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Question 13641Question →

Match each business organization or commercial body on the left with its defining structural scope and primary function on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Trade Association matches with the sector-specific organization of firms within a single line of trade; Chamber of Commerce matches with the geographically based multi-industry body issuing Certificates of Origin; Employers' Association matches with the body representing management in collective bargaining with trade unions; Export Promotion Council matches with the specialized government agency promoting foreign trade.

Each business organization is matched correctly based on its structural composition and legal/functional role in commerce: Trade Associations operate along single industry lines, Chambers of Commerce operate geographically across multiple industries while issuing legal export documents, Employers' Associations negotiate with trade unions, and Export Promotion Councils serve as statutory export facilitators.

Step-by-Step Solution

Analyze the structural boundary of a Trade Association

Identified as a specialized, single-industry association concerned with sector specific rules and price maintenance.

Trade Associations are restricted to member enterprises operating in one particular trade or industry.

Examine the geographic and administrative scope of a Chamber of Commerce

Identified as a multi-sector regional body handling Certificate of Origin issuance and commercial arbitration.

Chambers of Commerce bring together merchants and manufacturers across various sectors within a city or municipality.

Differentiate Employers' Associations and Export Promotion Councils

Employers' Associations deal with trade union negotiations (labor relations), while Export Promotion Councils execute statutory government export policies.

Understanding the distinct primary mandate of each commercial institution prevents functional misattribution.

Key Concept

Distinction between Trade Associations, Chambers of Commerce, Employers' Associations, and Export Promotion Councils

Question 13642Question →

If the matrix $P = \begin{pmatrix} k & 2 & 0 \\ 1 & 4 & 1 \\ 3 & 0 & 2 \end{pmatrix}$ has a determinant equal to $18$ , find the value of $k$ .

Show answer & explanation

Answer: 2

Answer

The value of

k

2

Expanding matrix

P

along the first row gives

\det(P) = k(8 - 0) - 2(2 - 3) + 0(0 - 12) = 8k + 2

. Setting

8k + 2 = 18

yields

8k = 16

, which simplifies to

k = 2

Step-by-Step Solution

Expand the matrix determinant along the first row.

\det(P) = k(8 - 0) - 2(2 - 3) + 0 = 8k + 2

Applying the cofactor expansion formula for a

3 \times 3

matrix across row 1.

Set the resulting determinant expression equal to the given value of 18.

8k + 2 = 18

The question specifies that the determinant of

P

is equal to

18

Solve the linear equation for

k

k = 2

Subtracting 2 from both sides yields

8k = 16

, and dividing by 8 gives

k = 2

Key Concept

Determinant of a

3 \times 3

Matrix

Question 13643Question →

A Nigerian importer agrees to purchase industrial equipment from a German supplier using a documentary collection under Documents Against Payment (D/P) terms. Arrange the following steps of the payment and document release process in their correct chronological sequence from initial agreement to final fund transfer.

Drag items to arrange them in the correct order

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Answer

The correct chronological order of the Documents Against Payment (D/P) process is: 1) Importer and exporter sign the sales contract agreeing to D/P terms; 2) Exporter ships goods and submits shipping documents with a bill of exchange to the remitting bank; 3) Remitting bank forwards documents to the collecting bank in the buyer's country; 4) Importer pays the bill to receive the shipping documents; 5) Collecting bank remits funds to the exporter's bank.

The correct sequence begins with contractual agreement between trading parties, followed by physical dispatch of goods and delivery of title documents to the remitting bank. The remitting bank transfers these to the collecting bank, which releases them to the importer only upon full cash settlement of the sight draft. Finally, the collected funds are remitted internationally back to the exporter's bank account.

Step-by-Step Solution

Identify the initiating phase of international trade transactions.

The sales contract setting payment terms (D/P) must be finalized prior to shipping or bank involvement.

Commercial agreements dictate the financial mechanism to be used by intermediary banks.

Trace the seller's actions post-contract.

The exporter ships goods, obtains title documents (e.g., Bill of Lading), draws a bill of exchange, and delivers them to the remitting bank.

The remitting bank requires valid shipping documents to execute collection instructions.

Follow the inter-bank transfer of documents.

The remitting bank sends documents to the collecting bank located in the buyer's country.

Financial collection requires a local presence in the importer's jurisdiction to present documents to the buyer.

Determine the condition for document release to the buyer.

The importer pays the sight bill at the collecting bank and receives the bill of lading.

Under D/P (Documents Against Payment) rules, document release is strictly contingent upon full immediate payment.

Identify the final settlement step.

The collecting bank remits proceeds to the remitting bank, which credits the seller.

Payment flows back through international banking channels to finalize the seller's reimbursement.

Key Concept

Documents Against Payment (D/P) Collection Process in International Trade

Question 13644Question →

In commercial operations, insurance performs distinct functions that support trade and enterprise. Match each insurance role listed on the left with the practical commercial scenario on the right that best illustrates it.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Collateral for business loans matches with pledging an endowment policy for a bank loan; Risk pooling and spreading of losses matches with collecting premiums from many to compensate the few suffering fire destruction; Facilitation of foreign trade matches with securing marine cargo insurance for international shipments.

Using insurance as collateral security is shown when an endowment life policy is pledged to secure a loan. Risk pooling is shown when premiums from many traders form a pool to compensate the few who sustain losses. Facilitating foreign trade is shown when marine cargo insurance covers perils during ocean shipping.

Step-by-Step Solution

Analyze the scenario of assigning an endowment life policy for bank credit.

Identify that using a policy to obtain financial credit illustrates insurance functioning as collateral security.

Lenders accept policy assignments as security because guaranteed cash values back the credit facility.

Examine the mechanism of collecting premiums from many policyholders to pay for catastrophic losses of a few.

Recognize this operation as risk pooling and spreading.

This spreads the financial burden of unexpected hazards across a broad group rather than leaving it on one business.

Evaluate the role of marine cargo insurance in shipping goods across sea routes.

Connect marine insurance directly to facilitating foreign trade.

International commerce carries high risk from sea perils; insurance coverage gives traders the security to conduct cross-border business.

Key Concept

Role and Importance of Insurance in Business and Commerce

Question 13645Question →

The Earth's crust is divided into structural layers with distinct chemical compositions, densities, and physical behaviors. Which of the following statements correctly distinguishes the compositional and structural characteristics of the sial layer from the sima layer?

Sial is predominantly composed of lighter granitic rocks rich in silica and alumina forming continental masses, whereas sima consists mainly of denser basaltic rocks rich in silica and magnesium forming oceanic basins.

Sial is formed exclusively through marine sedimentary deposition of metamorphic rocks like marble and slate, while sima originates entirely from atmospheric weathering processes.

Sial undergoes down-slope movement of loose materials under gravity known as weathering, whereas sima experiences in-situ mechanical breakdown known as mass wasting.

Sial forms a continuous, high-density basement layer across the outer core, while sima forms discontinuous blocks floating above the atmospheric envelope.

Show answer & explanation

Answer: Sial is predominantly composed of lighter granitic rocks rich in silica and alumina forming continental masses, whereas sima consists mainly of denser basaltic rocks rich in silica and magnesium forming oceanic basins.

Answer

The sialic layer forms the bulk of continental crust, composed mainly of granitic rocks high in silica and aluminum with lower density. Below sial (and forming the floor of ocean basins) lies sima, composed of denser basaltic rocks dominated by silica and magnesium.

Step-by-Step Solution

Analyze the structural and chemical components of the Earth's crust.

The outer lithospheric crust is subdivided into sial (upper continental crust) and sima (lower oceanic crust).

Geological studies establish distinct compositional profiles for continental versus oceanic lithospheric zones.

Compare the elemental and petrological makeup of both layers.

Sial stands for Silica + Alumina (granitic, density ~2.7 g/cm³), while Sima stands for Silica + Magnesium (basaltic, density ~3.0 g/cm³).

These chemical signatures determine why continental sial floats higher relative to denser oceanic sima.

Key Concept

Chemical and Petrological Differentiation of Earth's Crustal Layers (Sial vs. Sima)

Estimated Time:1m 0s

Question 13646Question →

In modern office automation systems, asynchronous collaboration software requires all remote participants to be online simultaneously to communicate and process shared business tasks.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. Asynchronous collaboration tools allow individuals to communicate and complete workflows independently at different times, whereas synchronous tools require simultaneous real-time participation.

The statement is false because asynchronous collaboration technologies are specifically designed to enable non-simultaneous interaction, allowing workers to contribute to shared digital workflows regardless of time zones or real-time availability.

Step-by-Step Solution

Define asynchronous collaboration in virtual business operations.

Asynchronous communication tools (e.g., email, message boards, shared document commenting systems) permit participants to view, edit, and respond to business tasks at their convenience rather than in real time.

Categorizing digital collaboration tools by time dependence is essential for understanding remote office workflows.

Compare asynchronous requirements with the claim in the stem.

The stem claims that simultaneous online presence is required, which describes synchronous tools (e.g., live video conferencing, telepresence) rather than asynchronous tools.

Identifying the mismatch between the term 'asynchronous' and the definition of real-time interaction determines that the statement is false.

Key Concept

Synchronous vs. Asynchronous Digital Collaboration in Virtual Offices

Question 13647Question →

A hotel proprietor employs a domestic steward to attend exclusively to his family's household chores and a warehouse supervisor to manage the hotel's central food and supply store. How are the services rendered by the domestic steward and the warehouse supervisor classified respectively?

Direct service occupation and commercial occupation

Commercial occupation and direct service occupation

Direct production occupation and trade occupation

Trade occupation and commercial auxiliary occupation

Show answer & explanation

Answer: Direct service occupation and commercial occupation

Answer

Direct service occupation and commercial occupation

Direct services consist of non-commercial personal services provided directly to consumers for personal satisfaction (such as household stewards, private drivers, and domestic cooks). Commercial occupations consist of trade (buying and selling) and auxiliaries to trade (warehousing, transport, banking, insurance, advertising). Therefore, the domestic steward rendered a direct service while the warehouse supervisor rendered a commercial service.

Step-by-Step Solution

Analyze the nature of the domestic steward's role

The steward works directly for a private household providing personal domestic satisfaction paid for by the employer.

Personal/household services that satisfy personal wants directly fall under direct service occupations.

Analyze the nature of the warehouse supervisor's role

The supervisor manages inventory storage for the business enterprise (warehousing).

Warehousing facilitates the distribution of goods and is a key auxiliary to trade, making it a commercial occupation.

Combine the respective classifications

The domestic steward is engaged in a direct service occupation, and the warehouse supervisor is engaged in a commercial occupation.

Matching the ordered pair yields 'Direct service occupation and commercial occupation'.

Key Concept

Classification of Tertiary Occupations into Commercial and Direct Services

Estimated Time:1m 0s

Question 13648Question →

Arrange the following economic activities in the correct chronological sequence to illustrate how raw timber moves through industry, commerce, and occupations from primary extraction to final consumption:

Drag items to arrange them in the correct order

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Answer

The correct sequence starts with primary extraction (felling mahogany trees), followed by initial manufacturing (sawmilling planks), advanced manufacturing/construction (building furniture), commercial auxiliaries (transportation, warehousing, and insurance), and ends with trade (retail sales to consumers).

The economic sequence flows logically from primary industry (extraction of timber) to secondary industry (sawmilling planks and manufacturing furniture), then through commercial auxiliary services (transport, storage, insurance), and finally to trade (retail sales). Each stage relies on specialized occupations that systematically link industry to commerce.

