Answer:
a. the investment earns 4%
b. yes
Step-by-step explanation:
The "rule of 72" says that an investment earning compound interest at x% will double in value after 72/x years. That is, ...
f(x) = 72/x
__
<h3>a.</h3>
We interpret f(4) to mean Becky's friend is interested in the doubling time for an investment that earns 4% interest.
__
<h3>b.</h3>
Using the above formula, ...
f(4) = 72/4 = 18
The friend's math is correct.
Answer
The missing length is 10
Step-by-step explanation:
Represent the missing length with x
The sides of the given shape are directly proportional.
Mathematically:
(15 + x) to (12 + 8) and x to 7
Represent as a ratio:


Convert to fraction

Cross Multiply:


Collect Like Terms


Solve for x


<em>The length of the missing side is 10</em>
Answer:
Step-by-step explanation:
given a point
the equation of a line with slope m that passes through the given point is
or equivalently
.
Recall that a line of the form
, the y intercept is b and the x intercept is
.
So, in our case, the y intercept is
and the x intercept is
.
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph
. Which means that 
The slope of the tangent line is given by the derivative of the function evaluated at
. Using the properties of derivatives, we get
. So evaluated at
we get 
Replacing the values in our previous findings we get that the y intercept is

The x intercept is

The triangle in consideration has height
and base
. So the area is

So regardless of the point we take on the graph, the area of the triangle is always 2.
If you choose 10 swimmers and 4 are Stingrays, you can say that Stingrays make up roughly 40% of the swimmers. If 20 Stingrays make up 40% of all the swimmers, we just have to find what number 20 is 40% of. That’s easy enough by cross multiplication:
20/x = 40/100
20/x = 4/10
20/x = 2/5
x = 50.
Double check by multiplying 50 * 0.4. Since 50 * 0.4 = 20, we know we have the right answer. There are about 50 swimmers on this team.