All practice questions

Question 13621Question →

What is the sum of the $y$ -values of the solution pairs that satisfy the simultaneous equations $y - x = 2$ and $y = x^2 - 3x + 5$ ?

4

6

8

15

Show answer & explanation

Answer: $8$

Answer

The sum of the

y

-values is 8.

Rearranging the linear equation gives

y = x + 2

. Equating this to the quadratic expression gives

x + 2 = x^2 - 3x + 5

, which simplifies to

x^2 - 4x + 3 = 0

. Solving for

x

yields

x = 1

and

x = 3

. Substituting these into

y = x + 2

gives

y = 3

and

y = 5

. The sum of these

y

-values is

3 + 5 = 8

.

Step-by-Step Solution

1

Express

y

in terms of

x

from the linear equation.

y = x + 2

Isolating

y

facilitates substitution into the quadratic equation.

2

Substitute

y = x + 2

into the quadratic equation and rearrange into standard form.

x + 2 = x^2 - 3x + 5 \implies x^2 - 4x + 3 = 0

Setting the two expressions for

y

equal to each other forms a single quadratic equation in

x

.

3

Solve the quadratic equation for

x

.

(x - 1)(x - 3) = 0 \implies x_1 = 1, x_2 = 3

Factoring gives the

x

-coordinates of the intersection points.

4

Calculate the corresponding

y

-values using

y = x + 2

.

y_1 = 1 + 2 = 3

and

y_2 = 3 + 2 = 5

Each

x

-value must be substituted into the linear equation to find its paired

y

-value.

5

Find the sum of the

y

-values.

y_1 + y_2 = 3 + 5 = 8

The question asks for the sum of the

y

-coordinates.

Key Concept

Simultaneous Linear and Quadratic Equations

Alternative Method

Using Vieta's formulas: once the quadratic equation for

x

is found as

x^2 - 4x + 3 = 0

, we know

x_1 + x_2 = 4

. Since

y_1 = x_1 + 2

and

y_2 = x_2 + 2

, the sum of the

y

-values is

y_1 + y_2 = (x_1 + 2) + (x_2 + 2) = (x_1 + x_2) + 4 = 4 + 4 = 8

.

Estimated Time:1m 30s

Question 13622Question →

A cocoa exporter in Ghana agrees to sell a shipment of raw cocoa beans to an overseas purchaser, but has serious concerns regarding both the buyer's creditworthiness and potential foreign exchange transfer restrictions in the buyer's country. To guarantee payment by having a bank in the exporter's own country add its independent undertaking to pay, which payment instrument should the exporter request?

Confirmed irrevocable letter of credit

Unconfirmed irrevocable letter of credit

Documentary collection under documents against acceptance

Bill of lading endorsed in blank

Show answer & explanation

Answer: Confirmed irrevocable letter of credit

Answer

The confirmed irrevocable letter of credit is the required payment instrument because it provides an additional guarantee from a bank in the seller's home country.

A confirmed irrevocable letter of credit involves an explicit guarantee from both the buyer's issuing bank and a confirming bank in the seller's home country. This protects the seller against buyer credit default as well as sovereign and foreign exchange transfer risks in the buyer's jurisdiction.

Step-by-Step Solution

1

Identify the risk exposure in the scenario

The exporter faces two distinct risks: buyer default risk and foreign country/political transfer risk.

Choosing the appropriate payment mechanism requires matching the instrument's security level against the specific commercial and sovereign risks identified.

2

Evaluate the protection level of foreign trade payment instruments

An unconfirmed credit protects only against buyer default via the foreign bank. A confirmed credit brings in a local confirming bank to cover foreign country/bank risks as well.

Confirmation adds an irrevocable commitment from a bank located in the exporter's jurisdiction.

3

Distinguish between payment instruments and shipping documents

Instruments like the Bill of Lading serve as transport/title documents rather than financial guarantees.

Titles to goods safeguard possession but do not constitute a bank guarantee of cash payment.

Key Concept

Confirmed Irrevocable Letter of Credit as a Risk Mitigation Tool in International Trade

Question 13623Question →

Which regulatory agency in Nigeria is directly responsible for registering, controlling, and certifying the safety and quality of processed food items, cosmetics, and pharmaceutical drugs before public sale?

National Agency for Food and Drug Administration and Control (NAFDAC)

Standards Organisation of Nigeria (SON)

Federal Competition and Consumer Protection Commission (FCCPC)

Nigerian Communications Commission (NCC)

Show answer & explanation

Answer: National Agency for Food and Drug Administration and Control (NAFDAC)

Answer

National Agency for Food and Drug Administration and Control (NAFDAC)

The National Agency for Food and Drug Administration and Control (NAFDAC) is specifically empowered by Nigerian statutory law to formulate standards, conduct tests, and regulate the manufacturing, importation, exportation, sale, and distribution of food, drugs, cosmetics, medical devices, and packaged water.

Step-by-Step Solution

1

Identify the target product categories in the stem.

The products are processed food items, cosmetics, and pharmaceutical drugs.

Different regulatory bodies in Nigeria hold distinct statutory mandates based on product classification.

2

Match statutory mandates of Nigerian regulatory agencies to the specific product categories.

NAFDAC holds exclusive statutory jurisdiction over food, drugs, cosmetics, chemicals, and medical devices.

This distinguishes NAFDAC from general industrial standards bodies like SON and general consumer protection agencies like FCCPC.

Key Concept

Statutory duties of NAFDAC in consumer protection

Estimated Time:45s

Question 13624Question →

A metal container with a volume of $200\text{ cm}^3$ at $30^\circ\text{C}$ is completely filled with an oil. The linear expansivity of the metal container is $2.0 \times 10^{-5}\text{ K}^{-1}$ and the real cubic expansivity of the oil is $6.0 \times 10^{-4}\text{ K}^{-1}$ . If the temperature of the system is raised to $80^\circ\text{C}$ , what volume of oil (in $\text{cm}^3$ ) will overflow?

Show answer & explanation

Answer: 5.4

Answer

The volume of oil that overflows is

5.4\text{ cm}^3

.

When a container filled to the brim with liquid is heated, both the liquid and container expand. The apparent cubic expansivity of the liquid is the difference between its real cubic expansivity and the volumetric expansivity of the vessel (3 * alpha). Subtracting 0.6 * 10^-4 K^-1 from 6.0 * 10^-4 K^-1 gives an apparent cubic expansivity of 5.4 * 10^-4 K^-1. Multiplying this by the initial volume of 200 cm^3 and the temperature rise of 50 K gives an overflow volume of 5.4 cm^3.

Step-by-Step Solution

1

Determine the temperature increase (\Delta T)

\Delta T = 80^\circ\text{C} - 30^\circ\text{C} = 50\text{ K}

Thermal expansion depends directly on the change in temperature.

2

Calculate the cubic expansivity of the container (\gamma_v)

\gamma_v = 3\alpha = 3 \times (2.0 \times 10^{-5}\text{ K}^{-1}) = 6.0 \times 10^{-5}\text{ K}^{-1} = 0.6 \times 10^{-4}\text{ K}^{-1}

The volumetric expansivity of an isotropic solid container is three times its linear expansivity.

3

Calculate the apparent cubic expansivity of the liquid (\gamma_a)

\gamma_a = \gamma_r - \gamma_v = 6.0 \times 10^{-4}\text{ K}^{-1} - 0.6 \times 10^{-4}\text{ K}^{-1} = 5.4 \times 10^{-4}\text{ K}^{-1}

Apparent expansivity accounts for the simultaneous expansion of the vessel containing the liquid.

4

Calculate the volume of liquid that overflows (\Delta V)

\Delta V = V_0 \times \gamma_a \times \Delta T = 200\text{ cm}^3 \times 5.4 \times 10^{-4}\text{ K}^{-1} \times 50\text{ K} = 5.4\text{ cm}^3

The overflow volume equals the apparent expansion of the liquid volume.

Key Concept

Real and Apparent Expansion of Liquids

Question 13625Question →

Two parallel resistors of values $6.0\text{ }\Omega$ and $12.0\text{ }\Omega$ are connected to a DC power source having an open-circuit voltage of $18.0\text{ V}$ and an internal resistance of $1.0\text{ }\Omega$ . What is the terminal potential difference supplied to the circuit?

14.4\text{ V}

18.0\text{ V}

3.6\text{ V}

17.0\text{ V}

Show answer & explanation

Answer: $14.4\text{ V}$

Answer

The terminal potential difference supplied to the circuit is

14.4\text{ V}

.

