9514 1404 393
Answer:
a) 600
b) see below
c) 1.26 hours
Step-by-step explanation:
a) The value of y when x=0 is the coefficient of the exponential term:
y = 600·3^(-0) = 600·1 = 600
There were 600 atoms to start.
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b) see attached for a graph
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c) The graph shows 150 atoms at t = 1.26, about 1.26 hours after the start of time counting.
If you want to find that value algebraically, substitute for y and solve for x. Logarithms are involved.
150 = 600·3^(-x)
150/600 = 3^(-x)
log(1/4) = -x·log(3)
x = -log(1/4)/log(3) = log(4)/log(3) ≈ 1.2618595
After about 1.26 hours, there were 150 atoms.
y = -2x + 1
y = -2x -3
none cuz they're both -2x
Answer: The value of the y-intercept is 
Step-by-step explanation:
The equation of the line in Slope-intercept form is:
Where "m" is the slope and "b" is the y-intercept.
In this case we know that the line passes through point 
and has a slope of 
. Then we can substitute the following values into :
Then:
And finally, we must solve for "b":
Answer:
The probability that a randomly chosen person has measles antibodies in his/her blood if the new test is positive = 0.9796
Step-by-step explanation:
The event that someone tests positive = P(T)
The event that someone has antibodies = P(A)
The event that someone does not have antibodies = P(A')
The new test was positive when administered to 96% of those who have the antibodies.
This probability = P(T n A) = 0.96
The new test gave positive results in 2% of those who do not have them.
This probability = P(T n A') = 0.02
The probability that a randomly chosen person has measles antibodies in his/her blood if the new test is positive = P(A|T)
This conditional probability is given as
P(A|T) = P(T n A) ÷ P(T)
P(T) is given as
P(T) = P(T n A) + P(T n A') = 0.96 + 0.02 = 0.98
P(A|T) = P(T n A) ÷ P(T) = 0.96 ÷ 0.98 = 0.9796
Hope this Helps!!!
