All practice questions

Question 161Question →

An electrical circuit in an automated test bench connects a $24\text{ V}$ direct-current power supply to two $12\,\Omega$ heating elements arranged in parallel. What is the total electric current delivered by the power supply to the entire circuit?

1\text{ A}

4\text{ A}

2\text{ A}

8\text{ A}

Show answer & explanation

Answer: $4\text{ A}$

Answer

4\text{ A}

In a parallel circuit with two identical

12\,\Omega

loads, the total equivalent resistance is halved to

6\,\Omega

. By Ohm's law (

I = \frac{V}{R}

), the total current drawn from the

24\text{ V}

source is

\frac{24\text{ V}}{6\,\Omega} = 4\text{ A}

. Alternatively, each branch draws

\frac{24\text{ V}}{12\,\Omega} = 2\text{ A}

, yielding a total current of

2\text{ A} + 2\text{ A} = 4\text{ A}

.

Step-by-Step Solution

1

Calculate the equivalent resistance of the two identical resistors connected in parallel.

R_{\text{eq}} = \frac{12\,\Omega}{2} = 6\,\Omega

When identical resistors are in parallel, the equivalent resistance equals the resistance of one branch divided by the total number of branches.

2

Apply Ohm's law (

I = \frac{V}{R_{\text{eq}}}

) using the total source voltage and equivalent resistance.

I_{\text{total}} = \frac{24\text{ V}}{6\,\Omega} = 4\text{ A}

Ohm's law defines the relationship between total circuit voltage, equivalent resistance, and total current.

Key Concept

Parallel circuit resistance and Ohm's law

Estimated Time:1m 0s

Question 162Question →

A military medical unit is inventorying a shipment of emergency first-aid kits. Upon inspection, they determine that $\frac{11}{25}$ of the kits have missing components, and an additional $2.5\%$ of the kits have expired medications. If the remaining kits are fully stocked and ready for deployment, what fractional portion of the total shipment is ready for deployment?

\frac{107}{200}

\frac{93}{200}

\frac{31}{100}

\frac{53}{65}

Show answer & explanation

Answer: $\frac{107}{200}$

Answer

The correct fractional portion of the total shipment that is ready for deployment is

\frac{107}{200}

.

To find the portion of kits ready for deployment, all given values must first be converted into a common format, such as percentages. The fraction of kits with missing components is

\frac{11}{25}

. To convert this to a percentage, multiply the numerator and denominator by

4

to get

\frac{44}{100}

, which is

44\%

. Adding this to the

2.5\%

of expired kits gives a total defective portion of

46.5\%

. Since the entire shipment represents

100\%

, the portion ready for deployment is

100\% - 46.5\% = 53.5\%

. Finally, this percentage must be converted back into a fraction.

53.5\%

is equivalent to

\frac{53.5}{100}

, which can be written as

\frac{535}{1000}

. Dividing both the numerator and denominator by

5

simplifies this fraction to its lowest terms,

\frac{107}{200}

.

Step-by-Step Solution

1

Convert the fraction of kits with missing components into a percentage.

\frac{11}{25} = \frac{44}{100} = 44\%

Converting all values to percentages makes it easier to add the different defective portions together.

2

Calculate the total percentage of defective kits in the shipment.

44\% + 2.5\% = 46.5\%

Adding the missing component percentage and the expired medication percentage gives the total portion that cannot be deployed.

3

Determine the percentage of kits that are ready for deployment.

100\% - 46.5\% = 53.5\%

The entire shipment is

100\%

. Subtracting the defective portion reveals the remaining ready portion.

4

Convert the final percentage back into a fully simplified fraction.

53.5\% = \frac{53.5}{100} = \frac{535}{1000} = \frac{107}{200}

The question specifically asks for the answer as a fractional portion.

Key Concept

Converting between fractions, decimals, and percentages to solve multi-step problems involving parts of a whole.