The option stating

14.4\text{ V}

is correct because the parallel combination of

6.0\text{ }\Omega

and

12.0\text{ }\Omega

gives an external equivalent resistance of

4.0\text{ }\Omega

. With an internal resistance of

1.0\text{ }\Omega

, the total circuit resistance is

5.0\text{ }\Omega

, resulting in a total current of

3.6\text{ A}

. The terminal voltage across the load is

3.6\text{ A} \times 4.0\text{ }\Omega = 14.4\text{ V}

.

Step-by-Step Solution

1

Calculate the equivalent resistance (

R_p

) of the parallel resistors.

R_p = \frac{6.0 \times 12.0}{6.0 + 12.0} = \frac{72.0}{18.0} = 4.0\text{ }\Omega

Resistors connected in parallel combine according to

\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}

.

2

Determine the total resistance (

R_{\text{total}}

) of the entire circuit, including internal resistance.

R_{\text{total}} = R_p + r = 4.0\text{ }\Omega + 1.0\text{ }\Omega = 5.0\text{ }\Omega

The internal resistance of the power source is in series with the external parallel load.

3

Calculate the total current (

I

) drawn from the power source.

I = \frac{E}{R_{\text{total}}} = \frac{18.0\text{ V}}{5.0\text{ }\Omega} = 3.6\text{ A}

Ohm's law for a complete circuit relates e.m.f., total resistance, and total current.

4

Calculate the terminal potential difference (

V

).

V = I \cdot R_p = 3.6\text{ A} \times 4.0\text{ }\Omega = 14.4\text{ V}

(or

V = E - I r = 18.0\text{ V} - 3.6\text{ V} = 14.4\text{ V}

)

Terminal voltage is the voltage across the external load or the e.m.f. minus the lost volts inside the cell.

Key Concept

Terminal Potential Difference and Internal Resistance

Question 13626Question →

A galvanometer with an internal resistance of $100\ \Omega$ gives a full-scale deflection for a current of $1.0\text{ mA}$ . It is converted into an ammeter capable of measuring up to $1.0\text{ A}$ by connecting a suitable shunt resistor across it. This converted ammeter is then connected in series with a load resistor of $4.40\ \Omega$ and a cell of electromotive force $3.0\text{ V}$ having an internal resistance of $0.50\ \Omega$ . What is the current reading indicated by the ammeter?

0.60\text{ A}

0.67\text{ A}

0.68\text{ A}

0.03\text{ A}

Show answer & explanation

Answer: $0.60\text{ A}$

Answer

The ammeter will indicate a current of

0.60\text{ A}

.

To find the ammeter reading, first calculate the effective ammeter resistance

R_A = \frac{I_g G}{I} = \frac{0.001 \times 100}{1.0} = 0.10\ \Omega

. The total circuit resistance is

R_{\text{total}} = R_A + R + r = 0.10 + 4.40 + 0.50 = 5.00\ \Omega

. Applying Ohm's law

I = \frac{E}{R_{\text{total}}} = \frac{3.0}{5.00} = 0.60\text{ A}

.

Step-by-Step Solution

1

Calculate the equivalent resistance of the converted ammeter (

R_A

).

R_A = \frac{I_g \times G}{I_{\text{max}}} = \frac{0.001\text{ A} \times 100\ \Omega}{1.0\text{ A}} = 0.10\ \Omega

The shunt resistor is connected in parallel with the galvanometer so that the potential difference across both components is equal.

2

Determine the total resistance (

R_{\text{total}}

) of the complete series circuit.

R_{\text{total}} = R_A + R + r = 0.10\ \Omega + 4.40\ \Omega + 0.50\ \Omega = 5.00\ \Omega

The ammeter, load resistor, and internal resistance of the cell are all connected in series.

3

Calculate the circuit current (

I

) using Ohm's law for a complete circuit.

I = \frac{E}{R_{\text{total}}} = \frac{3.0\text{ V}}{5.00\ \Omega} = 0.60\text{ A}

The total current flowing through the circuit is the electromotive force divided by the total resistance.

Key Concept

Galvanometer Conversion to Ammeter and Circuit Current Calculation

Estimated Time:2m 0s

Question 13627Question →

A merchant who holds an accepted 90-day credit instrument from a customer needs immediate liquidity to replenish inventory before the payment due date. The merchant approaches a money market institution to obtain cash immediately at a value lower than the face amount. Which money market operation is being demonstrated in this scenario?

