Tüm alıştırma soruları

Soru 1Soru →

A sales representative earns a base monthly salary of $2,400. They also earn a commission based on their total monthly sales volume. The commission structure is as follows: -$ 4\% $on the first$ 15,000 of sales
- $6\%$ on the next $25,000 of sales -$ 8.5\% $on any sales exceeding$ 40,000

In addition, if their total monthly sales exceed $50,000, they receive a one-time performance bonus of$ 750. Last month, the representative had a total sales volume of $54,200. What was the representative's total gross income for the month?

Cevabı ve açıklamayı göster

Cevap: 6457

Cevap

6457

The correct gross income is found by calculating the commission for each tier separately (

600 for the first tier,

1,500 for the second tier, and

1,207 for the third tier), summing them to get a total commission of

3,307, and then adding the base salary of

2,400 and the

750 performance bonus (awarded since sales exceeded

50,000) for a final total of

6,457.

Adım Adım Çözüm

1

Calculate the commission for the first tier (

0 to

15,000).

15,000 \times 0.04 =

600

The representative earns a 4% commission on the first $15,000 of sales.

2

Calculate the commission for the second tier (the next $25,000).

25,000 \times 0.06 =

1,500

The 6% rate applies to the next

25,000 of sales (covering sales from

15,000 to $40,000).

3

Calculate the commission for the third tier (sales exceeding $40,000).

54,200 -

40,000 =

14,200.

14,200 \times 0.085 = $1,207

The 8.5% rate applies to any sales exceeding the $40,000 threshold.

4

Sum the total commission.

600 +

1,500 +

1,207 =

3,307

Adding the amounts from all three tiers gives the total commission earned.

5

Calculate the total gross income by adding the base salary, total commission, and the performance bonus.

2,400 +

3,307 +

750 =

6,457

Total sales (

54,200) exceeded the

50,000 threshold, so the $750 bonus is awarded. Gross income includes base pay, total commission, and the bonus.

Anahtar Kavram

Calculating tiered commissions, applying percentages to multiple thresholds, and combining various income streams.

Soru 2Soru →

A transport aircraft flies at a constant cruising speed of $360\text{ miles per hour}$ . If it maintains this speed, what is the total distance it travels in $40\text{ minutes}$ , in miles?

Cevabı ve açıklamayı göster

Cevap: 240

Cevap

240

To find the distance, the time must first be converted to match the 'hours' unit in the speed rate. Forty minutes is equal to two-thirds of an hour. Multiplying the rate of

360\text{ miles per hour}

by

\frac{2}{3}\text{ of an hour}

yields a total distance of

240\text{ miles}

.

Adım Adım Çözüm

1

Convert the travel time from minutes to hours.

\frac{2}{3}\text{ hours}

The speed is given in miles per hour, so the time must be converted to hours to ensure the units cancel out correctly during multiplication.

2

Calculate the distance using the formula

Distance = Rate \times Time

.

240\text{ miles}

Multiplying the constant rate of

360\text{ mph}

by the travel time of

\frac{2}{3}\text{ hours}

yields the total distance traveled.

Anahtar Kavram

Calculating distance using a constant rate and performing a basic time unit conversion.

Alternatif Yöntem

You can also find the distance traveled per minute by dividing

360\text{ miles}

by

60\text{ minutes}

, which equals

6\text{ miles per minute}

. Then, multiply

6\text{ miles per minute}

by

40\text{ minutes}

to get

240\text{ miles}

.

Tahmini Süre:45s

Soru 3Soru →

Find the greatest integer value of $x$ that makes the following inequality true:

\frac{2}{3}(6x - 9) - 4(2x + 1) > \frac{1}{4}(8x - 20) - 3x

Cevabı ve açıklamayı göster

Cevap: -2

Cevap

The greatest integer value that satisfies the inequality is -2.

Expanding both sides yields

-4x - 10 > -x - 5

. Isolating

x

on one side gives

-3x > 5

. Dividing by -3 requires flipping the inequality symbol, resulting in

x < -\frac{5}{3}

(or

x < -1.67

). The greatest integer strictly less than -1.67 is -2.

Adım Adım Çözüm

1

Distribute the constants and fractions into the parentheses on both sides.

4x - 6 - 8x - 4 > 2x - 5 - 3x

Applying the distributive property removes the parentheses so like terms can be combined.

2

Combine like terms on each side of the inequality.

