Correct Answer: C. a continuosly higher proportion falls into working class category

Correct Answer: A) bereaved of the child

Explanation

The question is asking about a conversation between Nathan and David. Nathan tells David that God will show him mercy, but something else will happen too. The options list different things that could happen. The correct option is option A, which says that David will be bereaved of the child. This means that the child will die.

To better understand this question, we need to know who Nathan and David are. Nathan was a prophet in the Old Testament, and David was a king of Israel. The conversation being referred to in this question happened after David committed a grave sin with Bathsheba, another man's wife. Nathan confronted David about his sin, and in response, David repented and asked for God's forgiveness.

In the conversation referred to in the question, Nathan tells David that God will show him mercy, but that there will still be consequences for his sin. The consequence mentioned in the correct option, option A, is that David will lose his child. This punishment is a result of David's sin, but it is also an act of mercy from God, as it could have been much worse.

In summary, the correct option for this question is option A, which says that David will be bereaved of the child. This refers to the consequence of David's sin, which was losing his child. Nathan and David are important figures in the Old Testament, and this question relates to a conversation they had after David sinned with Bathsheba.

Correct Answer: B. hydrometer

Correct Answer: B. Equate marginal cost to marginal revenue

Correct Answer: B. the vain expectations of man

Explanation

(a) Resultant of the forces acting on the plane = (6i + 2j) + (5i + 4j) + (4i - j) = 15i + 5j

\(F = \frac{m \Delta v}{t}\)

Resultant force = \(\frac{mv}{t} \)

\(15i + 5j = \frac{5v}{t}\)

\(v = \frac{(15i + 5j). t}{5} = 3t i + t j\)

(b) velocity after 4 seconds = \(3(4) i + 4 j = 12 i + 4 j\)

\(\therefore |12i + 4j| = \sqrt{12^{2} + 4^{2}} = \sqrt{144 + 16}\)

= \(\sqrt{160} \)

= \(4\sqrt{10} m/s\)

Explanation

The probability of success (p) = \(\frac{3}{5}\) and the probability of failure (q) = 1 - \(\frac{3}{5} = \frac{2}{5}\)

The probability that at least two of them failed is

P(x \(\geq\) 2) = 1 - p(x < 2) = 1 - [P(x = 0)] + [P(x = 1)]= 1 - [(\(^{10}_{0}\)) (\(\frac{2}{5}\))\(^0\) (\(\frac{3}{5}\))\(^{10}\) + (\(^{10}_1\)) (\(\frac{2}{5}\))\(^1\) (\(\frac{3}{5}\))\(^9\)]

Which simplified to 1 - 0.046357401 = 0.9536 correct to four decimal places

(b) The probability that exactly half of them passes is P(x = 6) = (\(^{10}_{5}\)) (\(\frac{3}{5}\))\(^5\) (\(\frac{2}{5}\))\(^{5}\)

Simplified to give; 252 x 0.7776 x 0.01024 = 0.2007 correct to four decimal places

(c) The probability that at most two of them failed is

P(x \(\leq\) 2) = P(x = 0) + P(x = 1) + P(x = 2). In this case p = \(\frac{2}{5}\) q = \(\frac{3}{5}\) so that

p(x \(\leq\) 2) = (\(^{10}_{0}\)) (\(\frac{2}{5}\))\(^0\) (\(\frac{3}{5}\))\(^{10}\) + (\(^{10}_1\)) (\(\frac{2}{5}\))\(^1\) (\(\frac{3}{5}\))\(^9\) + (\(^{10}_{2}\)) (\(\frac{2}{5}\))\(^2\) (\(\frac{3}{5}\))\(^{8}\)

Which simplies to 0.1673 correct to four decimal places.

Correct Answer: A. product

Explanation

In marketing, a product is an object or system made available for consumer use; it is anything that can be offered to a market to satisfy the desire or need of a consumer. Product has a vital role in developing the strategy for the overall marketing mix which includes place, price and promotion.

Correct Answer: C) ethyl ethanoate

Explanation

In naming an ester (Alkanoate), The partially positive anion R+ is named first followed by the partially negative RCOO- cation (When split into ions). In a more elaborative Structure, the First Carbon is not bonded directly to the Oxygen atom as illustrated in the condensed Structural formula given in the question, instead it is linked to second carbon atom which carries the Ethanoate functional group and lastly, this is of course linked to an Alkyl group (R'). To put this in a clearer way, the Dense Structural Formula that is being referred to in this question as opposed to what was given originally in the question is: CH₃?COO?C₂H₅

Explanation

(a) Perimeter of a rectangle = 2(l + b)

\(2l + 2b = 280\)

But l = 2.5b,

\(2(2.5b) + 2b = 280 \implies 7b = 280\)

\(b = 40 m\)

\(\therefore l = 2.5(40) \)

= \(100 m\)

(b) Volume of pyramid = \(\frac{1}{3}l \times b \times h\)

= \(\frac{1}{3}(4.5) \times 2.5 \times 4 \)

= \(15 m^{3}\).