Discounting a bill of exchange

Subscribing to a corporate debenture

Underwriting an equity share issue

Trading government development stocks

Show answer & explanation

Answer: Discounting a bill of exchange

Answer

Discounting a bill of exchange

Discounting a bill of exchange allows the holder of a short-term commercial bill to receive immediate cash from a financial institution (like a commercial bank or discount house) before its maturity date. The institution deducts a small fee (discounting rate) from the face value and collects the full amount from the debtor upon maturity.

Step-by-Step Solution

1

Identify the nature of the transaction described in the scenario.

The scenario involves converting a short-term commercial credit debt (90-day maturity) into immediate liquid cash prior to maturity at a reduced (discounted) value.

The merchant holds a short-term trade instrument and requires funds before the maturity date.

2

Distinguish between money market and capital market instruments and operations.

Converting short-term bills into cash through financial intermediaries at a discount is the core operation known as discounting bills of exchange in the money market.

Options involving debentures, equity shares, and development stocks relate to long-term capital market securities.

Key Concept

Bill Discounting in the Money Market

Estimated Time:1m 0s

Question 13628Question →

The foreign trade transactions of a country for a specific fiscal year are presented below:

Item	Value ($ million)
Visible merchandise exports	620
Freight and insurance paid to foreign shipping lines	85
Visible merchandise imports	480
Banking and financial service fees received from abroad	110
Foreign direct investment inflows	150

Based on the statement above, what is the country's Balance of Trade position?

A surplus of

\$140\text{ million}

A surplus of

\$165\text{ million}

A surplus of

\$315\text{ million}

A deficit of

\$140\text{ million}

Show answer & explanation

Answer: A surplus of $\$140\text{ million}$

Answer

A surplus of

\$140\text{ million}

The Balance of Trade (BOT) is defined strictly as the difference between the monetary value of a nation's visible exports and visible imports over a given period. Subtracting visible merchandise imports (

\$480\text{ million}

) from visible merchandise exports (

\$620\text{ million}

) gives a favorable balance (surplus) of

\$140\text{ million}

. Freight charges, banking services, and investment inflows are excluded from BOT.

Step-by-Step Solution

1

Identify the relevant trade items required to calculate the Balance of Trade.

Visible merchandise exports =

\$620\text{ million}

; Visible merchandise imports =

\$480\text{ million}

. Invisible trade services and capital account movements are excluded.

The Balance of Trade (BOT) measures exclusively the net trade value of physical/visible goods.

2

Apply the Balance of Trade formula:

\text{Balance of Trade} = \text{Visible Exports} - \text{Visible Imports}

.

\text{BOT} = \$620\text{ million} - \$480\text{ million} = +\$140\text{ million}

.

Subtracting visible imports from visible exports yields a positive balance (surplus) of

\$140\text{ million}

.

Key Concept

Balance of Trade vs Balance of Payments

Question 13629Question →

Three independent cement manufacturing companies in Nigeria enter into a formal agreement to restrict market output quotas and fix minimum selling prices, while each enterprise maintains its separate legal identity and financial independence. What form of business combination does this agreement illustrate?

Cartel

Holding company

Vertical merger

Trust

Show answer & explanation

Answer: Cartel

Answer

The agreement illustrates a cartel.

A cartel is a horizontal combination of independent producers operating in the same industry who aggregate to control product supply and set uniform prices, while preserving their distinct ownership and legal autonomy.

Step-by-Step Solution

1

Analyze the operational relationship described in the scenario.

The firms are engaged in the same industry (cement manufacturing) and retain their separate legal identities and managerial autonomy.

Identifying ownership transfer and legal status determines whether the combination is an equity-based consolidation or a voluntary trade agreement.

2

Evaluate the contractual objectives of the alliance.

The primary objectives are restricting output quotas and enforcing uniform selling prices.

Contractual arrangements designed to eliminate price competition among independent producers in the same line of business define a cartel.

Key Concept

Cartels and Market Pool Agreements

Question 13630Question →

Despite the competitive pressure from large departmental stores, small-scale convenience shops located in residential neighborhoods continue to operate successfully. Which of the following represents a primary operational advantage that enables these small-scale producers and traders to survive?

