1) Carlos and Nathan ate lunch together in a park bench. At 1:00p.m., they left the bench and walked in different directions. By 1:05p.m., Carlos and Nathan were 60 meters apart. If they each continued walking in a straight line at the same speed as before, how far apart will they be at 1:20pm?
(I got 180 meters?)
2) A box contains 6 yellow pencils, 6 blue pencils, 8 black pencils, and 4 green pencils. One pencil is removed at random and not looked at, then another, and so on. How many pencils must be removed to be certain that at least one green pencil is taken?
(I don't know)
3)
9< 2^n < 36
How many different integer values of n satisfy the inequality above?
(I got 2?)
#1 they will be 240m apart. 60m per 5 min
They would be 180m farther apart than they were at 1:05
#2 There are 20 pencils which are not green.
So unless you take 21, you cannot be sure of a green.
#3 ok
Thank you!!
1) To solve this problem, we need to determine how far Carlos and Nathan will move in 15 minutes (from 1:05pm to 1:20pm).
Since they are walking away from each other at the same speed, the total distance between them will increase by the same amount of meters per minute. We can calculate this by dividing the initial distance of 60 meters by the time it took for them to separate, which is 5 minutes.
60 meters / 5 minutes = 12 meters per minute
Now we can calculate how far apart they will be at 1:20pm, which is 15 minutes after 1:05pm.
12 meters per minute * 15 minutes = 180 meters
So you are correct, they will be 180 meters apart at 1:20pm.
2) To find out the minimum number of pencils that need to be removed to guarantee taking at least one green pencil, we need to find the scenario where all non-green pencils have been picked before a green pencil.
The worst-case scenario is when we have removed all the other colored pencils except for the green pencils. So we need to calculate the sum of the other colored pencils and add 1 for the first green pencil.
6 yellow + 6 blue + 8 black + 1 green = 21 pencils
Therefore, you need to remove 21 pencils to be certain that at least one green pencil has been taken.
3) To find the number of different integer values that satisfy the inequality 9 < 2^n < 36, we need to determine the range of possible values for n.
Starting with the left inequality: 9 < 2^n, we can rewrite it as n > log base 2 of 9. Using a calculator to find the logarithm, we get n > 3.17 (approximately).
Moving on to the right inequality: 2^n < 36, we can rewrite it as n < log base 2 of 36. Using a calculator, we get n < 5.17 (approximately).
So the values of n that satisfy the inequality are integers greater than 3 and less than 5.
The only two integer values of n within this range are 4 and 5. Therefore, the answer is 2.