Step-by-Step Solution

Identify the primary industry activity.

Felling mature mahogany trees in a forest reserve is the initial extractive occupation.

Production begins with extracting raw natural resources from the environment.

Identify the primary-to-secondary processing stage.

Processing harvested timber into standardized wooden planks at a sawmilling plant comes next.

Raw materials must undergo basic processing before being converted into final products.

Identify the secondary manufacturing/construction stage.

Constructing finished household dining sets from wooden planks in a joinery factory follows.

This secondary industrial activity transforms processed inputs into finished durable goods, completing form utility creation.

Identify the commercial auxiliary services required before trade.

Transporting and warehousing finished furniture while securing transit insurance is the fourth step.

Auxiliaries to trade (transport, warehousing, insurance) facilitate the safe movement and storage of finished goods prior to exchange.

Identify the final trade activity.

Selling the dining sets to household buyers through retail furniture showrooms is the final step.

Retail trade completes the economic cycle by placing the finished product directly into the hands of final consumers.

Key Concept

Inter-relationship Between Industry, Commerce, and Occupation

Question 13649Question →

A projectile is launched from ground level with an initial speed of $40\text{ m/s}$ at an angle $\theta$ to the horizontal such that $\sin\theta = 0.8$ and $\cos\theta = 0.6$ . Taking the acceleration due to gravity $g = 10\text{ m/s}^2$ , what is the speed of the projectile in $\text{m/s}$ when it reaches a height of $35\text{ m}$ above the ground?

Show answer & explanation

Answer: 30

Answer

The speed of the projectile at a height of

35\text{ m}

above the ground is

30\text{ m/s}

The correct answer is

30\text{ m/s}

. The vertical component of velocity at height

35\text{ m}

is found using

v_y^2 = u_y^2 - 2gh = 32^2 - 2(10)(35) = 324

, giving

v_y = 18\text{ m/s}

. Since horizontal velocity component remains constant at

v_x = 24\text{ m/s}

, the overall speed magnitude is given by

v = \sqrt{v_x^2 + v_y^2} = \sqrt{24^2 + 18^2} = \sqrt{900} = 30\text{ m/s}

Step-by-Step Solution

Resolve initial velocity into horizontal and vertical components

u_x = 24\text{ m/s}

and

u_y = 32\text{ m/s}

Horizontal component

u_x = u\cos\theta = 40 \times 0.6 = 24\text{ m/s}

and vertical component

u_y = u\sin\theta = 40 \times 0.8 = 32\text{ m/s}

Calculate vertical velocity component at height

h = 35\text{ m}

v_y = 18\text{ m/s}

Using

v_y^2 = u_y^2 - 2gh

, we get

v_y^2 = 32^2 - 2(10)(35) = 1024 - 700 = 324

, yielding

v_y = 18\text{ m/s}

Calculate the magnitude of total velocity at height

h = 35\text{ m}

v = 30\text{ m/s}

Because air resistance is neglected, horizontal velocity remains constant (

v_x = u_x = 24\text{ m/s}

). Total speed is

v = \sqrt{v_x^2 + v_y^2} = \sqrt{24^2 + 18^2} = 30\text{ m/s}

Key Concept

Independence of perpendicular velocity components and calculation of instantaneous speed in projectile motion.

Question 13650Question →

In a photoelectric effect experiment, monochromatic light of frequency $f$ (where $f > f_0$ ) illuminates a sodium metal surface, causing the emission of photoelectrons with a maximum kinetic energy $K_{\text{max}}$ and producing a saturation photoelectric current $I$ . If the intensity of the incident light is quadrupled while maintaining the frequency constant, what are the new values of the maximum kinetic energy of the photoelectrons and the saturation photoelectric current?

