Answer:
46.22
Step-by-step explanation:
Class A total= 23 x 13= 299
Clas B total= 57 x 28= 1596
total score= 299 + 1596 = 1895
total mean= 1895 ÷ (13+28) = 1895 ÷ 41
= 46.22
Answer:
\[y < = 300\]
Step-by-step explanation:
Let x = number of out-of-state students at the college
Let y = number of in-state students at the college
As per the given problem, the constraints are as follows:
\[x < = 100\] --------- (1)
\[y = 3 * x\] --------- (2)
From the given equations (2), \[ x = y/3 \]
Substituting in (1):
\[y/3 < = 100\]
Or, \[y < = 300\] which is the constraint representing the incoming students.
Answer:
y = x - 3
Step-by-step explanation:
You have to complete the square to get it into vertex form. Do this by setting the function equal to zero and at the same time moving the constant over to the other side of the equals sign so you have this:
![x^{2} +4x=-10](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2B4x%3D-10)
. Now we can complete the square on the polynomial by taking half the linear term, squaring it, and adding it to both sides. Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so we add 4 to both sides:
![( x^{2} +4x+4)=-10+4](https://tex.z-dn.net/?f=%28%20x%5E%7B2%7D%20%2B4x%2B4%29%3D-10%2B4)
and simplify to get
![( x^{2} +4x+4)=-6](https://tex.z-dn.net/?f=%28%20x%5E%7B2%7D%20%2B4x%2B4%29%3D-6)
. In this process we have created a perfect square binomial on the left, which happens to be
![(x+2) ^{2}=-6](https://tex.z-dn.net/?f=%28x%2B2%29%20%5E%7B2%7D%3D-6%20)
. Now move the -6 back over by addition to get
![(x+2) ^{2} +6=y](https://tex.z-dn.net/?f=%28x%2B2%29%20%5E%7B2%7D%20%2B6%3Dy)
. The vertex is found at (-2, 6), the third choice down.
Each container is 50 pounds, forget about the second sentence it's just there to confuse you. One ton is 2,000 pounds, half of that is 1,000 lbs. 1,000 divided by 20 is 50. 50 pounds each.