Estimated Time:1m 30s

Question 163Question →

Match each buy-and-sell transaction to the correct dollar amount of profit or loss.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Tool set matches

\$25

Profit; Guitar matches

\$50

Loss; Blender matches

\$0

(Break-even); Winter coat matches

\$15

Profit.

Profit is correctly calculated when the selling price is higher than the cost price. A loss occurs when the selling price is lower than the cost price, and breaking even occurs when the two prices are identical.

Step-by-Step Solution

1

Calculate the difference between the selling price and the cost price for each transaction.

Tool set:

\$65 - \$40 = \$25

. Guitar:

\$150 - \$200 = -\$50

. Blender:

\$30 - \$30 = \$0

. Coat:

\$100 - \$85 = \$15

.

The difference determines the amount of money gained or lost on each item.

2

Determine if each result is a profit, loss, or break-even.

Positive values (

\$25

,

\$15

) are profits. The negative value (

-\$50

) is a loss. Zero (

\$0

) is a break-even.

A positive difference means money was made (profit), a negative difference means money was lost (loss), and zero means no change in value.

Key Concept

Calculating absolute profit or loss by finding the difference between selling price and cost price.

Question 164Question →

A base commander is distributing a total of $240$ new combat helmets to two platoons in a ratio of $5:3$ . How many helmets will the platoon with the smaller share receive?

Show answer & explanation

Answer: 90

Answer

The platoon with the smaller share will receive 90 helmets.

To find the smaller share, first add the ratio parts together to find the total number of parts (

5 + 3 = 8

). Next, divide the total number of helmets by the total parts (

240 \div 8 = 30

) to find the value of one part. Finally, multiply the value of one part by the smaller ratio number (

30 \times 3 = 90

).

Step-by-Step Solution

1

Find the total number of ratio parts

5 + 3 = 8

parts

To determine how many equal parts the total number of helmets is divided into.

2

Calculate the value of one part

240 \div 8 = 30

helmets per part

To find out how many helmets correspond to a single ratio unit.

3

Calculate the smaller share

3 \times 30 = 90

helmets

To find the number of helmets for the platoon receiving the smaller portion of the ratio.

Key Concept

Dividing a total quantity into a given ratio by finding the value of a single part.

Estimated Time:45s

Question 165Question →

A naval base allocates its quarterly maintenance budget among structural repairs, mechanical overhauls, and routine inspections in the ratio of $5:8:2$ . The amount allocated for mechanical overhauls is $\$45,000$ more than the amount allocated for routine inspections. Based on this information, calculate the total quarterly maintenance budget.

Fill in the blanks below

The total quarterly maintenance budget is $\$.

Show answer & explanation

Answer

The total quarterly maintenance budget is $112,500.

The difference between the mechanical overhaul and routine inspection allocations represents 6 parts of the total ratio (

8 - 2

). By dividing the given dollar difference (

\$45,000

) by 6, we find that a single ratio part is worth

\$7,500

. Since the entire maintenance budget is composed of 15 parts in total (

5 + 8 + 2

), multiplying 15 by

\$7,500

gives the correct total budget of

\$112,500

.

Step-by-Step Solution

1

Identify the number of ratio parts assigned to each category.

Structural =

5

parts, Mechanical =

8

parts, Routine =

2

parts.

This establishes the proportional distribution of the entire budget.

2

Determine the difference in parts between mechanical overhauls and routine inspections.

8

parts -

2

parts =

6

parts.

The problem provides the dollar amount for the difference between these two specific allocations, so we must find the corresponding difference in ratio parts.

3

Calculate the monetary value of a single ratio part.

\$45,000 \div 6 = \$7,500

per part.

Dividing the total monetary difference by the difference in parts gives the unit value of one part.

4

Find the total number of parts in the ratio and calculate the final budget.

Total parts =

5 + 8 + 2 = 15

. Total budget =

15 \times \$7,500 = \$112,500

.

Multiplying the total number of parts by the value of a single part yields the overall budget.

Key Concept

Using the monetary difference between two shares in a ratio to determine the value of a single unit, which is then used to find the total amount.

