The function P(x)= -0.008x2 + 0.815x-9.983 models the percentage of the U.S population whose age is xthat have earned an advanced degree. (more than a bachelors degree)in march 2003. A) What is the age for which the highest percentage of Americans have earned an advanced degree? What is the highestpercentage? B) Is the percentage of Americans who have earned an advanceddegree increasing or decreasing for individuals between the ages of40 and 50.

Determine whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) ${\displaystyle f\left(x\right)=-3x^2+7}$

c) $f(x)=\frac{x+1}{x+2}$
${\displaystyle d)f\left(x\right)=x^5+1}$

Find the linear approximation of the function $f(x)=\sqrt{1-x}$ at $a=0$ and use it to approximate the numbers $\sqrt{0.9}$ and $\sqrt{0.99}$.

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attend ance had been 27,000.When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?

I know how to use methods like system of linear equations to show that any vector in ${\displaystyle R^n}$ can be expressed in the form of unique linear combinations of a given set of n linearly independent vectors, but how to expand this result to that any given set of exactly n linearly independent vectors must form a basis of ${\displaystyle R^n}$ space? How to understand it conceptually?
I saw there are similar questions, but the answers in those posts do not really convince me.
Thanks in advance.

how do i find the difference quotient and simplify:
$f(x)=x^2-x+1,f(2+h)-f(2)/h$, h doesn't equal zero

In what connection have to be rational parameters and irrational number for $\frac{ax+b}{cx+d}$ to be rational number?