The mass of radioactive material remaining after 50 years would be 48.79 kilograms
<h3>How to determine the amount</h3>
It is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.
Given the radioactive decay formula as
m(t)=120e−0.018t
Where
t= 50 years
m(t) is the remaining amount
Substitute the value of t
Find the exponential value
m(t) = 48.788399
m(t) = 48.79 kilograms to 2 decimal places
Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms
Learn more about half-life here:
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The answer is a equals 6.
Answer:
The total distance of the round trip was 4 miles
Step-by-step explanation:
1. Let's check all the information given to answer the question correctly:
Speed of Dave walking to his friend's house = 4 mph
Speed of Dave biking from his friend's house = 10 mph
Time walking is 18 minutes longer than time biking
2. What was the total distance of the round trip?
Time walking = x
Time biking = x - 18
For solving x, we will use the following equation:
4x = 10 * (x - 18)
4x = 10x - 180
-6x = - 180
x = -180/-6 (Dividing by - 6)
x = 30
Dave walked 30 minutes and biked 12 minutes, now we can calculate the total distance, this way:
30 minutes = 0.5 hours and 12 minutes = 0.2 hours
Total distance = 4 *0.5 + 10 * 0.2
Total distance = 2 + 2
Total distance = 4 miles.
Problem: A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? How much does each person cost? Show this using y = mx + b form.
Solution:
Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.
Then, when there are 30 people on the bus (x = 30), the cost was $180 (y = 180). This means the point (x, y) = (30, 180).
Also, when there were 50 people on the bus, the cost was $220. So that is the point (50, 220).
You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.
The slope of the line joining two points is the rise divided by the run. That means
m = (y2 - y1) / (x2 - x1)
So we put in the values of (30, 180) and (50, 220):
m = (220 - 180) / (50 - 30)
m = 40 / 20
m = 2.
The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:
y = 2x + b.
This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:
220 = 2(50) + b
220 = 100 + b
b + 100 = 220
b = 120.
Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:
y = 2x + 120.
For the other questions, I can look at the equation I got. The y-intercept (b value) is $120. That means that we are adding $120 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.
Here's an example: if you had just 10 people on the bus, you'd pay $120 for the empty bus and $2 for each person. That's $20 for the people and $120 for the bus. That total is $140. Let's see if (10, 140) works in the equation we got:
y = 2x + 120
140 ?=? 2(10) + 120
140 ?=? 20 + 120
yes. 140 = 140. It does work.
Now you try it with your question.
