<span>Constraints (in slope-intercept form)
x≥0,
y≥0,
y≤1/3x+3,
y</span>≤ 5 - x
The vertices are the points of intersection between the constraints, or the outer bounds of the area that agrees with the constraints.
We know that x≥0 and y≥0, so there is one vertex at (0,0)
We find the other vertex on the y-axis, plug in 0 for x in the function:
y <span>≤ 1/3x+3
y </span><span>≤1/3(0)+3
y = 3.
There is another vertex at (0,3)
Find where the 2 inequalities intersect by setting them equal to each other
(1/3x+3) = 5-x Simplify Simplify Simplify
x = 3/2
Plugging in 3/2 into y = 5-x: 10/2 - 3/2 = 7/2
y=7/2
There is another vertex at (3/2, 7/2)
There is a final vertex where the line y=5-x crosses the x axis:
0 = 5 -x , x = 5
The final vertex is at point (5, 0)
Therefore, the vertices are:
(0,0), (0,3), (3/2, 7/2), (5, 0)
We want to maximize C = 6x - 4y.
Of all the vertices, we want the one with the largest x and smallest y. We might have to plug in a few to see which gives the greatest C value, but in this case, it's not necessary.
The point (5,0) has the largest x value of all vertices and lowest y value.
Maximum of the function:
C = 6(5) - 4(0)
C = 30</span>
Answer:
P(X = 3) = 0.14680064
Step-by-step explanation:
Formula=============================
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Given :
n = 8
p = 0.2
1 - p = 1 - 0.2 = 0.8
k = 3
Then
Answer:
<em>2(15+8)</em>
Step-by-step explanation:
Given the expression 30+16
We are to use GCF to rewrite the sum as a product.
Get the factor of each value first as shown;
30 = 2 * 15
16 = 2 * 8
substitute the factors back into the expression:
30+16 = (2*15)+(2*8)
Since 2 is common to both terms, then:
30+16 = 2(15+8)
<em></em>
<em>Hence the required sum of product of the terms is 2(15+8)</em>
Answer:
Hypotenuse: 100
Segment Adjacent to the leg: 36
x=60
Step-by-step explanation:
I submitted and it was correct
Answer:
106 and 107
Step-by-step explanation:
Integers are just numbers that doesn't have a decimal point.
1, 2, 3, 4, and 5 are integers.
1.123, 2.45312, 3.5, 7.9 are NOT integers
105 is between 106 and 107.