-4x - 10 > -x - 5

Simplifying both expressions makes it easier to isolate the variable.

3

Add

x

to both sides and add

10

to both sides to separate the variable terms from the constant terms.

-3x > 5

This isolates the

x

term on one side of the inequality.

4

Divide both sides by -3 and flip the inequality sign.

x < -\frac{5}{3}

When multiplying or dividing an inequality by a negative number, the direction of the inequality sign must be reversed.

5

Identify the greatest integer less than

-\frac{5}{3}

.

Since

-\frac{5}{3} \approx -1.67

, the integers strictly less than this are

-2, -3, -4, \dots

The greatest of these is

-2

.

The question specifically asks for the greatest integer value that makes the inequality true.

Anahtar Kavram

Solving complex linear inequalities involves applying the distributive property, combining like terms, and reversing the inequality symbol when dividing or multiplying by a negative number.

Soru 4Soru →

A mechanical winch uses a gear system where the driving gear and the driven gear have a revolution ratio of $4:7$ . If the driving gear completes $124$ revolutions during a lifting operation, how many revolutions does the driven gear complete?

Cevabı ve açıklamayı göster

Cevap: 217

Cevap

217

The correct answer is found by setting up a direct proportion based on the 4:7 ratio. Since the driving gear's 4 parts scale up to 124 actual revolutions, the scale factor is 31 (124 ÷ 4). Multiplying the driven gear's 7 parts by this same scale factor yields 217 revolutions.

Adım Adım Çözüm

1

Identify the known ratio

Driving : Driven = 4 : 7

This establishes the proportional relationship between the two gears.

2

Set up a proportion using the known quantity

4 / 7 = 124 / x

We know the driving gear completes 124 revolutions, which corresponds to the '4' in the ratio.

3

Find the scale factor

124 ÷ 4 = 31

This tells us how many times greater the actual operation is compared to the base ratio.

4

Calculate the unknown quantity

7 × 31 = 217

Applying the same scale factor to the driven gear maintains the proportional relationship.

Anahtar Kavram

Solving for an unknown part in a part-to-part relationship using scale factors.

Soru 5Soru →

A bakery owner purchases a commercial oven for $\$2,400$ . She pays $\$250$ for freight shipping and $\$150$ for professional installation. If she later sells the oven for a $15\%$ loss on her total initial investment, what is the selling price in dollars?

Cevabı ve açıklamayı göster

Cevap: 2380

Cevap

2380

The correct answer is found by first determining the total investment (

\$2,400 + \$250 + \$150 = \$2,800

), then finding the

15\%

loss (

0.15 \times \$2,800 = \$420

), and finally subtracting that loss from the total investment to get the selling price (

\$2,800 - \$420 = \$2,380

).

Adım Adım Çözüm

1

Calculate the total initial investment.

\$2,400 + \$250 + \$150 = \$2,800

All overhead costs must be added to the purchase price to find the true total cost.

2

Calculate the dollar amount of the

15\%

loss.

0.15 \times \$2,800 = \$420

The loss is based on the total initial investment, not just the purchase price.

3

Determine the final selling price.

\$2,800 - \$420 = \$2,380

Subtracting the loss amount from the total investment gives the selling price.

Anahtar Kavram

Calculating total cost including overhead, and applying a percentage loss to find the final selling price.

Alternatif Yöntem

Instead of calculating the loss and subtracting it, you can multiply the total investment by

85\%

(since

100\% - 15\% = 85\%

).

0.85 \times \$2,800 = \$2,380

.

Tahmini Süre:1m 0s

Soru 6Soru →

A Navy maintenance crew is applying a new non-slip coating to a ship's deck. A single standard drum of the coating covers exactly $12 \frac{3}{4}$ square yards of deck surface. If the crew needs to coat a helicopter landing pad that requires exactly $5 \frac{1}{3}$ times the amount of coating contained in a single drum, what is the total area of the helicopter landing pad in square yards?

Cevabı ve açıklamayı göster

Cevap: 68

Cevap

68

To find the total area, you must multiply the area covered by one drum (

12 \frac{3}{4}

square yards) by the relative size of the landing pad (

5 \frac{1}{3}

). Converting to improper fractions gives

\frac{51}{4} \times \frac{16}{3}

. Cross-canceling the terms yields

17 \times 4 = 68

square yards.

Adım Adım Çözüm

1

Convert the mixed numbers

12 \frac{3}{4}

and

5 \frac{1}{3}

to improper fractions.

12 \frac{3}{4} = \frac{12 \times 4 + 3}{4} = \frac{51}{4}

and

5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{16}{3}

.

Multiplication of mixed numbers requires converting them to improper fractions first.

2

Multiply the two improper fractions to find the total area.

\frac{51}{4} \times \frac{16}{3}

The total area is the area covered by one drum multiplied by the number of drum-equivalents required.

3

Simplify and compute the final product.

\frac{51 \times 16}{4 \times 3} = \left(\frac{51}{3}\right) \times \left(\frac{16}{4}\right) = 17 \times 4 = 68

.

Simplifying the fractions by cross-canceling before multiplying makes the calculation easier and provides the final area.

Anahtar Kavram

Multiplying mixed numbers by converting them to improper fractions in an applied context.

Soru 7Soru →

A hospital administrator places $\$12,000$ into a fixed-term savings certificate that earns an annual simple interest rate of $4.2\%$ . If no other deposits or withdrawals are made, what is the total accumulated balance, in dollars, of the certificate after exactly 30 months?

Cevabı ve açıklamayı göster

Cevap: 13260

Cevap

The total accumulated balance is 13260.

The correct answer is found by first converting the 30-month time period into 2.5 years (

30 \div 12 = 2.5

), and the

4.2\%

interest rate into the decimal

0.042

(

4.2 \div 100 = 0.042

). Using the simple interest formula

I = P \times R \times T

, the interest earned is

\$12,000 \times 0.042 \times 2.5 = \$1,260

. Adding this interest to the original principal of

\$12,000

gives a total accumulated balance of

\$13,260

.

Adım Adım Çözüm

1

Convert the interest rate to a decimal and the time period to years.

R = 4.2\% = 0.042

, and

T = 30 \text{ months} \div 12 \text{ months/year} = 2.5 \text{ years}

.

The standard simple interest formula requires the interest rate as a decimal and the time expressed in years.

2

Calculate the total interest earned using the simple interest formula

I = P \times R \times T

.

I = 12000 \times 0.042 \times 2.5 = 1260

This determines how much additional money the certificate earns over the 30-month period.

3

Calculate the total accumulated balance by adding the interest earned to the original principal.

Total Balance =

12000 + 1260 = 13260

The question asks for the total accumulated balance, which includes both the initial deposit (principal) and the earned interest.

Anahtar Kavram

Calculating simple interest over a fractional year and determining the total accumulated amount.

Soru 8Soru →

A technician is assembling a low-pass filter circuit and connects two inductors in series with values of $45\text{ mH}$ and $80\text{ mH}$ . Assuming there is no mutual magnetic coupling between the coils, what is the total equivalent inductance of the circuit in millihenries ( $\text{mH}$ )?

Cevabı ve açıklamayı göster

Cevap: 125

Cevap

125

When inductors are connected in series without mutual inductance, their magnetic opposition to current changes accumulates directly, meaning the total inductance is simply the sum of the individual inductances (

45\text{ mH} + 80\text{ mH} = 125\text{ mH}

).

Adım Adım Çözüm

1

Recall the formula for combining series inductances without mutual magnetic coupling.

L_{\text{total}} = L_1 + L_2

Like series resistors, total series inductance is the direct sum of individual inductances when there is no magnetic interaction.

2

Add the two individual inductance values together.

45\text{ mH} + 80\text{ mH} = 125\text{ mH}

Direct addition provides the equivalent total inductance in millihenries.

Anahtar Kavram

Inductors in series combine by direct addition, identical to the rule for resistors in series.

Tahmini Süre:45s

Soru 9Soru →

A circular swimming pool has a circumference of $20\pi$ feet. What is the diameter of the pool in feet?

Cevabı ve açıklamayı göster

Cevap: 20

Cevap

20

The formula for the circumference of a circle is

C = \pi d

. By substituting the given circumference of

20\pi

into the formula, we get

20\pi = \pi d

. Dividing both sides by

\pi

yields a diameter of

20

feet.

Adım Adım Çözüm

1

Identify the formula for the circumference of a circle.

C = \pi d

, where

C

is circumference and

d

is diameter.

This formula directly relates the given circumference to the unknown diameter.

2

Substitute the given value into the formula.

20\pi = \pi d

The problem states the circumference is

20\pi

feet.

