Question 33: Yakubu's scores in five out of six subjects are 95, 87, 85, 93, and 94. If he requires an average score of 90 to get promoted, what must be the minimum score in the sixth subject? Question 34: A right pyramid has a square base of side 10 cm. If the volume is 700 $cm^3$, find the height. Question 35: The bearing of F from G is 064°. What is the bearing of G from F?

1. Problem Description

Question 33: Yakubu's scores in five out of six subjects are 95, 87, 85, 93, and

9

4. If he requires an average score of 90 to get promoted, what must be the minimum score in the sixth subject?

Question 34: A right pyramid has a square base of side 10 cm. If the volume is 700 $cm^3$, find the height.

Question 35: The bearing of F from G is 064°. What is the bearing of G from F?

2. Solution Steps

Question 33:

Let $x$ be the score in the sixth subject.

The average score of the six subjects is given by

$\frac{95+87+85+93+94+x}{6}$.

We want this average to be at least

9

0. So, we have the inequality:

$\frac{95+87+85+93+94+x}{6} \ge 90$.

$95+87+85+93+94+x \ge 90 \times 6$.

$454+x \ge 540$.

$x \ge 540 - 454$.

$x \ge 86$.

Therefore, the minimum score in the sixth subject is

8

6.

Question 34:

The volume of a pyramid is given by the formula

$V = \frac{1}{3} \times base\_area \times height$.

The base is a square with side 10 cm. So, the base area is $10 \times 10 = 100$ $cm^2$.

The volume is given as 700 $cm^3$.

Let $h$ be the height. Then,

$700 = \frac{1}{3} \times 100 \times h$.

$700 = \frac{100h}{3}$.

$2100 = 100h$.

$h = \frac{2100}{100}$.

$h = 21$ cm.

Therefore, the height of the pyramid is 21 cm.

Question 35:

The bearing of F from G is 064°. This means that if you are standing at G and facing North, you need to rotate 64° clockwise to face F.

The bearing of G from F is the angle measured clockwise from North at F to G.

The difference between the bearings is 180°. Since 064° is less than 180°, we add 180° to 064°.

Bearing of G from F = 064° + 180° = 244°.

Therefore, the bearing of G from F is 244°.

3. Final Answer

Question 33: A. 86

Question 34: B. 21 cm

Question 35: C. 244°