All practice questions

Question 141Question →

A mechanic is reviewing a technical parts manual to replace damaged hardware on a heavy equipment mounting plate. The specification calls for a $3/8\text{-}16\text{ UNC} \times 1\text{-}1/2\text{ in}$ hex cap screw. In this standardized Unified National fastener callout, what does the number $16$ represent?

The outer diameter of the bolt head in sixteenths of an inch

The recommended metric wrench size of

16\text{ mm}

required for installation

The number of threads per inch along the bolt shank

The minimum tensile yield strength rating of

16\text{ ksi}

Show answer & explanation

Answer: The number of threads per inch along the bolt shank

Answer

The number of threads per inch along the bolt shank

In standard imperial fastener nomenclature (Unified Thread Standard), the number immediately following the nominal diameter indicates the thread pitch, defined as the number of threads per inch (TPI). In

3/8\text{-}16\text{ UNC} \times 1\text{-}1/2\text{ in}

,

16

specifies that there are

16

complete thread crests per inch along the shank.

Step-by-Step Solution

1

Analyze the standard SAE Unified National thread callout format

The standard nomenclature is formatted as: [Nominal Diameter] - [Threads Per Inch] [Thread Series] x [Fastener Length].

Deconstructing the callout reveals the distinct mechanical property defined by each segment.

2

Map each value from

3/8\text{-}16\text{ UNC} \times 1\text{-}1/2\text{ in}

to its corresponding dimension

3/8\text{ in}

is the nominal major diameter,

16

is the thread pitch (threads per inch),

\text{UNC}

indicates Unified National Coarse, and

1\text{-}1/2\text{ in}

is the overall length measured from under the bolt head.

The second parameter in imperial fractional fastener callouts always specifies the thread density per linear inch.

Key Concept

Standard Unified National (SAE) fastener callout nomenclature

Estimated Time:1m 0s

Question 142Question →

The engineering schematics outline four asymmetrical aerospace panels that must be manufactured with their exact mirror-image counterparts. Match each original panel and its designated reflection axis (Left) to its correctly mirrored counterpart (Right).

Click a left item, then click its matching right item

Show answer & explanation

Answer

Panel 1 matches Configuration C; Panel 2 matches Configuration A; Panel 3 matches Configuration D; Panel 4 matches Configuration B.

Each correct pairing applies the mathematical rules of geometric reflection based on the specified axis. Vertical axes invert left and right, horizontal axes invert top and bottom, and diagonal axes swap length and height dimensions.

Step-by-Step Solution

1

Analyze Panel 1's reflection across the vertical axis on its right.

Identify that the right triangle flips horizontally, placing the 90° angle on the bottom-right (Configuration C).

Vertical reflection lines invert the left-to-right orientation of all points.

2

Analyze Panel 2's reflection across the horizontal axis below it.

Identify that the F-shape flips upside down, placing the prongs at the bottom (Configuration A).

Horizontal reflection lines invert the top-to-bottom orientation of all points.

3

Analyze Panel 3's reflection across the vertical axis on its left.

Identify that the rectangular plate mirrors horizontally, moving the notch from top-left to top-right (Configuration D).

Vertical reflection lines invert horizontal positioning relative to the axis.

4

Analyze Panel 4's reflection across the diagonal axis.

Identify that the L-shape transposes coordinates, turning the tall vertical arm into a wide horizontal base (Configuration B).

Diagonal reflection lines (at 45 degrees) swap the horizontal and vertical axes of the shape.

Key Concept

Mental reflection of asymmetric 2D shapes across varying geometric axes (vertical, horizontal, diagonal).

Alternative Method

Instead of attempting to visualize the entire shape at once, select one distinct asymmetric feature (such as the 90-degree corner, the notch, or the longest arm) and mentally track its specific perpendicular distance and orientation across the given reflection axis.

Estimated Time:1m 30s

Question 143Question →

The speed at which light travels depends directly on the optical density and refractive index of the medium through which it passes. Arrange the following media in order of the speed of light within them, from slowest to fastest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

Diamond, Crown glass, Liquid water, Vacuum (from slowest to fastest)

Light travels fastest through empty space (

c \approx 3.00 \times 10^8\text{ m/s}

) where the refractive index is

1.00

. When entering denser transparent media, the wave interacts with the electromagnetic fields of atoms, causing an apparent slowdown proportional to the medium's index of refraction (

v = \frac{c}{n}

). Diamond has the highest index of refraction among the options (

n \approx 2.42

), making it the slowest, followed by crown glass (

n \approx 1.52

), liquid water (

n \approx 1.33

), and vacuum (

n = 1.00

).

Step-by-Step Solution

1

Identify the relationship between the index of refraction and the speed of light.

The speed of light in a medium is inversely proportional to its refractive index, given by

v = \frac{c}{n}

, where

c

is the speed of light in a vacuum and

n

is the refractive index.

Higher refractive indices indicate greater optical density and slower wave propagation speeds.

2

Rank the media by their refractive indices from highest to lowest.

Diamond (

n \approx 2.42

) > Crown glass (

n \approx 1.52

) > Liquid water (

n \approx 1.33

) > Vacuum (

n = 1.00

).

Ranking from highest index to lowest index establishes the reverse order of speed.

3

Invert the refractive index ranking to order the media from slowest speed to fastest speed.

Diamond (slowest,

\approx 1.24 \times 10^8\text{ m/s}

)

\rightarrow

Crown glass (

\approx 1.97 \times 10^8\text{ m/s}

)

\rightarrow

Liquid water (

\approx 2.25 \times 10^8\text{ m/s}

)

\rightarrow

Vacuum (fastest,

\approx 3.00 \times 10^8\text{ m/s}

).

Matches the required sequence criteria from slowest to fastest.

Key Concept

Inverse relationship between index of refraction and wave speed in optical media (

v = \frac{c}{n}

)

Estimated Time:1m 0s

Question 144Question →

During a ship repair project, a naval shipyard assigns 24 welders and 8 pipefitters to complete the structural work. What is the ratio of welders to pipefitters on this project, expressed in its simplest form?

3:1

1:3

3:4

1:4

Show answer & explanation

Answer: 3:1

Answer

3:1

The correct answer accurately extracts the given quantities (24 welders, 8 pipefitters), sets them up in the requested sequence (24 to 8), and successfully reduces the numbers to their simplest terms by dividing both by 8, yielding 3:1.

Step-by-Step Solution

1

Identify the two quantities that need to be compared based on the question.

Welders = 24, Pipefitters = 8

The question asks for the specific ratio of welders to pipefitters.

2

Set up the initial ratio in the exact order requested by the problem.

24:8

The order of terms in a ratio matters; it must strictly match 'welders to pipefitters'.

3

Simplify the ratio by dividing both numbers by their greatest common divisor (GCD).

The GCD of 24 and 8 is 8. Therefore, (24 ÷ 8) : (8 ÷ 8) = 3:1

Ratios are conventionally expressed in their lowest possible integer terms.

Key Concept

Basic Ratios

Estimated Time:45s

Question 145Question →

A vendor purchases a vintage jacket for $60$ dollars and later sells it at a market for $75$ dollars. What is the vendor's profit percentage on this item?

20\%

25\%

125\%

2.5\%

Show answer & explanation

Answer: $25\%$

Answer

The vendor's profit percentage is

25\%

.

The total profit is found by subtracting the cost price (

60

) from the selling price (

75

), resulting in a

15

dollar profit. To find the profit percentage, you must divide the profit by the original cost price (

15 \div 60 = 0.25

). Converting the decimal

0.25

to a percentage gives

25\%

.

Step-by-Step Solution

1

Calculate the dollar amount of the profit.

75 - 60 = 15

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

2

Divide the profit by the original cost price.

\frac{15}{60} = 0.25

Profit percentage is based on the original cost, not the final selling price.

3

Convert the resulting decimal to a percentage.

0.25 \times 100 = 25\%

The question asks for the final answer in percentage format.

Key Concept

Calculating profit percentage using the original cost as the base value.

Estimated Time:45s

Question 146Question →

A sound wave traveling through air at a constant temperature has a frequency of $250\text{ Hz}$ and a wavelength of $1.36\text{ m}$ . If the frequency of the sound source increases to $500\text{ Hz}$ , what is the new wavelength of the sound wave?

