Answer:
The probability that the last card dealt is an ace is 
.
Step-by-step explanation:
Given : A deck of ordinary cards is shuffled and 13 cards are dealt.
To find : What is the probability that the last card dealt is an ace?
Solution :
There are total 52 cards.
The total arrangement of cards is 52!.
There is 4 ace cards in total.
Arrangement for containing ace as the 13th card is 
.
The probability that the last card dealt is an ace is
Therefore, the probability that the last card dealt is an ace is .
Answer:
3.8
Step-by-step explanation:
A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains.
If a trip of 300 miles took 3 hour and 48 minutes, how much of it was through the mountains?
Let d = distance traveled at 37.5 (thru the mountains)
then
(300-d) = distance traveled at 90 mph
Write a time equation, time = dist/speed
change 3 hr 48 min to hrs: 3 + 48/60 = 3.8 hrs
plain time + mountain time = 3.8 hrs
%28300-d%29%2F90 + d%2F37.5 = 3.8
Multiply 90*37.5
3375*%28300-d%29%2F90 + 3375*d%2F37.5 = 3.8(3375)
cancel the denominator
37.5(300-d) + 90d = 12825
11250 - 37.5d + 90d = 12825
52.5d = 1575
d = 1575/52.5
d = 30 mi thru the mountains
Check this, find the distance on the plain
300-30 = 270 mi
Find the actual time at each speed
270/90 = 3 hrs
30/37.5 = .8 hrs
-----------------
total time: 3.8 hrs
Given two points 
, the slope of the line passing through the two points is
So, in your case, you have
Interval notation is used to write a set of real numbers from one value to another value.
On the left, you start with left parenthesis or left bracket.
Then you follow by two numbers separated by a comma.
You then finish with a right parenthesis or right bracket.
To include a number, use a square bracket.
To exclude a number use parenthesis.
To write the set of numbers, you need to list the smallest number in the set followed by the largest number in the set. An interval is always stated with two numbers, from the smallest in the set to the largest in the set. The numbers are always separated by a comma.
Examples:
1) All numbers from 6 to 10, including 6 and 10.
Algebra: 6 <= x <= 10
Interval: [6, 10]
Notice brackets since both 6 and 10 are included in this interval.
2) All number from 5 to 20, including 5 but not including 20.
Algebra 5 <= x < 20
Interval: [5, 20)
Bracket with 5 means include 5. Parenthesis with 20 means 20 is not included.
3) All numbers greater than or equal to 7.
Algebra: x >= 7
Interval: [7, ∞)
The 7 has a bracket because it is included. Infinity always has parenthesis.
With the infinity symbol, always use parenthesis, not square bracket.
4) All numbers less than -5.
Algebra: x < - 5
Interval: (-∞, 5)
Now for your problems.
10.
This is a line. Both the domain and range all all real numbers.
That means the interval is from negative infinity to positive infinity.
(-∞, ∞)
Both the domain and range are that same interval, all real numbers, from negative infinity to positive infinity.
13.
The domain is all real numbers as you can see the x-coordinates extend left forever and right forever. The domain is the same interval as the domain and range of problem 10.
The range is zero and all positive numbers.
You can think of it a all values of y such that y is greater than or equal to zero. Notice that zero is included in the interval.
[0, ∞)
Since zero is included, we use a left bracket, not left parenthesis.
With infinity, we alyways use parentheses, not brackets.
In exact form it would be 4/3
