N=11 because 4+10= 14 and 25-14 = 11
This pic is the answer i believe
Answer:
210
Step-by-step explanation:
Given:
Medals in sports = 40
Medals in dance = 25
Medals in music = 212
Total students that received medals = 55
Total students that received medals in all three categories = 6
Required:
How many students get medals in exactly two of these categories?
Take the following:
A = set of persons who got medals in sports.
B = set of persons who got medals in dance
C = set of persons who got medals in music.
Therefore,
n(A) = 40
n(B) = 25
n(C) = 212
n(A∪B∪C)= 55
n(A∩B∩C)= 6
To find how many students get medals in exactly two of these categories, we have:
n(A∩B) + n(B∩C) + n(A∩C) −3*n(A∩B∩C)
=n(A∩B) + n(B∩C) + n(A∩C) −3*6 ……............... (1)
n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)
Thus, n(A∩B)+n(B∩C)+n(A∩C)=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)
Using equation 1:
=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)−18
Substitute values in the equation:
= 40 + 25 + 212 + 6 − 55 − 18
= 283 - 73
= 210
Number of students that get medals in exactly two of these categories are 210
Answer:
(-10,-10)
Step-by-step explanation:
9x-9y=0
3x-4y=10
In elimination, we want both equations to have the same form and like terms to be lined up. We have that. We also need one of the columns with variables to contain opposites or same terms. Neither one of our columns with the variables contain this.
We can do a multiplication to the second equation so that the first terms of each are either opposites or sames. It doesn't matter which. I like opposites because you just add the equations together. So I'm going to multiply the second equation by -3.
I will rewrite the system with that manipulation:
9x-9y=0
-9x+12y=-30
----------------------Add them up!
0+3y=-30
3y=-30
y=-10
So now once you find a variable, plug into either equation to find the other one.
I'm going to use 9x-9y=0 where y=-10.
So we are going to solve for x now.
9x-9y=0 where y=-10.
9x-9(-10)=0 where I plugged in -10 for y.
9x+90=0 where I simplified -9(-10) as +90.
9x =-90 where I subtracted 90 on both sides.
x= -10 where I divided both sides by 9.
The solution is (x,y)=(-10,-10)
D. After 150 minutes, the 5 cent one is more.
Hope this helps!
