac{7}{12}

of the warehouse's capacity.

To find the amount of capacity added, subtract the initial capacity from the final capacity (

\frac{5}{6} - \frac{1}{4}

). Convert both fractions to a common denominator of 12, resulting in

\frac{10}{12}

and

\frac{3}{12}

. Subtracting these fractions gives

\frac{7}{12}

.

Step-by-Step Solution

1

Set up the subtraction expression to find the difference in capacity.

\frac{5}{6} - \frac{1}{4}

The fraction added is equal to the final capacity minus the initial capacity.

2

Find the lowest common denominator (LCD) for the fractions with denominators 6 and 4.

The LCD is 12.

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

3

Convert both fractions to equivalent fractions with a denominator of 12.

\frac{5}{6} = \frac{10}{12}

and

\frac{1}{4} = \frac{3}{12}

This standardizes the parts so they can be accurately subtracted.

4

Subtract the numerators and keep the common denominator.

\frac{10}{12} - \frac{3}{12} = \frac{7}{12}

The numerators represent the specific number of parts being subtracted from the whole.

Key Concept

Fraction Addition and Subtraction in Context

Question 3227Question →

Read the scenario below and calculate the final selling price.

Fill in the blanks below

A mechanic buys a used car for

\$3,500

and spends

\$500

on replacement parts. He marks up his total investment by

25\%

to set the asking price. A customer then negotiates a

10\%

discount off this asking price. The final selling price of the car is $\$.

Show answer & explanation

Answer

4500

The total investment is the sum of the car and parts (

\$4,000

). The

25\%

markup is calculated on this total base, resulting in a

\$5,000

asking price (

\$4,000 \times 1.25

). Finally, the

10\%

discount is calculated sequentially on the new

\$5,000

asking price, giving a final selling price of

\$4,500

(

\$5,000 \times 0.90

).

Step-by-Step Solution

1

Calculate the mechanic's total investment.

\$3,500 + \$500 = \$4,000

The markup is applied to the total cost, which includes both the initial purchase price and the cost of the replacement parts.

2

Calculate the asking price by applying the 25% markup to the total investment.

\$4,000 \times 1.25 = \$5,000

A

25\%

markup means the asking price is

125\%

of the total investment.

3

Calculate the final selling price by applying the 10% discount to the asking price.

\$5,000 \times 0.90 = \$4,500

The discount is taken off the new marked-up asking price, leaving

90\%

of that price to be paid.

Key Concept

Calculating successive percentage changes by updating the base amount for each step.

Question 3228Question →

In basic direct-current circuits, various fundamental electrical quantities describe the flow and use of electric energy. Match each electrical quantity on the left with its correct physical definition and standard unit on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Voltage matches the electrical potential difference driving charge (volts); Current matches the rate of charge flow (amperes); Resistance matches the opposition to current flow (ohms); Electrical Power matches the rate of energy transfer (watts).

Each electrical quantity is correctly matched to its standard SI unit and underlying physical definition based on Ohm's law and electrical power principles.

Step-by-Step Solution

1

Identify the definitions and units for potential difference and charge flow.

Voltage provides the electrical push measured in volts (

\text{V}

), while Current represents the flow rate of charge measured in amperes (

\text{A}

).

These are the two driving and kinematic parameters of an active circuit.

2

Identify the definitions and units for circuit opposition and energy rate.

Resistance opposes current flow and is measured in ohms (

\Omega

), while Electrical Power is the energy conversion rate measured in watts (

\text{W}

).

These relate the load characteristics and total work rate in the circuit.

Key Concept

Fundamental electrical properties, units of measurement, and definitions in direct-current circuits.

Estimated Time:45s

Question 3229Question →

A bimetallic strip made of two different metals bonded firmly along their lengths bends into an arc when heated evenly. Which of the following best explains why this bending occurs?

The two metals expand at different rates as their temperature increases.

Convection currents within the solid metals apply mechanical pressure to one side.

One metal conducts thermal energy while the other acts as a complete thermal insulator.

Heating causes a chemical reaction at the boundary that shrinks one of the metals.

