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timama [110]
4 years ago
12

Find the area of rectangle ABCD

Mathematics
1 answer:
zubka84 [21]4 years ago
8 0
Find the length of the rectangle with pythagoras
You can use point (0,0) and (3,3) as the reference points.
l = √(Δx² + Δy²)
l = √((3-0)² + (3-0)²)
l = √(3² + 3²)
l = √18

Find the width of the rectangle with pythagoras
You can use point (0,0) and (2,-2) as the reference points.
w = √(Δx² + Δy²)
w = √((-2-0)² + (2-0)²)
w = √((-2)² + 2²)
w = √(4 + 4)
w = √8

Find the area of rectangle
A = l × w
A = √18 × √8
A = √9 × √2 × √4 × √2
A = 3 × √2 × 2 × √2
A = 12

The area of the rectangle is 12 unit length
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3 years ago
Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let X and Y
harina [27]

Answer:

Expected revenue from the single trip is $ 13.14

Step-by-step explanation:

                              y

p(x,y)                   0               1                                 2                g(x)

x    0           0.025              0.015                       0.010            0.05

1                  0.050            0.030                        0.020           0.1  

2                   0.115             0.075                        0.050           0.24

3                  0.150              0.090                      0.060             0.3

<u>4                   0.100             0.060                     0.040              0.2 </u>

h(y)              0.325              0.27                       0.18  

E (x+Y) = E(X) +E(Y)

E(X)= ∑ xi g(x)i

       = ( 0*0.05) + (1*0.1) + (2* 0.24) + (3*0.3) + (4*0.2)

        = 0 + 0.1+ 0.48 + 0.9+0.8

        =2.28

E(Y)= ∑yi h(y)

      = (0* 0.325) + (1*0.27) + (2*0.18)    

       = 0 +0.27+ 0.36

        = 0.63

E (x+Y) = E(X) +E(Y)

             = 2.28 + 0.63

                = 2.91

But the equation is 3x+ 10y

E(3x+ 10y)= 3E(x) + 10 E(y)

                   = 3(2.28) + 10 (0.63)

                       = 6.84 +6.3

                         = 13.14

Expected revenue from the single trip is $ 13.14

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3 years ago
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