Aand b alternate rolling a pair of dice, stopping either when a rolls the sum 9 or when b rolls the sum 6. assuming that a rolls first, find the probability that the final roll is made by a.

There are 6*6 total combinations = 36 combinations.

For A: the probability that one rolls a 9 is 4/36

(9  = 3&6, 6&3, 4&5, 5&4) 

For B: the probability that one rolls a 6 is 5/36 

(6  = 3&3, 1&5, 5&1, 2&4, 4&2) 

So find the probability that final roll is made by A:
P(A wins) = P(A wins in first roll) + P(A wins in 3rd roll) +  
P(A wins) = 4/36 + (32/36)*(31/36)*(4/36) + (32/36)^2 *(31/36)^2 *(4/36) + ... 

Therefore we see that the common ratio is (32*31/36^2) 

Sum is = (4/36) / [1 - (32*31/36^2)] 
= 144 / 304 
= 9 / 19     (ANSWER)

725 parts per hour.

step-by-step explanation:

hi there, this answer is actually really simple.

you can set it up as 1450/2 or 3625/5 to find the answer.

they want to know how much per hour is being made, so you just divide.

1450/2=725.

and that's how many are produced per hour.

hope this . : )

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.