Show answer & explanation

Answer: The two metals expand at different rates as their temperature increases.

Answer

The two metals expand at different rates as their temperature increases.

Thermal expansion causes materials to expand upon heating, but different materials expand by different amounts for the same temperature change due to differing coefficients of thermal expansion. Because the two metal strips are bonded together, the metal that expands more forms the outer, longer curve of the arc, causing the entire strip to bend predictably.

Step-by-Step Solution

1

Identify the thermal property involved when solid objects change size upon heating.

Most solids undergo thermal expansion, increasing in length and volume as temperature rises.

Added thermal energy increases the average vibrational kinetic energy of atoms, pushing them slightly further apart.

2

Analyze how bonding two materials with different expansion rates affects the combined structure.

The metal with the higher coefficient of thermal expansion expands more in length than the metal with the lower coefficient.

Because the two strips are permanently joined, the longer expanded strip must curve around the shorter strip, resulting in a bent arc.

Key Concept

Thermal expansion and differential expansion in composite materials

Estimated Time:1m 0s

Question 3230Question →

When an ancient vertebrate organism undergoes permineralization to become a preserved body fossil, its remains pass through a distinct series of physical and chemical stages. What is the correct chronological sequence of these fossil formation events, ordered from the death of the organism to its eventual discovery?

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The proper chronological order of fossilization by permineralization is: rapid burial in sediment, soft tissue decay and sediment compaction, groundwater infiltration into pore spaces, mineral crystallization to form petrified rock, and surface exposure via uplift and weathering.

Fossilization through permineralization begins when an organism is rapidly buried by sediments, protecting it from surface destruction. Next, soft tissues decompose, leaving only hard skeletal elements as increasing sediment load compacts the surroundings. Mineral-bearing groundwater then seeps through the open pore spaces of the bones. Over time, dissolved minerals like silica or calcite precipitate out and crystallize, turning the bone structure into stone. Finally, geological forces lift the strata and surface weathering erodes the covering rock, bringing the fossil to the surface.

Step-by-Step Solution

1

Identify the initial preservation requirement.

Rapid burial beneath sediment prevents scavenging and biological decay.

Without immediate burial, remains are consumed or destroyed by physical weathering before preservation can begin.

2

Determine the intermediate chemical and physical transformation stages.

Soft tissues rot away, sediment layers compact into rock, and mineralized groundwater infiltrates the porous skeletal matrix.

Groundwater must gain access to internal bone cavities to deliver the dissolved minerals required for fossilization.

3

Trace the lithification and eventual surface discovery process.

Mineral precipitation hardens the bone into stone, followed by tectonic uplift and erosion exposing the fossil.

Permineralization must be completed deep underground before uplift and surface erosion can reveal the specimen.

Key Concept

Process of Fossil Formation by Permineralization

Estimated Time:1m 0s

Question 3231Question →

A contractor is assigned a specialized repair project with a labor budget of $12 \frac{1}{2}$ hours. The contractor works $3 \frac{3}{4}$ hours on Monday, $2 \frac{5}{8}$ hours on Tuesday, and $4$ hours and $10$ minutes on Wednesday. If no other time is spent on the project, how many hours of the budgeted time remain?

2 \frac{1}{40}

10 \frac{13}{24}

1 \frac{23}{24}

3

Show answer & explanation

Answer: $1 \frac{23}{24}$

Answer

The remaining time on the project budget is

1 \frac{23}{24}

hours.

To find the remaining time, first convert all time spent into fractions of an hour with a common denominator, sum them up, and subtract the total from the budgeted hours. Converting 10 minutes to a fraction of an hour yields

10/60 = 1/6

hour. The sum of the fractions is

3 \frac{3}{4} + 2 \frac{5}{8} + 4 \frac{1}{6}

. The lowest common denominator for 4, 8, and 6 is 24. Converting the fractions gives

3 \frac{18}{24} + 2 \frac{15}{24} + 4 \frac{4}{24} = 9 \frac{37}{24}

, which simplifies to

10 \frac{13}{24}

hours. Subtracting this from the budget requires regrouping:

12 \frac{12}{24} - 10 \frac{13}{24} = 11 \frac{36}{24} - 10 \frac{13}{24} = 1 \frac{23}{24}

hours.