The maximum kinetic energy remains

K_{\text{max}}

, and the saturation current becomes

4I

The maximum kinetic energy becomes

4K_{\text{max}}

, and the saturation current remains

I

The maximum kinetic energy becomes

4K_{\text{max}}

, and the saturation current becomes

4I

The maximum kinetic energy remains

K_{\text{max}}

, and the saturation current remains

I

Show answer & explanation

Answer: The maximum kinetic energy remains $K_{\text{max}}$ , and the saturation current becomes $4I$ .

Answer

The maximum kinetic energy remains

K_{\text{max}}

, and the saturation current becomes

4I

According to Einstein's photoelectric theory, light intensity corresponds to the rate of photon arrival. Quadrupling the intensity quadruples the number of photons striking the surface per second, thereby quadrupling the rate of emitted photoelectrons and resulting in a saturation current of

4I

. However, individual photon energy depends strictly on frequency (

E = hf

). Because frequency remains constant, the maximum kinetic energy of the photoelectrons remains unchanged at

K_{\text{max}}

Step-by-Step Solution

Apply Einstein's photoelectric equation to analyze the maximum kinetic energy.

K_{\text{max}} = hf - W_0

. Since both frequency

f

and work function

W_0

remain constant,

K_{\text{max}}

remains unchanged.

Photon energy depends only on frequency (

E = hf

), so intensity changes do not affect individual photon energies or the kinetic energy of emitted photoelectrons.

Analyze the relationship between light intensity and photoelectric current.

Intensity

I_{\text{light}}

is proportional to the number of incident photons per second. Quadrupling intensity increases photon flux by a factor of 4, quadrupling photoelectron rate to

4I

Each photon causes the emission of one photoelectron (assuming 100% quantum efficiency), making photoelectric current directly proportional to light intensity.

Key Concept

Independence of photoelectron kinetic energy from light intensity and direct proportionality of photoelectric current to light intensity.

Question 13651Question →

A group of manufacturers operating exclusively within the textile manufacturing sector establish a formal body to protect their specific industrial interests, maintain product standards, and engage in joint trade negotiations. Which type of commercial organization does this body represent?

A trade association

A chamber of commerce

A trade union

An export promotion council

Show answer & explanation

Answer: A trade association

Answer

The organization described is a trade association because its membership is restricted to businesses operating within a specific industry sector.

A trade association is an alliance of firms operating in the same industry or line of business (such as textile manufacturing) formed to advance their specific commercial interests, enforce quality standards, and represent their industry to government bodies.

Step-by-Step Solution

Analyze the organizational scope in the scenario

The membership consists exclusively of business owners within a single line of business (textile manufacturing).

Identifying membership restrictions distinguishes sector-specific bodies from general commercial associations.

Match the scope with the correct business organization

Trade associations represent specific industries or trades, whereas chambers of commerce cover multiple industries across a geographical region.

Trade associations exist to serve the common interests of firms within one particular industry.

Key Concept

Trade Association Structure and Scope

Estimated Time:45s

Question 13652Question →

A promoter intends to set up a modern glass manufacturing factory in Ogun State and requires a 12-year loan facility to import specialized industrial equipment. A commercial bank turned down the application due to the long repayment period required. Which financial institution is specifically mandated to provide this long-term industrial project financing?

Bank of Industry

Central Bank of Nigeria

Nigerian Export-Import Bank

Federal Mortgage Bank of Nigeria

Show answer & explanation

Answer: Bank of Industry

Answer

Bank of Industry

The Bank of Industry is mandated to provide medium to long-term funding, equity participation, and concessionary loans to large, medium, and small industrial enterprises in Nigeria.

Step-by-Step Solution

Identify the financial requirement

The requirement is a 12-year long-term loan facility for acquiring manufacturing plant equipment.

Commercial banks rely on short-term deposit liabilities and cannot support long-term capital investments without facing maturity mismatch.

Match the requirement to institutional mandates

The Bank of Industry is the primary Nigerian development finance institution created to fund industrial expansion, manufacturing, and processing enterprises with long-term loans.