3

Solve for the diameter (

d

).

d = 20

Dividing both sides of the equation by

\pi

isolates the value of

d

.

Anahtar Kavram

Circumference of a circle

Tahmini Süre:45s

Soru 10Soru →

A rectangular swimming pool measures $40$ feet in length and $30$ feet in width. A concrete deck of uniform width is built around the entire outer edge of the pool. If the area of the concrete deck alone is $296$ square feet, what is the width of the deck, in feet?

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

2

The correct width is found by setting up an equation for the total area. The deck adds its width to both sides of the pool's length and width, making the overall dimensions

40 + 2w

and

30 + 2w

. The area of the deck alone is the total area minus the pool's area. Solving the algebraic equation

(40 + 2w)(30 + 2w) - 1200 = 296

yields a positive root of

w = 2

.

Adım Adım Çözüm

1

Calculate the area of the pool.

40 \times 30 = 1200

square feet.

You need the baseline area of the inner rectangle before the deck is added.

2

Write algebraic expressions for the outer dimensions of the pool and deck combined.

Length

= 40 + 2w

, Width

= 30 + 2w

.

The deck has a uniform width

w

, which adds to both the top/bottom and left/right sides of the pool.

3

Formulate an equation for the area of the deck.

(40 + 2w)(30 + 2w) - 1200 = 296

.

The area of the deck alone is equal to the total area (pool plus deck) minus the area of the pool.

4

Expand the binomials and simplify into a standard quadratic equation.

1200 + 140w + 4w^2 - 1200 = 296 \implies 4w^2 + 140w - 296 = 0

.

Standard quadratic form (

ax^2 + bx + c = 0

) is required to solve for the unknown variable

w

.

5

Solve the quadratic equation for

w

.

Divide by

4

to get

w^2 + 35w - 74 = 0

. Factoring yields

(w + 37)(w - 2) = 0

, so

w = 2

.

Finding the positive root gives the actual physical width of the concrete deck.

Anahtar Kavram

Calculating the area of composite rectangular figures and solving quadratic equations derived from expanding geometric boundaries.

Soru 11Soru →

An armory has a total of $50$ training rifles on a rack. Exactly $15$ of these rifles are equipped with laser sights. If a recruit is randomly issued one of these training rifles, what is the probability, expressed as a decimal, that they receive a rifle with a laser sight?

Cevabı ve açıklamayı göster

Cevap: 0.3

Cevap

0.3

The probability of a single event is calculated by dividing the number of specific desired outcomes by the total number of possible outcomes. In this scenario, there are 15 rifles with laser sights out of a total of 50 rifles in the armory. Therefore, the probability is 15/50. To express this as a decimal, you can simplify the fraction by dividing the numerator and denominator by 5 to get 3/10, which easily converts to 0.3.

Adım Adım Çözüm

1

Determine the total number of possible outcomes.

50

This is the total number of training rifles available on the rack.

2

Determine the number of favorable outcomes.

15

This is the number of training rifles equipped with laser sights, which represents the target event.

3

Calculate the probability by dividing the favorable outcomes by the total possible outcomes.

15 / 50 = 3 / 10 = 0.3

The basic formula for single event probability is the ratio of target outcomes to total outcomes.

Anahtar Kavram

Single Event Probability

Soru 12Soru →

An outdoor construction project requires 15 pieces of lumber, each having nominal dimensions of $2\text{ inches}$ thick, $8\text{ inches}$ wide, and $12\text{ feet}$ long. What is the total number of board feet in these 15 pieces of lumber?

Cevabı ve açıklamayı göster

Cevap: 240

Cevap

240 board feet

The total board footage is calculated with the formula

\text{Board Feet} = \frac{\text{Thickness (in)} \times \text{Width (in)} \times \text{Length (ft)}}{12} \times \text{Quantity}

. Substituting the given project dimensions yields

\frac{2 \times 8 \times 12}{12} \times 15 = 16 \times 15 = 240\text{ board feet}

.

Adım Adım Çözüm

1

Calculate the board feet for a single board using nominal thickness and width in inches and length in feet

16 board feet per piece

One board foot is defined as the volume of a board 1 inch thick, 12 inches wide, and 1 foot long. Applying the formula

\text{BF} = \frac{\text{Thickness (in)} \times \text{Width (in)} \times \text{Length (ft)}}{12}

gives

\frac{2 \times 8 \times 12}{12} = 16\text{ BF}

.

