Answer:
There is a 99.99998% probability that at least one valve opens.
Step-by-step explanation:
For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
Calculate P(at least one valve opens).
This is 
Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:
So
Finally
There is a 99.99998% probability that at least one valve opens.
Answer:
6x - 5y = -5
Step-by-step explanation:
Your FIRST goal is to fill out y = mx + b with the values of m (your slope) and b (your y-intercept). First, find m by dividing the change in y in the two points given by their change in x. (43 - 31)/(35-25) = 12/10 = 6/5. Plug this in immediately for a "placeholder equation" of y = 6/5x + b, which you can plug either of your points into and solve for b.
43 = 6/5(35) + b
43 = 42 + b
1 = b
Your SLOPE-INTERCEPT equation is y = 6/5x + 1. However, you were asked for standard form. This means you must convert into ax + by = c, where a b and c are all whole numbers, and a is positive.
y = 6/5x + 1
-6/5x + y = 1
6/5x - y = -1
6x - 5y = -5, and this is your final answer.
Let me know if you need a more in-depth explanation on any part of this!
2/3 = 8/12. So the answer is 4/12
Answer:
lets call the children, c, and call adult, a,
c+a= 52 eq 1: a=52-c
c=3a eq 2
take a's value from eq 1 and plug it into eq 2
c=3(52-c)
c=156-3c
4c=156
c=39 the number of children that attended the ball game.
Step-by-step explanation:
Answer:
It would be 8 PM.
Step-by-step explanation:
If you keep decreasing 23 by 7 till you get to -5, it would have to be decreased 4 times to get to -5. This means that the time would have to go up 4 times the 45 minute rate, which would be 3 hours. 5 pm + 3 hours is 8 PM.