Step-by-Step Solution

1

Convert the time worked on Wednesday into a mixed number with a fraction of an hour.

4

hours and

10

minutes =

4 \frac{10}{60}

hours =

4 \frac{1}{6}

hours.

All quantities must be in the same unit (hours) and fraction format before adding.

2

Find a common denominator to add the hours worked on Monday, Tuesday, and Wednesday.

The lowest common denominator for

4

,

8

, and

6

is

24

. The fractions become

3 \frac{18}{24}

,

2 \frac{15}{24}

, and

4 \frac{4}{24}

.

Fractions can only be added when they share a common denominator.

3

Add the converted fractions to find the total time spent.

3 \frac{18}{24} + 2 \frac{15}{24} + 4 \frac{4}{24} = 9 \frac{37}{24}

. Since

\frac{37}{24} = 1 \frac{13}{24}

, the total is

10 \frac{13}{24}

hours.

Adding the individual shifts gives the combined total hours worked so far.

4

Subtract the total time spent from the budgeted time to find the remaining hours.

12 \frac{1}{2} - 10 \frac{13}{24} = 12 \frac{12}{24} - 10 \frac{13}{24}

. Regrouping

12 \frac{12}{24}

gives

11 \frac{36}{24}

. Subtracting yields

11 \frac{36}{24} - 10 \frac{13}{24} = 1 \frac{23}{24}

hours.

Subtracting the part used from the whole budget determines the remaining balance.

Key Concept

Adding and subtracting mixed numbers with unlike denominators in real-world contexts, including unit conversions and regrouping.

Estimated Time:2m 30s

Question 3232Question →

A string of decorative holiday lights is designed such that removing a single bulb causes all the other bulbs on the strand to go out immediately. Which type of electrical circuit does this light strand represent?

A parallel circuit, because each component operates on an independent branch

A series circuit, because all components share a single continuous path for electric current

A parallel circuit, because current stops dividing among multiple pathways

A short circuit, because electrical resistance in the wire drops to zero

Show answer & explanation

Answer: A series circuit, because all components share a single continuous path for electric current

Answer

A series circuit, because all components share a single continuous path for electric current

In a series circuit, all electrical loads are connected end-to-end along a single continuous path. Because electric current must travel through each component sequentially, removing or burning out any one bulb breaks the loop, creating an open circuit that immediately turns off all remaining bulbs.

Step-by-Step Solution

1

Identify the pathway configuration of the electrical components in the circuit

The circuit contains only one continuous conducting path connecting every bulb in sequence.

Understanding the number of paths for current flow determines whether a circuit is wired in series or in parallel.

2

Analyze the effect of removing a component on the circuit loop

Removing one bulb creates a gap (open circuit), halting the flow of charge through the entire path.

Electric current requires an uninterrupted closed loop from the power source back to the source to flow.

Key Concept

Series vs. Parallel Circuits and Current Pathways

Estimated Time:45s

Question 3233Question →

Solve the following problem by determining the missing value. Enter your final numerical answer in the blank provided.

Fill in the blanks below

A base exchange purchases a batch of tactical backpacks from a distributor. The exchange applies a markup of

60\%

over the distributor cost to determine the standard price. After a month, the backpacks are placed on clearance, reducing the standard price by

30\%

. A service member buys a backpack using a special coupon that takes an additional

15\%

off the clearance price. If the service member pays

\$66.64

for the backpack (which is tax-exempt), the original distributor cost of the backpack was $\$$.

Show answer & explanation

Answer

70

The original cost is found by translating the successive markup and discounts into multipliers:

1.60

for the

60\%

markup,

0.70

for the

30\%

discount, and

0.85

for the

15\%

discount. The product of these multipliers is

1.60 \times 0.70 \times 0.85 = 0.952

. This means the final price is

95.2\%

of the original cost. Setting

0.952C = \$66.64

and dividing gives the original distributor cost of

\$70

.

Step-by-Step Solution

1

Define a variable for the unknown original cost.

