Work out area of ABCD

Area of ABCD = 45.1 cm²

Step-by-step explanation:

From the figure attached,

Area of ABCD = Area of ΔBCD + Area of ΔABD

Area of ΔABD =

sin(55°) =

sin(55°) =

AB = 10sin(55°)

AB = 8.19 cm

cos(55°) =

              =

AD = 10cos(55°)

AD = 5.74cm

Area of ΔABD =

                        = 23.51 cm²

Area of ΔBCD =

                        =

tan(38°) =

BE =

Similarly, DE =

Since, BE + DE = 10 cm

CE(1.28 + 1.04) = 10

CE(2.32) = 10

CE = 4.31 cm

Area of ΔBCD =

                       = 21.55 cm²

Area of ABCD = Area of ΔBCD + Area of ΔABD

                        = 21.55 + 23.51

                        = 45.06

                        ≈ 45.1 cm²

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560