Answer:
A
Step-by-step explanation:
Answer:
142.932
Step-by-step explanation:
given that in triangle ABC, AC =24
Angle A = 30 and Angle B =45
If we draw altitude from C, we get
h = 24sin 30 = 12
Since BC = h (45, 45,90 triangle)
BC=12
By sine formula for triangle
Area of triangle
= 
Answer:
- <u><em>P(M) = 0.4</em></u>
Explanation:
<u>1. Build a two-way frequency table:</u>
To have a complete understanding of the scenary build a two-way frequency table.
Major in math No major in math Total
Major in CS
No major in CS
Total
Major in math No major in math Total
Major in CS
No major in CS
Total 200
- <u>80 plan to major in mathematics:</u>
Major in math No major in math Total
Major in CS
No major in CS
Total 80 200
- <u>100 plan to major in computer science</u>:
Major in math No major in math Total
Major in CS 100
No major in CS
Total 80 200
- <u>30 plan to pursue a double major in mathematics and computer science</u>:
Major in math No major in math Total
Major in CS 30 100
No major in CS
Total 80 200
- <u>Complete the missing numbers by subtraction</u>:
Major in math No major in math Total
Major in CS 30 70 100
No major in CS 100
Total 80 120 200
Major in math No major in math Total
Major in CS 30 70 100
No major in CS 50 50 100
Total 80 120 200
<u>2. What is P(M), the probability that a student plans to major in mathematics?</u>
- P(M) = number of students who plan to major in mathematics / number of students
Answer:
- 12 ft parallel to the river
- 6 ft perpendicular to the river
Step-by-step explanation:
The least fence is used when half the total fence is parallel to the river. That is, the shape of the rectangle is twice as long as it is wide.
72 = W(2W)
36 = W²
6 = W . . . . . . the width perpendicular to the river
12 = 2W . . . . the length parallel to the river
_____
<em>Development of this relation</em>
Let T represent the total length of the fence for some area A. Then if x is the length along the river, the width is y=(T-x)/2, and the area is ...
A = xy = x(T -x)/2
Note that the equation for area is that of a parabola with zeros at x=0 and at x=T. That is, for some fence length T, the area will be a maximum at the vertex of this parabola. That vertex is located halfway between the zeros, at ...
x = (0 +T)/2 = T/2
The corresponding area width (y) is ...
y = (T -T/2)/2 = T/4
Equivalently, the fence length T will be a minimum for some area A when x=T/2 and y=T/4. This is the result we used above.
