Between the probability of union and intersection, it's not clear what you're supposed to compute. (I would guess it's the probability of union.) But we do know that
For parts (a) and (b), you're given everything you need to determine
.
For part (c), if
and
are mutually exclusive, then
, so
. If the given probability is
, then you can find
. But if this given probability is for the intersection, finding
is impossible.
For part (d), if
and
are independent, then
.
Answer:
(5,-1) or x=5 y=-1
Step-by-step explanation:
I used the substitution method to solve this!
<em>1. Pick one of your equations and solve for one of the variables. I chose the first equation and solved for x.</em>
x-2y=7
(Move the -2y to the other side of the equation in order to get the x by itself. You do the opposite, so it becomes +2y.)
x=2y+7
<em>2. Now take your second equation and plug in what you got for x into the x variable.</em>
2(2y+7)+5y=5
(Multiple 2 by everything inside of the parentheses.)
4y+14+5y=5
(We want to get the y by itself, so move the 14 to the other side.)
4y+5y=-14+5
(Combine all the like terms.)
9y=-9
(Divide the 9 from the y. What you do to one side you must do to the other.)
y=-1
<em>3. Since you have one variable solved for. Now take the first equation and plug in your y.</em>
x-2(-1)=7
(Multiple -2 by -1)
x+2=7
(Move the 2 to the other side in order to get the x by itself.)
x=5
<em>4. If needed, plug in your x and y values into the equations in order to check your answer.</em>
Hope this could help!
Answer:
the system of equation has infinite solution
Step-by-step explanation:
, 
Solve the first equation for x_2
Subtract 5x1 on both sides
Now substitute -5x1 on second equation
0=0
So the system of equation has infinite solution
The formula for the volume of pyramid is,
Here, B is base area and height of pyramid.
The volume expression for group 4 is,
Here, expression,
represents the base area and 9 represent the height of pyramid.
So height of the pyramid created by group 4 is 9.
Answer: 9