Question 166Question →

A marine supply store purchases commercial GPS units at a wholesale price of $\$320.00$ each. The store applies a $75\%$ markup to establish the regular retail price. During a spring clearance event, the store offers a $20\%$ discount off the regular retail price. What is the final sale price of the GPS unit?

Fill in the blanks below

The final sale price of the GPS unit is $\$$.

Show answer & explanation

Answer

The final sale price is

\$448.00

.

The final sale price is calculated in two sequential steps. First, the

\$240.00

markup (

75\%

of the

\$320.00

wholesale cost) is added to establish a regular retail price of

\$560.00

. Second, the

20\%

discount is applied to the

\$560.00

retail price, which equals

\$112.00

. Subtracting this

\$112.00

discount from the

\$560.00

retail price yields a final sale price of

\$448.00

.

Step-by-Step Solution

1

Calculate the markup amount.

\$320.00 \times 0.75 = \$240.00

To find the dollar amount added to the wholesale cost.

2

Determine the regular retail price.

\$320.00 + \$240.00 = \$560.00

To establish the base price before the clearance discount is applied.

3

Calculate the discount amount.

\$560.00 \times 0.20 = \$112.00

To find the dollar amount subtracted during the clearance sale.

4

Find the final sale price.

\$560.00 - \$112.00 = \$448.00

To determine the final cost to the customer after applying the discount.

Key Concept

Calculating sequential percentage changes by applying a markup to a base price and a subsequent discount to the resulting retail price.

Question 167Question →

A ceramic space heater is connected to a standard $120\text{ V}$ electrical outlet. If the heating element has an internal resistance of $15\,\Omega$ , what is the electric current flowing through the circuit, in amperes ( $\text{A}$ )?

Show answer & explanation

Answer: 8

Answer

8 A

According to Ohm's Law (

V = IR

), the electric current (

I

) flowing through a circuit is found by dividing the potential difference (

V

) by the resistance (

R

). Dividing

120\text{ V}

by

15\,\Omega

gives an electric current of

8\text{ A}

.

Step-by-Step Solution

1

Identify the given electrical values from the problem statement.

Voltage

V = 120\text{ V}

and resistance

R = 15\,\Omega

.

Determining known quantities is required to choose the appropriate formula.

2

State Ohm's Law and isolate current (

I

).

I = \frac{V}{R}

Ohm's Law governs the relationship between potential difference, current, and resistance in an electrical circuit.

3

Divide voltage by resistance to calculate the current in amperes.

I = \frac{120\text{ V}}{15\,\Omega} = 8\text{ A}

Carrying out the arithmetic yields the resulting current in amperes.

Key Concept

Ohm's Law (

V = IR

) defines the relationship among voltage, current, and resistance, where current is directly proportional to voltage and inversely proportional to resistance.

Estimated Time:1m 0s

Question 168Question →

A field communications unit has a spool containing $30 \frac{1}{4}$ yards of specialized copper wire. They need to cut the wire into smaller segments that are each $1 \frac{3}{8}$ yards long to connect field radios. How many complete segments of wire can the unit cut?

Fill in the blanks below

The unit can cut complete segments of wire.

Show answer & explanation

Answer

22

The correct answer is 22 because you must divide the total amount of wire by the length of one segment. Converting both mixed numbers to improper fractions gives

\frac{121}{4}

and

\frac{11}{8}

. Dividing

\frac{121}{4}

by

\frac{11}{8}

is equivalent to multiplying

\frac{121}{4}

by

\frac{8}{11}

, which simplifies to exactly 22.

Step-by-Step Solution

1

Convert the total wire length from a mixed number to an improper fraction.

30 \frac{1}{4} = \frac{30 \times 4 + 1}{4} = \frac{121}{4}

yards.

Improper fractions are required to perform fraction division.

2

Convert the length of each segment from a mixed number to an improper fraction.

1 \frac{3}{8} = \frac{1 \times 8 + 3}{8} = \frac{11}{8}

yards.

