Answer: I'd be happy to help you with these problems!
1a.
i. Cardinal: There were 10 apples in the basket.
ii. Ordinal: He came in first place in the race.
iii. Nominal: My favorite color is blue.
i. 1997 in Roman numerals is MCMXCVII.
ii. 15-03-2023 in Roman numerals is XV-III-MMXXIII.
2a.
2√128 - √243 + 5√125 + √27 - √80 - 162 + √98
First, simplify the square roots:
2√64·2 - 3√81·3 + 5√25·5 + √9·3 - √16·5 - 162 + √49·2
Next, simplify further:
2·8√2 - 3·3√3 + 5·5√5 + 3√3 - 4√5 - 162 + 7√2
Combine like terms:
15√2 - √3 + 8√5 - 162 - 4√5 + 7√2
Simplify further:
22√2 + 4√5 - √3 - 162
b.
1.3555555555.... can be written as 1.36 in 7º.
c.
Village A has a funeral every 10 days, so it will have a funeral on March 4th, March 14th, March 24th, etc.
Village B has a funeral every 15 days, so it will have a funeral on March 4th, March 19th, April 3rd, etc.
Village C has a funeral every 20 days, so it will have a funeral on March 4th, March 24th, April 13th, etc.
To determine the next time all three villages will have a funeral on the same day, find the least common multiple of 10, 15, and 20.
10 = 2 x 5
15 = 3 x 5
20 = 2 x 2 x 5
The least common multiple is 2 x 2 x 3 x 5 = 60.
So, the next time all three villages will have a funeral on the same day is 60 days after March 4th, which is May 3rd, 2023.
Comment if you have any more questions.