Explanation:
1 inch = 25.4 mm
1 foot = 12 inches
1 mile = 5260 feet
1 cm = 0.01 m or 10 mm
Now Sammy's height is 5 feet and 5.3 inches.
(a) We need to find Sammy's height in inches.
Since, 1 foot = 12 inches
5 feet = 5 × 12 inches = 60 inches
Now, 5 feet and 5.3 inches = 60 inches + 5.3 inches = 65.3 inches
Sammy's height is 65.3 inches.
(b) We need to find Sammy's height in feet.
Since, 1 foot = 12 inches

So,

5 feet and 5.3 inches = 5 feet + 0.4416 feet = 5.44 feet
Sammy's height is 5.44 feet.
Answer : Yes, distance measurements based on the speed of light used for objects in space.
Explanation : A light year is measurement of distance that light travel in a one year.
In a one year light travels 9460000000000 kilometer.
We know that, speed of light is 
and time is 31536000 seconds in 1 year
so, distance = speed of light X time
Now, the light year is 
Example : The nearest star to earth is about 4.3 light year away.
Answer:
The vibrational frequency of the rope is 5 Hz.
Explanation:
Given;
number of complete oscillation of the rope, n = 20
time taken to make the oscillations, t = 4.00 s
The vibrational frequency of the rope is calculated as follows;

Therefore, the vibrational frequency of the rope is 5 Hz.
From Carnot's theorem, for any engine working between these two temperatures:
efficiency <= (1-tc/th) * 100
Given: tc = 300k (from question assuming it is not 5300 as it seems)
For a, th = 900k, efficiency = (1-300/900) = 70%
For b, th = 500k, efficiency = (1-300/500) = 40%
For c, th = 375k, efficiency = (1-300/375) = 20%
Hence in case of a and b, efficiency claimed is lesser than efficiency calculated, which is valid case and in case of c, however efficiency claimed is greater which is invalid.