Improper fractions are required to perform fraction division.

3

Set up the division problem to find the total number of segments.

\frac{121}{4} \div \frac{11}{8}

Dividing the total length by the length of a single segment gives the total number of segments.

4

Perform the division by multiplying the first fraction by the reciprocal of the second fraction.

\frac{121}{4} \times \frac{8}{11}

The rule for dividing fractions is to multiply by the reciprocal of the divisor.

5

Simplify the expression by cross-canceling and multiply.

\frac{121}{11} \times \frac{8}{4} = 11 \times 2 = 22

segments.

Simplifying before multiplying makes the calculation easier and yields the final whole number of segments.

Key Concept

Dividing mixed numbers in a real-world word problem context

Question 169Question →

A state map uses a scale where $1\text{ inch}$ represents $50\text{ miles}$ . If the straight-line distance between two cities on the map is $2.5\text{ inches}$ , what is the actual distance between the two cities?

20\text{ miles}

12.5\text{ miles}

125\text{ miles}

2.5\text{ miles}

Show answer & explanation

Answer: $125\text{ miles}$

Answer

125\text{ miles}

The map scale indicates that every 1 inch on the map corresponds to 50 actual miles. To find the real-world distance for a measurement of 2.5 inches on the map, you must multiply the map measurement by the scale factor: 2.5 × 50 = 125 miles.

Step-by-Step Solution

1

Set up a proportion or identify the scale factor from the problem description.

1\text{ inch} = 50\text{ miles}

This establishes how many real-world miles are represented by each inch on the map.

2

Multiply the measured map distance by the scale factor to find the actual distance.

2.5\text{ inches} \times 50\text{ miles/inch} = 125\text{ miles}

Since every inch represents 50 miles, 2.5 inches will represent 2.5 groups of 50 miles.

Key Concept

Using a linear scale factor to convert a map measurement to a real-world distance.

Question 170Question →

A technician spends $2$ hours diagnosing a communications system and $30$ minutes completing the repair. What is the ratio of the time spent diagnosing to the time spent repairing?

4:1

1:15

1:4

4:5

Show answer & explanation

Answer: $4:1$

Answer

The correct ratio is

4:1

.

To find the correct ratio, both times must be expressed in the same unit. Converting

2

hours gives

120

minutes. The requested ratio of diagnosing time to repairing time is

120:30

. Dividing both numbers by their greatest common divisor (

30

) yields the simplest form,

4:1

.

Step-by-Step Solution

1

Convert the diagnosing time to the same unit as the repair time.

2

hours =

2 \times 60

minutes =

120

minutes.

Ratios must compare quantities in the same units to be mathematically meaningful.

2

Set up the ratio of diagnosing time to repair time.

120

minutes :

30

minutes

The question specifically asks for the ratio of diagnosing time first, followed by repair time.

3

Simplify the ratio to its lowest terms.

120 : 30 = 4 : 1

Divide both parts of the ratio by their greatest common divisor, which is

30

.

Key Concept

To find a ratio between two real-world quantities, ensure they share the same units, express their relationship in the exact order requested, and simplify.

Question 171Question →

A portrait studio upgrades its lighting equipment. The manufacturer's base price for the lighting kit is $\$2,400.00$ . The regional distributor adds a $25\%$ markup to set the standard retail price. During a promotional event, the studio receives a $12\%$ discount off the standard retail price. What is the final price the studio pays for the lighting kit?

\$2,712.00

\$2,988.00

\$2,640.00

\$2,964.00

Show answer & explanation

Answer: $\$2,640.00$

Answer

The final price the studio pays for the lighting kit is

\$2,640.00

.

The correct final price is found by calculating the transactions in sequence. First, a 25% markup on the

2,400.00 base price adds

600.00, creating a retail price of

3,000.00. Then, a 12% discount is applied to that

3,000.00 retail price, which subtracts

360.00, resulting in a final price of

2,640.00.