Offering personal attention and maintaining flexible operating hours tailored to local customers

Spreading fixed overhead costs over a massive volume of output to lower unit costs

Eliminating worker boredom and monotony by implementing extensive labor specialization

Operating without paying any financial returns or rewards to the capital factor of production

Show answer & explanation

Answer: Offering personal attention and maintaining flexible operating hours tailored to local customers

Answer

Providing personal attention and maintaining flexible operating hours tailored to local customers.

Small-scale enterprises survive competition from large firms because their intimate size allows owners to maintain personal contact with customers, adapt quickly to individual requests, and operate flexible hours convenient for the local community.

Step-by-Step Solution

1

Analyze the operational characteristics of small-scale business enterprises.

Identified key advantages including low capital requirements, direct owner contact with customers, flexibility, and localized service.

Small firms compete primarily on non-price factors like convenience and personal relations rather than economies of scale.

2

Evaluate the choices against small-scale scale of production principles.

Personal attention and flexible working hours directly explain small business survival against large-scale firms.

Large firms suffer from standardized, impersonal operations, creating a market niche for small firms.

Key Concept

Survival factors of small-scale enterprises

Question 13631Question →

A water wave moving horizontally across the surface of a pond causes a floating cork to move vertically up and down. The cork completes one full oscillation every $0.50\text{ s}$ , and the horizontal distance between two consecutive wave crests is $1.2\text{ m}$ . What is the speed of propagation of the wave, and how is the wave classified?

2.4\text{ m s}^{-1}

, transverse mechanical wave

2.4\text{ m s}^{-1}

, longitudinal mechanical wave

0.60\text{ m s}^{-1}

, transverse mechanical wave

2.4\text{ m s}^{-1}

, transverse electromagnetic wave

Show answer & explanation

Answer: $2.4\text{ m s}^{-1}$ , transverse mechanical wave

Answer

2.4\text{ m s}^{-1}

, transverse mechanical wave

The frequency of oscillation is

f = \frac{1}{T} = \frac{1}{0.50\text{ s}} = 2.0\text{ Hz}

. Using the wave formula

v = f\lambda

, the propagation speed is

v = 2.0\text{ Hz} \times 1.2\text{ m} = 2.4\text{ m s}^{-1}

. Because the cork vibrates vertically while the wave propagates horizontally, the oscillations are perpendicular to the propagation direction, defining a transverse wave. Since water is required for propagation, it is a mechanical wave.

Step-by-Step Solution

1

Determine the frequency of the wave from the period.

The period

T = 0.50\text{ s}

, so frequency

f = \frac{1}{T} = \frac{1}{0.50} = 2.0\text{ Hz}

.

Frequency is the reciprocal of the time period of oscillation.

2

Calculate the wave speed using the wave equation.

v = f \lambda = 2.0\text{ Hz} \times 1.2\text{ m} = 2.4\text{ m s}^{-1}

.

Wave speed equals the product of frequency and wavelength.

3

Classify the wave based on particle motion and medium requirement.

Particle displacement is perpendicular to wave direction (transverse) and requires water as a medium (mechanical).

Perpendicular oscillation defines transverse waves, and medium dependence defines mechanical waves.

Key Concept

Wave speed calculation and wave classification based on vibration direction and medium requirements.

Question 13632Question →

The Nigeria Deposit Insurance Corporation (NDIC) is statutorily mandated to insure bank deposit liabilities and protect depositors in the event of bank failure in Nigeria.

True

False

Show answer & explanation

Answer: True

Answer

True

The statement is accurate because the Nigeria Deposit Insurance Corporation (NDIC) protects bank depositors against financial loss caused by bank failure and guarantees bank deposit liabilities up to statutory limits.

Step-by-Step Solution

1

Examine the regulatory body mentioned in the statement and its key statutory purpose.

The entity is the Nigeria Deposit Insurance Corporation (NDIC).

Understanding institutional roles is necessary to evaluate jurisdictional accuracy.

2

Compare the function described (protecting depositors and insuring bank liabilities) with the mandate of NDIC.

NDIC directly acts as a bank deposit insurer and supervisor, providing a financial safety net to depositors.

Securities regulation belongs to the SEC, whereas deposit protection belongs to the NDIC.

Key Concept

Primary Mandate of the Nigeria Deposit Insurance Corporation (NDIC)

Question 13633Question →

Match each Rochdale cooperative principle on the left with its correct operational definition on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Voluntary and Open Membership pairs with non-discriminatory entry/exit; Democratic Member Control pairs with equal voting power regardless of shares; Limited Interest on Capital pairs with capping financial returns on share capital; Patronage Dividend Distribution pairs with returning surplus according to transaction volume.

The Rochdale principles establish the foundational operating guidelines for cooperative societies. Open membership guarantees non-discrimination; democratic member control mandates equal voting rights ('one member, one vote'); limited interest on capital avoids profit-seeking speculation; and patronage dividends ensure surplus distribution rewards active member participation.

Step-by-Step Solution

1

Identify the core operational rule of cooperative governance.

Democratic Member Control relies on the 'one member, one vote' principle rather than share-weighted voting.

Cooperatives focus on member equality rather than financial ownership weight.

2

Determine how surplus is allocated in cooperative societies.

Surplus is distributed as a patronage dividend based on the value or volume of business done with the society.

This rewards active participation and usage of cooperative services rather than passive investment.

3

Examine capital return constraints and membership rules.

Limited Interest on Capital caps dividend rates on shares, while Voluntary and Open Membership ensures open access without arbitrary barriers.

These principles maintain the service-oriented, non-speculative nature of cooperatives.

Key Concept

Rochdale Principles of Cooperative Enterprise

Question 13634Question →

Match each economic activity on the left with its precise occupational sector or sub-classification on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Timber logging matches Primary (Extractive) Occupation; Processing iron ore matches Secondary (Manufacturing) Occupation; Commercial warehousing matches Tertiary (Commercial Service) Occupation; Personal medical consultation matches Tertiary (Direct Service) Occupation.

Each economic activity correctly aligns with its precise occupational sub-classification based on whether it extracts raw resources from nature (timber logging → primary extractive), processes raw materials into manufactured items (iron ore processing → secondary manufacturing), aids trade distribution (warehousing → tertiary commercial), or satisfies personal human needs directly (medical consultation → tertiary direct service).

Step-by-Step Solution

1

Identify activities involving direct raw material extraction from nature.

Timber logging extracts raw forest resources directly from natural reserves, placing it under Primary (Extractive) Occupation.

Primary occupations concentrate on gathering raw materials directly from natural land, water, or forest resources.

2

Identify industrial processing and transformation of raw materials.

Converting iron ore into steel sheets represents industrial processing, placing it under Secondary (Manufacturing) Occupation.

Secondary occupations process primary raw materials into usable industrial products or finished consumer goods.

3

Distinguish between commercial services aiding trade and direct personal services.

Commercial warehousing facilitates trade distribution (Tertiary Commercial Service), whereas personal medical consultation serves an individual directly (Tertiary Direct Service).

Commercial services support the distribution of commodities, while direct services provide non-trade personal care directly to human beings.

Key Concept

Classification of occupations into Primary, Secondary, and Tertiary sectors

Estimated Time:1m 30s

Question 13635Question →

A musical note played on an instrument produces a fundamental frequency of $440\text{ Hz}$ . Given that the speed of sound in air is $330\text{ m/s}$ , what is the wavelength, in meters, of the sound wave produced in air corresponding to its second overtone?

Show answer & explanation

Answer: 0.25

Answer

0.25 m

The fundamental frequency (

f_1 = 440\text{ Hz}

) is the first harmonic. The second overtone is the third harmonic, which has a frequency of

3 \times 440\text{ Hz} = 1320\text{ Hz}

. Substituting this into the wave speed equation

\lambda = \frac{v}{f}

gives

\lambda = \frac{330\text{ m/s}}{1320\text{ Hz}} = 0.25\text{ m}

.

Step-by-Step Solution

1

Determine the harmonic number for the second overtone

The second overtone is the third harmonic (

n = 3

)

Overtones are integer harmonics above the fundamental frequency (

n = 1

). Thus, the 1st overtone is

n = 2

and the 2nd overtone is

n = 3

.

2

Calculate the frequency of the second overtone

f_3 = 3 \times 440\text{ Hz} = 1320\text{ Hz}

The frequency of the

n

-th harmonic is

n

times the fundamental frequency.