2.72\text{ m}

1.36\text{ m}

0.68\text{ m}

0.34\text{ m}

Show answer & explanation

Answer: $0.68\text{ m}$

Answer

The new wavelength is

0.68\text{ m}

.

Wave speed in a given medium at constant temperature is constant (

v = f\lambda

). The initial speed is

250\text{ Hz} \times 1.36\text{ m} = 340\text{ m/s}

. When the frequency doubles to

500\text{ Hz}

, the wavelength must be halved:

340\text{ m/s} \div 500\text{ Hz} = 0.68\text{ m}

.

Step-by-Step Solution

1

Calculate the constant wave speed in air using the initial conditions

v = f_1 \times \lambda_1 = 250\text{ Hz} \times 1.36\text{ m} = 340\text{ m/s}

The speed of a mechanical wave depends entirely on the medium and remains constant at a fixed temperature.

2

Rearrange the wave equation to solve for the new wavelength

\lambda_2 = \frac{v}{f_2} = \frac{340\text{ m/s}}{500\text{ Hz}} = 0.68\text{ m}

Because wave speed is constant, an increase in frequency causes an inversely proportional decrease in wavelength.

Key Concept

Inverse relationship between frequency and wavelength in a constant medium (

v = f\lambda

)

Estimated Time:1m 0s

Question 147Question →

On a regional map, a scale of $1\text{ inch} = 12\text{ miles}$ is used. If a straight road is $1.5\text{ inches}$ long on the map, what is the actual length of the road?

0.125\text{ miles}

8\text{ miles}

18\text{ miles}

180\text{ miles}

Show answer & explanation

Answer: $18\text{ miles}$

Answer

The actual length of the road is

18\text{ miles}

.

The map uses a scale where each inch corresponds to

12

actual miles. To find the real distance, we multiply the map distance by the scale:

1.5 \times 12 = 18

. Therefore, the road is

18\text{ miles}

long in reality.

Step-by-Step Solution

1

Identify the scale ratio and the given map measurement.

The scale is

1\text{ inch} = 12\text{ miles}

, and the map measurement is

1.5\text{ inches}

.

This establishes the relationship between the drawing size and the real-world size.

2

Set up the calculation to find the actual distance.

Actual distance =

1.5\text{ inches} \times 12\text{ miles/inch}

.

Since every inch represents

12\text{ miles}

, multiplying the number of map inches by

12

will yield the actual miles.

3

Perform the multiplication.

1.5 \times 12 = 18\text{ miles}

.

Completing the arithmetic gives the final actual length of the road.

Key Concept

To find actual dimensions from a map, multiply the measured distance on the map by the given scale factor.

Question 148Question →

A family goes out for dinner, and the total cost of their meal is $\$85.00$ . They use a coupon for $20\%$ off the cost of the meal. A sales tax of $8\%$ is applied to the discounted price. They also decide to leave a $15\%$ tip based on the original pre-discount cost of the meal. What is the total amount the family paid?

\$82.95

\$83.64

\$86.19

\$87.55

Show answer & explanation

Answer: $\$86.19$

Answer

The total amount the family paid is

\$86.19

.

The correct answer accurately separates the bases for the different percentage calculations. The

20\%

discount reduces the

\$85.00

meal to

\$68.00

. The

8\%

tax is applied to that

\$68.00

base, adding

\$5.44

. The

15\%

tip is calculated on the original

\$85.00

base, adding

\$12.75

. The sum of the discounted meal, tax, and tip is

\$68.00 + \$5.44 + \$12.75 = \$86.19

.

Step-by-Step Solution

1

Calculate the discount amount and the new discounted price of the meal.

20\%

of

\$85.00 = 0.20 \times 85 = \$17.00

. The discounted price is

\$85.00 - \$17.00 = \$68.00

.

The coupon provides a

20\%

discount on the original meal cost, which must be deducted before applying the sales tax.

2

Calculate the sales tax based on the discounted price.

8\%

of

\$68.00 = 0.08 \times 68 = \$5.44

.

The problem states that the sales tax is applied to the discounted price, not the original price.

3

Calculate the tip based on the original pre-discount cost.

15\%

of

\$85.00 = 0.15 \times 85 = \$12.75

.

The problem explicitly states that the tip is based on the original pre-discount cost of the meal.

4

Add the discounted price, the sales tax, and the tip to find the total amount paid.

\$68.00 + \$5.44 + \$12.75 = \$86.19

.

The final total is the sum of the actual cost of the meal, the required tax, and the gratuity.

Key Concept

Calculating multi-step financial arithmetic involving discounts, taxes, and tips, ensuring each percentage is applied to the correct base amount.

Question 149Question →

A Boatswain's Mate needs $12$ gallons of deck paint for a resurfacing project. In the paint locker, they find three partially filled buckets containing $4 \frac{2}{3}$ gallons, $2 \frac{1}{4}$ gallons, and $1 \frac{5}{6}$ gallons of the correct paint. If they combine all the paint from these buckets, how many additional gallons of paint do they need to reach the required $12$ gallons?

3 \frac{1}{4}

4 \frac{3}{4}

4 \frac{5}{13}

8 \frac{3}{4}

Show answer & explanation

Answer: $3 \frac{1}{4}$

Answer

The Boatswain's Mate needs an additional

3 \frac{1}{4}

gallons of paint.

The correct result is found by first combining the available quantities of paint. Since the fractions have unlike denominators (

3

,

4

, and

6

), a common denominator of

12

is used:

4 \frac{8}{12} + 2 \frac{3}{12} + 1 \frac{10}{12} = 7 \frac{21}{12}

, which simplifies to

8 \frac{3}{4}

gallons. To determine the remaining amount needed, subtract this total from the required

12

gallons. By regrouping

12

as

11 \frac{4}{4}

, the final step becomes

11 \frac{4}{4} - 8 \frac{3}{4}

, yielding

3 \frac{1}{4}

gallons.

Step-by-Step Solution

1

Find a common denominator to add the fractions of paint currently available.

The least common denominator for

3

,

4

, and

6

is

12

. Convert the fractions:

4 \frac{2}{3} = 4 \frac{8}{12}

,

2 \frac{1}{4} = 2 \frac{3}{12}

, and

1 \frac{5}{6} = 1 \frac{10}{12}

.

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

2

Add the converted mixed numbers to find the total amount of paint on hand.

Add the whole numbers:

4 + 2 + 1 = 7

. Add the fractions:

\frac{8}{12} + \frac{3}{12} + \frac{10}{12} = \frac{21}{12}

. Combine them to get

7 \frac{21}{12}

. Simplify the improper fraction

\frac{21}{12}

to

1 \frac{9}{12}

, which adds to the whole number to become

8 \frac{9}{12}

. Reduced to simplest form, this is

8 \frac{3}{4}

gallons.

This establishes the total combined volume of paint from the three buckets.

3

Subtract the total paint on hand from the total paint required to find the difference.

Subtract

8 \frac{3}{4}

from

12

. To do this, borrow

1

from the whole number

12

to create a mixed number with a matching denominator:

11 \frac{4}{4} - 8 \frac{3}{4} = 3 \frac{1}{4}

gallons.

Subtracting the available amount from the required total determines exactly how much more paint is needed.

Key Concept

Adding mixed numbers with unlike denominators and correctly borrowing to subtract a mixed number from a whole number.

Question 150Question →

A military logistics center uses two automated packaging machines to assemble field ration kits. Machine A can assemble $450$ kits in $1.5$ hours. Machine B can assemble $90$ kits every $15$ minutes. If both machines operate simultaneously at their respective constant rates, how many total ration kits can they assemble in $4$ hours?

2,640

1,224

1,560

165

Show answer & explanation

Answer: $2,640$

Answer

They can assemble

2,640

ration kits in

4

hours.

The correct answer is found by standardizing the production rates into hourly unit rates, adding them together, and multiplying by the total time. Machine A produces at

300

kits/hr (

450 \div 1.5

). Machine B produces at

360

kits/hr (

90 \times 4

, since

15

minutes is a quarter of an hour). The combined hourly rate is

660

kits/hr. In

4

hours, they produce

660 \times 4 = 2,640

kits.