Step-by-Step Solution

1

Calculate the retail price by applying the 25% markup to the manufacturer's base price.

\$2,400.00 \times 0.25 = \$600.00

markup.

\$2,400.00 + \$600.00 = \$3,000.00

standard retail price.

The markup is a percentage of the base price and must be added to it to determine the retail price before any discounts can be applied.

2

Calculate the discount amount by applying the 12% discount to the standard retail price.

\$3,000.00 \times 0.12 = \$360.00

discount.

The promotional discount applies to the current retail price, not the original base price.

3

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

\$3,000.00 - \$360.00 = \$2,640.00

.

The final price is the retail price reduced by the calculated discount amount.

Key Concept

Calculating successive percentage changes requires updating the base value after each step. A discount applied after a markup must be calculated using the newly marked-up price.

Question 172Question →

A unit of $36$ combat engineers can construct a perimeter defense system in $3$ hours and $45$ minutes. If the commanding officer orders the defense system to be completed in exactly $1$ hour and $40$ minutes, how many combat engineers in total must be assigned to the task, assuming all engineers work at the same constant rate?

16

32

81

89

Show answer & explanation

Answer: 81

Answer

81

The problem describes an inverse proportion because decreasing the allotted time requires increasing the number of workers to accomplish the identical task. By converting all times to minutes, the total required work effort is calculated as

36

engineers

\times

225

minutes =

8,100

engineer-minutes. Dividing this constant work effort by the new strict time constraint of

100

minutes yields the total required personnel:

81

engineers.

Step-by-Step Solution

1

Convert both time durations entirely into minutes to establish a single, consistent unit of measure.

3

hours and

45

minutes =

(3 \times 60) + 45 = 225

minutes.

1

hour and

40

minutes =

(1 \times 60) + 40 = 100

minutes.

Converting to minutes prevents errors associated with mixed units and base-60 time fractions.

2

Set up an inverse proportion equation, recognizing that the total amount of work (personnel multiplied by time) remains constant.

\text{Engineers}_1 \times \text{Time}_1 = \text{Engineers}_2 \times \text{Time}_2 \Rightarrow 36 \times 225 = x \times 100

When completing a fixed task, the number of workers and the time required are inversely proportional.

3

Solve the equation to find the total number of engineers required for the new timeframe.

8,100 = 100x \Rightarrow x = \frac{8,100}{100} = 81

engineers.

Dividing the total required engineer-minutes (

8,100

) by the available minutes (

100

) determines the necessary workforce.

Key Concept

Inverse Proportions

Estimated Time:1m 30s

Question 173Question →

A landscaper purchases a used backpack leaf blower for $240. A week later, they sell the equipment to another contractor for$ 300. What is the landscaper's profit percentage?

25%

20%

125%

2.5%

Show answer & explanation

Answer: 25%

Answer

25%

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

240) from the selling price (

300), which equals

60. Then, divide that profit by the original cost (

240).

60 divided by

240 is 0.25, which translates to a 25% profit.

Step-by-Step Solution

1

Determine the dollar amount of the profit by subtracting the original purchase price from the selling price.

300 -

240 = $60

Profit is the positive difference between revenue (selling price) and expenses (cost price).

2

Set up a fraction or division problem placing the profit over the original cost price.

60 / 240

Profit percentage is always calculated relative to the original cost, not the final selling price.

3

Simplify the fraction and convert it into a percentage.

60 / 240 = 1 / 4 = 0.25 = 25%

Converting the decimal ratio to a percentage provides the final answer.

Key Concept

Profit Percentage Calculation

Alternative Method

You can also solve this by dividing the selling price by the cost price first (

300 /

240 = 1.25). Because 1.00 represents the original 100% cost, the decimal portion remaining (0.25) represents the profit, which is 25%.

Estimated Time:45s

Question 174Question →

A musician purchases a sound amplifier with an original price of $350.00$ . The store is offering a $15\%$ promotional discount on all electronics. After the discount is applied, a $6\%$ state sales tax is added to the purchase. What is the final total cost the musician pays?

318.50

355.10

315.35

371.00

Show answer & explanation

Answer: $315.35$

Answer

The final total cost is

315.35

.

To find the final cost, you must first calculate the 15% discount on the original

350 price (

350 \times 0.15 =

52.50). Subtracting this gives the discounted subtotal (

350 -

52.50 =

297.50). Next, calculate the 6% sales tax based strictly on this new subtotal (

297.50 \times 0.06 =

17.85). Finally, add the sales tax to the discounted subtotal to find the final total cost (

297.50 +

17.85 = $315.35).

Step-by-Step Solution

1

Calculate the discount amount.

350.00 \times 0.15 = 52.50

To find how much money is taken off the original price, multiply the original price by the decimal equivalent of the discount percentage.

2

Calculate the discounted price.

350.00 - 52.50 = 297.50

Subtract the discount amount from the original price to find the subtotal before tax.

3

Calculate the sales tax.

297.50 \times 0.06 = 17.85

Taxes are applied to the discounted purchase price. Multiply the subtotal by the decimal equivalent of the tax percentage.

4

Calculate the final total cost.

297.50 + 17.85 = 315.35

Add the calculated sales tax to the discounted price to find the total amount paid.

Key Concept

Calculating sequential percentages by applying a discount to an original base price, and then calculating tax based on the new discounted subtotal.

Question 175Question →

An emergency backup lighting system connects three identical $15\,\Omega$ indicator lamps in series across a $45\text{ V}$ direct-current power source. What is the electric current flowing through each lamp?

0.33\text{ A}

3.0\text{ A}

1.0\text{ A}

9.0\text{ A}

Show answer & explanation

Answer: $1.0\text{ A}$

Answer

1.0\text{ A}

In a series circuit, the total electrical resistance is the sum of all individual resistances in the path:

R_{\text{total}} = 15\,\Omega + 15\,\Omega + 15\,\Omega = 45\,\Omega

. Applying Ohm's law (

I = \frac{V}{R}

), the current drawn from the

45\text{ V}

source is

I = \frac{45\text{ V}}{45\,\Omega} = 1.0\text{ A}

. In any series circuit, the electric current is identical at every point, meaning exactly

1.0\text{ A}

flows through each lamp.

Step-by-Step Solution

1

Calculate the total equivalent resistance of the series circuit.

R_{\text{total}} = 15\,\Omega + 15\,\Omega + 15\,\Omega = 45\,\Omega

In a series circuit, the total electrical resistance equals the direct sum of all individual resistances.

2

Apply Ohm's law to determine the total circuit current.

I = \frac{V}{R_{\text{total}}} = \frac{45\text{ V}}{45\,\Omega} = 1.0\text{ A}

Current is calculated by dividing total source voltage by the total resistance of the circuit.

3

Determine the current flowing through each individual lamp.

I_{\text{lamp}} = 1.0\text{ A}

Because there is only one continuous path for electrical charge in a series circuit, the current is uniform through all components.

Key Concept

Ohm's law and total resistance in series circuits

Estimated Time:1m 0s

Question 176Question →

A base logistics center is processing a shipment of 2,400 supply crates. Over three days, the following portions of the total shipment were processed:

- Monday: $31.25\%$ of the total shipment
- Tuesday: $\frac{5}{12}$ of the total shipment
- Wednesday: $0.125$ of the total shipment

How many supply crates remain to be processed?

Show answer & explanation

Answer: 350

Answer

350

The total amount processed is found by converting all values to fractions:

31.25\%

becomes

\frac{5}{16}

and

0.125

becomes

\frac{1}{8}

. Adding these to

\frac{5}{12}

using a common denominator of 48 gives

\frac{41}{48}

processed. The remaining

\frac{7}{48}

of the 2,400 total crates equals 350 crates.

Step-by-Step Solution

1

Convert

31.25\%

and

0.125

to fractions.

31.25\% = \frac{5}{16}

and

0.125 = \frac{1}{8}

.