Specialized development banks receive targeted government and institutional capital designed specifically for long-term economic development.

Key Concept

Functions of Development Banks in Nigeria

Question 13653Question →

The impulse imparted to an object by a net force is equal to the time rate of change of the object's linear momentum.

True

False

Show answer & explanation

Answer: False

Answer

False. Impulse is equal to the total change in linear momentum (

J = \Delta p

), while the time rate of change of linear momentum (

\frac{\Delta p}{\Delta t}

) represents the net force.

The statement is false. By definition, impulse is the product of net force and the time interval during which it acts (

J = F \Delta t

), which equals the total change in linear momentum (

\Delta p

). In contrast, the time rate of change of momentum (

\frac{\Delta p}{\Delta t}

) is equal to the net applied force.

Step-by-Step Solution

Define impulse according to the Impulse-Momentum Theorem

Impulse (

J

) is defined as

J = F \Delta t = \Delta p

, which represents the total change in momentum.

Establishing the mathematical definition of impulse.

Identify the physical quantity equal to the time rate of change of momentum

Newton's Second Law states that force

F = \frac{\Delta p}{\Delta t}

, which is the time rate of change of linear momentum.

Distinguishing between force and impulse.

Evaluate the statement

Because impulse equals total change in momentum (

\Delta p

) rather than rate of change (

\frac{\Delta p}{\Delta t}

), the statement is false.

Concluding the true/false verification.

Key Concept

Impulse-Momentum Theorem vs Newton's Second Law

Question 13654Question →

A corporate legal team provides contractual advisory services to an ocean freight firm to facilitate international trade cargo logistics, whereas a private legal consultant is engaged directly by an individual to draft a personal family will. Under occupational classification, how are the services rendered by the corporate legal team and the private legal consultant categorized?

The corporate legal team renders a commercial service, while the private legal consultant renders a direct service.

The corporate legal team renders a direct service, while the private legal consultant renders a commercial service.

Both providers render commercial services because all legal practices operate under tertiary trade activities.

The corporate legal team engages in direct production, while the private legal consultant engages in secondary production.

Show answer & explanation

Answer: The corporate legal team renders a commercial service, while the private legal consultant renders a direct service.

Answer

The corporate legal team renders a commercial service, while the private legal consultant renders a direct service.

Commercial occupations comprise trade and auxiliaries to trade (services like transport, legal aid for shipping, banking, and insurance that facilitate trade). The corporate legal team serves a commercial entity in trade, making it a commercial service. Direct service occupations involve personal services provided directly to an individual for personal satisfaction, such as drafting a family will for a private client.

Step-by-Step Solution

Analyze the service performed by the corporate legal team

The services assist an ocean freight shipping firm involved in moving international trade goods, making it an auxiliary service to trade (commercial occupation).

Commercial occupations encompass trade and all activities directly supporting trade and exchange.

Analyze the service performed by the private legal consultant

The service is rendered directly to an individual for private personal needs (a family will) and paid for directly by the consumer.

Direct services are non-commercial personal services provided directly to the final consumer for personal satisfaction.

Compare the two occupational categories

The corporate legal team provides commercial service, while the private consultant provides direct service.

Occupations are classified by whether they support commercial exchange/distribution or provide direct personal satisfaction.

Key Concept

Commercial vs Direct Service Occupations

Question 13655Question →

A surveyor standing $255\text{ m}$ away from the base of a vertical canyon wall emits a short acoustic signal. If the speed of sound in air is $340\text{ m/s}$ , after what time interval will the surveyor detect the reflected echo?

0.75\text{ s}

1.50\text{ s}

1.33\text{ s}

3.00\text{ s}

Show answer & explanation

Answer: $1.50\text{ s}$

Answer

1.50\text{ s}

Sound must travel to the cliff face and reflect back to the surveyor, covering a total distance of

2 \times 255\text{ m} = 510\text{ m}

. Using the speed formula

t = \frac{d}{v}

, the elapsed time is

\frac{510\text{ m}}{340\text{ m/s}} = 1.50\text{ s}

Step-by-Step Solution

Determine the total distance traveled by the sound wave

s_{total} = 2 \times 255\text{ m} = 510\text{ m}

An echo requires sound to travel to the obstacle and reflect back to the source.

