This is middle school??? AinT no way
Answer:
21.759
Step-by-step explanation:
Given that :
Mean (m) = 25
Standard deviation (s) = 12.5
Sample size (n) = 40
α = 90%
The confidence interval is obtained using the relation:
Mean ± Zcritical * s/sqrt(n)
Zcritical at 90% confidence interval = 1.64
25 ± 1.64 * (12.5/sqrt(40))
Lower boundary : 25 - 1.64(1.9764235) = 21.75866546
Upper boundary : 25 + 1.64(1.9764235) = 28.24133454
(21.759, 28.241)
Hence, lower bound of confidence interval is : 21.759
Answer:
An equation represents the number of pieces of lasagna that are left after dinner is 
Step-by-step explanation:
Each piece of Lasagna is 1/6 of the pan
Let x be the number of pieces left
So, x pieces is
of the pan
We are given that After dinner 2/3 of a pan of lasagna is left.
So, 

x=4
So, Number of pieces left = 4
Hence An equation represents the number of pieces of lasagna that are left after dinner is 
We are given that there are a total of 78 students. If we set the following variables:

Then, the sum of all of these must be 78, that is:

Since there are 15 in chemistry and physics and 47 in chemistry, we may replace that into the equation and we get:

Simplifying:

Now we solve for P by subtracting 62 on both sides:

Therefore, there are 16 students in physics
Either would work, but substitution looks a bit easier.
The graph for these two is shown below.
I just put the equations in just as they are written. They did not have to be changed in any way. DESMOS is a wonderful program. Very powerful.
The blue line is 2x + y = - 6
The red line is y = x + 3
The best way to solve this other than a graph is to use substitution. Put the red graph into the blue one.
2x + y = - 6
2x +(x + 3) = - 6
2x + x + 3 = - 6
3x + 3 = - 6 Subtract 3 from both sides.
3x = - 6 - 3
3x = - 9
x = -9/3
x = -3
Now go back and solve for y
y = x + 3
y = -3 + 3
y = 0
Answer
The solution point is (-3,0) just what the graph shows.