Answer:
<em>Probability ≈ 0.0714</em>
Step-by-step explanation:
Consider permutation and combination;
Answer:
A) slope = p/q
Step-by-step explanation:
Slope of any given can be found using the formula, 
.
In this case, using similar triangles, the rise over the run of any of the given similar triangles will give us the slope of line AB.
This means, slope of line AB would be:
.
✅Therefore, slope of line AB = p/q
Answer:
Step-by-step explanation:
The equation of a straight line can be written as 
.
With the pair of coordinates (coordinates are written in the form 
) , the following can be written:
To solve for a variable, we can use elimination:
(subtract the second equation from the first)
(
is eliminated)
To solve for the other variable, we can use substitution:
is the linear equation for the line that passes through the points 
and 
Answer:
Vertex = (12,64)
The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
X-intercepts: 4 and 20
The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
Step-by-step explanation:
To find the vertex we can use the formula for the x-coordinate of the vertex:
x_v = -b/2a
Where a and b are coefficients of the quadratic equation (in this case, a = -1 and b = 24)
So we have that:
x_v = -24 / (-2) = 12
The vertex is 12 cups of coffee. Now we apply this value to find the y-coordinate of the vertex:
f(x) = -12^2 + 24*12 - 80 = 64
So the vertex is (12,64). The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
To find the x-intercepts, we need to make f(x) = 0 and find the values of x:
-x2 + 24x - 80 = 0
Delta = 24^2 - 80*4 = 256
sqrt(Delta) = 16
x1 = (-24 + 16)/(-2) = 4
x2 = (-24 - 16)/(-2) = 20
The x-intercepts are 4 and 20. The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