Step-by-Step Solution

1

Calculate the hourly unit rate for Machine A.

450 \div 1.5 = 300

kits per hour.

To compare and combine rates, both machines must be evaluated using the same unit of time (hours).

2

Calculate the hourly unit rate for Machine B.

90

kits per

15

minutes is equal to

90 \times 4 = 360

kits per hour.

There are

60

minutes in an hour, which is exactly four

15

-minute segments (

60 \div 15 = 4

). Therefore, multiplying the

15

-minute production rate by

4

gives the hourly rate.

3

Calculate the combined hourly rate.

300 + 360 = 660

kits per hour.

Since both machines operate simultaneously, their individual hourly rates are added together to find the total combined rate.

4

Calculate the total kits assembled in

4

hours.

660 \times 4 = 2,640

kits.

Multiply the combined hourly unit rate by the total operating time to find the final production amount.

Key Concept

Unit Rates

Question 151Question →

A commercial 3D printer extrudes $1.2$ kilograms of plastic filament every $45$ minutes of operation. Assuming the printer continues to operate at this exact constant rate, how many grams of filament will it extrude during a $3$ -hour continuous printing session?

4.8

80

300

4800

Show answer & explanation

Answer: $4800$

Answer

The printer will extrude 4800 grams of filament.

Solving this requires maintaining consistent units while scaling up the operation time. Converting the 3-hour print session into 180 minutes reveals that the printer operates for exactly 4 times the duration of the baseline 45-minute period (180 divided by 45 is 4). Because the relationship is a direct proportion, the mass of filament used also scales by a factor of 4. Multiplying 1.2 kilograms by 4 yields 4.8 kilograms. Finally, converting 4.8 kilograms into grams by multiplying by 1000 gives 4800 grams.

Step-by-Step Solution

1

Convert the target time period from hours to minutes to match the units of the given rate.

3 \text{ hours} = 3 \times 60 = 180 \text{ minutes}

Units must be consistent across the proportion equation to find the correct multiplier.

2

Set up a direct proportion to find the amount of filament extruded in kilograms over the new time period.

\frac{1.2 \text{ kg}}{45 \text{ min}} = \frac{x \text{ kg}}{180 \text{ min}} \Rightarrow x = 1.2 \times \left(\frac{180}{45}\right) = 1.2 \times 4 = 4.8 \text{ kg}

The mass of filament extruded scales directly with the time the machine operates.

3

Convert the resulting mass from kilograms to grams.

4.8 \text{ kg} = 4.8 \times 1000 = 4800 \text{ grams}

The question specifically asks for the final answer in grams.

Key Concept

Direct Proportions with Unit Conversions

Question 152Question →

A base cafeteria sells a lunch combo for $\$6.45$ . If a soldier buys $10$ combos for her unit and the order includes a fixed $\$3.50$ delivery fee, what is the total cost of the order?

\$68.00

\$99.50

\$64.50

\$64.85

Show answer & explanation

Answer: $\$68.00$

Answer

The total cost of the order is

\$68.00

.

The total cost is calculated in two steps. First, find the subtotal for the meals by multiplying the individual cost by the quantity:

10 \times \$6.45 = \$64.50

. Next, add the one-time fixed delivery fee to this subtotal:

\$64.50 + \$3.50 = \$68.00

.

Step-by-Step Solution

1

Calculate the total cost of the 10 lunch combos.

10 \times \$6.45 = \$64.50

Each combo costs

\$6.45

, so multiplying by the quantity gives the subtotal for the meals.

2

Add the fixed delivery fee to the subtotal.

\$64.50 + \$3.50 = \$68.00

The delivery fee is a one-time fixed charge that must be added to the subtotal to find the final cost.

Key Concept

Multiplying decimals by powers of 10 and accurately aligning decimals when adding currency amounts.

