Correct Answer: D. Lagos

Explanation

(a)(i) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 5, 7}

A' = U - A = {3, 4, 6, 8, 9, 10}

(ii) \(A \cap B = {1, 2, 5, 7} \cap {1, 3, 6, 7} = {1, 7}\)

\((A \cap B)' = {2, 3, 4, 5, 6, 8, 9, 10}\)

(iii) \(A \cup B = {1, 2, 5, 7} \cup {1, 3, 6, 7}\)

= \({1, 2, 3, 5, 6, 7}\)

\((A \cup B)' = {4, 8, 9,10}\)

(iv) {1, 3, 6}, {1, 3, 7}, {1, 6, 7} and {3, 6, 7}.

(b) The nth term of the sequence is given as

\(U_{n} = \frac{n + 1}{n(n + 2)}, n = 1, 2,3\)

For the 15th term,

\(U_{15} = \frac{16}{15 \times 17}\)

(c)(i) \(T_{n} = a + (n - 1)d\)

\(T_{n} = 3 + (n - 1)4 = 3 + 4n - 4\)

= \(4n - 1\)

(ii) \(4n - 1 > 100\)

\(4n > 100 + 1 \implies 4n > 101\)

\(n > 25.25\)

The least term greater than 100 = 26th term.

(a)(i) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 5, 7}

A' = U - A = {3, 4, 6, 8, 9, 10}

(ii) \(A \cap B = {1, 2, 5, 7} \cap {1, 3, 6, 7} = {1, 7}\)

\((A \cap B)' = {2, 3, 4, 5, 6, 8, 9, 10}\)

(iii) \(A \cup B = {1, 2, 5, 7} \cup {1, 3, 6, 7}\)

= \({1, 2, 3, 5, 6, 7}\)

\((A \cup B)' = {4, 8, 9,10}\)

(iv) {1, 3, 6}, {1, 3, 7}, {1, 6, 7} and {3, 6, 7}.

(b) The nth term of the sequence is given as

\(U_{n} = \frac{n + 1}{n(n + 2)}, n = 1, 2,3\)

For the 15th term,

\(U_{15} = \frac{16}{15 \times 17}\)

(c)(i) \(T_{n} = a + (n - 1)d\)

\(T_{n} = 3 + (n - 1)4 = 3 + 4n - 4\)

= \(4n - 1\)

(ii) \(4n - 1 > 100\)

\(4n > 100 + 1 \implies 4n > 101\)

\(n > 25.25\)

The least term greater than 100 = 26th term.

Correct Answer: D. 1200m

Explanation

pressure change for air = pressure change for mercury

hpg = Hpg

h x 0.00136 x g = (75 - 63) x 13.6 x g

h = \(\frac{12 \times 13.6}{0.00136}\)

= 120,000cm

= 1,200m

Correct Answer: A. Pigs

Correct Answer: A. forage crops

Correct Answer: B. B5

Correct Answer: A. Forte.

Correct Answer: B. 3.0m

Explanation

Here's how to solve the problem:

1. Understand the Magnification Formula:

For a lens, the magnification (M) is given by the ratio of the image height (h_i) to the object height (h_o), and also by the ratio of the negative of the image distance (v) to the object distance (u):

M = h_i / h_o = -v / u

2. Identify Given Values:

* The image is 24 times as large as the slide. This means the magnitude of the magnification is 24. For a real image formed by a projection lantern, the image is inverted, so M = -24.

* The screen is 72.0 m from the projecting lens. This is the image distance (v). Since the screen is where the real image is formed, v = +72.0 m.

* We need to find the position of the slide from the lens, which is the object distance (u).

3. Apply the Magnification Formula:

M = -v / u

-24 = -(72.0 m) / u

4. Solve for u:

-24 * u = -72.0 m

24 * u = 72.0 m

u = 72.0 m / 24

u = 3.0 m

The position of the slide from the lens is 3.0 m.

The final answer is 3.0m.

Correct Answer: D. experiences serious liquidity crisis

Correct Answer: B) New York City, United States

Explanation

From the options given, the correct answer is option B, which is New York City, United States. This is because the headquarters of the United Nations is located in New York City, and the Secretary-General's official residence is also located there. It should be noted that the United States has historically been a major contributor to the United Nations, and as such, it is not uncommon for many UN-related activities to take place in the US.

In summary, the official residence of the Secretary-General of the United Nations is located in New York City, United States, which is also where the headquarters of the United Nations is located