Correct Answer: D. commercialization

Explanation

Commercialization is the efficient running of a government enterprise with the major motive of making profit.

Correct Answer: C. made sacrifice to God

Correct Answer: C. Kano state

Correct Answer: B. Ghana

Explanation

After a temporary set back in 2021 due to a sharp decline in output, Ghana has reclaimed its position as the top Gold producer

Explanation

(a) Logic gate is an elementary building block of a digital circuit with the two binary conditions, i.e.; low (0) or high (1) which is a representation of different voltage levels.

OR

Logic gate is a logical circuit in digital devices with one or more inputs but only one output channel.

(b)(i) AND logic gate, OR logic gate and NOT logic gate.

(ii) NAND logic gate, XNOR logic gate, NOR logic gate and XOR logic gate.

(ci)

XOR Logic gate symbol .

(ii) Truth Table for XOR logic gate

(d) Uses of Logic Gate:

Logic gates are used as building blocks of digital electronic hardware

Logic gates are used in the construction of simple comparator.

Logic gates are used for decision making.

It is used in constructing alarms.

It is used in push-button lock circuit.

It is used in traffic light controller.

It is used in light-activated burglar.

It is used in safety thermostat, an automatic watering system.

It is used in the Arithmetic and Logic Unit (ALU).

It is used in error checking in FM transmission.

It is used in Micro-controller circuits.

Explanation

(a) Tie Edem and his wife. There are six people to arrange in 6! ways, Edem and his wife can be arranged in 2! ways.

\(\therefore\) Total number of ways = 2!6! = 1440 ways.

(b) 4 red, 5 black balls

Total = 9 balls.

\(p(red) = p = \frac{4}{9} ; p(black) = q = \frac{5}{9}\)

5 balls are selected. The binomial probability distribution function is

\((p + q)^{5} = p^{5} + 5p^{4}q + 10p^{3}q^{2} + 10p^{2}q^{3} + 5pq^{4} + q^{5}\)

(i) \(p(\text{red ball picked 3 times}) = 10p^{3}q^{2}\)

= \(10 \times (\frac{4}{9})^{3} \times (\frac{5}{9})^{2}\)

= \(10 \times \frac{64}{729} \times \frac{25}{81}\)

= \(0.271\)

(ii) \(p(\text{black ball at most 2 times}) = p(none) + p(once) + p(twice)\)

= \(10p^{3}q^{2} + 5p^{4}q + p^{5}\)

= \(\frac{16000}{59049} \times 5(\frac{4}{9})^{4} (\frac{5}{9}) + (\frac{4}{9})^{5}\)

= \(\frac{16000 + 6400 + 1024}{59049}\)

= \(\frac{23424}{59049}\)

= \(0.3967\)

Correct Answer: D. Paul and Barnabas

Correct Answer: A. were always angry with each other

Explanation

The phrase 'at daggers drawn' is an idiom which means to be bitterly hostile or at enmity with someone. It does not literally mean that they always wore daggers or were good at drawing daggers or were fighting everybody. Therefore, the option 'were always angry with each other' best describes the sentence.

Explanation

\(xy^{2} + x^{2} y = 4xy\)

Differentiating with respect to x,

\(2xy \frac{\mathrm d y}{\mathrm d x} + y^{2} + x^{2} \frac{\mathrm d y}{\mathrm d x} + 2xy = 4x \frac{\mathrm d y}{\mathrm d x} + 4y\)

\((2xy + x^{2} - 4x) \frac{\mathrm d y}{\mathrm d x} = 4y - y^{2} - 2xy\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{4y^{2} - y^{2} - 2xy}{2xy + x^{2} - 4x}\)

At (1, 3), Gradient = \(\frac{4(3) - (3)^{2} - 2(1)(3)}{2(1)(3) + 1^{2} - 4(1)}\)

= \(\frac{-3}{3}\)

= -1

Correct Answer: D. emphasis