Calculate the time taken using the wave speed formula

t = \frac{s_{total}}{v} = \frac{510\text{ m}}{340\text{ m/s}} = 1.50\text{ s}

Time is equal to total distance divided by the speed of propagation.

Key Concept

Echo reflection and two-way sound propagation distance

Estimated Time:1m 0s

Question 13656Question →

A Nigerian merchant receives a consignment of industrial machinery shipped from Germany. Which of the following foreign trade documents serves as the legal document of title, enabling the importer to claim physical possession of the cargo at the seaport?

Bill of Lading

Certificate of Origin

Consular Invoice

Indent

Show answer & explanation

Answer: Bill of Lading

Answer

Bill of Lading

The Bill of Lading is the definitive document of title in foreign trade. Issued by the shipowner or shipping agent, it acts as a receipt for goods loaded, evidence of the contract of carriage, and a negotiable instrument whose transfer passes legal ownership of the goods to the consignee.

Step-by-Step Solution

Identify the required legal function of the document in the foreign trade transaction.

The importer requires a document that proves legal ownership (document of title) to collect cargo from the shipping company.

In international shipping, carriers require proof of title before releasing goods.

Analyze the functions of key international trade documents.

The Bill of Lading represents the physical goods themselves, functioning as a transferable document of title, receipt, and contract of carriage.

Possession of an endorsed Bill of Lading gives the holder legal entitlement to claim the goods at the port of destination.

Key Concept

Document of Title in Foreign Trade

Question 13657Question →

A binary operation $\star$ defined on the set of real numbers $\mathbb{R} \setminus \left\{\frac{1}{2}\right\}$ is given by $a \star b = a + b - 2ab$ . If $x^{-1}$ represents the inverse of an element $x$ under $\star$ , what is the value of $x$ for which $x^{-1} = 3$ ?

\frac{3}{5}

\frac{2}{5}

\frac{1}{3}

-\frac{3}{5}

Show answer & explanation

Answer: $\frac{3}{5}$

Answer

The value of

x

\frac{3}{5}

First find the identity element

e

using

a \star e = a

, which gives

a + e - 2ae = a \implies e(1 - 2a) = 0 \implies e = 0

. Next, use the inverse definition

x \star x^{-1} = e \implies x + x^{-1} - 2x x^{-1} = 0

. Substituting

x^{-1} = 3

yields

x + 3 - 2x(3) = 0 \implies -5x + 3 = 0 \implies x = \frac{3}{5}

Step-by-Step Solution

Find the identity element

e

under the operation

\star

e = 0

By definition,

a \star e = a \implies a + e - 2ae = a \implies e(1 - 2a) = 0 \implies e = 0

for all

a \neq \frac{1}{2}

Set up the inverse equation for element

x

x \star x^{-1} = 0 \implies x + x^{-1} - 2x x^{-1} = 0

An element operating on its inverse yields the identity element

e = 0

Substitute

x^{-1} = 3

into the inverse equation and solve for

x

x + 3 - 6x = 0 \implies -5x + 3 = 0 \implies 5x = 3 \implies x = \frac{3}{5}

Substitute the given inverse value and perform simple linear algebraic rearrangement.

Key Concept

Identity and Inverse Elements in Binary Operations

Question 13658Question →

An electronics retailer in Lagos displays a notice stating 'Goods once sold cannot be returned or exchanged.' A customer purchases a defective television that fails to function upon installation and demands a refund or replacement. Which regulatory agency has the primary statutory mandate to void this restrictive disclaimer and enforce the consumer's right to redress?