2

Multiply the board footage per board by the total number of boards required

240 board feet

The total volume for 15 identical pieces is determined by multiplying:

16 \times 15 = 240\text{ BF}

.

Anahtar Kavram

Calculating board footage for multiple pieces of lumber using standard nominal dimension formulas

Alternatif Yöntem

Convert length to inches, compute total cubic inches for all 15 boards, and divide by 144 cubic inches per board foot:

\frac{2\text{ in} \times 8\text{ in} \times 144\text{ in} \times 15}{144} = 240\text{ board feet}

.

Tahmini Süre:1m 0s

Soru 13Soru →

A woodworker is purchasing solid oak lumber to construct a tabletop. The bill of materials calls for $5$ boards, each measuring a nominal $2\text{ inches}$ thick, $9\text{ inches}$ wide, and $8\text{ feet}$ long. What is the total volume of lumber needed, expressed in board feet?

Cevabı ve açıklamayı göster

Cevap: 60

Cevap

The total volume of lumber required is

60\text{ board feet}

.

One board foot is defined as

1\text{ in} \times 12\text{ in} \times 1\text{ ft} = 144\text{ in}^3

. Using the standard formula

\text{Board Feet} = \frac{\text{Thickness (in)} \times \text{Width (in)} \times \text{Length (ft)}}{12}

, each board contains

\frac{2 \times 9 \times 8}{12} = 12\text{ board feet}

. Multiplying by

5

pieces yields a total of

60\text{ board feet}

.

Adım Adım Çözüm

1

Calculate the board feet contained in one board using nominal thickness and width in inches and length in feet.

\text{Board Feet per piece} = \frac{2\text{ in} \times 9\text{ in} \times 8\text{ ft}}{12} = \frac{144}{12} = 12\text{ board feet}

One board foot represents the volumetric equivalent of a board

1\text{ inch}

thick,

12\text{ inches}

wide, and

1\text{ foot}

long (or

144\text{ cubic inches}

). Dividing by

12

converts inch-inch-foot dimensions directly to board feet.

2

Multiply the volume per board by the total quantity of boards.

\text{Total Board Feet} = 12\text{ board feet} \times 5 = 60\text{ board feet}

The project requires

5

identical boards of specified dimensions.

Anahtar Kavram

Calculation of board footage for dimensional lumber using nominal dimensions and the standard volume formula.

Tahmini Süre:1m 0s

Soru 14Soru →

A hand-cranked emergency siren uses a compound gear train to amplify the rotational speed of the crank. The crank is directly attached to Gear A, which has $50$ teeth. Gear A meshes with Gear B, which has $10$ teeth. Gear B shares a solid shaft with Gear C, which has $40$ teeth. Finally, Gear C meshes with Gear D, which has $10$ teeth and is directly attached to the siren's rotor. If the operator turns the crank at a constant speed of $30\text{ rpm}$ , what is the rotational speed of the siren's rotor?

Cevabı ve açıklamayı göster

Cevap: 600

Cevap

600 rpm

The system consists of two gear pairs that both increase speed. The first pair (

50

teeth driving

10

teeth) increases the speed by a factor of

5

. The second pair (

40

teeth driving

10

teeth) increases the speed by a factor of

4

. The total speed multiplier is

5 \times 4 = 20

. Multiplying the input speed of

30\text{ rpm}

by

20

yields the final output speed of

600\text{ rpm}

.

Adım Adım Çözüm

1

Determine the speed multiplier for the first gear pair.

Ratio =

50 / 10 = 5

Gear A drives Gear B. A larger gear driving a smaller gear increases rotational speed proportionally to their tooth count.

2

Determine the speed multiplier for the second gear pair.

Ratio =

40 / 10 = 4

Gear C drives Gear D. Both pairs are independent in tooth count, but Gear C rotates at the same speed as Gear B because they share a shaft.

3

Calculate the total mechanical advantage for speed.

Total multiplier =

5 \times 4 = 20

In a compound gear train, the total speed ratio is the product of the individual gear pair ratios.

4

Calculate the final output speed.

30 \times 20 = 600\text{ rpm}

Multiply the input speed by the total speed multiplier to find the output speed.

Anahtar Kavram

Compound Gear Trains and Speed Ratios

Soru 15Soru →

A family rents an RV for a cross-country road trip. The RV has a fuel tank capacity of $55$ gallons and averages $12$ miles per gallon. If the driver begins with a completely full tank and plans to leave exactly $10$ gallons of fuel in the tank as a safety reserve, what is the maximum number of miles the RV can travel before needing to refuel?