Let

C

represent the original distributor cost of the backpack.

Setting up a variable allows us to build an algebraic equation to track the successive price changes.

2

Calculate the multiplier for the

60\%

markup.

Standard Price =

C \times (1 + 0.60) = 1.60C

A markup increases the cost by that percentage, making the new price

160\%

of the original cost.

3

Apply the

30\%

clearance discount to the standard price.

Clearance Price =

1.60C \times (1 - 0.30) = 1.60C \times 0.70 = 1.12C

The clearance reduction applies to the newly established standard price, leaving

70\%

of that price.

4

Apply the additional

15\%

coupon discount to the clearance price.

Final Price =

1.12C \times (1 - 0.15) = 1.12C \times 0.85 = 0.952C

The coupon applies sequentially to the clearance price, meaning the customer pays

85\%

of that discounted amount.

5

Set the final price expression equal to the known amount paid and solve for

C

.

0.952C = 66.64 \Rightarrow C = \frac{66.64}{0.952} = 70

Equating the algebraic expression to the actual dollar amount allows us to isolate and calculate the original distributor cost.

Key Concept

Solving multi-step percentage changes by applying successive multipliers to find an unknown base value.

Question 3234Question →

A supply pump transfers $10$ gallons of aviation fuel every $15$ seconds. At this rate, how many gallons of fuel will it transfer in $3$ minutes?

120

270

12

2

Show answer & explanation

Answer: 120

Answer

120

The problem establishes a constant rate, which requires a direct proportion to solve. First, convert the

3

-minute time period into

180

seconds to match the units of the given rate. Then, set up the proportion

\frac{10}{15} = \frac{x}{180}

. Cross-multiplying

10

by

180

yields

1800

, and dividing that product by

15

results in

120

gallons.

Step-by-Step Solution

1

Harmonize the time units by converting minutes to seconds.

3

minutes

= 3 \times 60 = 180

seconds.

The initial rate is given in seconds, so the target time must also be in seconds to set up an accurate mathematical proportion.

2

Set up a direct proportion using the given rate.

10

gallons /

15

seconds

= x

gallons /

180

seconds.

The pump operates at a constant rate, meaning the ratio of volume to time remains equivalent.

3

Solve for the unknown volume

x

.

x = \frac{10 \times 180}{15} = \frac{1800}{15} = 120

gallons.

Cross-multiplying and dividing isolates the variable, providing the total gallons transferred.

Key Concept

Direct proportions represent situations where two quantities increase at the same relative rate. When setting up proportions, it is critical to ensure that corresponding units match.

Question 3235Question →

A sporting goods store owner buys a pair of running shoes from a manufacturer for $\$80.00$ . He applies a $30\%$ markup to the wholesale cost to determine the final retail price. What is the retail selling price of the running shoes?

\$24.00

\$104.00

\$110.00

\$82.40

Show answer & explanation

Answer: $\$104.00$

Answer

\$104.00

The correct answer accurately calculates the

30\%

markup as

\$24.00

(

\$80.00 \times 0.30

) and correctly adds this markup to the original wholesale cost (

\$80.00 + \$24.00

) to reach the final retail price of

\$104.00

.

Step-by-Step Solution

1

Calculate the markup amount by finding

30\%

of the wholesale cost.

\$80.00 \times 0.30 = \$24.00

The markup is a percentage of the original wholesale cost, which must be converted to a dollar amount.

2

Add the markup amount to the original wholesale cost to find the retail selling price.

\$80.00 + \$24.00 = \$104.00

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

Key Concept

Calculating a percentage of a quantity and adding it to the original value to determine a final marked-up price.

Alternative Method

Instead of calculating the markup and adding it to the wholesale cost, you can multiply the wholesale cost directly by

1.30

(which represents the

100\%

original cost plus the

30\%

markup). Thus,

\$80.00 \times 1.30 = \$104.00

.

Estimated Time:1m 0s

Question 3236Question →

During a routine vehicle maintenance check, a technician records four distinct observations about an engine and its fluid systems. Which of the following observations describes a physical change rather than a chemical change?

