Answer:
Carrie left Colorado at 2:45pm CST on Tuesday.
Step-by-step explanation:
The train travels a total of 24 hours to get from Colorado to Illinois, that is, it takes one complete day of travel to get from one city to the other.
So, if Carrie arrives Illinois at 2:45pm CST on Wednesday, she left Colorado exactly one day before that, in the same hour, so she left Colorado at 2:45pm CST on Tuesday.
Answer:
2,075,673,600 batting orders may occur.
Step-by-step explanation:
The order of the first eight batters in the batting order is important. For example, if we exchange Jonathan Schoop with Adam Jones in the lineup, that is a different lineup. So we use the permutations formula to solve this problem.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:

First 8 batters
8 players from a set of 16. So

Last batter:
Any of the four pitchers.
How many different batting orders may occur?
4*518918400 = 2,075,673,600
2,075,673,600 batting orders may occur.
Answer:
13.7
Step-by-step explanation:
3x=41
x is around 13.7
Answer:
There is only one real zero and it is located at x = 1.359
Step-by-step explanation:
After the 4th iteration the solution was repeating the first 3 decimal places. The formula for Newton's Method is

If our function is

then the first derivative is

I graphed this on my calculator to see where the zero(s) looked like they might be, and saw there was only one real one, somewhere between 1 and 2. I started with my first guess being x = 1.
When I plugged in a 1 for x, I got a zero of 5/3.
Plugging in 5/3 and completing the process again gave me 997/687
Plugging in 997/687 and completing the process again gave me 1.36976
Plugging in 1.36976 and completing the process again gave me 1.359454
Plugging in 1.359454 and completing the process again gave me 1.359304
Since we are looking for accuracy to 3 decimal places, there was no need to go further.
Checking the zeros on the calculator graphing program gave me a zero of 1.3593041 which is exactly the same as my 5th iteration!
Newton's Method is absolutely amazing!!!
Answer:
x = 12
Step-by-step explanation:
Solve for x:
(2 x)/5 - 4 = 8 - (3 x)/5
Put each term in (2 x)/5 - 4 over the common denominator 5: (2 x)/5 - 4 = (2 x)/5 - 20/5:
(2 x)/5 - 20/5 = 8 - (3 x)/5
(2 x)/5 - 20/5 = (2 x - 20)/5:
(2 x - 20)/5 = 8 - (3 x)/5
Put each term in 8 - (3 x)/5 over the common denominator 5: 8 - (3 x)/5 = 40/5 - (3 x)/5:
(2 x - 20)/5 = 40/5 - (3 x)/5
40/5 - (3 x)/5 = (40 - 3 x)/5:
(2 x - 20)/5 = (40 - 3 x)/5
Multiply both sides by 5:
2 x - 20 = 40 - 3 x
Add 3 x to both sides:
3 x + 2 x - 20 = (3 x - 3 x) + 40
3 x - 3 x = 0:
3 x + 2 x - 20 = 40
2 x + 3 x = 5 x:
5 x - 20 = 40
Add 20 to both sides:
5 x + (20 - 20) = 20 + 40
20 - 20 = 0:
5 x = 40 + 20
40 + 20 = 60:
5 x = 60
Divide both sides of 5 x = 60 by 5:
(5 x)/5 = 60/5
5/5 = 1:
x = 60/5
The gcd of 60 and 5 is 5, so 60/5 = (5×12)/(5×1) = 5/5×12 = 12:
Answer: x = 12