Cevabı ve açıklamayı göster

Cevap: 540

Cevap

540

The correct distance is found by first determining the amount of fuel that can actually be used for the trip. Out of the

55

gallons,

10

must remain in the tank, leaving

45

gallons available. At a rate of

12

miles for every gallon, the RV can travel

45

multiplied by

12

, which equals

540

miles.

Adım Adım Çözüm

1

Determine the usable fuel by subtracting the reserve from the total capacity.

55 - 10 = 45

gallons

The driver will not use the bottom 10 gallons of the tank, so this fuel cannot contribute to the travel distance.

2

Calculate the maximum distance using the usable fuel and the fuel efficiency rate.

45 \times 12 = 540

miles

Distance equals the amount of fuel used multiplied by the miles per gallon.

Anahtar Kavram

Fuel Efficiency and Range calculations involving partial tank usage and safety reserves.

Alternatif Yöntem

You could also calculate the total theoretical distance the RV could travel on a full tank (

55 \times 12 = 660

miles) and subtract the distance that would be covered by the

10

-gallon reserve (

10 \times 12 = 120

miles).

660 - 120 = 540

miles.

Tahmini Süre:1m 0s

Soru 16Soru →

A stained glass artist cuts a piece of glass into the shape of a right triangle. The two perpendicular legs of the triangle measure $30$ centimeters and $40$ centimeters. What is the total perimeter of this glass triangle in centimeters?

Cevabı ve açıklamayı göster

Cevap: 120

Cevap

120

The correct answer is found by first determining the length of the hypotenuse using the Pythagorean theorem. Since the legs are

30

and

40

, the hypotenuse is

\sqrt{30^2 + 40^2} = \sqrt{2500} = 50

. The perimeter is then calculated by adding the lengths of all three sides:

30 + 40 + 50 = 120

.

Adım Adım Çözüm

1

Use the Pythagorean theorem to find the length of the missing hypotenuse.

c = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50

centimeters.

The perimeter requires all three side lengths, but only the two legs are provided.

2

Calculate the total perimeter of the right triangle.

Perimeter =

30 + 40 + 50 = 120

centimeters.

The perimeter is the total distance around the outside of the shape, found by summing all side lengths.

Anahtar Kavram

Applying the Pythagorean theorem to find a missing side length, then using all three side lengths to calculate the perimeter of a right triangle.

Soru 17Soru →

A cabinetmaker uses the standard pennyweight formula, $\text{Length} = \frac{d}{4} + 0.5\text{ inches}$ , to determine fastener dimensions for sizes up to $10\text{d}$ , where $d$ represents the penny size number. What is the total length, in inches, of a $4\text{d}$ nail?

Cevabı ve açıklamayı göster

Cevap: 1.5

Cevap

The total length of a

4\text{d}

nail is

1.5\text{ inches}

.

Using the standard carpentry formula for nails between

2\text{d}

and

10\text{d}

(

\text{Length} = \frac{d}{4} + 0.5\text{ inches}

), substituting

d = 4

yields

\frac{4}{4} + 0.5 = 1 + 0.5 = 1.5\text{ inches}

.

Adım Adım Çözüm

1

Identify the variable

d

representing the penny rating.

d = 4

The question specifies a

4\text{d}

nail.

2

Substitute

d = 4

into the nail length formula

\text{Length} = \frac{d}{4} + 0.5

.

\text{Length} = \frac{4}{4} + 0.5

The standard empirical formula relates penny size to physical inch length.

3

Perform arithmetic evaluation to find the final length.

1.5\text{ inches}

Dividing

4

by

4

gives

1

, and adding

0.5

yields

1.5

.

Anahtar Kavram

Nail Pennyweight (d) Sizing System

Tahmini Süre:45s

Soru 18Soru →

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?

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Cevap: 21

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Soru 19Soru →

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?

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Cevap: 90

Cevap

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

).

Adım Adım Çözüm

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.

Anahtar Kavram

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

Tahmini Süre:45s

Soru 20Soru →

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 ( $\text{A}$ )?

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Cevap: 8

Cevap

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}

.

Adım Adım Çözüm

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.

Anahtar Kavram

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.

Tahmini Süre:1m 0s

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