Diesel fuel burning to form carbon dioxide, water vapor, and exhaust soot

Engine oil decreasing in viscosity and flowing more freely as operating temperature rises

Acidic combustion byproducts reacting with and corroding the steel exhaust manifold

A basic fuel additive neutralizing sulfuric acid present in fuel residues

Show answer & explanation

Answer: Engine oil decreasing in viscosity and flowing more freely as operating temperature rises

Answer

Engine oil decreasing in viscosity and flowing more freely as operating temperature rises

The observation describing engine oil thinning as temperature increases represents a physical change. Viscosity is a physical property governed by intermolecular forces; heating increases molecular motion and reduces resistance to flow without altering the chemical composition of the oil.

Step-by-Step Solution

1

Distinguish between physical and chemical changes

A physical change alters the form, state, or appearance of a substance without changing its chemical identity. A chemical change produces one or more new substances through bond breaking and formation.

Correct classification requires evaluating whether the molecular structure of the substance is modified.

2

Evaluate the fluid behavior under temperature change

When engine oil is heated, thermal energy reduces intermolecular attractions, causing the fluid to thin (lower viscosity). The chemical structure of the hydrocarbon base oil remains identical.

Since no new substance is formed and the process is reversible upon cooling, the change in flow properties is purely physical.

Key Concept

Physical versus chemical changes in matter

Estimated Time:45s

Question 3237Question →

An equipment container weighs $120\text{ N}$ on Earth, where the acceleration due to gravity is approximately $10\text{ m/s}^2$ . The container is transported to an orbital space station where it is in a weightless environment. If an astronaut applies a constant net horizontal force of $36\text{ N}$ to the container, what is its resulting acceleration?

0.3\text{ m/s}^2

30\text{ m/s}^2

3\text{ m/s}^2

3\text{ m/s}

Show answer & explanation

Answer: $3\text{ m/s}^2$

Answer

3\text{ m/s}^2

Mass measures an object's inertia and does not change when moving between Earth and orbit. Using the Earth weight

W = 120\text{ N}

and gravity

g = 10\text{ m/s}^2

, the container's mass is

m = 12\text{ kg}

. In orbit, applying a net force of

36\text{ N}

yields an acceleration of

a = F/m = 36\text{ N} / 12\text{ kg} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Determine the mass of the container from its Earth weight

\text{Mass } m = \frac{W}{g} = \frac{120\text{ N}}{10\text{ m/s}^2} = 12\text{ kg}

Weight is the force of gravity acting on mass (

W = mg

). Mass is an intrinsic property of the object and remains unchanged regardless of location.

2

Apply Newton's Second Law of Motion (

F = ma

) in the orbital environment

a = \frac{F_{\text{net}}}{m} = \frac{36\text{ N}}{12\text{ kg}} = 3\text{ m/s}^2

Although the container is weightless in orbit, its inertia (mass) remains

12\text{ kg}

. A net force produces an acceleration inversely proportional to that mass.

Key Concept

Newton's Second Law (

F = ma

) and the distinction between mass (inertia) and weight (gravitational force).

Estimated Time:1m 0s

Question 3238Question →

Thermal energy transfer and thermodynamic properties govern many practical engineering and natural systems. Match each thermal physics principle with the real-world application that most directly relies on it.

Click a left item, then click its matching right item

Show answer & explanation

Answer

High specific heat capacity matches engine water cooling; Latent heat of vaporization matches sweating/evaporative cooling; Thermal conduction matches a copper base plate on an electronic heat sink; Radiation reflection matches a shiny foil emergency blanket.

Each principle is paired with its primary physical mechanism: high specific heat capacity explains water's resistance to rapid temperature spikes in cooling systems; latent heat of vaporization explains how phase transitions remove heat during evaporation; conduction explains direct contact heat flow through solid copper; and radiation reflection explains how metallic foil redirects infrared waves.

Step-by-Step Solution

1

Analyze the role of coolant fluids in temperature regulation

Water requires a large amount of heat energy to raise its temperature (

4.184\text{ J}/(\text{g}\cdot^\circ\text{C})

), demonstrating high specific heat capacity.

Identify the property responsible for heat absorption without rapid temperature spikes.