Working in a single format (fractions) is the most precise way to add parts of a whole without losing exact values.

2

Find the least common denominator (LCD) for

\frac{5}{16}

,

\frac{5}{12}

, and

\frac{1}{8}

.

The LCD for 16, 12, and 8 is 48.

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

3

Convert each fraction to have a denominator of 48 and sum them together.

\frac{15}{48} + \frac{20}{48} + \frac{6}{48} = \frac{41}{48}

This calculates the total fraction of the shipment that has already been processed over the three days.

4

Subtract the processed fraction from 1 to find the remaining fraction.

1 - \frac{41}{48} = \frac{7}{48}

The question asks for the remaining amount of crates, not the completed amount.

5

Multiply the remaining fraction by the total number of crates (2,400).

\frac{7}{48} \times 2400 = 7 \times 50 = 350

This converts the fractional remainder back into the actual physical quantity of crates.

Key Concept

Converting percentages and decimals to fractions to efficiently sum portions of a whole, and applying a fractional remainder to a total quantity.

Question 177Question →

A reservist drives $15$ miles one-way to the armory. Her vehicle consumes $0.4$ gallons of fuel for this one-way trip. If fuel costs $\$3.50$ per gallon, what is the total cost of fuel for the round trip?

\$1.40

\$28.00

\$2.80

\$52.50

Show answer & explanation

Answer: $\$2.80$

Answer

The total cost of fuel for the round trip is

\$2.80

.

The round trip consists of two legs, so the vehicle consumes

0.4 \times 2 = 0.8

gallons of fuel in total. Multiplying the total fuel by the price per gallon (

0.8 \times \$3.50

) results in a total cost of

\$2.80

.

Step-by-Step Solution

1

Determine the total fuel consumed for the round trip.

0.4 \text{ gallons} \times 2 = 0.8 \text{ gallons}

The

0.4

gallons is for a one-way trip, but the total cost requested is for a round trip.

2

Calculate the total cost of the fuel.

0.8 \text{ gallons} \times \$3.50/\text{gallon} = \$2.80

Multiplying the total fuel volume by the price per gallon gives the overall cost.

Key Concept

Multi-step decimal multiplication involving money and adjusting quantities for a round trip.

Alternative Method

Calculate the cost of a one-way trip first by multiplying

0.4

gallons by

\$3.50

to get

\$1.40

, then double this amount for the round trip to get

\$2.80

.

Estimated Time:45s

Question 178Question →

Electrical circuits and power distribution systems utilize specialized components to regulate, convert, and protect electrical energy. Which functional description correctly matches each electrical component?

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match Fuse with interrupting excessive current by melting a sacrificial strip, Transformer with altering alternating-current voltage levels through electromagnetic induction, Capacitor with storing separated electric charge across an insulating dielectric layer, and Diode with restricting current flow primarily to a single direction.

Each component is correctly paired with its defining physical mechanism: a fuse provides overcurrent protection by melting its internal element; a transformer modulates AC voltage via mutual electromagnetic induction; a capacitor accumulates electrostatic charge across separated plates; and a diode rectifies or guides current in a single direction.

Step-by-Step Solution

1

Identify the protective mechanism of a fuse.

A fuse contains a thin wire designed to melt under overcurrent conditions, matching the description of interrupting excessive current by melting a sacrificial strip.

Fuses protect wiring and equipment from dangerous current overloads and short circuits.

2

Identify the electromagnetic function of a transformer.

A transformer transfers energy between AC circuits through mutual magnetic flux, matching the description of altering AC voltage levels through electromagnetic induction.

Transformers rely on changing magnetic fields produced by alternating current to induce voltage across windings.

3

Identify the electrostatic storage mechanism of a capacitor.

A capacitor holds electrostatic charge on opposing plates separated by a dielectric, matching the description of accumulating and storing separated electric charge.

Capacitors maintain potential difference by holding static charge rather than dissipating or converting it.

4

Identify the unidirectional conducting property of a diode.