Question 153Question →

Understanding magnetic behaviors and electromagnetic interactions is fundamental in physical science. Match each magnetic concept on the left with its correct scientific description on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Ferromagnetic substance matches the material strongly attracted to magnets and easily magnetized; Magnetic domain matches the microscopic region where atomic magnetic fields are aligned; Magnetic field lines match the lines of force mapping direction and strength from north to south; and Electromagnetic induction matches the process of generating an electric current via a changing magnetic field.

Each physical concept is paired with its precise scientific description: ferromagnetic substances describe materials like iron and nickel that exhibit strong magnetic attraction; magnetic domains are the microscopic aligned clusters of atomic dipoles; magnetic field lines map the invisible field geometry from north to south; and electromagnetic induction refers to current generation induced by a changing magnetic environment.

Step-by-Step Solution

1

Identify the definition of a ferromagnetic substance

Matches the description of a material such as iron or nickel that is strongly attracted to magnets and can be magnetized

Ferromagnetism is the basic mechanism by which certain materials form permanent magnets or are attracted to magnets.

2

Identify the definition of a magnetic domain

Matches the description of a microscopic region within a solid where atomic magnetic fields are aligned

Domains are localized zones of uniform magnetic orientation within ferromagnetic materials.

3

Identify the definition of magnetic field lines

Matches the description of continuous lines of force emerging from north and entering south to indicate direction and strength

Field lines visually communicate the direction of the magnetic force and its magnitude through line spacing.

4

Identify the definition of electromagnetic induction

Matches the description of the process of generating an electric current in a conductor via a changing magnetic field

Relative movement between a magnetic field and a conductor produces an induced current.

Key Concept

Core concepts of magnetism, magnetic domains, field mapping, and electromagnetic induction

Estimated Time:1m 0s

Question 154Question →

A sporting goods store acquires a shipment of professional-grade kayaks at a wholesale cost of $\$450.00$ each. The store applies a $60\%$ markup to establish the regular retail price. During an end-of-season clearance event, the kayaks are discounted by $25\%$ off the regular retail price. What is the final sale price of a single kayak?

\$607.50

\$695.00

\$540.00

\$702.00

Show answer & explanation

Answer: $\$540.00$

Answer

\$540.00

The correct sale price is found by first adding the

60\%

markup to the

\$450.00

wholesale cost, resulting in a retail price of

\$720.00

. Then, the

25\%

discount is applied to the

\$720.00

retail price, creating a discount amount of

\$180.00

. Subtracting this discount from the retail price leaves a final sale price of

\$540.00

.

Step-by-Step Solution

1

Calculate the markup amount by finding

60\%

of the wholesale cost.

\$450.00 \times 0.60 = \$270.00

The store increases the wholesale price by

60\%

to set the regular retail price.

2

Add the markup amount to the wholesale cost to find the regular retail price.

\$450.00 + \$270.00 = \$720.00

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

3

Calculate the discount amount by finding

25\%

of the regular retail price.

\$720.00 \times 0.25 = \$180.00

The discount is based on the current retail price, not the wholesale cost.

4

Subtract the discount amount from the retail price to find the final sale price.

\$720.00 - \$180.00 = \$540.00

The final price is the retail price minus the discount.

Key Concept

Calculating sequential percentage changes by correctly identifying the new base value for each step.

Estimated Time:1m 0s

Question 155Question →

Match each military logistical operation to its correct unit rate. Pay close attention to the requested units of measurement and necessary conversions.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: Supply truck with 12 miles per gallon, Drainage system with 60 gallons per minute, Packaging line with 420 rations per hour, and Generator with 12.5 milliliters per minute.

Each scenario requires identifying the total quantity of the numerator (miles, gallons, rations, milliliters) and dividing it by the corresponding total of the denominator (gallons, minutes, hours). In every case, this necessitates at least one preliminary conversion or calculation step.

Step-by-Step Solution

1

Calculate the fuel efficiency of the supply truck in miles per gallon.

Total distance =

45 \times 4 = 180

miles. Unit rate =

180 / 15 = 12

miles per gallon.

The fuel efficiency is found by dividing the total distance traveled by the total gallons of fuel consumed, requiring a preliminary distance calculation.

2

Calculate the pumping rate of the drainage system in gallons per minute.

