Answer:
A = P x r^t
Step-by-step explanation:
A = Amount (e.g. number of organisms in population after certain period of time)
P = Principal/ Initial Value (e.g. the starting population)
r = rate as a decimal (e.g. if a population increases over certain period of time by 20%, r would equal 1.2)
t = time in whichever units you need.
Example of problem using formula:
A population of 2000 decreases by 20% every year, find the population size after 5 years.
A = ?
P = 2000
r = 0.8
t = 5
A = Pxr^t
A = 2000 x 0.8^5
A = 655.36
Hope this helped!
Answer:
B. The graph rises on the left side.
Step-by-step explanation:
The limit provided on the image is interpreted as; The limit of the function f(x) as x approaches negative infinity is infinity.
X is approaching negative infinity, this means that along the x-axis we are moving towards the left where the values of x become increasingly negative.
On the other hand, f(x) is approaching positive infinity, meaning that along the y-axis we are moving upwards where the values of y become increasingly positive.
This typically implies that as we move towards the left the graph of f(x) is moving upwards or basically the graph rises on the left side.
Lagrangian:

where the function we want to minimize is actually

, but it's easy to see that

and

have critical points at the same vector

.
Derivatives of the Lagrangian set equal to zero:




Substituting the first three equations into the fourth gives


Solving for

, we get a single critical point at

, which in turn gives the least distance between the plane and (0, 2, 5) of

.
Answer:
.Option A
Step-by-step explanation:
Given that an instructor was interested in seeing if there was a difference in the average amount of time that men and women anticipate studying for an Introduction to Statistics course in the summer.
Minitab results are

Since p value >0.05 our alpha significant level we accept null hypothesis that
difference in means =0
With a p-value of 0.817, that there is no statistically significant evidence of a difference in average anticipated amount of time studying between the men and women
.Option A
The image I included should help you solve the problem