A diode conducts forward-bias current while blocking reverse-bias current, matching the description of restricting current flow to a single direction.

Diodes are fundamental semiconductor components used in rectification and polarity protection.

Key Concept

Functional characteristics and operating principles of fundamental electrical circuit components

Estimated Time:1m 0s

Question 179Question →

An aviation maintenance team is preparing a specialized anti-icing fluid blend consisting of glycol, water, and an additive in the ratio of $8:3:1$ by volume. If the team needs to prepare a total of $60$ gallons of this fluid, how many more quarts of glycol are required than water?

25

100

150

160

Show answer & explanation

Answer: 100

Answer

100

To solve this, first find the total number of parts in the ratio by adding

8 + 3 + 1 = 12

parts. Since the total volume is

60

gallons, each part represents

60 \div 12 = 5

gallons. Glycol accounts for

8

parts and water accounts for

3

parts, making a difference of

5

parts. The difference in gallons is

5 \times 5 = 25

gallons. Finally, convert gallons to quarts by multiplying by

4

(

1

gallon =

4

quarts), which gives

25 \times 4 = 100

quarts.

Step-by-Step Solution

1

Determine the total number of parts in the ratio.

8 + 3 + 1 = 12

parts

To find the volume of a single part, the total parts must be known.

2

Calculate the volume of one part in gallons.

60 \div 12 = 5

gallons per part

Dividing the total volume by the total parts gives the value of one part.

3

Find the difference in volume between glycol and water in gallons.

Glycol is

8

parts and water is

3

parts. Difference =

5

parts.

5 \times 5 = 25

gallons.

The question asks for the exact difference between the two components.

4

Convert the difference from gallons to quarts.

25 \times 4 = 100

quarts

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

4

quarts in a gallon.

Key Concept

Dividing a total amount into a multi-part ratio and converting between standard units of measurement.

Question 180Question →

A remote weather-monitoring station is powered by a $36\text{ V}$ direct-current solar battery bank. Two identical communication transmitters are connected in parallel across the power terminals. If the monitoring station draws a total current of $4\text{ A}$ when both transmitters are operating simultaneously, what is the electrical resistance of each individual transmitter?

9\,\Omega

4.5\,\Omega

18\,\Omega

180\,\Omega

Show answer & explanation

Answer: $18\,\Omega$

Answer

The electrical resistance of each individual transmitter is

18\,\Omega

.

In a parallel circuit, each identical branch draws an equal share of the total current. With a total current of

4\text{ A}

split evenly across two identical paths, each transmitter draws

2\text{ A}

. Applying Ohm's law (

R = \frac{V}{I}

) across one branch with the full

36\text{ V}

potential difference yields

R = \frac{36\text{ V}}{2\text{ A}} = 18\,\Omega

.

Step-by-Step Solution

1

Calculate the total equivalent resistance of the parallel circuit using Ohm's Law.

R_{\text{eq}} = \frac{V}{I_{\text{total}}} = \frac{36\text{ V}}{4\text{ A}} = 9\,\Omega

The total resistance of the entire circuit relates the total supply voltage to the total current drawn from the battery bank.

2

Determine the resistance of each individual transmitter from the parallel combination formula.

\frac{1}{R_{\text{eq}}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \implies R = 2 \times R_{\text{eq}} = 2 \times 9\,\Omega = 18\,\Omega

When two identical resistors are connected in parallel, their equivalent resistance is equal to half the resistance of a single component.

Key Concept

Ohm's law and equivalent resistance in parallel circuits

Alternative Method

Determine the current per branch directly: because the two transmitters are identical and in parallel across the

36\text{ V}

source, each receives the full supply voltage and carries half the total current (

I_{\text{branch}} = \frac{4\text{ A}}{2} = 2\text{ A}

). Then apply Ohm's law directly to a single branch:

R = \frac{V}{I_{\text{branch}}} = \frac{36\text{ V}}{2\text{ A}} = 18\,\Omega

.

Estimated Time:1m 0s

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