Total time =

60 + 20 = 80

minutes. Unit rate =

4,800 / 80 = 60

gallons per minute.

The units requested are gallons per minute, so the total time must first be completely converted into minutes before dividing the volume.

3

Calculate the production rate of the packaging line in rations per hour.

Rate per minute =

315 / 45 = 7

rations/min. Rate per hour =

7 \times 60 = 420

rations per hour.

To find the hourly rate from a minute-based rate, first find the rate per minute, then scale it up by multiplying by the number of minutes in an hour (

60

).

4

Calculate the consumption rate of the generator in milliliters per minute.

Volume =

18 \times 1,000 = 18,000

mL. Time =

24 \times 60 = 1,440

minutes. Unit rate =

18,000 / 1,440 = 12.5

mL/min.

Both given quantities require unit conversions (liters to milliliters, and hours to minutes) before performing the final division to find the required rate.

Key Concept

Calculating unit rates involving multi-step operations and dimensional analysis (unit conversions).

Question 156Question →

A city planner is reviewing a map of a proposed municipal park. The map uses a scale where $\frac{1}{2}$ inch represents $30$ feet. If the park occupies an area of $15$ square inches on the map, what will be the actual area of the park in square yards?

300

6,000

18,000

54,000

Show answer & explanation

Answer: 6,000

Answer

The actual area of the park is 6,000 square yards.

To solve this problem efficiently, first convert the linear scale to yards:

\frac{1}{2}\text{ inch} = 30\text{ feet}

means

1\text{ inch} = 60\text{ feet}

, which equals

20\text{ yards}

. Because we are dealing with area, we must square the linear scale to find the area scale factor:

1\text{ square inch} = 20^2\text{ square yards} = 400\text{ square yards}

. Finally, multiply the given map area by this factor:

15\text{ square inches} \times 400 = 6,000\text{ square yards}

.

Step-by-Step Solution

1

Determine the linear scale factor for one full inch.

1\text{ inch} = 60\text{ feet}

The map scale is given as

\frac{1}{2}\text{ inch} = 30\text{ feet}

. Multiplying both sides by 2 gives the equivalent measurement for 1 inch.

2

Convert the linear scale into yards to match the requested final unit.

1\text{ inch} = 20\text{ yards}

Since there are 3 feet in a yard, dividing 60 feet by 3 yields 20 yards. This simplifies calculations by converting units early.

3

Calculate the area scale factor by squaring the linear scale.

1\text{ square inch} = 400\text{ square yards}

Area is a two-dimensional measurement. The linear scale must be squared (

20 \times 20 = 400

) to establish the relationship between map area and actual area.

4

Calculate the actual area of the park.

15 \times 400 = 6,000\text{ square yards}

Multiply the map area by the area scale factor to find the true dimensions.

Key Concept

Scale Factors for Area and Unit Conversions

Alternative Method

Instead of converting to yards early, you can find the actual area in square feet first. The area scale factor in feet is

60^2 = 3,600\text{ square feet per square inch}

. Multiply by the map area:

15 \times 3,600 = 54,000\text{ square feet}

. Then convert to square yards by dividing by 9:

54,000 \div 9 = 6,000\text{ square yards}

.

Estimated Time:1m 30s

Question 157Question →

A floor plan for a new office space is drawn using a scale of $1\text{ inch} = 6\text{ feet}$ . If the main conference room is $3.5\text{ inches}$ long on the floor plan, what is the actual length of the conference room in feet?

Show answer & explanation

Answer: 21

Answer

21

The scale indicates that every

1\text{ inch}

on the drawing corresponds to

6\text{ feet}

in reality. Therefore, a length of

3.5\text{ inches}

on the drawing represents an actual length of

3.5 \times 6 = 21\text{ feet}

.

Step-by-Step Solution

1

Identify the given scale and drawing measurement.

Scale:

1\text{ inch} = 6\text{ feet}

, Drawing length:

3.5\text{ inches}

.

These are the key values needed to calculate the actual length.

2

Multiply the drawing length by the scale factor.

3.5 \times 6 = 21

Since each inch represents

6\text{ feet}

, multiplying the number of inches by

6

gives the total actual feet.

