See attachment and show work. you. will mark

a. Let c and b represent the numbers of capped and broken bottles, respectively. Here is the system of equations.

... c + b = 15 . . . . 15 bottles have come Erica's way

... 4c -2b = 6 . . . .Erica's net pay for the day is 6 cents

b. By substitution, we can write an expression for b in terms of c:

... b = 15 - c

Then put it into the second equation:

... 4c - 2(15-c) = 6

... 6c - 30 = 6 . . . . eliminate parentheses

... 6c = 36 . . . . . . .add 30

... c = 6 . . . . . . . . . divide by 6

... b = 15 - 6 = 9 . . find the value of b

Erica has capped 6 bottles and broken 9.

Here's one way to do it by elimination. We can divide the second equation by 2 to put it into standard form:

... 2c - b = 3

Now, adding it to the first equation gives

... (2c -b) + (c +b) = (3) + (15)

... 3c = 18 . . . . . simplify. Notice the b variable has been eliminated

... c = 6 . . . . . . . divide by 3

... 6 + b = 15

... b = 9 . . . . . . substitute into the first equation and solve for b by subtracting 6

Erica has capped 6 bottles and broken 9. (same solution as above)

y=mx+b is the final answer!   : )

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