Correct Answer: A. 8

Explanation

\(^{n}C_{3} = \frac{n!}{(n - 3)! 3!}\)

\(^{n}P_{2} = \frac{n!}{(n - 2)!}\)

\(\frac{^{n}C_{3}}{^{n}P_{2}} = \frac{n!}{(n - 3)! 3!} ÷ \frac{n!}{(n - 2)!}\)

\(\frac{n!}{(n - 3)! 3!} \times \frac{(n - 2)!}{n!} = \frac{(n - 2)!}{(n - 3)! 3!}\)

Note that \((n - 2)! = (n - 2) \times (n - 2 - 1)! = (n - 2)(n - 3)!\)

\(\frac{(n - 2)(n - 3)!}{(n - 3)! 3!} = 1\)

\(\frac{n - 2}{3!} = 1 \implies n - 2 = 6\)

\(n = 2 + 6 = 8\)

Correct Answer: D. which

Correct Answer: C. 15

Correct Answer: D. 80

Explanation

Sum of ∠s in a pentagon = (n - 2)180 = 540°

x° + 2x° + x° + 60° + x° + 10° + x° - 10° = 540°

6x° + 60° = 540°; x = 80°

Correct Answer: A. performance of the ancestors

Correct Answer: C. predators

Correct Answer: C. 75.0J

Explanation

K.E = P.E = mgh = 0.3 x 10 x 100 - 0.3 x 10 x 75 = 75J

Correct Answer: A)

20cm\(^3\)

Explanation

The reaction between hydrogen and oxygen can be described by the following balanced chemical equation:

\(2H_{2(g)} + O_{2(g)} \rightarrow 2H_2O_{(g)}\)

In this reaction, 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water vapor. This can also be interpreted in terms of volume, as 2 volumes of hydrogen gas react with 1 volume of oxygen gas to produce 2 volumes of water vapor at constant temperature and pressure (based on Avogadro's Law).

Given that 70 cm\(^3\) of hydrogen is sparked with 25 cm\(^3\) of oxygen at S.T.P. (Standard Temperature and Pressure), we can determine the limiting reactant and the volume of the residual gas.

To do this, we first need to compare the volume ratio of hydrogen to oxygen with the stoichiometric ratio from the balanced chemical equation. The stoichiometric ratio is 2:1 (hydrogen:oxygen), while the volume ratio is 70:25 or 2.8:1.

Since the volume ratio of hydrogen to oxygen is greater than the stoichiometric ratio, there is an excess of hydrogen, and oxygen is the limiting reactant.

From the stoichiometric ratio, 1 volume of oxygen reacts with 2 volumes of hydrogen. Therefore, the 25 cm\(^3\) of oxygen reacts with 50 cm\(^3\) of hydrogen. This leaves 20 cm\(^3\) of hydrogen unreacted (70 cm\(^3\) - 50 cm\(^3\)).

As a result, the total volume of the residual gas is 20 cm\(^3\) (unreacted hydrogen), which corresponds toOption A: 20 cm\(^3\).

Correct Answer: D) Believed that there was no other god able to deliver

Explanation

The question is asking about the effect that the faith of Shadrach, Meshach and Abednego had on King Nebuchadnezzar and his subjects. These three men were Jews who were taken into captivity and exiled to Babylon. King Nebuchadnezzar had ordered that everyone should worship an idol he had made, but Shadrach, Meshach and Abednego refused to do so because it was against their faith. They were then thrown into a fiery furnace, but they were miraculously saved by God.

The question is asking us to choose the option that best describes the effect that their faith had on King Nebuchadnezzar and his subjects. Option A states that they refrained from persecuting the Jews in exile, Option B states that they were converted, Option C states that they forsook their gods, and Option D states that they believed that there was no other god able to deliver, which is the correct answer.

The faith of Shadrach, Meshach and Abednego had a profound effect on King Nebuchadnezzar and his subjects. When they saw that these men were saved from the fiery furnace by their God, they believed that there was no other god who could do such a thing. This caused them to have a greater respect for the God of the Jews and to acknowledge His power. It did not necessarily mean that they converted to Judaism or forsook their own gods, but it did cause them to recognize the superiority of the God of the Jews.

In summary, the correct answer to this question is Option D, which states that the effect that the faith of Shadrach, Meshach and Abednego had on King Nebuchadnezzar and his subjects was that they believed that there was no other god able to deliver.

Correct Answer: B. apathy