Key Concept

Using a scale factor to convert a drawing measurement to an actual measurement.

Question 158Question →

Match each military supply and maintenance inventory count to its correctly simplified ratio.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches pair each scenario to its mathematically simplified ratio.

Each correct match is found by writing the quantities in the requested order and then dividing all terms by their greatest common factor.

Step-by-Step Solution

1

Identify the quantities to be compared in the exact order requested by each scenario.

The numerical values are extracted in the correct sequence.

Ratios represent a specific relationship, and the order of the terms must match the order requested in the text.

2

Write the initial unsimplified ratios for all scenarios.

The initial ratios are

24:8

,

10:15

,

20:5

, and

10:5:15

.

This establishes the mathematical baseline before simplification.

3

Find the greatest common factor (GCF) for the numbers in each ratio and divide.

The simplified ratios are

3:1

,

2:3

,

4:1

, and

2:1:3

.

Ratios should always be expressed in their simplest terms.

Key Concept

Basic Ratios and Simplification

Question 159Question →

Read the scenario and perform the necessary calculations. Enter the exact numerical values in the blanks.

Fill in the blanks below

A customer purchases a premium spa package for

\$250.00

. The local municipality applies a

6\%

sales tax to the base price of all spa services. After the tax is added, the customer decides to leave a

20\%

tip based on the new, post-tax total on the receipt.

The amount of the tip is $\$

and the final total cost paid by the customer is

\$$.

Show answer & explanation

Answer

The amount of the tip is 53 (or 53.00) and the final total cost is 318 (or 318.00).

The correct amounts are found by sequentially applying the percentages according to the narrative. First, a

6\%

tax on the

\$250.00

base price adds

\$15.00

, resulting in a

\$265.00

subtotal. The

20\%

tip is then applied to this

\$265.00

subtotal, resulting in a

\$53.00

tip. Adding this tip to the subtotal gives the final cost of

\$318.00

.

Step-by-Step Solution

1

Calculate the sales tax amount on the base price.

\$15.00

Multiply the base price (

\$250.00

) by the tax rate (

0.06

).

2

Determine the post-tax total.

\$265.00

Add the tax amount (

\$15.00

) to the base price (

\$250.00

) to find the amount upon which the tip will be calculated.

3

Calculate the tip amount.

\$53.00

Multiply the post-tax total (

\$265.00

) by the tip rate (

0.20

).

4

Calculate the final total cost.

\$318.00

Add the tip amount (

\$53.00

) to the post-tax total (

\$265.00

).

Key Concept

Calculating sales tax on a base price and applying a tip percentage to the sequential post-tax total.

Question 160Question →

Determine the correct numerical values to complete the statement.

Fill in the blanks below

An aviation mechanic calibrates

8

flight instruments in

3

hours. If a squadron requires

20

instruments to be calibrated, and the mechanic works at the same constant rate, it will take hours and minutes to complete the task.

Show answer & explanation

Answer

It will take 7 hours and 30 minutes.

Because the work rate is constant, the number of instruments calibrated is directly proportional to the time taken. Setting up the proportion 8/3 = 20/x yields x = 7.5 hours. Converting the remaining 0.5 hours to minutes gives 30 minutes, resulting in a total required time of 7 hours and 30 minutes.

Step-by-Step Solution

1

Set up a direct proportion comparing the number of instruments to the time in hours.

\frac{8 \text{ instruments}}{3 \text{ hours}} = \frac{20 \text{ instruments}}{x \text{ hours}}

When a rate is constant, the ratio of work completed to time taken remains equivalent.

2

Cross-multiply the terms to create a linear equation.

8x = 3 \times 20

Cross-multiplying is the standard algebraic method to solve for an unknown in a proportional relationship.

3

Simplify the equation and solve for

x

.

8x = 60 \Rightarrow x = \frac{60}{8} = 7.5 \text{ hours}

Isolating

x

provides the total required time expressed in hours.

4

Convert the decimal portion of the hours into minutes.

0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}

The question specifically requires the final answer to be formatted in hours and minutes.

Key Concept

Direct proportions with unit conversion

Estimated Time:1m 30s

Answer

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