Question

1.On a scale drawing, the length of a farm land is 20cm. what is the actual length of the farm land if the scale is 1cm represents 50m?

100m
200m
500m
1000m
2. Convert 432 base 5 to a number in base 10
171
117
115
112
119. Add the binary numbers 10112 and 11012
11000
10111
10001
10110
120. Find the simple interest on $300.00 for 4 years at 6% per annum.
$12.00
$72.00
$24.00
$48.00

Answer 1

a. 1000m

b. 117

c. 11000 to base 2

d. $72

Explanation:

a. On the scale drawing, the farm land has a length of 20cm.

In real life, using the scale, 1cm represents 50m, thus, the length of 20cm will be 50 * 20 = 1000 m

b. Convert 432 in base 5 to base ten

That would be;

(4 * 5^2) + (3 * 5^1) + (2 * 5^0)

= 100 + 15 + 2 = 117

c. Please check attachment

To do this addition, we should recall that the terms we can have is only 0 and 1.

Also addition of 1 + 1 in base 2 gives 10; and thus we put down 0 and add the 1 to the next set on the left. We keep doing this till we reach the final leftward term where 1 + 1 + 1 equals 3, but we can’t write this and we need to convert to base 2. 3 to base 2 is 11.

This gives us a final answer of 11000

d. Mathematically, the simple interest can be calculated using the formula;

I = PRT/100

where P is the principal which is $300 according to the question

R is the rate which is 6%

T is time which is 4 years

Plugging these values into the equation, we have;

I = (300 * 6 * 4)/100 = 7200/100 = $72