Answer: -2/5
Step-by-step explanation:
To find the slope, we set the function use y = mx + b forms.
2x + 5y = 10
5y = -2x + 10 Minus 2x in both side
y = -2/5x + 10/5 Divide 5 from both side
y = -2/5x + 2
In the y = mx + b, the m before variable x is always the slope, so -2/5 is the slope for 2x + 5y = 10.
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:
A) 25
Step-by-step explanation:
You use x= -b/2a in order to get your maximum so x= -10/ 2(-5) and you get x=1. You plug 1 into the function as h(1)=-5(1)^2 + 10(1)+ 20 which gets you 25
D. (I used 3.14 as pi so my answer was a little off so I just went with the one closest to my answer)
D = {16, 19, 21}
E = {16, 18, 19, 20}
D ∩ E = {16, 19}