Answer:
Given that,
The number of grams A of a certain radioactive substance present at time, in years
from the present, t is given by the formula

a) To find the initial amount of this substance
At t=0, we get


We know that e^0=1 ( anything to the power zero is 1)
we get,

The initial amount of the substance is 45 grams
b)To find thehalf-life of this substance
To find t when the substance becames half the amount.
A=45/2
Substitute this we get,


Taking natural logarithm on both sides we get,







Half-life of this substance is 154.02
c) To find the amount of substance will be present around in 2500 years
Put t=2500
we get,




The amount of substance will be present around in 2500 years is 0.000585 grams
The diameter is the line that goes through the middle of a circle and the radius goes from the center to a point in the circle so r = d/2 or d =2r
C. d/2
Answer:
Z=-2
This value means that the score of Rachel 550 it's 2 deviations below the mean of the population
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
represent the population mean for the Graduate Record Exam (GRE)
represent the population standard deviation for Graduate Record Exam (GRE)
2) Solution to the problem
Let X the random variable that represent the Graduate Record Exam (GRE) of a population, and for this case we know the distribution for X is given by:
Where
and
We want to find the z score for a score of 550. And in order to do this we need to apply the formula for the z score given by:
If we apply this formula to our probability we got this:

So the answer for our case would be Z=-2
This value means that the score of Rachel 550 it's 2 deviations below the mean of the population