3

Calculate the wavelength using the wave speed equation

\lambda = \frac{v}{f_3} = \frac{330\text{ m/s}}{1320\text{ Hz}} = 0.25\text{ m}

Wavelength is determined by dividing the speed of sound by the wave frequency.

Key Concept

Harmonics, Overtones, and Wave Equation

Question 13636Question →

A farmer plants two types of crops, maize and cassava, in separate fields. The probability that the maize crop yields a successful harvest is $\frac{3}{8}$ , and the probability that the cassava crop yields a successful harvest is $\frac{1}{2}$ . Assuming that the harvest outcomes of the two crops are independent, what is the probability that at least one of the crops yields a successful harvest?

\frac{3}{16}

\frac{11}{16}

\frac{7}{8}

\frac{5}{16}

Show answer & explanation

Answer: $\frac{11}{16}$

Answer

The probability that at least one of the crops yields a successful harvest is

\frac{11}{16}

.

The probability of at least one successful harvest is given by the union of the two events,

P(M \cup C) = P(M) + P(C) - P(M \cap C)

. Since the harvests are independent, the joint probability is

P(M \cap C) = P(M) \times P(C) = \frac{3}{8} \times \frac{1}{2} = \frac{3}{16}

. Substituting these values gives

\frac{3}{8} + \frac{1}{2} - \frac{3}{16} = \frac{6}{16} + \frac{8}{16} - \frac{3}{16} = \frac{11}{16}

.

Step-by-Step Solution

1

Identify given probabilities and event relationship

Let

M

be maize success and

C

be cassava success:

P(M) = \frac{3}{8}

and

P(C) = \frac{1}{2}

. The events are independent.

Establishing the basic event probabilities and independence condition is essential for applying compound probability laws.

2

Calculate the joint probability of both events occurring

P(M \cap C) = P(M) \times P(C) = \frac{3}{8} \times \frac{1}{2} = \frac{3}{16}

.

For independent events, the multiplication law states that the probability of both occurring is the product of their individual probabilities.

3

Apply the addition law of probability for the union of two events

P(M \cup C) = P(M) + P(C) - P(M \cap C) = \frac{3}{8} + \frac{1}{2} - \frac{3}{16} = \frac{6}{16} + \frac{8}{16} - \frac{3}{16} = \frac{11}{16}

.

The probability that at least one crop succeeds corresponds to the union

P(M \cup C)

, which requires subtracting the intersection to prevent double counting.

Key Concept

Addition Law of Probability and Multiplication Law for Independent Events

Question 13637Question →

A $4.0\text{ }\mu\text{F}$ capacitor and a $6.0\text{ }\mu\text{F}$ capacitor are connected in parallel. This parallel combination is connected in series with a $10.0\text{ }\mu\text{F}$ capacitor across a $60.0\text{ V}$ d.c. power supply. What is the total energy stored in the combination?

9.0 \times 10^{-3}\text{ J}

3.6 \times 10^{-2}\text{ J}

3.48 \times 10^{-3}\text{ J}

2.23 \times 10^{-2}\text{ J}

Show answer & explanation

Answer: $9.0 \times 10^{-3}\text{ J}$

Answer

The total energy stored in the combination is

9.0 \times 10^{-3}\text{ J}

.

First, find the equivalent capacitance of the parallel branch by adding

4.0\text{ }\mu\text{F}

and

6.0\text{ }\mu\text{F}

to get

10.0\text{ }\mu\text{F}

. Next, combine this result in series with the

10.0\text{ }\mu\text{F}

capacitor to obtain a total circuit capacitance of

5.0\text{ }\mu\text{F}

(or

5.0 \times 10^{-6}\text{ F}

). Substituting

C_{eq} = 5.0 \times 10^{-6}\text{ F}

and

V = 60.0\text{ V}

into

E = \frac{1}{2} C_{eq} V^2

gives

9.0 \times 10^{-3}\text{ J}

.

Step-by-Step Solution

1

Calculate the equivalent capacitance of the parallel branch.

C_p = C_1 + C_2 = 4.0\text{ }\mu\text{F} + 6.0\text{ }\mu\text{F} = 10.0\text{ }\mu\text{F}

Capacitors in parallel add directly.

2

Calculate the total equivalent capacitance of the entire circuit.

