Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
We will simplify this first a bit by dividing 2000 by 1150 to get
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.
Answer:
The ratio of the number of female teachers to the number of male teachers is 18:5.
Step-by-step explanation:
First: Review how to write a ratio:
To write a ratio, take the two quantities, and put them on both sides of a colon (:). So, our two quantities our 18 and 5. But, they need to be in a specific order:
There are 18 female teachers and 5 male teachers at Ashley's school. What is the ratio of the number of female teachers to the number of male teachers?
Since, they mentioned the number of female teachers first, we put the quantity of female teachers first. So we will write 18 first and 5 after. So, the ratio is 18:5.
Thank you for reading
Topic: Ratios
The expression has 2 factors, and the second factor has 2 terms.
<h3 /><h3>How many factors has the expression?</h3>
We can write an expression of N factors as:
Here, the expression is:
4*(8x + 5)
This expression has 2 factors, which are:
4 and (8x + 5)
Now, if we look at the only factor 8x + 5, we have two terms (the terms are the parts that are added), the terms are:
8x and 5.
If you want to learn more about factors and terms:
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Answer:
2000 meters
Step-by-step explanation:
When the motorboat is moving downstream, its speed relative to the ground is 18 km/h, so its speed relative to the raft is 15 km/h.
When the motorboat is moving upstream, its speed relative to the ground is 12 km/h, so its speed relative to the raft is again 15 km/h.
Converted to m/min, the relative speed is:
15 km/h × (1000 m/km) × (1 h / 60 min) = 250 m/min
It takes the motorboat 16 minutes to travel to the front of the raft and back. Since the speed is the same in both directions, the motorboat takes 8 minutes to travel the length of the raft.
So the length of the raft is 250×8 = 2000 meters.
