Tell whether the question is a statistical question. Explain. How many songs are on your MP3 player?

A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function ${\displaystyle h\left(t\right)=-16t^2+24t}$. Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.

Let $A\subset \mathbb{R}$ be Lebesgue measurable such that $0<\lambda (A)<\mathrm{\infty }$ and consider the function $f:\mathbb{R}\to [0,\mathrm{\infty })$, $f(x)=\lambda (A\cap (-\mathrm{\infty },x))$. I would like to compute $\underset{x\to \mathrm{\infty }}{lim}f(x)$.
I have already proved that f is continuous (I have in fact showed that it is Lipschitz continuous), but I am not really sure if this allows me to say that $\underset{x\to \mathrm{\infty }}{lim}f(x)=\lambda (A\cap (-\mathrm{\infty },\mathrm{\infty }))=\lambda (A)$. Intuitively, I am sure that this is right, but I am not sure whether the fact that $f$ is continuous is enough to write this. I feel that I am somehow assuming that the Lebesgue measure $\lambda$ is continuous in some sense. Could you please tell me if my conclusion is right and if the mere continuity of $f$ is enough for it?

Turn 0.75 into a fraction.

$e^{itH}$ notation
recently I saw the notation $e^{itH}$, and just wondering how should I interpret it?
In my understanding, $u(t,x)=e^{itH}{u}_0$ is, for example, a solution to Schrodinger-type equation $i{\mathrm{\partial }}_{t}u=-Hu$ with the initial data $u_0$. In case $H=\mathrm{\Delta }$, the solution to Schrodinger equation is known to involve the Schrodinger kernel in the integrand. In such case, does $e^{itH}$ is a short-hand notation for the operator involving the Schrodinger kernel?
Or should I interpret $e^{itH}$ as the Taylor series with $H^k$ terms involved? In this case, does the (operator) series converge once applied to the element in the domain of H?
Also, I would be very glad to get a reference to read more on this type of operators. Thank you very much!

Rationalise the denominator and simplify $\frac{3\sqrt{2}-4}{3\sqrt{2}+4}$
Does someone have an idea how to work ${\displaystyle \frac{3\sqrt{2}-4}{3\sqrt{2}+4}}$ by rationalising the denominator method and simplifying?

When is a Morphism between Curves a Galois Extension of Function Fields
It is known that the category of normal projective curves and dominant morphisms between them is equivalent to the opposite category of fields of transcendence degree 1 over C and algebraic extensions, so that birational invariants of curves are actually invariants of the function fields, etc.
In algebraic geometry, we have nice interpretations of what it means for an extension of function fields to be separable or purely inseparable (even if these ideas are difficult to visualize since they only occur in prime characteristic). Is there a similar geometric way to view Galois extensions? (Or, I suppose, normal extensions?). Does the fact that a Galois extension of degree n is a splitting field of a degree n polynomial have any geometric meaning?