C_{eq} = \frac{C_p \times C_3}{C_p + C_3} = \frac{10.0\text{ }\mu\text{F} \times 10.0\text{ }\mu\text{F}}{10.0\text{ }\mu\text{F} + 10.0\text{ }\mu\text{F}} = 5.0\text{ }\mu\text{F} = 5.0 \times 10^{-6}\text{ F}

The parallel combination

C_p

is connected in series with

C_3

.

3

Calculate the total energy stored using

E = \frac{1}{2} C_{eq} V^2

.

E = \frac{1}{2} (5.0 \times 10^{-6}\text{ F}) (60.0\text{ V})^2 = 9.0 \times 10^{-3}\text{ J}

The energy stored in a capacitive circuit depends on the net capacitance and applied potential difference.

Key Concept

Equivalent capacitance of mixed networks and stored energy in capacitors

Question 13638Question →

Arrange the following commercial documents in the exact chronological sequence in which they are issued during a standard home trade transaction, from initial transaction setup to final payment completion.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct chronological sequence of commercial documents in home trade is Letter of Inquiry, Quotation, Delivery Note, Invoice, and Receipt.

The transaction begins when a buyer inquires about goods (Letter of Inquiry). The seller responds with price and terms details (Quotation). Upon agreement and dispatch, goods are delivered with a verification document (Delivery Note). The seller then bills the buyer (Invoice), and finally provides proof of payment once settled (Receipt).

Step-by-Step Solution

1

Identify the transaction initiation document

Letter of Inquiry

Trade begins when a buyer inquires about available goods, prices, and terms from a seller.

2

Identify the seller's initial response document

Quotation

The seller replies to the inquiry by stating prices, trade discounts, and delivery conditions.

3

Identify the document accompanying physical dispatch

Delivery Note

When goods are shipped, the seller includes a document for the buyer to check off items received against items sent.

4

Identify the formal demand for payment

Invoice

After or during goods delivery, the seller sends a summary bill specifying the net amount owed.

5

Identify the proof of final settlement

Receipt

Once the buyer pays the invoice amount, the seller issues a document confirming payment receipt.

Key Concept

Chronological Workflow of Home Trade Commercial Documents

Estimated Time:1m 0s

Question 13639Question →

Funds spent by foreign visitors on hotel accommodation and local guided tours are classified as visible trade because the service consumption occurs physically within the host nation.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. Payments made by foreign visitors for local accommodation, dining, and guided tours represent intangible service transactions, placing them under invisible trade rather than visible trade.

Tourism involves commercial transactions for intangible services (hospitality, transportation, and recreation). In international commercial records, revenue derived from selling non-physical services to foreign nationals is categorized under invisible trade.

Step-by-Step Solution

1

Analyze the nature of tourism products

Accommodation, tour guiding, and entertainment are services rather than physical merchandise.

Commerce categorizes trade based on tangibility; items are either tangible goods or intangible services.

2

Apply international trade classification rules

Earnings from serving international visitors represent invisible export receipts.

Visible trade is confined to tangible commodities, whereas service-based transactions constitute invisible trade.

Key Concept

Classification of Tourism as Invisible Trade

Question 13640Question →

According to the kinetic theory of gases, the pressure exerted by an ideal gas on the walls of its container is primarily caused by which of the following mechanisms?

The continuous elastic collisions of gas molecules with the walls of the container

The gravitational attraction pulling gas molecules toward the base of the container

Strong attractive intermolecular forces acting between adjacent gas particles

Inelastic collisions between gas molecules resulting in loss of total kinetic energy

Show answer & explanation

Answer: The continuous elastic collisions of gas molecules with the walls of the container

Answer

The pressure of an ideal gas is caused by the continuous elastic collisions of gas molecules with the container walls.

The correct answer states that pressure is caused by the continuous elastic collisions of gas molecules with the walls of the container. In kinetic theory, each wall collision imparts impulse to the container surface, yielding a net average force per unit area.

Step-by-Step Solution

1

Identify the microscopic origin of gas pressure in kinetic theory.

Gas molecules are in constant, random motion and frequently collide with the inner walls of the container.

Each collision results in a change of momentum of the gas molecule.

2

Relate molecular momentum change to force and pressure.

By Newton's second law, the rate of change of momentum produces a force on the wall, and force per unit area equals pressure.

Continuous elastic collisions create a steady macroscopic pressure on the walls.

Key Concept

Origin of Gas Pressure in Kinetic Theory

Estimated Time:45s

Answer

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