Carlos has 2 dollars more than half of the total amount of money his brother has. If x represents the amount of money Carlos's b
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Answer: Choice D) set of even integers
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Explanation:
U = universal set = {all positive integers} = {1, 2, 3, 4, 5, ...}
A = {stuff in set U that is odd} = {1, 3, 5, 7, 9, ...}
= {stuff in set U but NOT from set A} = {2, 4, 6, 8, ...}
= {set of even numbers from set U}
In set theory, the complement is simply the complete opposite. If the number 7 is found in set A for instance, then 7 is not going to live in the complement
The opposite of the odd numbers is the set of even numbers.
Therefore, we go for <u>choice D</u> as our final answer.
Side note: if we union set A with its complement then we get the universal set as a result.
1. For this problem I found the details of the ships in another source. Let us use the steamboat for going to the island and then switch to the tall ship when going back. We know that the steamboat makes the trip in 5 hours, the tall ship makes it in 10 hours, and that the tall ship is 10 knots slower than the steamboat.
2. We'll actually be good with whatever we choose but we just chose those two aforementioned boats because they will be the two most appropriate and inexpensive boats that can safely transport you back and forth the island. The details of the two boats have also been given for us to analyze.
3. As previously stated, travelling to the island would take us 5 hours while going back would take us 10 hours. We also know that the tall ship is 10 knots slower than the steamboat however we do not know the actual speed of any boat. Luckily, we can use the fact that the distance they will travel would be the same and that the trip time multiplied by the speed equals distance traveled.
4. For this item we just assign the variable x as the speed of the steamboat and use the fact that the tall boat is 10 knots slower than the steamboat to write its speed in terms of the variable x. With this information, we can find out that the tall boat's speed is (x-10) knots.
Speed of the steamboat: x knots
Speed of the tall boat: (x-10) knots
5. Since we know the trip time and we have already designated variables for the speed, we will just multiply these two to find out the distance. Given that the distance traveled for both boats is the same, we will just equate the expressions for both boats.
6.
Based on our calculations, the value for x is 20. This would tell us that the speed of the steamboat (which we designated as x earlier) is equal to 20 knots.
7. Since we designated the second boat (tall boat) to have a speed of (x-10) knots, we just use the value of x that we got in the previous item and subtract 10 from it.
Speed of the tall boat:
knots
8. For this item, we are only asked to provide the cost per hour for the boats we've picked. We already know the trip time of the two boats (as mentioned before) and we are already given the costs for each one therefore we just divide the two units to compute for the cost per hour.
Steamboat:
Tall boat:
2. We'll actually be good with whatever we choose but we just chose those two aforementioned boats because they will be the two most appropriate and inexpensive boats that can safely transport you back and forth the island. The details of the two boats have also been given for us to analyze.
3. As previously stated, travelling to the island would take us 5 hours while going back would take us 10 hours. We also know that the tall ship is 10 knots slower than the steamboat however we do not know the actual speed of any boat. Luckily, we can use the fact that the distance they will travel would be the same and that the trip time multiplied by the speed equals distance traveled.
4. For this item we just assign the variable x as the speed of the steamboat and use the fact that the tall boat is 10 knots slower than the steamboat to write its speed in terms of the variable x. With this information, we can find out that the tall boat's speed is (x-10) knots.
Speed of the steamboat: x knots
Speed of the tall boat: (x-10) knots
5. Since we know the trip time and we have already designated variables for the speed, we will just multiply these two to find out the distance. Given that the distance traveled for both boats is the same, we will just equate the expressions for both boats.
6.
Based on our calculations, the value for x is 20. This would tell us that the speed of the steamboat (which we designated as x earlier) is equal to 20 knots.
7. Since we designated the second boat (tall boat) to have a speed of (x-10) knots, we just use the value of x that we got in the previous item and subtract 10 from it.
Speed of the tall boat:
8. For this item, we are only asked to provide the cost per hour for the boats we've picked. We already know the trip time of the two boats (as mentioned before) and we are already given the costs for each one therefore we just divide the two units to compute for the cost per hour.
Steamboat:
Tall boat: