Which expressions are equivalent to -4(-25y + 4 + 50y - 8)? Select all that apply. A - 100 y - 4 -2123y - 5 + 27y - 3) B C (100y
1 answer:
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Answer:
Step-by-step explanation:
The given system is:
Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.
This gives me the system:
We could solve the first equation for and replace the second
with that.
Let's do that.
Subtract on both sides:
So we are replacing the second in the second equation with
which gives us:
Now recall the first equation we arranged so that was the subject. I'm referring to
.
We can now find given that
using the equation
.
Let's do that.
with
:
So the solution is (8,-1).
We can check this point by plugging it into both equations.
If both equations render true for that point, then we have verify the solution.
Let's try it.
with
:
is a true equation so the "solution" looks promising still.
with
:
is also true so the solution has been verified since both equations render true for that point.
Answer:
0.0588 = 5.88% probability that a middle-aged man with diabetes is very active
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Has diabetes.
Event B: Is very active.
Probability of having diabetes:
To find this probability, we take in consideration that:
It also found that men who were very active (burning about 3,500 calories daily) were a fourth as likely to develop diabetes compared with men who were sedentary. Assume that one-fifth of all middle-aged men are very active, and the rest are classified as sedentary.
So the probability of developing diabetes is:
x of 4/5 = x of 0.8(not active)
x/4 = 0.25x of 1/5 = 0.2(very active). So
Probability of developing diabetes while being very active:
0.25x of 0.2. So
What is the probability that a middle-aged man with diabetes is very active?
0.0588 = 5.88% probability that a middle-aged man with diabetes is very active
Use the law of cosines:
We have:
substitute: