Answer:
The half-life of the substance is about 288 days.
Step-by-step explanation:
The exponential decay function:
Can determine the amount <em>A</em> of a radioactive substance present at time <em>t. A₀ </em>represents the initial amount and <em>P</em> is the half-life of the substance.
We are given that a substance loses 70% of its radioactivity in 500 days, and we want to determine the period of the half-life.
In other words, we want to determine <em>P. </em>
Since the substance has lost 70% of its radioactivity, it will have only 30% of its original amount. This occured in 500 days. Therefore, <em>A</em> = 0.3<em>A₀</em> when <em>t</em> = 500 (days). Substitute:
Divide both sides by <em>A₀:</em>
We can take the natural log of both sides:
Using logarithmic properties:
So:
Take the reciprocal of both sides:
Use a calculator:
The half-life of the substance is about 288 days.
Answer:
x = 4
Step-by-step explanation:
12x + 5 = 4x + 37, first subtract both sides by 5 and subtract both sides by 4x
8x = 32, next divide 8 from both sides
x = 4
Answer:
k = 5
n = 10
p = 0.5
Step-by-step explanation:
Let X be a discrete random variable. The binomial probability formula is used to calculate the probability of obtaining k-successes in "n" independent trials for an experiment with probability of success p and probability of failure q.
The binomial formula is the following:
Where:
k = number of successes
n = number of trials
p = probability of success
q = probability of failure.
So, for the given problem
k = 5 Because you want to get the probability of getting 5 "heads"
n = 10 Because the experiment is repeated 10 times
p = 0.5 Because the probability of obtaining a "heads" when flipping a coin is 50%
q = 0.5
Total play = 20
Nancy win = 12
Ratio would be: 12/20 = 6/10 = 3/5
So, your answer is 3/5
Answer:
1=4(2)-7
Step-by-step explanation:
y=mx+b
b=where it crosses the y-axis
m=slope
1=4(2)-7
