Joseph has two pieces of rope. the longer piece is one foot less than four times the length of the smaller piece. together the two pieces measure 14 feet. how long is each piece of rope?

The answer to your question is: x = 57/5 and y = 13/5

Step-by-step explanation:

Data

x = longer piece = 1 foot less than four times of the smaller piece

y = smaller piece

Equations

                 x - 1 = 4y           (1)

                 x + y = 14           (2)           Clear y from the first equation

                y = (x - 1) / 4                       solve by substitution in 2

                x + (x - 1) / 4 = 14

               4x + x - 1 = 56

               5x = 57

                  x = 57 / 5    feet

               y = (57/5 - 1 ) / 4

               y = ((57-5)/5)/4

               y = 52/2 = 26/10 = 13/5

step-by-step explanation:

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