They lost 15 yards because once you multiply 3*5=15.
If you want to check if (1,2) is a solution to the system, you have to plug the x and y values back into both equations. If they work for one equation, but not the other, than the coordinates are not a solution to the system.
3(1) - 4(2) = -5
3 - 8 = -5
-5 = -5
2 = 4(1) - 2
2 = 4 - 2
2 = 2
Since both of these checks are true, then (1,2) is a solution to the system.
In order to determine the expression that should be multiplied to n^2 to get 5n^3, divide 5n^3 by n^2. First for the numerical coefficient, 5 divide 1 is 5. For the variable n, n^3/n^2 is n. Thus, the term that should be multiplied to n^2 is 5n.
Answer:
a) 336
b) 593775
c) 83160
d) P=0.14
e) P=0.0019
Step-by-step explanation:
We have wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet.
a) If he wants to serve 3 bottles of zinfandel and serving order is important. We get:
C=8·7·6=336
b) {30}_C_{6}=\frac{30!}{6!(30-6)!}
{30}_C_{6}=593775
c) {8}_C_{2} · {10}_C_{2} · {12}_C_{2}=
=\frac{8!}{2!(8-2)!} · \frac{10!}{2!(10-2)!} · \frac{12!}{2!(12-2)!}
=28 · 45 · 66
=83160
d) We calculate the number of possible combinations:
{30}_C_{6}=593775
We calculate the number of favorable combinations:
{8}_C_{2} · {10}_C_{2} · {12}_C_{2}=83160
The probability that this results in two bottles of each variety being is
P=83160/593775
P=0.14
e) We calculate the number of possible combinations:
{30}_C_{6}=593775
We calculate the number of favorable combinations:
{8}_C_{6} + {10}_C_{6} + {12}_C_{6}= 28+210+924=1162
The probability is
P=1162/593775
P=0.0019