Federal Competition and Consumer Protection Commission (FCCPC)

Standards Organisation of Nigeria (SON)

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

Central Bank of Nigeria (CBN)

Show answer & explanation

Answer: Federal Competition and Consumer Protection Commission (FCCPC)

Answer

Federal Competition and Consumer Protection Commission (FCCPC)

The Federal Competition and Consumer Protection Commission (FCCPC) is legally empowered under the FCCPA to protect consumers against unfair commercial practices, invalidate oppressive trade disclaimers (like 'goods sold are non-returnable'), and mandate remedies such as repairs, replacements, or refunds.

Step-by-Step Solution

Analyze the nature of the consumer grievance

The store is attempting to enforce an illegal 'no return/refund' disclaimer on a defective product, violating statutory consumer rights.

Under Nigerian consumer protection laws, disclaimers excluding liability for defective goods are unlawful and unenforceable.

Identify the agency responsible for general consumer rights and redress enforcement

The Federal Competition and Consumer Protection Commission (FCCPC) holds the statutory authority to protect consumer rights and outlaw unfair trade terms.

While technical bodies like SON handle quality standards and NAFDAC handles regulated consumables, the FCCPC oversees general market conduct and consumer complaint resolution.

Key Concept

Consumer Protection Rights and Enforcement Agencies in Nigeria

Question 13659Question →

When a constant net external force is applied to a body for a given time interval, the magnitude of the change in the body's linear momentum depends only on the magnitude of the applied force and the time duration, and is completely independent of the mass of the body.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True. By the impulse-momentum theorem (

\Delta p = F \Delta t

), the change in linear momentum is equal to the applied impulse, which depends only on force magnitude and time duration, regardless of the body's mass.

The statement is correct because impulse is defined as the product of net force and time interval (

J = F \Delta t

), and by the impulse-momentum theorem, impulse equals the change in momentum (

\Delta p = J

). Neither net force nor time interval depends on the mass of the body.

Step-by-Step Solution

Express Newton's Second Law of Motion in terms of linear momentum.

F = \frac{\Delta p}{\Delta t}

, where

F

is the net force and

\Delta p

is the change in linear momentum over time

\Delta t

Newton's second law states that the net force acting on an object equals the rate of change of its linear momentum.

Rearrange the equation to isolate the change in momentum (

\Delta p

\Delta p = F \Delta t

Multiplying both sides by

\Delta t

gives the impulse-momentum relationship.

Evaluate the dependence of

\Delta p

on the body's mass.

The expression

\Delta p = F \Delta t

contains only force and time, with no mass term (

m

Although a heavier body experiences smaller acceleration than a lighter body under the same force, both undergo the exact same total change in linear momentum over identical time intervals.

Key Concept

Impulse-Momentum Theorem and Newton's Second Law

Question 13660Question →

Match each organizational body on the left with its primary function and scope of operation on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Trade Association matches with protecting commercial interests within a single industry sector; Chamber of Commerce matches with promoting economic interests across diverse sectors in a geographic region; Trade Union matches with representing employees in negotiations with employers.

A Trade Association focuses strictly on a single industry line to protect member businesses. A Chamber of Commerce operates on a regional/geographic basis uniting multiple industries to foster local commerce and provide administrative services like Certificates of Origin. A Trade Union represents employees negotiating labor conditions.

Step-by-Step Solution

Identify the organizational scope of a Trade Association

Trade Associations are sector-specific groups representing business owners in one line of trade.

This differentiates them from multi-sector geographical associations.

Identify the organizational scope of a Chamber of Commerce

Chambers of Commerce cover a city or region and include businesses from all sectors, offering administrative services like Certificates of Origin.

This establishes their multi-sector and geographic focus.

Distinguish business associations from employee bodies

Trade Unions represent workers/employees rather than business employers.

This avoids confusing business organizations with labour unions.

Key Concept

Distinction between Trade Associations, Chambers of Commerce, and Trade Unions based on scope and functions.

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