2

Examine the mechanism of evaporative cooling

Sweat absorbing energy to undergo a phase change from liquid to vapor demonstrates latent heat of vaporization.

Phase transitions at constant temperature absorb latent heat from surrounding tissue.

3

Evaluate heat transfer across solid interfaces in contact

Thermal energy moving directly through a dense metallic copper plate into a heat sink operates by conduction.

Conduction is the primary mode of thermal transfer through stationary solids.

4

Determine how reflective barriers preserve body warmth

Shiny aluminized foil redirecting electromagnetic infrared radiation back to a person demonstrates radiation reflection.

Radiant heat transfers via electromagnetic waves without requiring a physical medium and can be reflected by polished surfaces.

Key Concept

Thermodynamic properties and heat transfer mechanisms in applied physical systems

Estimated Time:1m 0s

Question 3239Question →

Solve the following word problem and enter your final answer. You may use a mixed number, improper fraction, or decimal format.

Fill in the blanks below

A Navy seaman is painting the exterior of a ship. He uses

3 \frac{1}{2}

gallons of gray paint on the port side and

2 \frac{1}{4}

gallons on the starboard side. In total, he used gallons of paint.

Show answer & explanation

Answer

5 3/4

To find the total amount of paint used, the two quantities must be added together. By finding a common denominator of 4, the fraction

\frac{1}{2}

is converted to

\frac{2}{4}

. Adding the fractions

\frac{2}{4}

and

\frac{1}{4}

yields

\frac{3}{4}

. Adding the whole numbers 3 and 2 gives 5. The combined total is

5 \frac{3}{4}

gallons.

Step-by-Step Solution

1

Set up the addition problem to combine the two quantities of paint.

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

The total amount of paint used is the sum of the paint used on both sides of the ship.

2

Find a common denominator for the fractional parts (2 and 4).

The least common multiple of 2 and 4 is 4.

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

3

Convert the first fraction to an equivalent fraction with a denominator of 4.

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

This allows the fractional parts to be added seamlessly.

4

Add the whole numbers and the fractions.

Whole numbers:

3 + 2 = 5

. Fractions:

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

. Final total:

5 \frac{3}{4}

.

Combining the separate sums gives the total value of the mixed numbers.

Key Concept

Adding mixed numbers with unlike denominators

Question 3240Question →

An industrial cleaning solvent requires a mixture of Chemical A and Chemical B in a ratio of $5:2$ by volume. If a worker uses $300$ milliliters of Chemical B, how many liters of the final cleaning solvent will be produced?

1050

0.75

1.05

10.5

Show answer & explanation

Answer: 1.05

Answer

1.05

The correct answer accurately scales the mixture from parts to a total volume. Since the ratio of Chemical A to B is 5:2, there are 7 total parts in the mixture. Chemical B makes up 2 of these 7 parts. Setting up the proportion 2/7 = 300/x gives a total volume of 1050 mL. Converting this volume to liters by dividing by 1000 results in 1.05 liters.

Step-by-Step Solution

1

Identify the ratio of Chemical B to the total mixture.

The mixture has 5 parts Chemical A and 2 parts Chemical B, making 7 total parts. The ratio of Chemical B to the total is 2:7.

To find the total volume based on the volume of one component, we need the part-to-whole relationship.

2

Set up and solve a proportion to find the total volume in milliliters.

2 / 7 = 300 / x. Cross-multiplying gives 2x = 2100, which simplifies to x = 1050 milliliters.

Direct proportions allow us to scale the ratio up to find the actual combined volume of the mixture.

3

Convert the total volume from milliliters to liters.

1050 / 1000 = 1.05 liters.

The question explicitly requires the final answer to be stated in liters.

Key Concept

Direct proportions and unit conversions in part-to-whole relationships

Alternative Method

Instead of setting up a formal proportion, use the unitary method. If 2 parts represent 300 mL, then 1 part equals 150 mL (300 / 2). The total mixture requires 7 parts, so the total volume is 7 * 150 = 1050 mL. Converting to liters gives 1.05 L.

Estimated Time:1m 30s

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer