Answer:
Inverse Function: f^-1(x) = 9/4x + 9
Step-by-step explanation:
To find the inverse function we can interchange the position of the variables x and y, and then solve for y;
y = 4/9x - 4 => x = 4/9y - 4,
x = 4/9y - 4,
4/9y = x + 4,
y = 9/4x + 9/4(4),
y = 9/4x + 9/ f^-1(x) = 9/4x + 9
Answer:
The area of triangle K is 16 times greater than the area of triangle J
Step-by-step explanation:
we know that
If Triangle K is a scaled version of Triangle J
then
Triangle K and Triangle J are similar
If two triangles are similar, then the ratio of its areas is equal to the scale factor squared
Let
z -----> the scale factor
Ak ------> the area of triangle K
Aj -----> the area of triangle J
so

we have

substitute



therefore
The area of triangle K is 16 times greater than the area of triangle J
We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.
From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words,
.
We also know that E=5% or E=0.05
Also, since,
is not given, we will assume that
=0.5. This is because, the formula that we use will have
in the expression and that will be maximum only when
=0.5. (For any other value of
, we will get a value less than 0.25. For example if,
is 0.4, then
and thus,
.).
We will now use the formula

We will now substitute all the data that we have and we will get



which can approximated to n=271.
So, the brand manager needs a sample size of 271
Let the numbers be x and y.
x*y=HCF*LCM=6*60=360
thus
y=360/x
next we find the list of combinations of x and y and test if they satisfy the conditions above:
(6,60),(12,30),(18,20),(24,15)
out of the above, only (6,60) and (12,30) satisfy both conditions. Thus our answer is:
(6,60) or (12,30)