-2x - 8 > -12
-2x - 8 + 2x > -12 + 2x ...... add 2x to both sides
-8 > -12 + 2x
-8+12 > -12+2x+12 .... add 12 to both sides
4 > 2x
2x < 4 ..... flip both sides so that the x term is on the left side
2x/2 < 4/2 .... divide both sides by 2
x < 2
This describes the set of x values such that x is less than 2.
The largest integer that x can be is x = 1. The value of x cannot be 2 because we don't have an "or equal to" as part of the inequality sign.
Final Answer: 1
There was 3000 general admission tickets sold and 500 kid ticket sold.
How did I get this?
First, we need to see what information we have.
$2.50 = General admission tickets = (G)
$0.50 = kids tickets = (K)
There were 6x as many general admission tickets sold as kids. G = 6K
We need two equations:
G = 6K
$2.50G + $.50K = $7750
Since, G = 6K we can substitute that into the 2nd equation.
2.50(6K) + .50K = 7750
Distribute 2.50 into the parenthesis
15K + .50K = 7750
combine like terms
15.50K = 7750
Divide both sides by 15.50, the left side will cancel out.
K = 7750/15.50
K = 500 tickets
So, 500 kid tickets were sold.
Plug K into our first equation (G = 6k)
G = 6*500
G = 3000 tickets
So, 3000 general admission tickets were sold,
Let's check this:
$2.50(3000 tickets) = $7500 (cost of general admission tickets)
$.50(500 tickets) = $250 (cost of general admission tickets)
$7500 + $250 = $7750 (total cost of tickets)
Answer:
pradis has more orange slices
reason:The ratio of apple slices to the total number of slices on Praxis plate is 4 to 11. This means for every 11 slices in Praxis plate, 4 of them are apple slices and 7 of them are orange slices. This also shows the total number of slices in Praxis plate is a multiple of 11.
First possibility of total number of slices in Praxis plate is 11. Another possibility of total number of slices in Praxis plate is 11 x 2 = 22. Since, it is given that total number of slices are not more than 20, so 22 slices are not possible in Praxis plate. So, the only possibility is 11 slices. From here we can conclude that: Number of slices in Pam Plate:
The ratio of the total number of slices to orange slices on Pam plate is 13 to 6. This means for every 13 slices in Pam's plate there are 6 orange slices and 7 apple slices. This also show the total number of slices in Pam's plate is a multiple of 13.
The first possibility of total number of slices in Pam's plate is 13. The next possibility is 13 x 2 = 26 slices. But since the number of slices cannot be above 20, the only possibility is that there are 13 slices in Pam's plate. From here we can conclude that:
If A and B are independent, then 
.
a.
b. I'm guessing the ? is supposed to stand for intersection. We can use DeMorgan's law for complements here:
c. DeMorgan's law can be used here too:
